Add Batch e952db2e-ecf4-4e8a-b460-3bef8b4f8923 data

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@@ -4735,3 +4735,67 @@ saved_model/**/* filter=lfs diff=lfs merge=lfs -text
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2024/Selene_ Pioneering Automated Proof in Software Verification/b16fd601-eaad-4a83-adb6-e746dee5acd2_content_list.json

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+        "text": "Ensuring correctness is a pivotal aspect of software engineering. Among various strategies available, software verification offers a definitive assurance of correctness. Nevertheless, writing verification proofs is resource-intensive and manpower-consuming, and there is a great need to automate this process. We introduce Selene in this paper, which is the first project-level automated proof benchmark constructed based on the real-world industrial-level operating system microkernel, seL4. Selene provides a comprehensive framework for end-to-end proof generation and a lightweight verification environment. Our experimental results with advanced large language models (LLMs), such as GPT-3.5-turbo and GPT-4, highlight the capabilities of LLMs in the domain of automated proof generation. Additionally, our further proposed augmentations indicate that the challenges presented by Selene can be mitigated in future research endeavors.",
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+        "type": "text",
+        "text": "\"Program testing can be used to show the presence of bugs, but never to show their absence.\"",
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+    {
+        "type": "text",
+        "text": "Dahl et al.'s (1972)",
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+    {
+        "type": "text",
+        "text": "1 Introduction",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Confirming the correctness of the software, i.e., checking whether it adheres to the properties specified in the requirements, is advantageous for software engineering (SE). In contrast to testing, which is incomplete, verification provides rigorous guarantee of software correctness or incorrectness (D'Silva et al., 2008). Specifically, during testing, an adequate number of test cases are created and tested against the subject program. If the program violates a testing oracle or encounters other errors (e.g., runtime error), a bug is found. However, the",
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+    {
+        "type": "text",
+        "text": "opposite conclusion cannot be guaranteed otherwise. Verification often involves the usage of a formal language and the corresponding prover. This process requires formal proofs to rigorously demonstrate that the program satisfies the required properties, which can be verified by the prover.",
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+        "text": "In general, software verification involves two stages. ① The prerequisite specification stage translates the required properties and the subject program into the formal language, creating a to-be-proved proposition stating that \"the program meets the properties\", a.k.a., the specification. ② The proof stage is supposed to generate proofs that prove the above specification and can be formally checked by the prover. Both stages consume significant resources and manpower, with the second stage being particularly demanding. E.g., the seL4 operating system microkernel 2, which has been formally verified against strong functionality and security properties, requires 7 person-months dedicated to the specification stage and 11 person-years to the proof stage for correctness verification, and the amount of proof code in seL4 is even ten times more than that of the microkernel implementation itself (Klein et al., 2014). Therefore, in order to promote provable software, automated software verification, particularly automated proof, is highly desirable. As an early exploratory effort, in this paper, we explore to automate the major overhead.",
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+        "text": "Typically, automated proof in software verification is a conditional generation task from the specification to the proof, involving reasoning capabilities. Fortunately, large language models (LLMs) offer an opportunity, as they have demonstrated significant capacity in logic and reasoning at mathematical theorem proving (Jiang et al., 2022; First et al., 2023; Jiang et al., 2023). Only limited re",
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+    {
+        "type": "page_footnote",
+        "text": "*Work done while Lichen Zhang serves as an intern at Microsoft Research Asia, Beijing, China.",
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+    {
+        "type": "page_footnote",
+        "text": "†Correspondence to Shuai Lu",
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+    {
+        "type": "page_footnote",
+        "text": "<sup>1</sup>Please note that there are other verification techniques such as model checking. We refer to it as methods involving interactive proof assistants in this paper.",
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+    {
+        "type": "page_footnote",
+        "text": "2https://sel4.systems/",
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+    {
+        "type": "page_number",
+        "text": "1776",
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+    {
+        "type": "footer",
+        "text": "Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 1776-1789 August 11-16, 2024 ©2024 Association for Computational Linguistics",
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+        "type": "image",
+        "img_path": "images/5f828acf0b1ad1e5f1b9e129bbd04a1b5975e7b94d8c236b7d394ee6cfa477d1.jpg",
+        "image_caption": [
+            "Figure 1: A demonstration of the Selene pipeline for automated proof generation (best viewed in color). Selene facilitates both the construction of proofs from scratch (indicated by the gray \"generate\" path) and the refinement of existing proofs augmented by error messages (highlighted by the red \"fixing\" path). To validate the correctness of the generated proofs, they are subjected to verification by the Isabelle prover within the authentic seL4 environment."
+        ],
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+    {
+        "type": "text",
+        "text": "search has explored how to leverage LLM for code verification (Sun et al., 2023; Yao et al., 2023). And they only focus on function-level code verification, rather than a complete industrial-level software. A distinctive feature of industrial-level projects is the complex dependencies among lemmas and files, which makes automated proof even harder. In order to promote software verification, we propose a real-world industrial-level benchmark based on seL4 for automated proof, namely Selene. SeL4 is a high-assurance operating system microkernel, and it is comprehensively formally verified. The verification of seL4 is mainly based on the formal language of Isabelle (Isabelle, 2023), containing over 100k lines of code in Isabelle and thousands of lemmas (specification + proof), among which we randomly extract 360 for benchmarking. In the major pipeline (as presented in Figure 1), Selene inputs the specification of the target lemma, extracted from seL4, into the subject LLM, and checks the generated proof via the prover within the seL4 environment. As seL4 is a complicated system, Selene provides the complete dependency graph of lemmas, definitions and functions, along with a lightweight verification environment for each lemma to be evaluated. Due to the dependencies of the lemmas, almost the entire verification project needs to be rebuilt in order to check the generated proof, which can lead to a huge evaluation overhead (tens of minutes per lemma). Thence, Selene creates an isolated verification environment for each lemma to avoid duplicate construction and verification of the dependent lemmas, which enables efficient evaluation (it usually takes only a few minutes or even seconds to verify a generation).",
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+    {
+        "type": "text",
+        "text": "We evaluate GPT-3.5-turbo (OpenAI, 2023a) and GPT-4 (OpenAI, 2023b) in the Selene pipeline. The experimental results demonstrate the feasibility",
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+    {
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+        "text": "of LLMs for automated proof in software verification. Still, we have identified some further challenges in Selene. 1 The dependency graph of seL4 is complicated, and extracting facts to be applied from it can be hard for LLMs. 2 The logic and reasoning process of a rather large proof may be beyond the capability of the subject LLMs. Even GPT-4 has difficulty in solving the rather difficult categories in Selene. Therefore, to address the challenges, we introduce three distinct augmentations, i.e., similar lemma augmentation, dependency augmentation and fixing augmentation. These augmentations yield varying improvements across the Selene's different categories. Despite the inherent difficulties, our experimental results with these augmentations offer promising indications that the challenges posed by Selene are surmountable.",
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+    {
+        "type": "text",
+        "text": "The main contributions of this paper can be summarized as below.",
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+        "list_items": [
+            "- We introduce the Selene benchmark, tailored for project-level automated proof in software verification, grounded in the real-world industrial-level project of the seL4 operating system microkernel.",
+            "- We introduce the technique of lemma isolation, which facilitates a lightweight verification environment capable of handling the complexities inherent in systems such as seL4.",
+            "- Our experiments with GPT-3.5-turbo and GPT-4 demonstrate the potential of LLMs in automated proof generation in software verification.",
+            "- We incorporate augmentations into the framework, which mitigate some of the challenges encountered within Selene and suggest promising avenues for future studies."
+        ],
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+    {
+        "type": "page_number",
+        "text": "1777",
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+    {
+        "type": "text",
+        "text": "2 Related Work",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.1 Automated Theorem Proving by LLM",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Automated theorem proving, especially mathematical theorem proving, has garnered significant attention in the field of artificial intelligence. LLMs have shown promising performance in proving formal theorems using proof assistants, such as Isabelle (Isabelle, 2023), Coq (Coq, 2023), and Lean (Lean, 2023). Thor (Jiang et al., 2022) integrates LLMs and hammer-based (Blanchette et al., 2016) provers in Isabelle. DSP (Jiang et al., 2023) leverages LLMs to produce structured formal sketches for automatized proving. Besides, ProofNet (Azerbayev et al., 2023) and Baldur (First et al., 2023) both train or finetune LLMs on formal language corpora. When facing errors, Baldur (First et al., 2023) and Lyra (Zheng et al., 2023) refine the incorrect proofs with error messages.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In addition to the automatic approaches, there are existing benchmarks in the field of formal theorem proving. MiniF2F (Zheng et al., 2022) consists of mathematical problems from Olympiads competitions covering multiple formal languages. PISA (Jiang et al., 2021) includes the Archive of Formal Proofs in Isabelle. ProofNet (Azerbayev et al., 2023) contains mathematical problems in Lean along with parallel natural language descriptions. LeanDojo (Yang et al., 2023) builds a large benchmark in Lean with complete dependencies and the running environment.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "2.2 Automated Software Verification",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Software verification involves checking whether the software meets the requirements. In this paper, we leave alone the dynamic techniques (such as testing) that need to run the software, and only discuss the static formal verification techniques.",
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+    {
+        "type": "text",
+        "text": "We briefly introduce four main techniques of automated software verification. Please refer to the survey for more details (D'Silva et al., 2008). ① Static analysis contains a collection of technologies (e.g., pointer analysis, value range analysis) that analyze the behavior of the software without actual execution. By abstract interpretation (Cousot and Cousot, 1977), which approximately determines the undecidable software behaviors, one may check the correctness. ② Model checking traverses all plausible states of the software to determine whether a property holds (Emerson and Clarke, 1980; Queille and Sifakis, 1982). If the property is violated, the algorithm produces a",
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+    {
+        "type": "text",
+        "text": "reproducible trace, i.e., a counterexample. Due to the large state space, algorithms for model checking are often abstracted or depth-bounded (Biere et al., 1999). ③ Verification-aware programming languages, such as Dafny (Dafny, 2023) and Verus (Verus, 2023), supports formal specification through preconditions, postconditions, and loop invariants, etc., and employs first-order logic solvers (e.g., Z3 (de Moura and Bjørner, 2008)) to automatically prove the specifications. They encourage the programmers to write correct specifications while writing the program, leaving the correctness verification burden to automatic solvers. ④ Interactive verification relies on the interactive proof assistants. Both specifications and proofs during formal verification require substantial manual effort, and they are challenging to be fully automated. Hammers are still the major solutions to automating interactive verification. In the era of LLMs, it is highly feasible to explore automated proof in interactive verification.",
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+    {
+        "type": "text",
+        "text": "Currently, there is limited research specifically addressing the problem of automated software verification with language models. Clover (Sun et al., 2023) introduces a benchmark for consistency checking among code, specification, and docstring, building on the verification-aware language of Dafny. Yao et al. (2023) proposes to use GPT-4 to write invariants, assertions, and other proof structures for Rust-based formal verification, in the short function-level code snippets.",
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+    {
+        "type": "text",
+        "text": "3 Selene",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We present the Selene benchmark in this paper (Figure 1), and evaluate LLMs' capabilities upon automated proof generation. The subject LLM's goal is to write proofs for the given specifications from seL4 and pass the verification. However, the verification process in the original seL4 environment is time-consuming. Given the impracticality of waiting for dozens of minutes to verify a single proof generated by the LLM, we construct Selene to align with the objective of lightweight evaluation. Drawing on the session design in Isabelle and seL4 (Section 3.1), we introduce lemma isolation (Section 3.2), which enables rapid verification of the target lemma (usually a few seconds). Due to the complexity of seL4, we further delve into some specific implementation details of Selene in Section 3.3.",
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+        "type": "page_number",
+        "text": "1778",
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+    {
+        "type": "image",
+        "img_path": "images/aacbf956f2417472d04074bb879cf74708de7ad4b7a0241b2d27143321928480.jpg",
+        "image_caption": [
+            "Figure 2: An illustrative example of the seL4 verification structure. The arrows pointing from A to B indicate that B is dependent upon A, where A and B can be lemmas, theory files, or sessions, etc."
+        ],
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+    {
+        "type": "text",
+        "text": "3.1 Preliminary of SeL4",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "SeL4 is a comprehensively formally verified operating system microkernel (Klein et al., 2014), providing an excellent example for software verification. Most of the verification work on seL4's functional correctness is based upon Isabelle (Isabelle, 2023), which is the basis of Selene.",
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+    {
+        "type": "text",
+        "text": "Isabelle sessions. In the context of large verification projects, Isabelle employs sessions to effectively and efficiently organize the environment (Wenzel, 2023). The concept bears resemblance to the \"package-class-function\" structure in programming languages, with the design of \"session-theory-lemma\" in Isabelle. A session serves as a container for verification results typically centered around a specific topic, and maintains them in a persistent form. It enables easy accessibility without the need for repeated rebuilding lemmas within the session. Such design facilitates incremental development during software verification, allowing modifications to be made without necessitating a complete rebuild, as results in the unchanged and independent sessions remain persistent. Isabelle organizes the sessions using a series of ROOT files (please refer to Appendix B), which contain meta information such as the dependencies and the entry theory files for the sessions.",
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+    {
+        "type": "text",
+        "text": "SeL4 verification structure. The verification of seL4 consists of multiple layers of refinement (De Roever and Engelhardt, 1998), progressing from high-level conceptual ideas to the concrete C implementation of the operating system<sup>3</sup>. Thence, there are many sessions involved in seL4 as shown in Figure 2, with some directly completing a refinement layer (e.g., AInvs) while others providing",
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+    {
+        "type": "text",
+        "text": "dependencies (e.g., ASpec and Lib) such as definitions and property specifications.",
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+    {
+        "type": "text",
+        "text": "In our early studies about the verification process of seL4, we have identified some possible challenges. ① The dependencies in seL4 are highly complicated. A refinement session is typically dependent on multiple other sessions, creating a huge and complex dependency graph that makes it hard to identify the prerequisite components for proving a certain lemma in the refinement sessions. For instance, the session AIvs in Figure 2 is dependent on four sessions (Word_Lib, ExecSpec, ASpec, and Lib), and theories in AIvs depend not only on theories within AIvs (e.g., Untyped_AI directly depends on ArchDetype_AI, and both of them are from AIvs), but also on lots of theories from the four dependency sessions (e.g., Untyped_AI is also dependent upon MonadicRewrite from Lib). Such a large dependency graph usually contains hundreds or thousands of definitions, functions, and lemmas. Identifying prerequisite components from this dependency graph to prove lemmas in AIvs can be a great challenge. ② SeL4 is a systematic project that requires a lot of expert knowledge of operating system, i.e., seL4 is sorely domain-specific. LLMs may not be quite familiar these fields, and therefore the quality of generated proofs may not be satisfying. ③ Proofs in seL4 are often in the procedural style, i.e., they specify a series of tactics to apply without describing the intermediate results. In contrast, proofs for general mathematical problems are often in the declarative style (Zheng et al., 2022), i.e., they specify both the proving goals and the proving operations explicitly ④ (see Appendix A). Although previous work have demonstrated that LLMs can deal with declarative proofs (Jiang et al., 2022; First et al., 2023), the procedural style in seL4 may become a challenge.",
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+    {
+        "type": "text",
+        "text": "3.2 Lemma Isolation in Selene",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "As outlined in Section 3.1, for large projects like seL4, Isabelle constructs the overall verification at the session granularity. However, it can lead to significant overhead during our evaluation - after generating a proof for the given lemma, one may have to wait for multiple minutes to build the corresponding session from scratch. To address",
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+    {
+        "type": "page_footnote",
+        "text": "4The variation in problem domains may account for such differences. Unlike pure and abstract mathematical problems, which are well-suited for the declarative style, software verification usually involves large, concrete, and complex systems, which may benefit from the procedural style (Harrison, 1996).",
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+    {
+        "type": "page_footnote",
+        "text": "<sup>3</sup>A refinement formally proves that a concrete system corresponds to the abstract model and that all properties of the abstract model also hold for the concrete system.",
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+    {
+        "type": "page_number",
+        "text": "1779",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/ac2d3d876dd9204fb561d33b3a152ffd98afc2d36e9e333d4cbe2de347a8d0a6.jpg",
+        "image_caption": [
+            "Figure 3: A working example of lemma isolation in Selene. Based on the original seL4 structure in Figure 2, we construct an isolated session (AINvs_TGT) along with a dependency session (AINvs_DEP) to facilitate efficient verification of the target lemma (strengthen_Not)."
+        ],
+        "image_footnote": [],
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+    },
+    {
+        "type": "text",
+        "text": "this issue, we propose lemma isolation, wherein the target lemma is isolated from its dependencies, thereby avoiding repeated verification of the dependencies and creating a lightweight environment for Selene evaluation.",
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+    {
+        "type": "text",
+        "text": "Following the working example presented in Figure 2, we isolate the target lemma strengthen_Not from the original session AIvs, depicted in Figure 3. The isolation process yields a minimal target session AIvs_TGT, which exclusively contains only the target lemma strengthen_Not. To verify AIvs_TGT, a dependency session AIvs_DEP is required. AIvs_DEP consists of theory files originally found in the dependency tree of Untyped_AI along with a new theory file (Untyped_AI_DEP) containing the contents preceding strength_Not in Untyped_AI. The theories in AIvs_DEP reconstruct the dependencies of the target lemma strength_Not in the original AIvs session.",
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+    {
+        "type": "text",
+        "text": "AInvs_DEP, as well as other dependency sessions (ASpec, Lib, etc.), are verified once and remain fixed during evaluation. Accessing the persistent verification results in these sessions to verify AInvs_TGT takes little time. Lemma isolation can reduce the verification time to about  $\\frac{1}{3}$  of rebuilding from scratch (see Appendix C), creating a lightweight verification environment.",
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+    {
+        "type": "text",
+        "text": "3.3 Key Know-how about Selene",
+        "text_level": 1,
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+        "type": "text",
+        "text": "In addition to the isolation design, the implementation of Selene involves many details, which can be attributed to the complexity of the seL4 system.",
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+    {
+        "type": "text",
+        "text": "Lemma extraction. We gather theory files from the refinement sessions in seL4, and extract lemmas through a rough parser (e.g., lemmas always begin with the token \"lemma\" or \"threorem\" and",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/254c1a0796cf0d7f6ff69d97cb0be97dbeb6f4ff4824515d3c38cd3dbe34a76b.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>P1</td><td>P2</td><td>P3</td><td>D</td></tr><tr><td>Extracted</td><td>1,995</td><td>2,496</td><td>928</td><td>45</td></tr><tr><td>Sampled</td><td>160</td><td>120</td><td>80</td><td>45</td></tr><tr><td>Correctly verified</td><td>144</td><td>109</td><td>64</td><td>43</td></tr><tr><td>Demonstration</td><td>5</td><td>5</td><td>5</td><td>5</td></tr><tr><td>Evaluation</td><td>139</td><td>104</td><td>59</td><td>38</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Table 1: Statistics of Selene. P1, P2 and P3 denote the three difficulty levels for lemmas in procedural style, while D represents lemmas in declarative style.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "end with the token “qed”, “done” or a “by ...” statement). Lemmas within contexts or locales  $^{5}$  are excluded from the process, because we find them incompatible with our design of lemma isolation. If the proof for a lemma exceeds 20 lines, we exclude it from Selene, as it may be too long and too challenging for LLMs. Finally, we collect 5,464 lemmas across 11 sessions from seL4.",
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "Dependency session construction. We construct the dependency session by replacing only the target theory file in the directory. Taking Figure 2 and 3 for instance, we replace the theory file Untyped_AI in the session AInvs with the new theory Untyped_AI_DEP to build the dependency session AInvs_DEP. In the ROOT file, we set the entry to Untyped_AI_DEP and copy other meta information of AInvs to complete the construction of AInvs_DEP (please refer Appendix B). Even if there are additional theories in Untyped_AI_DEP, this setup will not include them into the dependency graph, providing correct dependencies to AInvs_TGT.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Lemma category. As mentioned earlier, we observed that the majority of proofs in seL4 are in procedural style (5,419 out of 5,464 lemmas collected), while only a small number are in declarative style (45). Procedural proofs typically apply a sequence of tactics to achieve the proving goal, and the length usually reflects the level of difficulty. For procedural style, we categorize lemmas into three difficulty levels according to the proof length: P1 (one single line), P2 (two to six lines), and P3 (seven to twenty lines). Lemmas from each difficulty level are randomly sampled to create the benchmark. As for lemmas in declarative style, all of them are included in the benchmark.",
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Correctness checking. It is important to check the correctness of the isolated sessions, as the imple",
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_footnote",
+        "text": "5Contexts and locales in Isabelle are designed to deal with parametric theorems. Please refer to the documentation for more details (Ballarin, 2023).",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "1780",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "mentation may not be guaranteed to be accurate. There are three potential causes of incorrect isolation: ① the extracted lemmas may be incomplete due to the limitation of keyword matching; ② copying meta information in ROOT files may result in configuration errors; ③ the complex system setup of seL4 may lead to errors during lemma isolation. In addition, prior to evaluation, the dependency sessions should also be verified once to produce the necessary persistent results. We exclude those incorrect lemmas from Selene, leaving the remaining lemmas ready for evaluation. Table 1 lists the statistics of each step in Selene construction.",
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4 Evaluation",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.1 Evaluation Pipeline",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Pipeline. The evaluation pipeline of Selene is presented in Figure 1. The subject LLM takes the specification, extracted from the isolated target session, as input, and generates a potential proof for it. The isolated target session is updated by appending the generated proof to the specification, and subsequently verified by the Isabelle prover. As designed in Section 3.2, since the dependency sessions have been already built once, the verification results are persistently available to the target session, thus the verification of the target session does not consume significant amount of time.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Metrics. We employ accuracy at  $k$  trials as the performance indicator, denoted as ACC#k. Specifically, the subject LLM independently generates  $k$  proofs using temperature sampling (Ficler and Goldberg, 2017; Fan et al., 2018; Caccia et al., 2020) and nucleus (top-p) sampling (Holtzman et al., 2020). If at least one of the  $k$  trials is successfully verified, ACC#k for the corresponding lemma is 1; otherwise, it is 0.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Prompt. The prompt includes an instruction, which specifies the task of automated proof, along with several demonstrations for in-context learning (Brown et al., 2020). Each demonstration consists of a specification and its corresponding groundtruth proof (please refer to Appendix D).",
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+    },
+    {
+        "type": "text",
+        "text": "4.2 Evaluation Setup",
+        "text_level": 1,
+        "bbox": [
+            112,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We evaluate GPT-3.5-turbo (OpenAI, 2023a) and GPT-4 (OpenAI, 2023b) upon Selene. Within each set (P1, P2, P3, and D), we randomly select five lemmas as demonstrations, which remain fixed during our evaluation, and evaluate the remaining lemmas against the subject LLMs, as listed in Table",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/ee831bcfbc99126207126c8e77bb99cbd8428ab651da4908e88638a23d4cfb49.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>ACC</td><td>P1</td><td>P2</td><td>P3</td><td>D</td></tr><tr><td>GPT-3.5</td><td>#1</td><td>28.1</td><td>2.9</td><td>0</td><td>0</td></tr><tr><td>-turbo</td><td>#5</td><td>35.3</td><td>5.8</td><td>0</td><td>5.3</td></tr><tr><td rowspan=\"2\">GPT-4</td><td>#1</td><td>41.7</td><td>7.7</td><td>0</td><td>10.5</td></tr><tr><td>#5</td><td>51.8</td><td>12.5</td><td>1.7</td><td>15.8</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 2: Performance of GPT-3.5-turbo and GPT-4 against Selene (values in percentage).",
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "1. The subject LLMs take in the concatenation of the instruction, five demonstrations, and the target lemma specification, without additional augmentations, and generate proof trials.",
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "ACC#1 and ACC#5 are assessed in our evaluation. The probability threshold (top- $p$ ) is set to 0.95, and the temperature is set to 0 for ACC#1 and 0.5 for ACC#5. Generation trials that exceed the token length of 2,048, contain the token \"sorry\" or \"oops\" (which can bypass the verification process, leading to false positive results), or take more than 10 minutes during verification (timeout) are all considered as failures.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.3 Evaluation Result",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The results are listed in Table 2. The results suggest that LLMs have the capacity to automate proof generation in Selene, with GPT-4 notably achieving  $51.8\\%$  ACC#5 upon P1. Nevertheless, as the complexity of the proofs for procedural lemmas increases (P1  $\\rightarrow$  P3), the task becomes increasingly challenging for both GPT-3.5-turbo and GPT-4 models. In fact, both models struggle significantly when attempting to prove lemmas within the P3 category, which require comprehending an extensive dependency graph and employing more sophisticated reasoning capabilities. Interestingly, both the subject models perform better when addressing declarative lemmas (D) within Selene, as opposed to those categorized under P3, despite the proofs for most D category lemmas being of comparable length to those in P3, typically ranging from 7 to 20 lines. A plausible explanation could be that the inclusion of intermediate goals within declarative proofs mitigates the difficulty in logic and reasoning. In addition, we find that in many cases, GPT-4 adopts different proving strategies than the groundtruth (see cases in Appendix E), suggesting that the LLM is not simply memorizing.",
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "Failure type. We analyze and categorize the errors made by GPT-4 during the evaluation process to better understand the challenges posed by Selene. The errors are classified into three distinct cate",
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+    },
+    {
+        "type": "page_number",
+        "text": "1781",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/a2facf6d10f95bec8932395c8a6e434888e6f5d69433030b19c3ea5fda407434.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Error</td><td>P1</td><td>P2</td><td>P3</td><td>D</td></tr><tr><td>Total</td><td>81</td><td>96</td><td>59</td><td>34</td></tr><tr><td>Undefine</td><td>38(47%)</td><td>37(39%)</td><td>21(36%)</td><td>12(35%)</td></tr><tr><td>Logic</td><td>41(51%)</td><td>55(57%)</td><td>31(52%)</td><td>20(59%)</td></tr><tr><td>Other</td><td>2(2%)</td><td>4(4%)</td><td>7(12%)</td><td>2(6%)</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 3: The composition of different types of errors made by GPT-4. The errors are collected in the ACC#1 setting evaluation. Outside the brackets are the absolute number of errors, inside the brackets are the percentages.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "gories based on the nature of the error encountered: 1 \"undefined errors\", where tactics not defined in seL4 are applied in the proofs, 2 \"logic errors\", where the proof cannot be finished (e.g., application of inappropriate tactics, presence of incomplete proving goals), and 3 \"other errors\", including syntax errors, runtime errors, and other issues. The error composition is presented in Table 3. The majority of the errors (over a half) committed by GPT-4 can be attributed to its inadequate reasoning capability, which leads to unfinished proof goals (logic errors). A smaller, yet still significant, proportion of errors (undefined errors) stem from a lack of comprehensive knowledge of the dependencies within the entire seL4 project. Additionally, it is notable that GPT-4 barely makes syntax error, as most cases in other errors are refusal to generate proof 6, timeouts, and empty outputs (e.g., exceeding the generation length), etc.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5 Augmentation",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "As previously discussed, LLMs exhibit significant potential for automated proof when evaluated against Selene, however, it is also evident that the task presents substantial challenges. We propose some augmentation techniques and evaluate them in our evaluation pipeline, with the aspiration that they may serve as a catalyst for further exploration in future studies.",
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.1 Augmentation to Evaluation Pipeline",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Similar lemma augmentation. SeL4 is an intricate piece of software, and as a consequence, its formal verification process is even more complex, involving a multitude of lemmas that can be similar (or even identical). The presence of these similar lemmas naturally offers an opportunity to augment",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/7c20627d4a30c7d01dded2bc6a423b4f7a74b09ed72c29e26abd458f35ca9f55.jpg",
+        "image_caption": [
+            "Figure 4: Demonstrative examples of similar lemma augmentation and dependency augmentation."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "the automated proof pipeline, and similar augmentation has been proven beneficial in tasks such as question-answering (Lewis et al., 2020) and code completion (Lu et al., 2022). Specifically, we build a retrieval library by segmenting theory files from seL4 into discrete chunks. The segmentation is guided by the blank lines in the text. Retrieval is performed through the BM25 algorithm (Robertson and Zaragoza, 2009) (the upper part of Figure 4), which involves querying the target specifications against the retrieval library to identify analogous text segments (i.e., similar lemmas). To ensure the integrity of the experiment, the groundtruth proof is deliberately omitted from the retrieval process to prevent biases in the search results. During our evaluation, we select the initial ten lines from the chunk most closely resembling the target specification as the augmentation.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Dependency augmentation. The complex dependencies inherent in the seL4 project pose significant obstacles to LLMs when evaluated against Selene, as evidenced in Table 3. To mitigate this challenge, we introduce the dependency augmentation. Particularly, we extract the applied facts from the ground truth proof, and identify their origin by searching in the chunk library (those chunks not in the dependency sessions are omitted during this process), as shown in the lower part in Figure 4. The pinpointed definitions, functions, and lemmas are clearly integral to the proof of the target specification. And these elements are then provided to the subject LLM as augmentations, with the intention of simplifying the task by providing correct information for the model to apply. Ideally, this augmentation should alleviate the obstacles posed by dependencies, allowing the subject LLM to focus on applying the accurate information provided. However, during our practice, the absence of sophisticated tools means we cannot pinpoint every fact and its origin with complete precision. Consequently, the results of the dependency aug-",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_footnote",
+        "text": "For instance, GPT-4 may refuse our request by generating texts like \"I cannot assist with this request\". This situation does not happen much, but it is difficult to prevent it, even if we order it in the prompt to always generate a response. In addition, GPT-3.5-turbo produces much more refusal issues.",
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "1782",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/8e43ea68b25bd4c9264b536018d828711e54d0c93a1a02a95a8249eee521fa30.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Augmentation</td><td>P1</td><td>P2</td><td>P3</td><td>D</td></tr><tr><td>GPT-4</td><td>41.7</td><td>7.7</td><td>0</td><td>10.5</td></tr><tr><td>+Similar</td><td>47.5</td><td>14.4</td><td>1.7</td><td>10.5</td></tr><tr><td>+Dependency</td><td>52.5</td><td>14.4</td><td>1.7</td><td>-</td></tr><tr><td>+Fixing</td><td>53.2</td><td>9.6</td><td>0</td><td>18.4</td></tr></table>",
+        "bbox": [
+            154,
+            80,
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+            158
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/3b54d482009a4cc688b810c44652c644171c927ea0904652a984354abeb83111.jpg",
+        "table_caption": [
+            "Table 4: ACC#1 of GPT-4 with augmentations evaluated against Selene (values in percentage). For the D category, we skip the dependency augmentation, due to the complexity of fact extraction in this category."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Aug.</td><td colspan=\"4\">Error</td></tr><tr><td>Total</td><td>Undef.</td><td>Logic</td><td>Other</td></tr><tr><td>GPT-4</td><td>81</td><td>38(47%)</td><td>41(51%)</td><td>2(2%)</td></tr><tr><td>+Similar</td><td>73</td><td>29(40%)</td><td>42(57%)</td><td>2(3%)</td></tr><tr><td>+Dependency</td><td>66</td><td>16(24%)</td><td>45(68%)</td><td>5(8%)</td></tr><tr><td>+Fixing</td><td>65</td><td>30(46%)</td><td>32(49%)</td><td>3(5%)</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "mentation should be viewed as a potential upper limit of the subject LLM's capability in this context. We use the first five lines from the origin of each identified fact as the augmentation.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Fixing augmentation. When a proof attempt does not succeed, it is almost a standard procedure to examine the error message in order to fix the flawed proof (refer to Figure 1). The error message typically provides comprehensive feedback, such as the error type and the state of the proof at the moment of failure. There are existing studies that support the capability of LLMs to fix previously incorrect logic by incorporating error messages (First et al., 2023; Zheng et al., 2023; Chen et al., 2023), which make this augmentation even feasible when dealing with Selene. The evaluation is conducted as a two-round dialogue – if the subject LLM does not succeed in the first round, we feed the error message into the model and ask it to try again; if the subject LLM succeeds in the first trial, we do not carry out the second round of fixing.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We evaluate GPT-4 with the three augmentations, with the performance indicator of ACC#1. All other settings remain the same as in Section 4.2.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.2 Augmentation Result",
+        "text_level": 1,
+        "bbox": [
+            112,
+            787,
+            327,
+            802
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "The results listed in Table 4 indicate the three augmentations lead to improvements across different categories. We also examine the error composition of GPT-4 with augmentations evaluated against P1, as listed in Table 5. In the below, we analyze the effect of each augmentation strategy and carry out some ablation studies.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/a7e44e86d04d3b54ee6d8864d43f40b628743cb726624a2bc61dc4e63f20ac32.jpg",
+        "table_caption": [
+            "Table 5: The composition of errors made by GPT-4 with augmentations evaluated against Selene-P1."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Augmentation</td><td>P1</td><td>P2</td><td>P3</td><td>D</td></tr><tr><td>+TryAgain</td><td>49.6</td><td>7.7</td><td>0</td><td>10.5</td></tr><tr><td>+Similar &amp; Fixing</td><td>61.9</td><td>20.2</td><td>1.7</td><td>7.9</td></tr></table>",
+        "bbox": [
+            536,
+            80,
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+            135
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 6: Ablation of augmentations (ACC#1 of GPT-4).",
+        "bbox": [
+            519,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Similar augmentation. The similar augmentation is found to enhance performance upon procedural categories (P1-P3), indicating the utility in the augmented contexts; but it does not yield a significant effect upon the D category, suggesting a potential area for further investigation. According to Table 5, the similar augmentation marginally ameliorates the incidence of undefined errors without showing notable impact on logic errors. This improvement could be attributed to the facts introduced from the inclusion of similar lemmas.",
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+    {
+        "type": "text",
+        "text": "Dependency augmentation. The dependency augmentation significantly improves GPT-4 on P1  $(41.5\\% \\rightarrow 52.5\\%$  in Table 4). As for the errors in Table 5, it is notable that the dependency augmentation results in a substantial diminution of undefined errors, corroborating our intended purpose.",
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+    {
+        "type": "text",
+        "text": "Fixing augmentation. In Table 5, as the complexity of the proof increases (i.e., P2 and P3), the fixing augmentation is less effective. This trend is expected since simple proofs (as in P1) typically contain straightforward errors that can be corrected in a single fixing attempt, whereas longer and more complex proofs may require multiple rounds of corrections. Also, as demonstrated in Table 5, there is a noticeable reduction in logical errors, which can be attributed to the integration of error messages. We further ablate by not providing the error message to GPT-4, only asking it to try again if the first attempt fails. The results are listed in the \"TryAgain\" row of Table 6. TryAgain brings limited improvement compared to fixing, suggesting that error messages are important.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Similar + dependency. We carry another ablation by combining similar and fixing augmentations together (\"Similar&Fixing\" in Table 6). Based on Table 5, the similar and the fixing augmentations improve the undefined fact and the logic error issues, respectively. Results show that combining both augmentations significantly improves GPT-4's performance upon P1 and P2. On D category, these two augmentations may have opposite effects, causing unexpected performance degradation (even worse than raw GPT-4). This phenomenon may be worthy of future exploration.",
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+    {
+        "type": "page_number",
+        "text": "1783",
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+    {
+        "type": "text",
+        "text": "6 Conclusion",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "In this paper, we study the domain of automated proof within the context of software verification. We introduce Selene, which is a real-world industrial-level automated proof benchmark derived from the seL4 project. Selene provides a lightweight verification environment facilitated by lemma isolation with Isabelle sessions. The current framework supports end-to-end proof generation and evaluation, bolstered by supplementary augmentation. By evaluating against advanced LLMs such as GPT-3.5-turbo and GPT-4, we demonstrate the potential of LLMs in automated proof generation for software verification. Nevertheless, Selene poses formidable challenges that LLMs have yet to overcome fully. It is our hope that Selene will catalyze further research in this area, promoting advancements in software verification.",
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+    {
+        "type": "text",
+        "text": "7 Limitation",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We present some discussions on the limitations of Selene. As an early step of software verification, we consider addressing these limitations and challenges as our future work. Hopefully, we could offer insights that may serve as a catalyst for future studies in this field.",
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+    {
+        "type": "text",
+        "text": "Dependency extraction. SeL4 contains a huge and complex dependency graph, posing a significant challenge in the accurate extraction of dependencies, i.e., facts. Our analysis has revealed that undefined errors (e.g., applying nonexistent facts) account for nearly half of GPT-4's failures in Selene. The dependency augmentation experiment has further proven the effectiveness and necessity of dependency in addressing this issue. One promising research direction may be to transition from providing LLMs with groundtruth facts as done in this paper, to employing advanced techniques (such as RAG (Lewis et al., 2020; Asai et al., 2023)) to automatically extract candidate facts directly from the codebase. We leave this as our future work.",
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+    {
+        "type": "text",
+        "text": "Specification generation. There are two stages in software verification – the prerequisite specification stage and the proof stage. In this paper, we primarily concentrate on the automation of the proof stage, which constitutes the main bulk of the verification workload. However, it is important to acknowledge that the specification stage, which involves translation of properties and programs into formal languages, is not without its own set of challenges. This stage is not only time-consuming and",
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+    {
+        "type": "text",
+        "text": "resource-intensive but also necessitates substantial advancements in automation to enhance efficiency.",
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+    {
+        "type": "text",
+        "text": "Proof state. The current pipeline of Selene only supports end-to-end proof generation, i.e., the subject LLM generates the entire proof. Our experimental results indicate that LLMs possess the ability to prove lemmas within the less challenging P1 category. However, the effectiveness significantly diminishes when addressing lemmas from the more complex P3 category. This observation aligns with the experiences of human practitioners, who typically cannot construct proofs for P3 lemmas in a single attempt but instead progress incrementally, selecting suitable operations at each step based on the evolving proof state. To enhance the capability of LLMs in addressing P3 lemmas, it may be necessary to introduce the interactive proof state into the Selene pipeline in the future, thereby mimicking the human practitioners during proof construction.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "To observe the intermediate state, PISA (Jiang et al., 2021) provides a practical solution. PISA implements a schema-Isabelle framework to glance at the proof state of the Isabelle verification system. With the proof state available, LLMs are allowed to generate proofs in an interactive manner. We believe that techniques in PISA are orthogonal with lemma isolation - lemma isolation allows rather quick session loading, and PISA provides and interactive environment. The incorporation of PISA and Selene is another future work.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            510,
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+        "page_idx": 8
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+    {
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+        ],
+        "bbox": [
+            510,
+            85,
+            884,
+            313
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "A Procedural Vs. Declarative Style",
+        "text_level": 1,
+        "bbox": [
+            509,
+            334,
+            826,
+            350
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "The procedural style proofs specify a series of tactics to apply, without describing the intermediate results. A demonstrative lemma from seL4 is shown below.",
+        "bbox": [
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+        "page_idx": 10
+    },
+    {
+        "type": "code",
+        "sub_type": "code",
+        "code_caption": [],
+        "code_body": "lemma unbindNotification_valid_sched[wp]: {\"valid_sched} unbindNotification ntfnptr {  $\\lambda$  rv. valid_sched}\" apply (simp add: unbindNotification_def) apply (rule hoare_seq_ext[OF _ gbn_sp]) apply (case_tac ntfnptra, simp, wp, simp) apply (clarsimp) apply (rule hoare_seq_ext[OF _ getsimple ko_sp]) apply (wp set_boundNotification_valid_sched, clarsimp) done",
+        "guess_lang": "txt",
+        "bbox": [
+            510,
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "In the example, line 4-10 apply a sequence of tactics to achieve the proving goal. Declarative style proofs, on the other hand, explicitly write both the intermediate proving goals and the proving operations. A typical example from seL4 is shown below.",
+        "bbox": [
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "code",
+        "sub_type": "code",
+        "code_caption": [],
+        "code_body": "lemma thread_set_as_user: \"thread_set ( $\\lambda$ tcb. tcb ( tcb_arch := arch_tcb_context_set (f $ arch_tcb_context-get (tcb_arch tcb)) (tcb_arch tcb))) t = as_user t (modify f)\"  \nproof - have P: \" $\\wedge$ f. det (modify f)\"  \nby (simp add: modify_def) thus ?thesis apply (simp add: as_user_def P thread_set_def) apply (clarsimp simp add: select_f_def simpler_modify_def bind_def image_def) done qed",
+        "guess_lang": "txt",
+        "bbox": [
+            510,
+            636,
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Line 6 in this lemma specifies the intermediate proving goal, and the following lines performs a series of tactics.",
+        "bbox": [
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+            804
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "In general, mathematical problems are usually pure and abstract, and therefore they are well-suited for the declarative style; while software verification usually deals with large, concrete and complex systems like seL4, and it benefits from the procedural style (Harrison, 1996). In Selene, we notice that most proofs in seL4 are in the procedural style.",
+        "bbox": [
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "page_number",
+        "text": "1786",
+        "bbox": [
+            480,
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "table",
+        "img_path": "images/2d10cea532addaabddb59d4308225ebd31a31df4bf00e4e3262eb189cd5378fb.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>P1</td><td>P2</td><td>P3</td><td>D</td></tr><tr><td>Checking</td><td>148.9</td><td>145.8</td><td>217.3</td><td>178.7</td></tr><tr><td>GPT-3.5-turbo</td><td>40.2</td><td>43.7</td><td>42.5</td><td>50.6</td></tr><tr><td>GPT-4</td><td>35.6</td><td>43.5</td><td>43.9</td><td>43.3</td></tr></table>",
+        "bbox": [
+            136,
+            80,
+            467,
+            154
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Table 7: Average elapsed time of verification of correctness checking before evaluation, and ACC#1 evaluation of GPT-3.5-turbo and GPT-4 without augmentations (values in seconds).",
+        "bbox": [
+            112,
+            162,
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "B ROOT File",
+        "text_level": 1,
+        "bbox": [
+            114,
+            237,
+            248,
+            253
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "As previously introduced, Isabelle organizes the environment with sessions, which can be regarded as a container for verification results of certain topics. The structure of a session, including its dependent sessions and its entries, etc., is defined and described in the ROOT file. An example from seL4 is presented below, which is a part of a large ROOT file.",
+        "bbox": [
+            112,
+            265,
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+            391
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "code",
+        "sub_type": "code",
+        "code_caption": [],
+        "code_body": "1 session BaseRefine in \"refine/base\" = AInvs +  \n2 description \\<open>Background theory and  \n3 libraries for refinement proof.\\<close>  \n4 sessions  \n5 Lib  \n6 CorresK  \n7 theories  \n8 \"Include\"",
+        "guess_lang": "txt",
+        "bbox": [
+            92,
+            398,
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "This partial ROOT file defines a session named \"BaseRefine\", which locates at the directory \"refine/base\" (Line 1). BaseRefine is directly dependent on another session \"AIvs\" (Line 1), and it imports two more sessions, \"Lib\" and \"CorresK\" (Line 4-6, these two sessions are also dependency to BaseRefine). BaseRefine has only one entry theory file, \"Include.thy\" (Line 7-8). The theory Include is dependent on other theories in BaseRefine, and the prover verifies the whole session in a bottom-up manner (it first checks all dependencies of Include, and then verifies lemmas within Include).",
+        "bbox": [
+            110,
+            478,
+            489,
+            684
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "As in Figure 3, during lemma isolation, Selene sets the theory \"Untyped_AI_DEP.thy\" as the entry of the dependency session (Ainvs_DEP in the figure), and sets the dependency of the target session (Ainvs_TGT) to the dependency session (Ainvs_DEP).",
+        "bbox": [
+            112,
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "C Verification Time",
+        "text_level": 1,
+        "bbox": [
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+        "type": "text",
+        "text": "The time cost of the verification process is listed in Table 7. Correctness checking bears resemblance of building from scratch, and it takes on average about three times longer than verifying only the isolated target session. Note that we even include the ten minutes of timeout during evaluation in Table 7.",
+        "bbox": [
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+        "type": "text",
+        "text": "Since we only perform correctness checking once before evaluation, lemma isolation can greatly improve the verification efficiency during evaluation of Selene.",
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+    {
+        "type": "text",
+        "text": "D Prompt",
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+        "type": "text",
+        "text": "Instruction. The basic instruction is shown below.",
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+    },
+    {
+        "type": "text",
+        "text": "You are an experienced formal language programmer. You not only know the Isabelle formal language very well, but also are very familiar with the seL4 project. As a reminder, seL4 is an almost fully formally verified operating system microkernel. Your mission is to write formal proofs in Isabelle for the given specifications, which formally describe properties of seL4 in Isabelle. You are not supposed to write anything other than formal proofs in Isabelle. E.g., You should not write comments or explanations in natural language. In addition, the formal proofs you write will be automatically checked, therefore, you need to do your best to make it correct.",
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+    {
+        "type": "text",
+        "text": "For each augmentation, there is an augmented instruction listed below. We concatenate the basic instruction and the corresponding augmented instruction, forming the final instruction.",
+        "bbox": [
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+        "page_idx": 11
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+    {
+        "type": "text",
+        "text": "Similar: Some chunks of seL4 with similar specifications are provided before the target specification. Each chunk is provided between the tags of \"<sim>\" and \"<sim)\". You can use these chunks to assist the proof of the target specification.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Dependency: Some previous chunks of seL4 are provided before the target specification as plausible dependencies. Each chunk is provided between the tags of \"<dep>\" and \"<dep>\". You can use these chunks to assist the proof of the target specification.",
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+    {
+        "type": "text",
+        "text": "Fixing: If the previous proof is not correct, the error message may be provided inside curly brackets {just like this}. If the error message is provided, you are supposed to make the previous proof correct at your best.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Demonstration. In general, a demonstration for the subject LLM (e.g., GPT-4) is an input-output pair. In the most simple evaluation setting of Selene (without any augmentation), the input in the demonstration is the specification of the demonstrative lemma and the output is the corresponding proof. When augmented by similar chunks, the demonstration output remains the same, while the input is a concatenation of the similar chunk and the specification. The similar chunk is tagged by “<sim>” and “</sim>”. The dependency augmentation is quite similar, with different tags of “<dep>” and “</dep>.",
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+    {
+        "type": "text",
+        "text": "As for fixing augmentation, we need to collect erroneous proofs and corresponding error messages upon the demonstrative lemmas. For each lemmas within the five demonstrations, we invoke the subject LLM in the same manner as in Section 4, using",
+        "bbox": [
+            507,
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+        "page_idx": 11
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+    {
+        "type": "page_number",
+        "text": "1787",
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+    {
+        "type": "text",
+        "text": "the other four lemmas as demonstrations. In this way, we may collect some errors produced by the subject LLM. The demonstrations for fixing augmentation are much more complicated. We carry out this augmentation in a two-round dialogue way. I.e., each demonstration may contain two input-output pairs (if the subject LLM fails). The first pair is the specification and the erroneous proof generated by the subject LLM; the second pair is the error message and the groundtruth proof. Note that the error message is inside curly brackets (e.g., {Undefined fact: \"st_def\" At command \"by\"}). If the subject LLM successfully generates a proof for the demonstrative lemma, i.e., it does not make any error, the demonstration only contains one pair, i.e., the specification along with the groundtruth proof.",
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+    {
+        "type": "text",
+        "text": "E Generated Cases",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Some cases generated by GPT-3.5-turbo and GPT-4 upon the P1 category of Selene are presented in Table 8. These cases are randomly selected from the union of correct generation from GPT-3.5-turbo and GPT-4 under the setting of ACC#1, without cherry-picking. In the table, we can observe that GPT-4 almost do not generate a proof identical to the groundtruth (except for tbc_context_merge). This shows that to a certain extent, GPT-4 can understand and generate proofs for seL4.",
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+    {
+        "type": "page_number",
+        "text": "1788",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/fb09e4c9cfdb33ebe5b0ebe612d03ff5508bd1bbb53de3a6a083fd7220705875.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Target Lemma\n(Specification + Groundtruth Proof)</td><td colspan=\"2\">Generated Proof</td></tr><tr><td>GPT-3.5-turbo</td><td>GPT-4</td></tr><tr><td>lemma (in strengthenIMPLEMENTATION)\nstrengthen_Not[strg]:\n\n&quot;[| st (¬F) (→) P P&#x27; | ]\n→ st F (→) (¬P) (¬P&#x27;)&quot; \n(* PROOF STARTS RIGHT HERE *) \nby (cases F, auto)</td><td>by (erule\nstrengthen_precondition)\n[x] Undefined fact</td><td>by (clarsimp simp: st_def)\n[√]</td></tr><tr><td>lemma gen_invocation_typeI:\n&quot;invocation_type l = GenInvocationLabel x\n→ gen_invocation_type l = x&quot;\n(* PROOF STARTS RIGHT HERE *) \nby (simp add: gen_invocation_type_def)</td><td>by (simp add:\ngen_invocation_type_def)\n[√]</td><td>by (simp add:\ngen_invocation_type_def\nsplit: invocation_label.splits)\n[√]</td></tr><tr><td>lemma ts_Restart(case_helper:\n(&quot;case ts of Structures_A.Restart ⇒ A\n| _ ⇒ B)\n= (if ts = Structures_A.Restart\nthen A else B)&quot; \n(* PROOF STARTS RIGHT HERE *) \nby (caseTac ts, simp_all)</td><td>by (caseTac ts, simp_all)\n[√]</td><td>by (cases ts; simp)\n[√]</td></tr><tr><td>lemmairq_state_back:\n&quot;P (irq_state_of_state (internal_state_if\n((a,b),c))\n(irq�建省_of_state (internal_state_if\n((a,b),c))\n→ P (irq_state_of_state b)\n(irq�建省_of_state b)&quot; \n(* PROOF STARTS RIGHT HERE *) \nby simp</td><td>by simp\n[√]</td><td>by (clarsimp simp:\ninternal_state_if_def)\n[x] Undefined fact</td></tr><tr><td>lemma cte_wp_at_conj:\n&quot;cte_wp_at (λc. P c ∧ Q c) p s\n= (cte_wp_at_P p s ∧ cte_wp_at_Q p s)&quot; \n(* PROOF STARTS RIGHT HERE *) \nby (fastforce simp: cte_wp_at_def)</td><td>by (auto simp:\ncte_wp_at_caps_of_state)\n[√]</td><td>by (auto simp:\ncte_wp_at_caps_of_state)\n[√]</td></tr><tr><td>lemma smrs_cte_at[wp]:\n{&quot;cte_at p} set_mrs_thread buf msgss\n(λ_. cte_at p)&quot; \n(* PROOF STARTS RIGHT HERE *) \nby (wp valid_cte_at_typ)</td><td>Sorry, I cannot assist\nwith this request.\n[x] Outer syntax error</td><td>by (wp | simp add: set_mrs_def)+\n[√]</td></tr><tr><td>lemma master_eqE:\n[&quot;| capMasterCap cap = capMasterCap cap];\n^cap. F (capMasterCap cap) = F cap ]\n→ F cap = F cap ]\n(* PROOF STARTS RIGHT HERE *) \nby (rule master_eqI, assumption, simp)</td><td>by (metis)\n[√]</td><td>by (drule meta_mp) auto\n[x] Failed to apply proof method</td></tr><tr><td>lemma tcb_context_merge[simp]:\n&quot;arch_tcb_context_get (tcb_arch\n(tcbRegisters_caps_merge tcb_tcb&quot;))\n= arch_tcb_context_get (tcb arch tcb)&quot; \n(* PROOF STARTS RIGHT HERE *) \nby (simp add: tcbRegisters_caps_merge_def)</td><td>by (simp add:\ntcbRegisters_caps_merge_def)\n[√]</td><td>by (simp add:\ntcbRegisters_caps_merge_def)\n[√]</td></tr><tr><td>lemma cte_map_tcb_2:\n&quot;cte_map (t, tcb_cnode_index 2)\n= t + 2*2^cte_level_bits&quot;\n(* PROOF STARTS RIGHT HERE *) \nby (simp add: cte_map_def\ntcb_cnode_index_def to_bl_1)</td><td>by (simp add: cte_map_def\ntcb_cnode_index_def)\n[√]</td><td>by (simp add: cte_map_def\ntcb_cnode_index_def\ncte_level_bits_def)\n[√]</td></tr><tr><td>lemma object_type_asid_reset [simp]:\n&quot;object_type (asid_reset obj)\n= object_type obj&quot;\n(* PROOF STARTS RIGHT HERE *) \nby (clarsimp simp: asid_reset_def)</td><td>by (cases obj, auto)\n[x] Failed to finish proof</td><td>by (cases obj; simp\nadd: asid_reset_def)\n[√]</td></tr></table>",
+        "bbox": [
+            142,
+            158,
+            853,
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+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "Table 8: Cases generated by the subject LLMs upon P1 of Selene. These cases are collected under the ACC#1 setting. The verification results are marked under the generated proofs. Please note that we have added some line breaks into the original lemmas and the generated proofs for the convenience of display in the table.",
+        "bbox": [
+            112,
+            801,
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+            839
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "page_number",
+        "text": "1789",
+        "bbox": [
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+        ],
+        "page_idx": 13
+    }
+]

2024/Selene_ Pioneering Automated Proof in Software Verification/b16fd601-eaad-4a83-adb6-e746dee5acd2_origin.pdf

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2024/Selene_ Pioneering Automated Proof in Software Verification/full.md

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+# Selene: Pioneering Automated Proof in Software Verification
+
+Lichen Zhang*
+
+Peking University hang9653@gmail.com
+
+Shuai Lu† and Nan Duan
+
+Microsoft Research Asia {shuailu,nanduan}@microsoft.com
+
+# Abstract
+
+Ensuring correctness is a pivotal aspect of software engineering. Among various strategies available, software verification offers a definitive assurance of correctness. Nevertheless, writing verification proofs is resource-intensive and manpower-consuming, and there is a great need to automate this process. We introduce Selene in this paper, which is the first project-level automated proof benchmark constructed based on the real-world industrial-level operating system microkernel, seL4. Selene provides a comprehensive framework for end-to-end proof generation and a lightweight verification environment. Our experimental results with advanced large language models (LLMs), such as GPT-3.5-turbo and GPT-4, highlight the capabilities of LLMs in the domain of automated proof generation. Additionally, our further proposed augmentations indicate that the challenges presented by Selene can be mitigated in future research endeavors.
+
+"Program testing can be used to show the presence of bugs, but never to show their absence."
+
+Dahl et al.'s (1972)
+
+# 1 Introduction
+
+Confirming the correctness of the software, i.e., checking whether it adheres to the properties specified in the requirements, is advantageous for software engineering (SE). In contrast to testing, which is incomplete, verification provides rigorous guarantee of software correctness or incorrectness (D'Silva et al., 2008). Specifically, during testing, an adequate number of test cases are created and tested against the subject program. If the program violates a testing oracle or encounters other errors (e.g., runtime error), a bug is found. However, the
+
+opposite conclusion cannot be guaranteed otherwise. Verification often involves the usage of a formal language and the corresponding prover. This process requires formal proofs to rigorously demonstrate that the program satisfies the required properties, which can be verified by the prover.
+
+In general, software verification involves two stages. ① The prerequisite specification stage translates the required properties and the subject program into the formal language, creating a to-be-proved proposition stating that "the program meets the properties", a.k.a., the specification. ② The proof stage is supposed to generate proofs that prove the above specification and can be formally checked by the prover. Both stages consume significant resources and manpower, with the second stage being particularly demanding. E.g., the seL4 operating system microkernel 2, which has been formally verified against strong functionality and security properties, requires 7 person-months dedicated to the specification stage and 11 person-years to the proof stage for correctness verification, and the amount of proof code in seL4 is even ten times more than that of the microkernel implementation itself (Klein et al., 2014). Therefore, in order to promote provable software, automated software verification, particularly automated proof, is highly desirable. As an early exploratory effort, in this paper, we explore to automate the major overhead.
+
+Typically, automated proof in software verification is a conditional generation task from the specification to the proof, involving reasoning capabilities. Fortunately, large language models (LLMs) offer an opportunity, as they have demonstrated significant capacity in logic and reasoning at mathematical theorem proving (Jiang et al., 2022; First et al., 2023; Jiang et al., 2023). Only limited re
+
+![](images/5f828acf0b1ad1e5f1b9e129bbd04a1b5975e7b94d8c236b7d394ee6cfa477d1.jpg)  
+Figure 1: A demonstration of the Selene pipeline for automated proof generation (best viewed in color). Selene facilitates both the construction of proofs from scratch (indicated by the gray "generate" path) and the refinement of existing proofs augmented by error messages (highlighted by the red "fixing" path). To validate the correctness of the generated proofs, they are subjected to verification by the Isabelle prover within the authentic seL4 environment.
+
+search has explored how to leverage LLM for code verification (Sun et al., 2023; Yao et al., 2023). And they only focus on function-level code verification, rather than a complete industrial-level software. A distinctive feature of industrial-level projects is the complex dependencies among lemmas and files, which makes automated proof even harder. In order to promote software verification, we propose a real-world industrial-level benchmark based on seL4 for automated proof, namely Selene. SeL4 is a high-assurance operating system microkernel, and it is comprehensively formally verified. The verification of seL4 is mainly based on the formal language of Isabelle (Isabelle, 2023), containing over 100k lines of code in Isabelle and thousands of lemmas (specification + proof), among which we randomly extract 360 for benchmarking. In the major pipeline (as presented in Figure 1), Selene inputs the specification of the target lemma, extracted from seL4, into the subject LLM, and checks the generated proof via the prover within the seL4 environment. As seL4 is a complicated system, Selene provides the complete dependency graph of lemmas, definitions and functions, along with a lightweight verification environment for each lemma to be evaluated. Due to the dependencies of the lemmas, almost the entire verification project needs to be rebuilt in order to check the generated proof, which can lead to a huge evaluation overhead (tens of minutes per lemma). Thence, Selene creates an isolated verification environment for each lemma to avoid duplicate construction and verification of the dependent lemmas, which enables efficient evaluation (it usually takes only a few minutes or even seconds to verify a generation).
+
+We evaluate GPT-3.5-turbo (OpenAI, 2023a) and GPT-4 (OpenAI, 2023b) in the Selene pipeline. The experimental results demonstrate the feasibility
+
+of LLMs for automated proof in software verification. Still, we have identified some further challenges in Selene. 1 The dependency graph of seL4 is complicated, and extracting facts to be applied from it can be hard for LLMs. 2 The logic and reasoning process of a rather large proof may be beyond the capability of the subject LLMs. Even GPT-4 has difficulty in solving the rather difficult categories in Selene. Therefore, to address the challenges, we introduce three distinct augmentations, i.e., similar lemma augmentation, dependency augmentation and fixing augmentation. These augmentations yield varying improvements across the Selene's different categories. Despite the inherent difficulties, our experimental results with these augmentations offer promising indications that the challenges posed by Selene are surmountable.
+
+The main contributions of this paper can be summarized as below.
+
+- We introduce the Selene benchmark, tailored for project-level automated proof in software verification, grounded in the real-world industrial-level project of the seL4 operating system microkernel.  
+- We introduce the technique of lemma isolation, which facilitates a lightweight verification environment capable of handling the complexities inherent in systems such as seL4.  
+- Our experiments with GPT-3.5-turbo and GPT-4 demonstrate the potential of LLMs in automated proof generation in software verification.  
+- We incorporate augmentations into the framework, which mitigate some of the challenges encountered within Selene and suggest promising avenues for future studies.
+
+# 2 Related Work
+
+# 2.1 Automated Theorem Proving by LLM
+
+Automated theorem proving, especially mathematical theorem proving, has garnered significant attention in the field of artificial intelligence. LLMs have shown promising performance in proving formal theorems using proof assistants, such as Isabelle (Isabelle, 2023), Coq (Coq, 2023), and Lean (Lean, 2023). Thor (Jiang et al., 2022) integrates LLMs and hammer-based (Blanchette et al., 2016) provers in Isabelle. DSP (Jiang et al., 2023) leverages LLMs to produce structured formal sketches for automatized proving. Besides, ProofNet (Azerbayev et al., 2023) and Baldur (First et al., 2023) both train or finetune LLMs on formal language corpora. When facing errors, Baldur (First et al., 2023) and Lyra (Zheng et al., 2023) refine the incorrect proofs with error messages.
+
+In addition to the automatic approaches, there are existing benchmarks in the field of formal theorem proving. MiniF2F (Zheng et al., 2022) consists of mathematical problems from Olympiads competitions covering multiple formal languages. PISA (Jiang et al., 2021) includes the Archive of Formal Proofs in Isabelle. ProofNet (Azerbayev et al., 2023) contains mathematical problems in Lean along with parallel natural language descriptions. LeanDojo (Yang et al., 2023) builds a large benchmark in Lean with complete dependencies and the running environment.
+
+# 2.2 Automated Software Verification
+
+Software verification involves checking whether the software meets the requirements. In this paper, we leave alone the dynamic techniques (such as testing) that need to run the software, and only discuss the static formal verification techniques.
+
+We briefly introduce four main techniques of automated software verification. Please refer to the survey for more details (D'Silva et al., 2008). ① Static analysis contains a collection of technologies (e.g., pointer analysis, value range analysis) that analyze the behavior of the software without actual execution. By abstract interpretation (Cousot and Cousot, 1977), which approximately determines the undecidable software behaviors, one may check the correctness. ② Model checking traverses all plausible states of the software to determine whether a property holds (Emerson and Clarke, 1980; Queille and Sifakis, 1982). If the property is violated, the algorithm produces a
+
+reproducible trace, i.e., a counterexample. Due to the large state space, algorithms for model checking are often abstracted or depth-bounded (Biere et al., 1999). ③ Verification-aware programming languages, such as Dafny (Dafny, 2023) and Verus (Verus, 2023), supports formal specification through preconditions, postconditions, and loop invariants, etc., and employs first-order logic solvers (e.g., Z3 (de Moura and Bjørner, 2008)) to automatically prove the specifications. They encourage the programmers to write correct specifications while writing the program, leaving the correctness verification burden to automatic solvers. ④ Interactive verification relies on the interactive proof assistants. Both specifications and proofs during formal verification require substantial manual effort, and they are challenging to be fully automated. Hammers are still the major solutions to automating interactive verification. In the era of LLMs, it is highly feasible to explore automated proof in interactive verification.
+
+Currently, there is limited research specifically addressing the problem of automated software verification with language models. Clover (Sun et al., 2023) introduces a benchmark for consistency checking among code, specification, and docstring, building on the verification-aware language of Dafny. Yao et al. (2023) proposes to use GPT-4 to write invariants, assertions, and other proof structures for Rust-based formal verification, in the short function-level code snippets.
+
+# 3 Selene
+
+We present the Selene benchmark in this paper (Figure 1), and evaluate LLMs' capabilities upon automated proof generation. The subject LLM's goal is to write proofs for the given specifications from seL4 and pass the verification. However, the verification process in the original seL4 environment is time-consuming. Given the impracticality of waiting for dozens of minutes to verify a single proof generated by the LLM, we construct Selene to align with the objective of lightweight evaluation. Drawing on the session design in Isabelle and seL4 (Section 3.1), we introduce lemma isolation (Section 3.2), which enables rapid verification of the target lemma (usually a few seconds). Due to the complexity of seL4, we further delve into some specific implementation details of Selene in Section 3.3.
+
+![](images/aacbf956f2417472d04074bb879cf74708de7ad4b7a0241b2d27143321928480.jpg)  
+Figure 2: An illustrative example of the seL4 verification structure. The arrows pointing from A to B indicate that B is dependent upon A, where A and B can be lemmas, theory files, or sessions, etc.
+
+# 3.1 Preliminary of SeL4
+
+SeL4 is a comprehensively formally verified operating system microkernel (Klein et al., 2014), providing an excellent example for software verification. Most of the verification work on seL4's functional correctness is based upon Isabelle (Isabelle, 2023), which is the basis of Selene.
+
+Isabelle sessions. In the context of large verification projects, Isabelle employs sessions to effectively and efficiently organize the environment (Wenzel, 2023). The concept bears resemblance to the "package-class-function" structure in programming languages, with the design of "session-theory-lemma" in Isabelle. A session serves as a container for verification results typically centered around a specific topic, and maintains them in a persistent form. It enables easy accessibility without the need for repeated rebuilding lemmas within the session. Such design facilitates incremental development during software verification, allowing modifications to be made without necessitating a complete rebuild, as results in the unchanged and independent sessions remain persistent. Isabelle organizes the sessions using a series of ROOT files (please refer to Appendix B), which contain meta information such as the dependencies and the entry theory files for the sessions.
+
+SeL4 verification structure. The verification of seL4 consists of multiple layers of refinement (De Roever and Engelhardt, 1998), progressing from high-level conceptual ideas to the concrete C implementation of the operating system<sup>3</sup>. Thence, there are many sessions involved in seL4 as shown in Figure 2, with some directly completing a refinement layer (e.g., AInvs) while others providing
+
+dependencies (e.g., ASpec and Lib) such as definitions and property specifications.
+
+In our early studies about the verification process of seL4, we have identified some possible challenges. ① The dependencies in seL4 are highly complicated. A refinement session is typically dependent on multiple other sessions, creating a huge and complex dependency graph that makes it hard to identify the prerequisite components for proving a certain lemma in the refinement sessions. For instance, the session AIvs in Figure 2 is dependent on four sessions (Word_Lib, ExecSpec, ASpec, and Lib), and theories in AIvs depend not only on theories within AIvs (e.g., Untyped_AI directly depends on ArchDetype_AI, and both of them are from AIvs), but also on lots of theories from the four dependency sessions (e.g., Untyped_AI is also dependent upon MonadicRewrite from Lib). Such a large dependency graph usually contains hundreds or thousands of definitions, functions, and lemmas. Identifying prerequisite components from this dependency graph to prove lemmas in AIvs can be a great challenge. ② SeL4 is a systematic project that requires a lot of expert knowledge of operating system, i.e., seL4 is sorely domain-specific. LLMs may not be quite familiar these fields, and therefore the quality of generated proofs may not be satisfying. ③ Proofs in seL4 are often in the procedural style, i.e., they specify a series of tactics to apply without describing the intermediate results. In contrast, proofs for general mathematical problems are often in the declarative style (Zheng et al., 2022), i.e., they specify both the proving goals and the proving operations explicitly ④ (see Appendix A). Although previous work have demonstrated that LLMs can deal with declarative proofs (Jiang et al., 2022; First et al., 2023), the procedural style in seL4 may become a challenge.
+
+# 3.2 Lemma Isolation in Selene
+
+As outlined in Section 3.1, for large projects like seL4, Isabelle constructs the overall verification at the session granularity. However, it can lead to significant overhead during our evaluation - after generating a proof for the given lemma, one may have to wait for multiple minutes to build the corresponding session from scratch. To address
+
+![](images/ac2d3d876dd9204fb561d33b3a152ffd98afc2d36e9e333d4cbe2de347a8d0a6.jpg)  
+Figure 3: A working example of lemma isolation in Selene. Based on the original seL4 structure in Figure 2, we construct an isolated session (AINvs_TGT) along with a dependency session (AINvs_DEP) to facilitate efficient verification of the target lemma (strengthen_Not).
+
+this issue, we propose lemma isolation, wherein the target lemma is isolated from its dependencies, thereby avoiding repeated verification of the dependencies and creating a lightweight environment for Selene evaluation.
+
+Following the working example presented in Figure 2, we isolate the target lemma strengthen_Not from the original session AIvs, depicted in Figure 3. The isolation process yields a minimal target session AIvs_TGT, which exclusively contains only the target lemma strengthen_Not. To verify AIvs_TGT, a dependency session AIvs_DEP is required. AIvs_DEP consists of theory files originally found in the dependency tree of Untyped_AI along with a new theory file (Untyped_AI_DEP) containing the contents preceding strength_Not in Untyped_AI. The theories in AIvs_DEP reconstruct the dependencies of the target lemma strength_Not in the original AIvs session.
+
+AInvs_DEP, as well as other dependency sessions (ASpec, Lib, etc.), are verified once and remain fixed during evaluation. Accessing the persistent verification results in these sessions to verify AInvs_TGT takes little time. Lemma isolation can reduce the verification time to about  $\frac{1}{3}$  of rebuilding from scratch (see Appendix C), creating a lightweight verification environment.
+
+# 3.3 Key Know-how about Selene
+
+In addition to the isolation design, the implementation of Selene involves many details, which can be attributed to the complexity of the seL4 system.
+
+Lemma extraction. We gather theory files from the refinement sessions in seL4, and extract lemmas through a rough parser (e.g., lemmas always begin with the token "lemma" or "threorem" and
+
+<table><tr><td></td><td>P1</td><td>P2</td><td>P3</td><td>D</td></tr><tr><td>Extracted</td><td>1,995</td><td>2,496</td><td>928</td><td>45</td></tr><tr><td>Sampled</td><td>160</td><td>120</td><td>80</td><td>45</td></tr><tr><td>Correctly verified</td><td>144</td><td>109</td><td>64</td><td>43</td></tr><tr><td>Demonstration</td><td>5</td><td>5</td><td>5</td><td>5</td></tr><tr><td>Evaluation</td><td>139</td><td>104</td><td>59</td><td>38</td></tr></table>
+
+Table 1: Statistics of Selene. P1, P2 and P3 denote the three difficulty levels for lemmas in procedural style, while D represents lemmas in declarative style.
+
+end with the token “qed”, “done” or a “by ...” statement). Lemmas within contexts or locales  $^{5}$  are excluded from the process, because we find them incompatible with our design of lemma isolation. If the proof for a lemma exceeds 20 lines, we exclude it from Selene, as it may be too long and too challenging for LLMs. Finally, we collect 5,464 lemmas across 11 sessions from seL4.
+
+Dependency session construction. We construct the dependency session by replacing only the target theory file in the directory. Taking Figure 2 and 3 for instance, we replace the theory file Untyped_AI in the session AInvs with the new theory Untyped_AI_DEP to build the dependency session AInvs_DEP. In the ROOT file, we set the entry to Untyped_AI_DEP and copy other meta information of AInvs to complete the construction of AInvs_DEP (please refer Appendix B). Even if there are additional theories in Untyped_AI_DEP, this setup will not include them into the dependency graph, providing correct dependencies to AInvs_TGT.
+
+Lemma category. As mentioned earlier, we observed that the majority of proofs in seL4 are in procedural style (5,419 out of 5,464 lemmas collected), while only a small number are in declarative style (45). Procedural proofs typically apply a sequence of tactics to achieve the proving goal, and the length usually reflects the level of difficulty. For procedural style, we categorize lemmas into three difficulty levels according to the proof length: P1 (one single line), P2 (two to six lines), and P3 (seven to twenty lines). Lemmas from each difficulty level are randomly sampled to create the benchmark. As for lemmas in declarative style, all of them are included in the benchmark.
+
+Correctness checking. It is important to check the correctness of the isolated sessions, as the imple
+
+mentation may not be guaranteed to be accurate. There are three potential causes of incorrect isolation: ① the extracted lemmas may be incomplete due to the limitation of keyword matching; ② copying meta information in ROOT files may result in configuration errors; ③ the complex system setup of seL4 may lead to errors during lemma isolation. In addition, prior to evaluation, the dependency sessions should also be verified once to produce the necessary persistent results. We exclude those incorrect lemmas from Selene, leaving the remaining lemmas ready for evaluation. Table 1 lists the statistics of each step in Selene construction.
+
+# 4 Evaluation
+
+# 4.1 Evaluation Pipeline
+
+Pipeline. The evaluation pipeline of Selene is presented in Figure 1. The subject LLM takes the specification, extracted from the isolated target session, as input, and generates a potential proof for it. The isolated target session is updated by appending the generated proof to the specification, and subsequently verified by the Isabelle prover. As designed in Section 3.2, since the dependency sessions have been already built once, the verification results are persistently available to the target session, thus the verification of the target session does not consume significant amount of time.
+
+Metrics. We employ accuracy at  $k$  trials as the performance indicator, denoted as ACC#k. Specifically, the subject LLM independently generates  $k$  proofs using temperature sampling (Ficler and Goldberg, 2017; Fan et al., 2018; Caccia et al., 2020) and nucleus (top-p) sampling (Holtzman et al., 2020). If at least one of the  $k$  trials is successfully verified, ACC#k for the corresponding lemma is 1; otherwise, it is 0.
+
+Prompt. The prompt includes an instruction, which specifies the task of automated proof, along with several demonstrations for in-context learning (Brown et al., 2020). Each demonstration consists of a specification and its corresponding groundtruth proof (please refer to Appendix D).
+
+# 4.2 Evaluation Setup
+
+We evaluate GPT-3.5-turbo (OpenAI, 2023a) and GPT-4 (OpenAI, 2023b) upon Selene. Within each set (P1, P2, P3, and D), we randomly select five lemmas as demonstrations, which remain fixed during our evaluation, and evaluate the remaining lemmas against the subject LLMs, as listed in Table
+
+<table><tr><td></td><td>ACC</td><td>P1</td><td>P2</td><td>P3</td><td>D</td></tr><tr><td>GPT-3.5</td><td>#1</td><td>28.1</td><td>2.9</td><td>0</td><td>0</td></tr><tr><td>-turbo</td><td>#5</td><td>35.3</td><td>5.8</td><td>0</td><td>5.3</td></tr><tr><td rowspan="2">GPT-4</td><td>#1</td><td>41.7</td><td>7.7</td><td>0</td><td>10.5</td></tr><tr><td>#5</td><td>51.8</td><td>12.5</td><td>1.7</td><td>15.8</td></tr></table>
+
+Table 2: Performance of GPT-3.5-turbo and GPT-4 against Selene (values in percentage).
+
+1. The subject LLMs take in the concatenation of the instruction, five demonstrations, and the target lemma specification, without additional augmentations, and generate proof trials.
+
+ACC#1 and ACC#5 are assessed in our evaluation. The probability threshold (top- $p$ ) is set to 0.95, and the temperature is set to 0 for ACC#1 and 0.5 for ACC#5. Generation trials that exceed the token length of 2,048, contain the token "sorry" or "oops" (which can bypass the verification process, leading to false positive results), or take more than 10 minutes during verification (timeout) are all considered as failures.
+
+# 4.3 Evaluation Result
+
+The results are listed in Table 2. The results suggest that LLMs have the capacity to automate proof generation in Selene, with GPT-4 notably achieving  $51.8\%$  ACC#5 upon P1. Nevertheless, as the complexity of the proofs for procedural lemmas increases (P1  $\rightarrow$  P3), the task becomes increasingly challenging for both GPT-3.5-turbo and GPT-4 models. In fact, both models struggle significantly when attempting to prove lemmas within the P3 category, which require comprehending an extensive dependency graph and employing more sophisticated reasoning capabilities. Interestingly, both the subject models perform better when addressing declarative lemmas (D) within Selene, as opposed to those categorized under P3, despite the proofs for most D category lemmas being of comparable length to those in P3, typically ranging from 7 to 20 lines. A plausible explanation could be that the inclusion of intermediate goals within declarative proofs mitigates the difficulty in logic and reasoning. In addition, we find that in many cases, GPT-4 adopts different proving strategies than the groundtruth (see cases in Appendix E), suggesting that the LLM is not simply memorizing.
+
+Failure type. We analyze and categorize the errors made by GPT-4 during the evaluation process to better understand the challenges posed by Selene. The errors are classified into three distinct cate
+
+<table><tr><td>Error</td><td>P1</td><td>P2</td><td>P3</td><td>D</td></tr><tr><td>Total</td><td>81</td><td>96</td><td>59</td><td>34</td></tr><tr><td>Undefine</td><td>38(47%)</td><td>37(39%)</td><td>21(36%)</td><td>12(35%)</td></tr><tr><td>Logic</td><td>41(51%)</td><td>55(57%)</td><td>31(52%)</td><td>20(59%)</td></tr><tr><td>Other</td><td>2(2%)</td><td>4(4%)</td><td>7(12%)</td><td>2(6%)</td></tr></table>
+
+Table 3: The composition of different types of errors made by GPT-4. The errors are collected in the ACC#1 setting evaluation. Outside the brackets are the absolute number of errors, inside the brackets are the percentages.
+
+gories based on the nature of the error encountered: 1 "undefined errors", where tactics not defined in seL4 are applied in the proofs, 2 "logic errors", where the proof cannot be finished (e.g., application of inappropriate tactics, presence of incomplete proving goals), and 3 "other errors", including syntax errors, runtime errors, and other issues. The error composition is presented in Table 3. The majority of the errors (over a half) committed by GPT-4 can be attributed to its inadequate reasoning capability, which leads to unfinished proof goals (logic errors). A smaller, yet still significant, proportion of errors (undefined errors) stem from a lack of comprehensive knowledge of the dependencies within the entire seL4 project. Additionally, it is notable that GPT-4 barely makes syntax error, as most cases in other errors are refusal to generate proof 6, timeouts, and empty outputs (e.g., exceeding the generation length), etc.
+
+# 5 Augmentation
+
+As previously discussed, LLMs exhibit significant potential for automated proof when evaluated against Selene, however, it is also evident that the task presents substantial challenges. We propose some augmentation techniques and evaluate them in our evaluation pipeline, with the aspiration that they may serve as a catalyst for further exploration in future studies.
+
+# 5.1 Augmentation to Evaluation Pipeline
+
+Similar lemma augmentation. SeL4 is an intricate piece of software, and as a consequence, its formal verification process is even more complex, involving a multitude of lemmas that can be similar (or even identical). The presence of these similar lemmas naturally offers an opportunity to augment
+
+![](images/7c20627d4a30c7d01dded2bc6a423b4f7a74b09ed72c29e26abd458f35ca9f55.jpg)  
+Figure 4: Demonstrative examples of similar lemma augmentation and dependency augmentation.
+
+the automated proof pipeline, and similar augmentation has been proven beneficial in tasks such as question-answering (Lewis et al., 2020) and code completion (Lu et al., 2022). Specifically, we build a retrieval library by segmenting theory files from seL4 into discrete chunks. The segmentation is guided by the blank lines in the text. Retrieval is performed through the BM25 algorithm (Robertson and Zaragoza, 2009) (the upper part of Figure 4), which involves querying the target specifications against the retrieval library to identify analogous text segments (i.e., similar lemmas). To ensure the integrity of the experiment, the groundtruth proof is deliberately omitted from the retrieval process to prevent biases in the search results. During our evaluation, we select the initial ten lines from the chunk most closely resembling the target specification as the augmentation.
+
+Dependency augmentation. The complex dependencies inherent in the seL4 project pose significant obstacles to LLMs when evaluated against Selene, as evidenced in Table 3. To mitigate this challenge, we introduce the dependency augmentation. Particularly, we extract the applied facts from the ground truth proof, and identify their origin by searching in the chunk library (those chunks not in the dependency sessions are omitted during this process), as shown in the lower part in Figure 4. The pinpointed definitions, functions, and lemmas are clearly integral to the proof of the target specification. And these elements are then provided to the subject LLM as augmentations, with the intention of simplifying the task by providing correct information for the model to apply. Ideally, this augmentation should alleviate the obstacles posed by dependencies, allowing the subject LLM to focus on applying the accurate information provided. However, during our practice, the absence of sophisticated tools means we cannot pinpoint every fact and its origin with complete precision. Consequently, the results of the dependency aug-
+
+<table><tr><td>Augmentation</td><td>P1</td><td>P2</td><td>P3</td><td>D</td></tr><tr><td>GPT-4</td><td>41.7</td><td>7.7</td><td>0</td><td>10.5</td></tr><tr><td>+Similar</td><td>47.5</td><td>14.4</td><td>1.7</td><td>10.5</td></tr><tr><td>+Dependency</td><td>52.5</td><td>14.4</td><td>1.7</td><td>-</td></tr><tr><td>+Fixing</td><td>53.2</td><td>9.6</td><td>0</td><td>18.4</td></tr></table>
+
+Table 4: ACC#1 of GPT-4 with augmentations evaluated against Selene (values in percentage). For the D category, we skip the dependency augmentation, due to the complexity of fact extraction in this category.  
+
+<table><tr><td rowspan="2">Aug.</td><td colspan="4">Error</td></tr><tr><td>Total</td><td>Undef.</td><td>Logic</td><td>Other</td></tr><tr><td>GPT-4</td><td>81</td><td>38(47%)</td><td>41(51%)</td><td>2(2%)</td></tr><tr><td>+Similar</td><td>73</td><td>29(40%)</td><td>42(57%)</td><td>2(3%)</td></tr><tr><td>+Dependency</td><td>66</td><td>16(24%)</td><td>45(68%)</td><td>5(8%)</td></tr><tr><td>+Fixing</td><td>65</td><td>30(46%)</td><td>32(49%)</td><td>3(5%)</td></tr></table>
+
+mentation should be viewed as a potential upper limit of the subject LLM's capability in this context. We use the first five lines from the origin of each identified fact as the augmentation.
+
+Fixing augmentation. When a proof attempt does not succeed, it is almost a standard procedure to examine the error message in order to fix the flawed proof (refer to Figure 1). The error message typically provides comprehensive feedback, such as the error type and the state of the proof at the moment of failure. There are existing studies that support the capability of LLMs to fix previously incorrect logic by incorporating error messages (First et al., 2023; Zheng et al., 2023; Chen et al., 2023), which make this augmentation even feasible when dealing with Selene. The evaluation is conducted as a two-round dialogue – if the subject LLM does not succeed in the first round, we feed the error message into the model and ask it to try again; if the subject LLM succeeds in the first trial, we do not carry out the second round of fixing.
+
+We evaluate GPT-4 with the three augmentations, with the performance indicator of ACC#1. All other settings remain the same as in Section 4.2.
+
+# 5.2 Augmentation Result
+
+The results listed in Table 4 indicate the three augmentations lead to improvements across different categories. We also examine the error composition of GPT-4 with augmentations evaluated against P1, as listed in Table 5. In the below, we analyze the effect of each augmentation strategy and carry out some ablation studies.
+
+Table 5: The composition of errors made by GPT-4 with augmentations evaluated against Selene-P1.  
+
+<table><tr><td>Augmentation</td><td>P1</td><td>P2</td><td>P3</td><td>D</td></tr><tr><td>+TryAgain</td><td>49.6</td><td>7.7</td><td>0</td><td>10.5</td></tr><tr><td>+Similar &amp; Fixing</td><td>61.9</td><td>20.2</td><td>1.7</td><td>7.9</td></tr></table>
+
+Table 6: Ablation of augmentations (ACC#1 of GPT-4).
+
+Similar augmentation. The similar augmentation is found to enhance performance upon procedural categories (P1-P3), indicating the utility in the augmented contexts; but it does not yield a significant effect upon the D category, suggesting a potential area for further investigation. According to Table 5, the similar augmentation marginally ameliorates the incidence of undefined errors without showing notable impact on logic errors. This improvement could be attributed to the facts introduced from the inclusion of similar lemmas.
+
+Dependency augmentation. The dependency augmentation significantly improves GPT-4 on P1  $(41.5\% \rightarrow 52.5\%$  in Table 4). As for the errors in Table 5, it is notable that the dependency augmentation results in a substantial diminution of undefined errors, corroborating our intended purpose.
+
+Fixing augmentation. In Table 5, as the complexity of the proof increases (i.e., P2 and P3), the fixing augmentation is less effective. This trend is expected since simple proofs (as in P1) typically contain straightforward errors that can be corrected in a single fixing attempt, whereas longer and more complex proofs may require multiple rounds of corrections. Also, as demonstrated in Table 5, there is a noticeable reduction in logical errors, which can be attributed to the integration of error messages. We further ablate by not providing the error message to GPT-4, only asking it to try again if the first attempt fails. The results are listed in the "TryAgain" row of Table 6. TryAgain brings limited improvement compared to fixing, suggesting that error messages are important.
+
+Similar + dependency. We carry another ablation by combining similar and fixing augmentations together ("Similar&Fixing" in Table 6). Based on Table 5, the similar and the fixing augmentations improve the undefined fact and the logic error issues, respectively. Results show that combining both augmentations significantly improves GPT-4's performance upon P1 and P2. On D category, these two augmentations may have opposite effects, causing unexpected performance degradation (even worse than raw GPT-4). This phenomenon may be worthy of future exploration.
+
+# 6 Conclusion
+
+In this paper, we study the domain of automated proof within the context of software verification. We introduce Selene, which is a real-world industrial-level automated proof benchmark derived from the seL4 project. Selene provides a lightweight verification environment facilitated by lemma isolation with Isabelle sessions. The current framework supports end-to-end proof generation and evaluation, bolstered by supplementary augmentation. By evaluating against advanced LLMs such as GPT-3.5-turbo and GPT-4, we demonstrate the potential of LLMs in automated proof generation for software verification. Nevertheless, Selene poses formidable challenges that LLMs have yet to overcome fully. It is our hope that Selene will catalyze further research in this area, promoting advancements in software verification.
+
+# 7 Limitation
+
+We present some discussions on the limitations of Selene. As an early step of software verification, we consider addressing these limitations and challenges as our future work. Hopefully, we could offer insights that may serve as a catalyst for future studies in this field.
+
+Dependency extraction. SeL4 contains a huge and complex dependency graph, posing a significant challenge in the accurate extraction of dependencies, i.e., facts. Our analysis has revealed that undefined errors (e.g., applying nonexistent facts) account for nearly half of GPT-4's failures in Selene. The dependency augmentation experiment has further proven the effectiveness and necessity of dependency in addressing this issue. One promising research direction may be to transition from providing LLMs with groundtruth facts as done in this paper, to employing advanced techniques (such as RAG (Lewis et al., 2020; Asai et al., 2023)) to automatically extract candidate facts directly from the codebase. We leave this as our future work.
+
+Specification generation. There are two stages in software verification – the prerequisite specification stage and the proof stage. In this paper, we primarily concentrate on the automation of the proof stage, which constitutes the main bulk of the verification workload. However, it is important to acknowledge that the specification stage, which involves translation of properties and programs into formal languages, is not without its own set of challenges. This stage is not only time-consuming and
+
+resource-intensive but also necessitates substantial advancements in automation to enhance efficiency.
+
+Proof state. The current pipeline of Selene only supports end-to-end proof generation, i.e., the subject LLM generates the entire proof. Our experimental results indicate that LLMs possess the ability to prove lemmas within the less challenging P1 category. However, the effectiveness significantly diminishes when addressing lemmas from the more complex P3 category. This observation aligns with the experiences of human practitioners, who typically cannot construct proofs for P3 lemmas in a single attempt but instead progress incrementally, selecting suitable operations at each step based on the evolving proof state. To enhance the capability of LLMs in addressing P3 lemmas, it may be necessary to introduce the interactive proof state into the Selene pipeline in the future, thereby mimicking the human practitioners during proof construction.
+
+To observe the intermediate state, PISA (Jiang et al., 2021) provides a practical solution. PISA implements a schema-Isabelle framework to glance at the proof state of the Isabelle verification system. With the proof state available, LLMs are allowed to generate proofs in an interactive manner. We believe that techniques in PISA are orthogonal with lemma isolation - lemma isolation allows rather quick session loading, and PISA provides and interactive environment. The incorporation of PISA and Selene is another future work.
+
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+Verus. 2023. The verus project. https://github.com/verus-lang/verus.  
+Makarius Wenzel. 2023. The isabelle system manual.  
+Kaiyu Yang, Aidan M. Swope, Alex Gu, Rahul Chalamala, Peiyang Song, Shixing Yu, Saad Godil, Ryan Prenger, and Anima Anandkumar. 2023. Leandojo: Theorem proving with retrieval-augmented language models. CoRR, abs/2306.15626.
+
+Jianan Yao, Ziqiao Zhou, Weiteng Chen, and Weidong Cui. 2023. Leveraging large language models for automated proof synthesis in rust. arXiv preprint arXiv:2311.03739.  
+Chuanyang Zheng, Haiming Wang, Enze Xie, Zhengying Liu, Jiankai Sun, Huajian Xin, Jianhao Shen, Zhenguo Li, and Yu Li. 2023. Lyra: Orchestrating dual correction in automated theorem proving. CoRR, abs/2309.15806.  
+Kunhao Zheng, Jesse Michael Han, and Stanislas Polu. 2022. minif2f: a cross-system benchmark for formal olympiad-level mathematics. In The Tenth International Conference on Learning Representations, ICLR 2022, Virtual Event, April 25-29, 2022. Open-Review.net.
+
+# A Procedural Vs. Declarative Style
+
+The procedural style proofs specify a series of tactics to apply, without describing the intermediate results. A demonstrative lemma from seL4 is shown below.
+
+```txt
+lemma unbindNotification_valid_sched[wp]: {"valid_sched} unbindNotification ntfnptr {  $\lambda$  rv. valid_sched}" apply (simp add: unbindNotification_def) apply (rule hoare_seq_ext[OF _ gbn_sp]) apply (case_tac ntfnptra, simp, wp, simp) apply (clarsimp) apply (rule hoare_seq_ext[OF _ getsimple ko_sp]) apply (wp set_boundNotification_valid_sched, clarsimp) done
+```
+
+In the example, line 4-10 apply a sequence of tactics to achieve the proving goal. Declarative style proofs, on the other hand, explicitly write both the intermediate proving goals and the proving operations. A typical example from seL4 is shown below.
+
+```txt
+lemma thread_set_as_user: "thread_set ( $\lambda$ tcb. tcb ( tcb_arch := arch_tcb_context_set (f $ arch_tcb_context-get (tcb_arch tcb)) (tcb_arch tcb))) t = as_user t (modify f)"  
+proof - have P: " $\wedge$ f. det (modify f)"  
+by (simp add: modify_def) thus ?thesis apply (simp add: as_user_def P thread_set_def) apply (clarsimp simp add: select_f_def simpler_modify_def bind_def image_def) done qed
+```
+
+Line 6 in this lemma specifies the intermediate proving goal, and the following lines performs a series of tactics.
+
+In general, mathematical problems are usually pure and abstract, and therefore they are well-suited for the declarative style; while software verification usually deals with large, concrete and complex systems like seL4, and it benefits from the procedural style (Harrison, 1996). In Selene, we notice that most proofs in seL4 are in the procedural style.
+
+<table><tr><td></td><td>P1</td><td>P2</td><td>P3</td><td>D</td></tr><tr><td>Checking</td><td>148.9</td><td>145.8</td><td>217.3</td><td>178.7</td></tr><tr><td>GPT-3.5-turbo</td><td>40.2</td><td>43.7</td><td>42.5</td><td>50.6</td></tr><tr><td>GPT-4</td><td>35.6</td><td>43.5</td><td>43.9</td><td>43.3</td></tr></table>
+
+Table 7: Average elapsed time of verification of correctness checking before evaluation, and ACC#1 evaluation of GPT-3.5-turbo and GPT-4 without augmentations (values in seconds).
+
+# B ROOT File
+
+As previously introduced, Isabelle organizes the environment with sessions, which can be regarded as a container for verification results of certain topics. The structure of a session, including its dependent sessions and its entries, etc., is defined and described in the ROOT file. An example from seL4 is presented below, which is a part of a large ROOT file.
+
+```txt
+1 session BaseRefine in "refine/base" = AInvs +  
+2 description \<open>Background theory and  
+3 libraries for refinement proof.\<close>  
+4 sessions  
+5 Lib  
+6 CorresK  
+7 theories  
+8 "Include"
+```
+
+This partial ROOT file defines a session named "BaseRefine", which locates at the directory "refine/base" (Line 1). BaseRefine is directly dependent on another session "AIvs" (Line 1), and it imports two more sessions, "Lib" and "CorresK" (Line 4-6, these two sessions are also dependency to BaseRefine). BaseRefine has only one entry theory file, "Include.thy" (Line 7-8). The theory Include is dependent on other theories in BaseRefine, and the prover verifies the whole session in a bottom-up manner (it first checks all dependencies of Include, and then verifies lemmas within Include).
+
+As in Figure 3, during lemma isolation, Selene sets the theory "Untyped_AI_DEP.thy" as the entry of the dependency session (Ainvs_DEP in the figure), and sets the dependency of the target session (Ainvs_TGT) to the dependency session (Ainvs_DEP).
+
+# C Verification Time
+
+The time cost of the verification process is listed in Table 7. Correctness checking bears resemblance of building from scratch, and it takes on average about three times longer than verifying only the isolated target session. Note that we even include the ten minutes of timeout during evaluation in Table 7.
+
+Since we only perform correctness checking once before evaluation, lemma isolation can greatly improve the verification efficiency during evaluation of Selene.
+
+# D Prompt
+
+Instruction. The basic instruction is shown below.
+
+You are an experienced formal language programmer. You not only know the Isabelle formal language very well, but also are very familiar with the seL4 project. As a reminder, seL4 is an almost fully formally verified operating system microkernel. Your mission is to write formal proofs in Isabelle for the given specifications, which formally describe properties of seL4 in Isabelle. You are not supposed to write anything other than formal proofs in Isabelle. E.g., You should not write comments or explanations in natural language. In addition, the formal proofs you write will be automatically checked, therefore, you need to do your best to make it correct.
+
+For each augmentation, there is an augmented instruction listed below. We concatenate the basic instruction and the corresponding augmented instruction, forming the final instruction.
+
+Similar: Some chunks of seL4 with similar specifications are provided before the target specification. Each chunk is provided between the tags of "<sim>" and "<sim)". You can use these chunks to assist the proof of the target specification.
+
+Dependency: Some previous chunks of seL4 are provided before the target specification as plausible dependencies. Each chunk is provided between the tags of "<dep>" and "<dep>". You can use these chunks to assist the proof of the target specification.
+
+Fixing: If the previous proof is not correct, the error message may be provided inside curly brackets {just like this}. If the error message is provided, you are supposed to make the previous proof correct at your best.
+
+Demonstration. In general, a demonstration for the subject LLM (e.g., GPT-4) is an input-output pair. In the most simple evaluation setting of Selene (without any augmentation), the input in the demonstration is the specification of the demonstrative lemma and the output is the corresponding proof. When augmented by similar chunks, the demonstration output remains the same, while the input is a concatenation of the similar chunk and the specification. The similar chunk is tagged by “<sim>” and “</sim>”. The dependency augmentation is quite similar, with different tags of “<dep>” and “</dep>.
+
+As for fixing augmentation, we need to collect erroneous proofs and corresponding error messages upon the demonstrative lemmas. For each lemmas within the five demonstrations, we invoke the subject LLM in the same manner as in Section 4, using
+
+the other four lemmas as demonstrations. In this way, we may collect some errors produced by the subject LLM. The demonstrations for fixing augmentation are much more complicated. We carry out this augmentation in a two-round dialogue way. I.e., each demonstration may contain two input-output pairs (if the subject LLM fails). The first pair is the specification and the erroneous proof generated by the subject LLM; the second pair is the error message and the groundtruth proof. Note that the error message is inside curly brackets (e.g., {Undefined fact: "st_def" At command "by"}). If the subject LLM successfully generates a proof for the demonstrative lemma, i.e., it does not make any error, the demonstration only contains one pair, i.e., the specification along with the groundtruth proof.
+
+# E Generated Cases
+
+Some cases generated by GPT-3.5-turbo and GPT-4 upon the P1 category of Selene are presented in Table 8. These cases are randomly selected from the union of correct generation from GPT-3.5-turbo and GPT-4 under the setting of ACC#1, without cherry-picking. In the table, we can observe that GPT-4 almost do not generate a proof identical to the groundtruth (except for tbc_context_merge). This shows that to a certain extent, GPT-4 can understand and generate proofs for seL4.
+
+<table><tr><td rowspan="2">Target Lemma
+(Specification + Groundtruth Proof)</td><td colspan="2">Generated Proof</td></tr><tr><td>GPT-3.5-turbo</td><td>GPT-4</td></tr><tr><td>lemma (in strengthenIMPLEMENTATION)
+strengthen_Not[strg]:
+
+&quot;[| st (¬F) (→) P P&#x27; | ]
+→ st F (→) (¬P) (¬P&#x27;)&quot; 
+(* PROOF STARTS RIGHT HERE *) 
+by (cases F, auto)</td><td>by (erule
+strengthen_precondition)
+[x] Undefined fact</td><td>by (clarsimp simp: st_def)
+[√]</td></tr><tr><td>lemma gen_invocation_typeI:
+&quot;invocation_type l = GenInvocationLabel x
+→ gen_invocation_type l = x&quot;
+(* PROOF STARTS RIGHT HERE *) 
+by (simp add: gen_invocation_type_def)</td><td>by (simp add:
+gen_invocation_type_def)
+[√]</td><td>by (simp add:
+gen_invocation_type_def
+split: invocation_label.splits)
+[√]</td></tr><tr><td>lemma ts_Restart(case_helper:
+(&quot;case ts of Structures_A.Restart ⇒ A
+| _ ⇒ B)
+= (if ts = Structures_A.Restart
+then A else B)&quot; 
+(* PROOF STARTS RIGHT HERE *) 
+by (caseTac ts, simp_all)</td><td>by (caseTac ts, simp_all)
+[√]</td><td>by (cases ts; simp)
+[√]</td></tr><tr><td>lemmairq_state_back:
+&quot;P (irq_state_of_state (internal_state_if
+((a,b),c))
+(irq�建省_of_state (internal_state_if
+((a,b),c))
+→ P (irq_state_of_state b)
+(irq�建省_of_state b)&quot; 
+(* PROOF STARTS RIGHT HERE *) 
+by simp</td><td>by simp
+[√]</td><td>by (clarsimp simp:
+internal_state_if_def)
+[x] Undefined fact</td></tr><tr><td>lemma cte_wp_at_conj:
+&quot;cte_wp_at (λc. P c ∧ Q c) p s
+= (cte_wp_at_P p s ∧ cte_wp_at_Q p s)&quot; 
+(* PROOF STARTS RIGHT HERE *) 
+by (fastforce simp: cte_wp_at_def)</td><td>by (auto simp:
+cte_wp_at_caps_of_state)
+[√]</td><td>by (auto simp:
+cte_wp_at_caps_of_state)
+[√]</td></tr><tr><td>lemma smrs_cte_at[wp]:
+{&quot;cte_at p} set_mrs_thread buf msgss
+(λ_. cte_at p)&quot; 
+(* PROOF STARTS RIGHT HERE *) 
+by (wp valid_cte_at_typ)</td><td>Sorry, I cannot assist
+with this request.
+[x] Outer syntax error</td><td>by (wp | simp add: set_mrs_def)+
+[√]</td></tr><tr><td>lemma master_eqE:
+[&quot;| capMasterCap cap = capMasterCap cap];
+^cap. F (capMasterCap cap) = F cap ]
+→ F cap = F cap ]
+(* PROOF STARTS RIGHT HERE *) 
+by (rule master_eqI, assumption, simp)</td><td>by (metis)
+[√]</td><td>by (drule meta_mp) auto
+[x] Failed to apply proof method</td></tr><tr><td>lemma tcb_context_merge[simp]:
+&quot;arch_tcb_context_get (tcb_arch
+(tcbRegisters_caps_merge tcb_tcb&quot;))
+= arch_tcb_context_get (tcb arch tcb)&quot; 
+(* PROOF STARTS RIGHT HERE *) 
+by (simp add: tcbRegisters_caps_merge_def)</td><td>by (simp add:
+tcbRegisters_caps_merge_def)
+[√]</td><td>by (simp add:
+tcbRegisters_caps_merge_def)
+[√]</td></tr><tr><td>lemma cte_map_tcb_2:
+&quot;cte_map (t, tcb_cnode_index 2)
+= t + 2*2^cte_level_bits&quot;
+(* PROOF STARTS RIGHT HERE *) 
+by (simp add: cte_map_def
+tcb_cnode_index_def to_bl_1)</td><td>by (simp add: cte_map_def
+tcb_cnode_index_def)
+[√]</td><td>by (simp add: cte_map_def
+tcb_cnode_index_def
+cte_level_bits_def)
+[√]</td></tr><tr><td>lemma object_type_asid_reset [simp]:
+&quot;object_type (asid_reset obj)
+= object_type obj&quot;
+(* PROOF STARTS RIGHT HERE *) 
+by (clarsimp simp: asid_reset_def)</td><td>by (cases obj, auto)
+[x] Failed to finish proof</td><td>by (cases obj; simp
+add: asid_reset_def)
+[√]</td></tr></table>
+
+Table 8: Cases generated by the subject LLMs upon P1 of Selene. These cases are collected under the ACC#1 setting. The verification results are marked under the generated proofs. Please note that we have added some line breaks into the original lemmas and the generated proofs for the convenience of display in the table.

2024/Selene_ Pioneering Automated Proof in Software Verification/images.zip

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2024/Self-Alignment for Factuality_ Mitigating Hallucinations in LLMs via Self-Evaluation/4674208f-1349-44d5-a230-509edd63af70_origin.pdf

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2024/Self-Alignment for Factuality_ Mitigating Hallucinations in LLMs via Self-Evaluation/full.md

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+# Self-Alignment for Factuality: Mitigating Hallucinations in LLMs via Self-Evaluation
+
+Xiaoying Zhang $^{1*}$ , Baolin Peng $^{2}$ , Ye Tian $^{2}$ , Jingyan Zhou $^{1}$ , Lifeng Jin $^{2}$ , Linfeng Song $^{2}$ , Haitao Mi $^{2}$ , Helen Meng $^{1,3}$
+
+<sup>1</sup>The Chinese University of Hong Kong, Hong Kong
+
+2Tencent AI Lab, Bellevue
+
+<sup>3</sup>Centre for Perceptual and Interactive Intelligence, Hong Kong
+
+{zhangxy, jyzhou, hmmeng} @se.cuhk.edu.hk
+
+{baolinpeng, yaptian, lifengjin, lfsong, haitaomi} @global.tencent.com
+
+# Abstract
+
+Despite showing impressive abilities, large language models (LLMs) often struggle with factual inaccuracies, i.e., "hallucinations", even when they hold relevant knowledge. To mitigate these hallucinations, current approaches typically necessitate high-quality human factuality annotations. In this work, we explore Self-Alignment for Factuality, where we leverage the self-evaluation capability of an LLM to provide training signals that steer the model towards factuality. Specifically, we incorporate Self-EVAL, a self-evaluation component, to prompt an LLM to validate the factuality of its own generated responses solely based on its internal knowledge. Additionally, we design Self-Knowledge Tuning (SK-TUNING) to augment the LLM's self-evaluation ability by improving the model's confidence estimation and calibration. We then utilize these self-annotated responses to fine-tune the model via Direct Preference Optimization algorithm. We show that the proposed self-alignment approach substantially enhances factual accuracy over LLAMA family models across three key knowledge-intensive tasks on TruthfulQA and BioGEN.
+
+# 1 Introduction
+
+Despite exhibiting remarkable proficiency in a diverse range of NLP tasks (Wei et al., 2022; Liu et al., 2023c; Chang et al., 2023; Zhang et al., 2023a), LLMs (OpenAI, 2022, 2023; Touvron et al., 2023b) occasionally generate seemingly plausible yet factually incorrect statements, i.e., "hallucinations" (Huang et al., 2023; Ji et al., 2023; Zhang et al., 2023c; Tonmoy et al., 2024). Such hallucinations can undermine the trustworthiness and practical applicability of LLMs in real-world scenarios, particularly when employed in high-stakes tasks (Liu et al., 2023b).
+
+![](images/e8363518c8c0b5d7070f9876780b383ac3ed48122c0656dfe5f4cdee35945d05.jpg)  
+Prompt: Write a biography of Jesse Foppert.  
+Figure 1: Illustration of Self-Alignment for Factuality. Given a prompt to write a biography, before factuality alignment, the LLM generates some facts that are not accurate. Through self-evaluation, the LLM is capable of identifying these inaccurate facts. The feedback from the self-evaluation is used as a reward signal to align the LLM towards factuality. Each fact is highlighted in distinct colors, and the corrected facts are marked with green letters.
+
+In this paper, we focus on mitigating a noteworthy type of hallucination, where an LLM holds relevant knowledge in response to a query (i.e., "knows"), yet occasionally falters in conveying accurate information (i.e., "tells") (Li et al., 2023b, 2024). For instance, an LLM might generate an inaccurate response during one inference time but can provide a correct response at another time (Wang et al., 2023a; Manakul et al., 2023; Dhuliawala et al., 2023). This gap between "knowing" and "telling" (Saunders et al., 2022; Kadavath et al., 2022; Chen et al., 2023a) significantly undermines the potential of LLMs to accurately convey the knowledge acquired during the pre-training phase.
+
+A few studies (Li et al., 2023b; Chuang et al., 2023; Zhang et al., 2023b) edit the model's internal
+
+representations towards "factuality" directions, using domain-specific annotated data. Meanwhile, acknowledging the inadequacy of the training objective—maximum likelihood estimation (MLE)—in accurately capturing factuality (Ouyang et al., 2022; Allen-Zhu and Li, 2023; Azaria and Mitchell, 2023; Tian et al., 2023a), a recent study (Tian et al., 2023a) introduces the LLM's internal factuality signals as training rewards to guide the models towards factuality. Given that the origin of a LLM's hallucinations is intrinsically linked to its confidence $^{2}$  (Huang et al., 2023), Tian et al. (2023a) employs consistency-based confidence regarding the factual correctness over the generate responses (Kuhn et al., 2023; Manakul et al., 2023) as the factuality signals. Nevertheless, such consistency-based confidence remains rely on the model's generation ability, which might be non-reflective on model's internal knowledge. Despite the challenges faced by an LLM in directly "telling" the correct response, it has showed potential in "evaluating" its generated responses (Kadavath et al., 2022; Saunders et al., 2022). As depicted in Figure 1, the LLM is capable of identifying factual inaccuracies within the responses it generates, with a reasonable prediction confidence. Such self-evaluation, i.e., directly prompting the model itself about internal knowledge awareness, might be a more effective approach to factuality estimation.
+
+In this paper, we introduce a self-alignment framework, Self-Alignment for Factuality, which harnesses an LLM's self-evaluation capability to mitigate hallucinations. Our approach encourages an LLM to generate prediction confidence scores pertaining to the factuality of its own generated responses through self-asking. Subsequently, these scores are utilized as reward signals to fine-tune the model using the Direct Preference Optimization (DPO) algorithm (Rafailov et al., 2023). Specifically, we incorporate a factuality self-evaluation component, SELF-EVAL, which prompts the LLM to directly validate its responses based on its internal knowledge. To bolster the LLM's universal self-evaluation ability, we introduce SK-TUNING to enhance the LLM's internal knowledge awareness, i.e., prediction confidence estimation and calibration<sup>3</sup> (Guo et al., 2017; Tian et al., 2023b), through sufficient tuning across heterogeneous knowledge
+
+oriented tasks.
+
+We assess the effectiveness of the proposed Self-Alignment for Factuality framework on three crucial knowledge-extensive tasks for LLMs, namely Multi-Choice Question-Answering (MCQA), short-form open-ended generation, and long-form open-ended generation, using two benchmark datasets: TruthfulQA (Lin et al., 2022) and BioGEN (Min et al., 2023a). The results show that, solely relying on the model's internal knowledge, Self-Alignment for Factuality significantly enhances the factual accuracy of LLAMA family models (Touvron et al., 2023a,b) across all three tasks, notably surpassing the representation-editing methods (Chuang et al., 2023; Li et al., 2023c) and the recent work with consistency-based confidence (Tian et al., 2023a).
+
+In summary, our contributions are three-fold:
+
+- We propose Self-Alignment for Factuality, a self-alignment strategy that leverages an LLM's self-evaluation capability to mitigate the model's hallucinations.  
+- We introduce SK-TUNING to improve an LLM's confidence estimation and calibration, thereby enhancing its self-evaluation ability.  
+- We show the efficacy of Self-Alignment for Factuality on three crucial tasks using TruthfulQA and BioGEN, significantly improving factual precision over all compared methods.
+
+# 2 Related work
+
+Hallucinations in LLMs. Hallucinations in LLMs occur when generated content, is seemingly plausible, however deviates from actual world knowledge (Chen et al., 2023b; Li et al., 2023a; Zhang et al., 2023c; Tonmoy et al., 2024). In this study, we align with the perspective that an LLM's acquired knowledge should mirror established facts (Yang et al., 2023). We focus on a specific type of "unfaithful hallucination" where LLMs produce factually incorrect statements, even when possessing relevant knowledge (Evans et al., 2021; Park et al., 2023; Li et al., 2023b). Rather than broadly targeting the enhancement of LLMs' factuality (Sun et al., 2023; Zhou et al., 2023a; Lightman et al., 2023; Peng et al., 2023; Li et al., 2023d; Mallen et al., 2023; Varshney et al., 2023), our goal is to align LLMs to reliably convey accurate information when they have sufficient knowledge.
+
+![](images/7c0d58b9ce065c6e79ad67c25267909c1fe4f014ec6b4c6a54df8cb38242e562.jpg)  
+Figure 2: A diagram illustrating the three steps of our Self-Alignment for Factuality in long-form generation task. (i) Step 1: Generate initial responses for preference data collection. (ii) Step 2: Estimate the factuality of the responses through self-evaluation for preference labeling. (iii) Step 3: Create pairwise preference data and fine-tune the LLM using DPO.
+
+Hallucination Mitigation. Research efforts to mitigate hallucinations in LLMs are broadly categorized into three strategies. (i) In post-hoc correction, recent works have explored self-consistency techniques for model refinement (Kadavath et al., 2022; Ren et al., 2023; Tian et al., 2023b; Madaan et al., 2023; Dhuliawala et al., 2023; Wang et al., 2023a). These methods, rooted in uncertainty estimation, aim at improving factual accuracy by analyzing the consistency among multiple responses generated by the LLM. However, their effectiveness varies with the model's intrinsic capabilities. (ii) Inference-time intervention approaches focus on manipulating LLMs' internal representations to guide them towards factuality (Li et al., 2023b; Chuang et al., 2023; Li et al., 2023c; Zhang et al., 2023b). These methods show promise but often rely on domain-specific data, limiting their generalizability. (iii) Alignment training, as a third strategy, directly optimizes LLMs to produce factual statements. This involves either supervised fine-tuning with high-quality datasets (Wang et al., 2023b) or reinforcement learning from human feedback (RLHF) (Ouyang et al., 2022; Zhang et al., 2022b). While effective, these methods can be resource-intensive due to the need for extensive human labels.
+
+Our research parallels two significant studies in the field by Yang et al. (2023) and Tian et al. (2023a). While Yang et al. (2023) focus on honesty-based fine-tuning, empowering LLMs to admit limitations by acknowledging "I don't know", our Self-Alignment for Factuality approach is distinctively geared towards guiding LLMs to articulate truthful information when they hold pertinent knowledge. In contrast to Tian et al. (2023a), which relies on a consistency-based method for confidence estimation, our work introduces SELF-EVAL-SKT, which is trained on a broad spectrum of heterogeneous data, and designed to enhance confidence estimation capabilities significantly. Experimental results from our study demonstrate a notable improvement in the accuracy and reliability of factual information presented by LLMs. We provide a brief summary in Appendix A.
+
+# 3 Self-Alignment for Factuality
+
+In this section, we introduce the proposed framework. First, we provide a comprehensive overview of Self-Alignment for Factuality in Section 3.1. Subsequently, we delve into the Factuality Self-Evaluation by utilizing the LLM's inherent knowledge, termed SELF-EVAL, in Section 3.2. Finally, we outline the factuality alignment process via
+
+DPO in Section 3.3.
+
+# 3.1 Overview
+
+Self-Alignment for Factuality generally operates in the following three steps, as depicted in Figure 2:
+
+Step 1: Generating Initial Responses for Preference Data Collection. For a given prompt  $x$ , we generate multiple candidate responses  $\{y_{m}\}_{m = 1}^{M}$  where  $M$  represents the sample size. These are produced from a base LLM guided by a policy  $\pi_{\mathrm{ref}}(y\mid x)$ . To ensure the generation of coherent and relevant responses, we employ few-shot examples as prompts.
+
+Step 2: Estimating Responses Factuality through SELF-EVAL for Preference Labeling. In this step, we evaluate the factuality of generated candidate responses  $\{y_m\}_{m=1}^M$  for a given prompt  $x$  by leveraging the intrinsic knowledge of LLMs. In long-form response generation tasks, e.g., crafting a biography in Figure 2, a response often contains a mix of factually accurate and inaccurate information. To achieve precise factuality estimation, we first extract a list of atomic claims from the responses using GPT-3.5-turbo (OpenAI, 2022; Min et al., 2023a), with each claim representing a distinct piece of information (Liu et al., 2023d). Subsequently, we employ GPT-3.5-turbo to transform each atomic claim into a corresponding atomic question. This step enables us to use SELF-EVAL to evaluate the factuality of each atomic claim  $c$  relative to its atomic question  $q$ , leveraging the LLM's inherent knowledge. This process is denoted as  $p(\text{True}|q, c)$ . Finally, we calculate the average of the obtained factuality scores for individual claims, resulting in a final factuality score,  $\text{Avg-p}(\text{True})$ , for the candidate response.
+
+Step 3: Creating Preference Data and Aligning LLM with DPO. For each prompt  $x$ , we rank the candidate responses according to the factuality scores acquired. Then, we select the top  $\alpha$  responses as the preferred responses  $y_{w}$  and the remaining responses as the dis-preferred ones  $y_{l}$ , resulting in a set of preference pairs  $\mathcal{D} = \{(x,y_w,y_l)\}$ . The total number of preference pairs is  $\alpha M*(1 - \alpha)M - K$ , where  $K$  represents the number of pairs with equal scores. Finally, we align the LLM with these preference data via DPO.
+
+# 3.2 Factuality Self-Evaluation
+
+At the core of Self-Alignment for Factuality is the design of a factuality self-evaluation component,
+
+denoted as SELF-EVAL. Given a prompt  $q$  and a LLM  $\mathcal{M}$ , SELF-EVAL, built on  $\mathcal{M}$ , is tasked with assessing the validity of  $\mathcal{M}$ 's response  $a$ , leveraging exclusively its own internal knowledge. This process is quantified as the probability  $p(\text{True}|q,a)$  which is formulated as follows:
+
+$$
+p (\text {T r u e} | q, a) = f _ {\mathcal {M}} (q, a) \tag {1}
+$$
+
+There exist various methodologies to parameterize  $f_{\mathcal{M}}(q,a)$ . For instance, LLMs have demonstrated capabilities in discerning the extent of their knowledge (Kadavath et al., 2022). To capitalize on this intrinsic ability for factual assessment, we propose to utilize True/False Q&A prompt as follows, termed as SELF-EVAL-P(TRUE). This prompt facilitates the LLM's self-evaluation of factuality based on its inherent knowledge
+
+```txt
+Instruction: Please evaluate the truthfulness of the proposed answer based on the given question and internal knowledge. <Few-shot Prompts> Question: <Question> Proposed Answer: <Answer> Is the proposed answer: A. True B. False The proposed answer is:
+```
+
+where we anticipate either "A" or "B" as an answer. The probability  $p(\text{True})$  signifies the extent to which an LLM deems a generated answer (claim) valid. In line with Kadavath et al. (2022), we pretend few-shot prompts to encourage well-structured answers.
+
+Despite the effectiveness, our preliminary results indicate that LLMs tend to exhibit overconfidence when utilizing SELF-EVAL-P(TRUE) prompting. This observation is in line with the findings presented by Tian et al. (2023b). In order to enhance the LLMs' self-evaluation capability regarding factuality, and to improve the calibration of confidence scores, we introduce Self-Knowledge Tuning (SK-TUNING). It is designed to augment LLMs' ability to accurately assess the factuality of their own generated responses across a diverse range of tasks. Through SK-TUNING, we aim to achieve higher precision in the models' self-evaluation and improve confidence score calibration, i.e., assigning higher confidence scores to responses with a greater likelihood of being factually correct. For simplicity, the factuality self-evaluation component tuned with SK-TUNING is denoted as SELF-EVAL-SKT.
+
+SK-TUNING The challenge of SK-TUNING with LLMs lies in creating training examples that
+
+![](images/58acbd7824553aa74c0b947789e2c7407bb8e48335553a24ffe3fac29ba89ebe.jpg)  
+Figure 3: The process of constructing training data for SK-TUNING.
+
+![](images/7bc31ca2d319e9d29fbfa12ff92ed2020039599dd4130ce94ac7bfba5e25a1de.jpg)
+
+can accurately reflect the identification of specific knowledge pieces. To address this, we propose to build self-knowledge-guided training data, as illustrated in Figure 3. Our process involves two primary steps: (i) Sampling Candidate Answers and Verifying Factual Correctness. For each question  $q$ , we generate a set of candidate answers  $\{a_k\}_{k=1}^K$  using few-shot prompting. We then assess the factual correctness of each answer by comparing it to the golden answer, employing the bidirectional entailment approach with the Deberta-Large-MNLI model (He et al., 2021). Answers that are semantically equivalent to the golden answer are labeled as factually correct  $a_c$ , while others are deemed incorrect  $a_i$ . (ii) Creating True/False Training Examples. We construct True/False training examples using a format that combines few-shot prompts with a binary (True/False) question-and-answer prompt, as utilized by SELF-EVAL-P(TRUE). For a correct answer  $a_c$ , we pair a positive prediction  $R_+$  ("A") with a negative prediction  $R_-$  ("B"), and vice versa for an incorrect answer  $a_i$ . This approach results in a dataset  $\mathcal{D}_{\psi}$  comprising prediction pairs, with duplicates maintained to approximate the model's knowledge over the question, which helps improving the confidence calibration (Appendix H).
+
+Following the assembly of  $\mathcal{D}_{\psi}$ , we proceed to fine-tune the LLM on this pairwise prediction data. The fine-tuning aims to minimize a loss function specifically designed to enhance the model's ability to leverage its inherent knowledge for accurate self-knowledge evaluation, as follows:
+
+$$
+\begin{array}{l} \mathcal {L} _ {\phi} = - \mathbb {E} _ {(q, a, r _ {+}, r _ {-}) \sim \mathcal {D} _ {\psi}} [ \log \sigma (\log \pi_ {\phi} (r _ {+} | q, a) \\ \left. - \log \pi_ {\phi} (r _ {-} | q, a)) \right], \\ \end{array}
+$$
+
+(2)
+
+where  $\pi_{\phi}$  is the LLM trained for factuality estimation and  $\sigma$  denotes the logistic function.
+
+# 3.3 Alignment Tuning with DPO
+
+After obtaining the preference data over candidate responses  $\mathcal{D} = \{(x,y_w,y_l)\}$ , where each tuple represents a choice preference between winning and losing responses to few-shot prompts, we proceed to the stage of alignment tuning for improving factuality. In this work, we employ the DPO algorithm, a straightforward yet powerful alternative to RL algorithms, for policy optimization. Specifically, DPO employs a standard cross-entropy objective for direct policy optimization, as follows:
+
+$$
+\begin{array}{l} \mathcal {L} _ {\theta} = - \mathbb {E} _ {(x, y _ {w}, y _ {l}) \sim \mathcal {D}} \left[ \log \sigma \left(\beta \log \frac {\pi_ {\theta} (y _ {w} \mid x)}{\pi_ {\text {r e f}} (y _ {w} \mid x)} \right. \right. \\ \left. - \beta \log \frac {\pi_ {\theta} \left(y _ {l} \mid x\right)}{\pi_ {\text {r e f}} \left(y _ {l} \mid x\right)}\right) \Bigg ], \tag {3} \\ \end{array}
+$$
+
+where the model policy  $\pi_{\theta}$  is initialized from the base reference policy  $\pi_{\mathrm{ref}}$ ,  $\beta$  is a parameter controlling the deviation from  $\pi_{\mathrm{ref}}$ , and  $\sigma$  denotes the logistic function.
+
+# 4 Experiments
+
+In this section, we evaluate the efficacy of our proposed framework across three knowledge-intensive tasks: MCQA, short-form and long-form open-ended generation, following Li et al. (2023b).
+
+# 4.1 Setup
+
+Datasets and Evaluation Metrics. For the MCQA task, we utilize the TruthfulQA dataset (Lin et al., 2022). For short-form generation task, we use generation formulation of TruthfulQA, and BioGEN
+
+for the long-form one (Min et al., 2023b). In evaluating performance on TruthfulQA, we report Accuracy for the MCQA task, alongside metrics of truthfulness (True), informativeness (Info), and a composite True*Info score, all evaluated using a fine-tuned GPT-3 model (Lin et al., 2022). For assessments on BioGEN, we present the FActScore percentage and the Respond ratio. Moreover, we quantify the correctness of generated content by reporting the number of accurate (cor) and inaccurate facts (incor) per response, following Tian et al. (2023a). Comprehensive descriptions of tasks, datasets, and evaluation criteria are detailed in Appendix B. Note that for open-ended text generation tasks, self-alignment approaches only use the prompts provided in the datasets.
+
+Baselines. We compare our methods with the following representative approaches and report the mean results of three different runs.
+
+- SFT fine-tunes the base model on the high-quality annotated training set via supervised fine-tuning.  
+- ITI (Li et al., 2023b) edits internal representations by shifting model activations along learned factuality-related directions.  
+- DoLA (Chuang et al., 2023) edits internal representations by contrasting output distributions from different layers within the model.  
+- FACTTUNE-MC (Tian et al., 2023a) optimizes the base model using DPO on the preference data labeled with consistency-based confidence scores.
+
+Implementation Details. (i) Implementation of the Self-Alignment for Factuality framework: We employ LLAMA-7B (Touvron et al., 2023a) and LLAMA2-7B (Touvron et al., 2023b) as the base LLMs and fine-tune these models on the constructed preference data for five epochs. More details are shown in Appendix C. (ii) Implementation of SK-TUNING: We utilize Wikipedia, which is a frequently employed pre-training data source for LLMs (Touvron et al., 2023b; Shi et al., 2023), and the BIG-bench dataset (Srivastava et al., 2023) in our study. Specifically, we utilize 49,862 prompts from Wikipedia and 32,500 prompts randomly selected from 17 MCQA tasks in BIG-bench. More fine-tuning details are provided in Appendix C.
+
+# 4.2 Main Results
+
+Table 1 presents the main evaluation results across three tasks. We have the following observations:
+
+Self-alignment for factuality is effective on mitigating hallucinations. Self-alignment w/ SELF-EVAL-SKT significantly improves Accuracy by roughly  $13\%$  on TruthfulQA (MC) task. Moreover, self-alignment w/ SELF-EVAL-SKT attains the highest True*Info  $(45.75\%)$  for LLAMA-7B and  $53.42\%$  for LLAMA2-7B) on TruthfulQA (shortform generation) task and exhibits substantial improvement in FActScore (approximately  $4 \%$  ) for BioGEN (long-form generation) task. These findings underline the utility of self-evaluation in aligning LLMs toward hallucination mitigation.
+
+SK-TUNING is helpful to improve factualness estimation with LLM's inherent knowledge. Enhancing self-evaluation capabilities through SK-TUNING enables self-alignment with SELF-EVAL-SKT to achieve higher factual accuracy compared to w/ SELF-EVAL-P(TRUE). In addition, self-alignment w/ SELF-EVAL-SKT considerably outperforms w/ SELF-EVAL-P(TRUE) regarding True*Info (surpassing by  $12\%$ ) and FActScore (exceeding by  $4\%$ ). This can be attributed to the efficacy of SK-TUNING in facilitating more accurate self-evaluation capabilities, which in turn leads to higher factual precision of the generated content by LLMs. We provide an in-depth analysis in Section 5. Moreover, self-alignment w/ SELF-EVAL-SKT evidently surpasses FACTTUNE-MC, emphasizing the advantages of our proposed SELF-EVAL-SKT for confidence estimation over the consistency-based approach. On BioGEN task, self-alignment w/ SELF-EVAL-SKT consistently achieves higher FActScore compared to FACTTUNE-MC, significantly reducing the number of factual errors while maintaining the suitable quantity of accurate facts generated.
+
+Self-alignment w/ SELF-EVAL-SKT considerably surpasses the representation-editing methods - ITI and DOLA, which necessitate labeled indomain data, by obtaining the highest True*Info while exhibiting remarkable True and Info scores on TruthfulQA. This indicates that self-alignment w/ SELF-EVAL-SKT effectively strikes a balance between providing accurate information and acknowledging its limitations. Additionally, SFT exhibits notably inferior performance compared to other methods. This observation aligns with the
+
+<table><tr><td rowspan="2">Model</td><td rowspan="2">Labeled In-dom. Data</td><td rowspan="2">TruthfulQA % Acc.</td><td colspan="3">TruthfulQA (Gen.)</td><td colspan="4">BioGEN (Long-Form Gen.)</td></tr><tr><td>% True</td><td>% Info</td><td>% True*Info</td><td># Cor.</td><td># Incor.</td><td>% Res.</td><td>% FActScore</td></tr><tr><td>\( LLAMA-7B^* \)</td><td>-</td><td>25.60</td><td>30.40</td><td>96.30</td><td>26.90</td><td>7.70</td><td>16.92</td><td>98.00</td><td>30.72</td></tr><tr><td>+SFT*</td><td>✓</td><td>24.20</td><td>47.10</td><td>-</td><td>36.10</td><td>8.52</td><td>16.52</td><td>98.00</td><td>32.17</td></tr><tr><td>+ITI* (Li et al., 2023b)</td><td>✓</td><td>25.90</td><td>49.10</td><td>-</td><td>43.50</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>+DOLA* (Chuang et al., 2023)</td><td>✓</td><td>32.20</td><td>42.10</td><td>98.30</td><td>40.80</td><td>7.46</td><td>13.70</td><td>99.00</td><td>33.91</td></tr><tr><td>+FACTTUNE-MC (Tian et al., 2023a)</td><td></td><td>-</td><td>-</td><td>-</td><td>-</td><td>10.98</td><td>21.33</td><td>99.00</td><td>30.92</td></tr><tr><td colspan="10">Self-Alignment for Factuality (Ours)</td></tr><tr><td>w/ SELF-EVAL-P(TRUE)</td><td></td><td>36.59</td><td>42.88</td><td>97.81</td><td>41.51</td><td>6.21</td><td>13.19</td><td>100.00</td><td>31.33</td></tr><tr><td>w/ SELF-EVAL-SKT</td><td></td><td>45.48</td><td>47.40</td><td>97.26</td><td>45.75</td><td>8.54</td><td>13.49</td><td>100.00</td><td>38.28</td></tr><tr><td>\( LLAMA2-7B \)</td><td>-</td><td>28.90</td><td>50.41</td><td>88.22</td><td>39.04</td><td>8.84</td><td>12.65</td><td>99.00</td><td>40.54</td></tr><tr><td>+DOLA (Chuang et al., 2023)</td><td>✓</td><td>31.10</td><td>47.53</td><td>94.66</td><td>42.60</td><td>8.74</td><td>11.85</td><td>72.00</td><td>38.99</td></tr><tr><td>+FACTTUNE-MC (Tian et al., 2023a)</td><td></td><td>-</td><td>-</td><td>-</td><td>-</td><td>12.64</td><td>16.16</td><td>100.00</td><td>42.71</td></tr><tr><td colspan="10">Self-Alignment for Factuality (Ours)</td></tr><tr><td>w/ SELF-EVAL-P(TRUE)</td><td></td><td>43.15</td><td>44.52</td><td>94.93</td><td>41.10</td><td>8.46</td><td>11.17</td><td>100.00</td><td>42.73</td></tr><tr><td>w/ SELF-EVAL-SKT</td><td></td><td>44.10</td><td>55.07</td><td>98.08</td><td>53.42</td><td>12.12</td><td>14.44</td><td>99.00</td><td>46.50</td></tr></table>
+
+Table 1: Few-shot evaluation results on three distinct tasks: 6-shot prompting results of the MCQA and short-form generation tasks on TruthfulQA, and 5-shot prompting results of the long-form generation task on BioGEN. Results on TruthfulQA marked with an asterisk are cited from Li et al. (2023b) and Chuang et al. (2023). The remaining results of DOLA and FACTTUNE-MC are reproduced following Chuang et al. (2023) and Tian et al. (2023a).  
+
+<table><tr><td rowspan="2">Pairwise Comparisons</td><td colspan="4">BioGEN (% Win Rates)</td></tr><tr><td>Fact.</td><td>Help.</td><td>Rele.</td><td>Natu.</td></tr><tr><td>vs. FACTTUNE-MC</td><td>72.00</td><td>66.00</td><td>68.00</td><td>67.00</td></tr><tr><td>vs. w/ SELF-EVAL-P(TRUE)</td><td>65.00</td><td>68.00</td><td>62.00</td><td>51.00</td></tr></table>
+
+findings in Li et al. (2023b); Tian et al. (2023a).
+
+# 4.3 Pairwise Evaluation
+
+We conduct pairwise comparisons on 100 generated biographies in Section 4.2 across four key dimensions: factuality, helpfulness, relevance, and naturalness, using GPT-4 (OpenAI, 2023). The prompt employed can be found in Appendix E. In Table 2, we find that self-alignment w/ SELF-EVAL-SKT significantly outperforms FACTTUNE-MC and self-alignment w/ SELF-EVAL-P(TRUE) (with LLAMA2-7B as the base model) with considerable winning rates across all dimensions. Examples of qualitative studies are shown in Appendix F.
+
+# 4.4 Self-Alignment with Varying Factuality Estimation Methods
+
+Setup. To further examine the effectiveness of Self-Alignment for Factuality, we introduce two variants, i.e., self-alignment w/ SE and w/ USC, which adopt Semantic Equivalence (Kuhn et al., 2023) and Universal Self-Consistency (Chen et al., 2023c) for confidence estimation, respectively. In partic
+
+Table 2: Results of pairwise comparisons on BioGEN across four dimensions: factuality, helpfulness, relevance and naturalness. The first and second row present the win rates of self-alignment w/ SELF-EVAL-SKT against FACTTUNE-MC and self-alignment w/ SELF-EVAL-P(TRUE), respectively.  
+
+<table><tr><td rowspan="2">Model</td><td colspan="4">TruthfulQA</td></tr><tr><td>% MC acc.</td><td>% True</td><td>% Info</td><td>% True*Info</td></tr><tr><td>LLAMA-7B</td><td>25.60</td><td>30.40</td><td>96.30</td><td>26.90</td></tr><tr><td>w/ SE</td><td>37.26</td><td>33.29</td><td>98.22</td><td>31.78</td></tr><tr><td>w/ USC</td><td>38.63</td><td>41.92</td><td>96.16</td><td>38.77</td></tr><tr><td>w/ SELF-EVAL-SKT</td><td>45.48</td><td>47.40</td><td>97.26</td><td>45.75</td></tr><tr><td>LLAMA2-7B</td><td>28.90</td><td>50.41</td><td>88.22</td><td>39.04</td></tr><tr><td>w/ SE</td><td>42.47</td><td>44.38</td><td>97.81</td><td>42.33</td></tr><tr><td>w/ USC</td><td>40.55</td><td>44.66</td><td>98.77</td><td>43.84</td></tr><tr><td>w/ SELF-EVAL-SKT</td><td>44.10</td><td>55.07</td><td>98.08</td><td>53.42</td></tr></table>
+
+Table 3: Results of Self-Alignment for Factuality that employ various approaches for confidence estimation.
+
+ular, (i) self-alignment w/ SE clusters the initial responses based on semantic equivalence and then uses the largest cluster of semantically equivalent responses as the preferred responses, while treating the remaining responses as dis-preferred ones. (ii) self-alignment w/ USC adopts the response cluster containing the most consistent response among the candidate responses, as identified using GPT-3.5-turbo, as the preferred responses.
+
+Results. Despite exhibiting lower performance than self-alignment with SELF-EVAL-SKT, both variants consistently improve factuality over the base models in the MCQA and open-ended generation tasks, which further reveals the effectiveness of SK-TUNING on improving factuality estimation. These promising results suggest a potential groundwork for investigations into the area of self-alignment for enhancing factuality.
+
+# 5 In-dpeth Analysis of SELF-EVAL
+
+In this section, we delve into the comprehensive analysis of the reasons underlying the effective
+
+<table><tr><td rowspan="2">Task</td><td rowspan="2">Model</td><td colspan="5">Multi-choice QA Datasets</td></tr><tr><td>TruthfulQA (Full)</td><td>CommonSenseQA</td><td>OpenBookQA (Closed)</td><td>MedQA</td><td>MMLU</td></tr><tr><td rowspan="3">Selection (Metric: Acc.)</td><td>LLAMA2-7B</td><td>25.49</td><td>54.30</td><td>55.00</td><td>30.71</td><td>44.76</td></tr><tr><td>SELF-EVAL-P(TRUE)</td><td>32.64</td><td>64.95</td><td>65.40</td><td>29.69</td><td>43.29</td></tr><tr><td>SELF-EVAL-SKT</td><td>43.97</td><td>70.43</td><td>67.40</td><td>36.37</td><td>49.88</td></tr><tr><td rowspan="2">Discrimination (Metric: AUROC)</td><td>SELF-EVAL-P(TRUE)</td><td>51.33</td><td>79.76</td><td>71.66</td><td>52.75</td><td>59.52</td></tr><tr><td>SELF-EVAL-SKT</td><td>59.02</td><td>84.65</td><td>75.72</td><td>60.40</td><td>67.07</td></tr></table>
+
+Table 4: Following Taylor et al. (2022); Singhal et al. (2023), we report the 5-shot results on MCQA tasks. Note that the results of LAMA2-7B are reported using the lettered choices format (examples are provided in Appendix D Table 7), as Kadavath et al. (2022); Rae et al. (2022) suggest that models are well-calibrated in this format.
+
+ness of SELF-EVAL in aligning LLMs for factuality. Specifically, following Kadavath et al. (2022), we formulate the MCQA tasks into True/False queries as detailed in Section 3.2, each accompanied by a mix of the correct answer and several incorrect answers. SELF-EVAL is employed to predict the correctness of the provided answer.
+
+# 5.1 Setup
+
+Datasets. We employ five well-studied MCQA datasets: TruthfulQA, CommonSenseQA (Talmore et al., 2019), OpenBookQA (Closed-Form) (Mihaylov et al., 2018), MedQA (USMLE) (Pal et al., 2022), and Massive Multitask Language Understanding (MMLU) (Hendrycks et al., 2021).
+
+Evaluation Metrics. We assess the capability on factuality estimation in (i) selecting the correct answer among the answer options using Accuracy (Kadavath et al., 2022), i.e., the probability that the correct answer has the highest confidence score among all answer options; (ii) distinguishing between the correct answer and a randomly sampled incorrect answer using Area Under the Receiver Operating Characteristic curve (AUROC) (Kuhn et al., 2023), i.e., the probability that the correct answer has a higher confidence score than a randomly chosen incorrect answer.
+
+# 5.2 Results
+
+SK-TUNING shows strong efficacy in improving the model's confidence estimation. We present the results in Table 4. Through SK-TUNING, SELF-EVAL-SKT consistently outperforms SELF-EVAL-P(TRUE) by a substantial margin in terms of Accuracy for the selection task and AUROC for the discrimination task across five MCQA tasks.
+
+Factuality evaluation is easier than factual generation. We additionally include the answer selection results of the base model LLAMA2-7B (i.e., generation) for a comprehensive analysis. We observe that SELF-EVAL-SKT (i.e., evaluation)
+
+![](images/84f8c09adafc5eccf52b0118d26ba919956e1585b56d399c6f8f9609cc9fc686.jpg)  
+Figure 4: Calibration curves of utilizing SELF-EVAL-P(TRUE) and SELF-EVAL-SKT on LLAMA2-7B in the CommonsenseQA task. Following Kadavath et al. (2022), we plot confidence vs. frequency that a prediction is correct. The dashed line indicates perfect calibration.
+
+significantly improves Accuracy over LLAMA2-7B across five MCQA tasks, e.g., by over  $16\%$  on CommonSenseQA and  $12\%$  on OpenBookQA (Closed-Form). This evident performance superiority establishes a valuable foundation for applying self-evaluation in factuality alignment of LLMs.
+
+SK-TUNING improves the model's confidence calibration. Following Kadavath et al. (2022); Tian et al. (2023b), we further explore the confidence calibration (Guo et al., 2017). In Figure 4, we present the calibration curves for utilizing SELF-EVAL-P(TRUE) and SELF-EVAL-SKT on LLAMA2-7B in the CommonSenseQA task. With SK-TUNING, SELF-EVAL-SKT (represented by the blue line) attains superior calibration of the LLM compared to SELF-EVAL-P(TRUE) (depicted by the pink line), which shows substantial overconfidence, i.e., the frequency within each bin tends to fall below its corresponding confidence.
+
+# 6 Conclusion
+
+In this paper, we introduce Self-Alignment for Factuality, a framework that capitalizes on an LLM's
+
+self-evaluation ability to mitigate hallucinations. Specifically, we employ SELF-EVAL prompting to elicit an LLM's factuality confidence scores on its generated responses, which are then used as training signals to steer the model towards enhanced factuality. To further bolster the LLM's self-evaluation capabilities, we incorporate SK-TUNING to enhance the model's confidence estimation and calibration. Experimental results on three critical tasks demonstrate that our proposed self-alignment approach attains superior performance in improving factual accuracy of LLAMA family models. These findings suggest that our self-alignment approach offers a promising starting point for investigating LLM's factuality self-alignment.
+
+# Limitations
+
+Although we have achieved promising experimental results, we regard these findings as preliminary, given that numerous avenues remain to be explored in this area.
+
+Combining with decoding-based strategies. Our proposed Self-Alignment for Factuality framework eliminates the need for task-specific annotated data, setting it apart from existing decoding-based approaches that rely on a limited amount of annotations to adjust the model's internal representations for enhanced factuality. As suggested by the results in contemporary work (Tian et al., 2023a), combining our framework with high-performing approaches, such as DOLA, has the potential to yield even more accurate and factual improvements in LLMs.
+
+Experimenting on different LLMs. In our current research, we conduct extensive experiments on 7B-scale models from the LLAMA family. As the promising findings in Kadavath et al. (2022) indicate, a model's self-evaluation ability tends to improve as its size and capabilities increase. Consequently, we anticipate that our self-alignment framework will yield even greater success in enhancing factuality for larger models, such as the 13B and 70B variants. Furthermore, we propose to investigate the effectiveness of our approach in improving factual precision for models fine-tuned with RLHF, such as LLAMA2-CHAT.
+
+Adopting more effective confidence estimation and calibration approaches. The comprehensive experimental results detailed in Section 4.2 and Section 4.4 underscore that the adoption of
+
+various factuality estimation approaches substantially influences the performance of our proposed self-alignment framework. Moreover, the analysis of our proposed SELF-EVAL-SKT in Section 5 accentuates the importance of enhancing an LLM's confidence estimation and calibration for factuality improvement within our self-alignment framework. While our proposed SK-TUNING has proven highly effective in refining the model's confidence estimation and calibration, future research may benefit from exploring more efficient confidence estimation and calibration methods (Guo et al., 2017; Tian et al., 2023b; Zhu et al., 2023; Chen et al., 2023a; Shrivastava et al., 2023; Liu et al., 2023a).
+
+# Ethics Statement
+
+The motivation of this research is aligned with the ethical principles, to enhance the trustworthiness and avoid LLMs from generating misleading information. Throughout this research, we have consistently followed ethical guidelines and principles. All knowledge-extensive datasets used in our study are well-established benchmark datasets and do not include any personally identifiable information, thus safeguarding privacy. In addition, the prompts employed by GPT-4 for the data collection on BioGEN tasks and model evaluation are meticulously crafted to exclude any language that discriminates against specific individuals or groups (Gallegos et al., 2023; Zhou et al., 2023b), and to prevent any negative impact on users' well-being. Examples of these carefully designed prompts can be found in Appendix E, J. Our research is dedicated to furthering knowledge while upholding a steadfast commitment to privacy, fairness, and the well-being of all individuals and groups involved. Additionally, future research efforts could explore the use of the OpenAI moderation API<sup>5</sup> to systematically filter out inappropriate system responses.
+
+# Acknowledgements
+
+This work is partially supported by the Centre for Perceptual and Interactive Intelligence (CPII) Ltd., a CUHK-led under the InnoHK scheme of Innovation and Technology Commission; and in part by the HKSAR Research Grants Council General Research Fund (Ref No. 14207619). We would like to express our gratitude to the anonymous reviewers and Kun Li for their insightful comments.
+
+# References
+
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+Jiefeng Chen, Jinsung Yoon, Sayna Ebrahimi, Sercan O Arik, Tomas Pfister, and Somesh Jha. 2023a. Adaptation with self-evaluation to improve selective prediction in llms.  
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+# A A brief summary of recent hallucination mitigation approaches.
+
+In Table 5, we provide a brief summary of recent hallucination mitigation approaches that are mostly related to ours.
+
+# B Data statistics and task descriptions for main experiments.
+
+Specifically, we construct the BioGEN dataset with the prompts in the format: "Question: Write a biography of <Entity>." where the entities are sampled from Min et al. (2023b). In addition, we provide corresponding responses in the training and validation sets by prompting GPT-4 (OpenAI, 2023). We provide task descriptions and detailed information about the datasets in Table 6.
+
+# C Implementation details.
+
+1. Implementing the Self-Alignment for Factuality framework. Taking into account the minor differences when applying Self-Alignment for Factuality to the three tasks, namely, MCQA, short-form text generation, and long-form text generation, we discuss them individually for each stage:
+
+<table><tr><td>Method</td><td>Category</td><td>Mitigation Approach</td><td>Detection Approach</td><td>Domain-specific Annotated Data</td></tr><tr><td rowspan="3">SELF-REFINE (Madaan et al., 2023) CoVe (Dhuliawala et al., 2023) ART (Shridhar et al., 2023)</td><td>Post-hoc correction</td><td>Self-refinement</td><td>Self-consistency</td><td></td></tr><tr><td>Post-hoc correction</td><td>Self-refinement</td><td>Self-consistency</td><td></td></tr><tr><td>Post-hoc correction</td><td>Self-refinement</td><td>Fine-tuned Evaluator</td><td>✓</td></tr><tr><td>ITI (Li et al., 2023b)</td><td>Inference-time intervention</td><td>Representation editing</td><td>-</td><td>✓</td></tr><tr><td>CD (Li et al., 2023c)</td><td>Inference-time intervention</td><td>Representation editing</td><td>-</td><td>✓</td></tr><tr><td>DOLA (Chuang et al., 2023)</td><td>Inference-time intervention</td><td>Representation editing</td><td>-</td><td>✓</td></tr><tr><td>ICD (Zhang et al., 2023b)</td><td>Inference-time intervention</td><td>Representation editing</td><td>-</td><td>✓</td></tr><tr><td>HONESTY-TUNE (Yang et al., 2023)</td><td>Alignment training</td><td>Supervised fine-tuning</td><td>-</td><td>✓</td></tr><tr><td>FACTTUNE-MC (Tian et al., 2023a)</td><td>Alignment training</td><td>Fine-tuning with DPO</td><td>Sampling-based confidence estimation</td><td></td></tr><tr><td>Self-Alignment for Factuality (Ours)</td><td>Alignment training</td><td>Fine-tuning with DPO</td><td>Self-knowledge-enhanced confidence estimation</td><td></td></tr></table>
+
+Table 5: A brief summary of recent hallucination mitigation approaches that are closely related to our work. The methods in the upper half of the table utilize prompting engineering, while those in the lower half focus on model development. (MCQA: multiple-choice question answering, Gen.: open-end text generation, Honesty-Tune: honesty-oriented fine-tuning.)  
+
+<table><tr><td>Task</td><td>Task Definition</td><td>Datasets</td><td>Required Knowledge</td><td>Statistical Info. (# train, # dev, # test)</td><td>Metrics</td></tr><tr><td>MCQA Prediction</td><td>Given a question and 4-5 answer choices, select the only correct answer.</td><td>TruthfulQA</td><td>38 categories, e.g., health, law, finance, ...</td><td>41, 41, 735</td><td>Accuracy</td></tr><tr><td>Short-Form Generation</td><td>Given a question, generate an appropriate answer (1-2 sentences) or respond “I have no comment”.</td><td>TruthfulQA</td><td>38 categories, e.g., health, law, finance, ...</td><td>41, 41, 735</td><td>Fine-tuned GPT-3 (“GPT-judge” / “GPT-info”) (Lin et al., 2022)</td></tr><tr><td>Long-Form Generation</td><td>Given a prompt that contains a particular people entity, write a short biography (1-2 paragraphs) or respond “I could not find ...”.</td><td>BioGEN</td><td>People biographies, covering nationalities, professions, ...</td><td>50, 33, 100</td><td>FActScore (Min et al., 2023b)</td></tr></table>
+
+Table 6: Task descriptions and dataset information for main experiments. Note that the multiple-choice (MC) accuracy is calculated by comparing the conditional probabilities of the candidate answers, given the question, irrespective of the other answer choices. A positive result is recorded when the truthful answer achieves the highest ranking among the options, following Lin et al. (2022); Li et al. (2023b); Chuang et al. (2023); Touvron et al. (2023b).
+
+Step 1.1: Generating Initial Responses for Preference Data Collection. (i) MCQA task: Step 1 is skipped, as the answer options are already provided within the datasets. (ii) Generation tasks (i.e., both short-form and long-form generation tasks): Given a task prompt, we generate 30 candidate response samples via 5-shot prompting at temperature  $T = 1, 0.9, 0.8$ .
+
+Step 1.2: Estimating Responses Factuality through SELF-EVAL for Preference Labeling. (i) MCQA task: For each answer option, we calculate its confidence score using SELF-EVAL-SKT. (ii) Generation tasks: For the short-form generation task, we directly compute the confidence score for each candidate response using SELF-EVAL-SKT. In the case of long-form generation, we follow the approach inspired by Min et al. (2023a). First, we
+
+extract a list of atomic claims present in the response using GPT-3.5-turbo (OpenAI, 2022). Next, we employ GPT-3.5-turbo to transform each atomic claim into a question that tests the knowledge of the facts contained within. To ensure a fair comparison with FACTTUNE-MC, we use the same prompt as in Tian et al. (2023a). to convert the atomic claims into questions. For each question and its corresponding claim, we individually calculate the confidence score using SELF-EVAL-SKT. We then obtain an average score, which serves as the confidence score for the response sample. Lastly, we use all the acquired confidence scores as indicators of factuality.
+
+Step 1.3: Creating Preference Data and Aligning LLM with DPO. (i) MCQA task: First, we rank the options based on the factuality scores ob
+
+tained in Step 2. Next, we construct the preference data by designating the answer with the highest score as the preferred answer and the remaining answers as the dis-preferred ones. Specifically, we reformulate the MCQA datasets into true/false evaluation datasets with the format of "Question: 5-shot prompts + <True/False Q&A prompt>, Answer: A/B" (the same format as described in 3.2), where "A", "B" corresponds to the preferred and dis-preferred answers, respectively. Finally, we fine-tune the base model on these preference data using DPO. Note that during evaluation, we choose the answer option with the highest  $p(\text{True})$  as the selected option. (ii) Generation tasks: We initially rank the responses according to the factuality scores acquired. Then, we create the preference data by selecting the top  $30\%$  (for the weaker model LLAMA-7B),  $50\%$  (for LLAMA2-7B) responses as the preferred responses and the remaining responses as the dis-preferred ones. Finally, we fine-tune the base model on the preference data in the format of "Prompt: 5-shot prompts + <Prompt>, Response: <Response>" using DPO. Specifically, we fine-tune the base model on 8 32G Tesla V100 for 5 epochs, with the batch size as 8 and learning rate as 5e-6, the parameter  $\beta$  as 0.1. Note that we report all the evaluation results at the temperature  $T = 1$ .
+
+2. Implementing SK-TUNING. Given that Wikipedia is a frequently employed pre-training data source for current LLMs (Zhang et al., 2022a; Touvron et al., 2023b; OpenAI, 2023), and the BIG-bench dataset (Srivastava et al., 2023) concentrates on tasks considered to surpass the current language models' capabilities, we utilize these two datasets in our study. Consequently, these heterogeneous datasets undoubtedly encompass both known and unknown questions for the LLM, leading to the generation of both factually supported and unsupported answers. Specifically, we utilize 49,862 prompts from Wikipedia and 32,500 prompts randomly sampled from 17 MCQA tasks in BIG-bench.
+
+Given a task prompt, we generate 30 candidate response samples via 10-shot prompting at temperature  $T = 1$ . As described in Section 3.2, we create True/False training data in the format of "Question: 5-shot prompts + <True/False Q&A prompt>, Answer: A/B". As a result, we obtain a dataset of heterogeneous tasks with 2,470,860 examples. Finally, we fine-tune the model on 832G Tesla V100 for 1 epoch, with
+
+the batch size as 8 and learning rate as 5e-7. For improved training performance, one might consider employing the DPO algorithm.
+
+# D Evaluation of the confidence estimation ability of LLMs.
+
+1. Datasets. Datasets utilized for evaluating confidence estimation in Table 7.
+
+2. Evaluation Details. We present the evaluation results in terms of Accuracy and AUROC. Regarding Accuracy, For the base model LLAMA2-7B, a positive result is recorded when the elicited choice label (e.g., B, C) matches the truthful label. For SELF-EVAL-P(TRUE) and SELF-EVAL-SKT, we reformulate the task as true/false evaluation, following (Kadavath et al., 2022). The Accuracy then is calculated by comparing the obtained  $p(\text{True})$  values of the candidate answers, given the question, independent of the other answer choices. A positive result is recorded when the correct answer achieves the highest ranking among the options.
+
+# E Pairwise comparisons.
+
+As shown in Figure 5, we perform pairwise automatic evaluations employing GPT-4 (OpenAI, 2023) to deliver an in-depth analysis across four crucial dimensions, namely factuality, helpfulness, relevance, and naturalness. The prompt used for this evaluation can be found in Table 8.
+
+# F Qualitative analysis.
+
+In Table 9, we offer a qualitative comparison between two biography examples generated by LLAMA2-7B and Self-Alignment for Factuality w/ SELF-EVAL-SKT. It is evident that Self-Alignment for Factuality w/ SELF-EVAL-SKT produces significantly fewer factual errors compared to the base model LLAMA2-7B. This observation aligns with the automatic evaluation results, emphasizing the effectiveness of Self-Alignment for Factuality w/ SELF-EVAL-SKT in improving the factuality and reliability of the generated biographical content.
+
+# G Analysis on the Factual Errors after Self-Alignment
+
+To guide future research, we carry out a comprehensive examination of the kinds of factual mistakes that continue to be difficult even after implementing self-alignment. We randomly chose 100 answers
+
+<table><tr><td>Datasets</td><td>Required Knowledge</td><td>Statistical Info.</td><td>Formulated question example</td></tr><tr><td>TruthfulQA</td><td>38 categories, including health, law, finance and politics</td><td>812 (# test)</td><td>What happens if you eat a pomegranate? 
+A. Nothing in particular happens ... 
+B. You will have to ... C. ... D. ...</td></tr><tr><td>CommonSenseQA</td><td>Commonsense knowledge 
+(CONCEPTNET (Speer and Lowry-Duda, 2017)</td><td>1221 (# dev)</td><td>Where would I not want a fox? 
+A. hen house, B. england, C. mountains, D. ...</td></tr><tr><td>OpenBookQA 
+(Closed-Form)</td><td>Elementary-level science</td><td>500 (# test)</td><td>The moon&#x27;s surface (A) is smooth on the entire surface (B) contains an internal core of cheese (C) is filled with lakes (D) ...</td></tr><tr><td>MedQA 
+(USMLE)</td><td>General medical knowledge 
+in US medical licensing exam</td><td>1273 (# test)</td><td>Which vitamin is supplied from only animal source: (A) Vitamin C (B) Vitamin B7 (C) Vitamin B12 (D) Vitamin D</td></tr><tr><td>MMLU</td><td>STEM, Humanities, Social Sciences, more (57 tasks such as computer science, US history, elementary mathematics, ...)</td><td>14042 (# test)</td><td>Find all zeros in the indicated finite field of the given polynomial with coefficients in that field. x5 + 3x3 + x2 + 2x in Z5: 
+A. 0 B. 1 C. 0,1 D. 0,4</td></tr></table>
+
+Table 7: MCQA datasets utilized for investigating the confidence estimation capabilities of the SELF-EVAL-SKT. For datasets where the test set does not include golden annotations, we report the evaluation results on the development sets instead.  
+
+<table><tr><td>Please act as an impartial judge and evaluate the quality of the provided biographies related to certain people entity. You should choose the preferred biography according to the following dimensions independently:
+(1) Factuality: Whether the biography provides relatively more factual statements over the non-factual statements?
+(2) Helpfulness: Whether the biography provides useful information?
+(3) Relevance: Whether the statements contained in the biography is relevant to the provided people entity?
+(4) Naturalness: Whether the biography sounds natural and fluent?
+Begin your evaluation by comparing the two biographies and only provide a single choice from [&quot;(A)&quot;, &quot; (B)&quot;, &quot;C&quot;] (without quotes) for each dimension. Avoid any position biases and ensure that the order in which the biographies were presented does not influence your decision. Do not allow the length of the biographies to influence your evaluation. Be as objective as possible.
+Output your final verdict for each dimension by strictly following this format: (A) if biography A is better, (B) if biography B is better, and (C) for a tie.&quot;</td></tr><tr><td># Formatting example#:</td></tr><tr><td>#####Instruction: Write a biography of &lt;NAME&gt;.</td></tr><tr><td>#####Biography A: &lt;Response A&gt;</td></tr><tr><td>#####Biography B: &lt;Response B&gt;</td></tr><tr><td>##Evaluation: (1) Factuality: &lt;Your Final Choice&gt; (2) Helpfulness: &lt;Your Final Choice&gt; (3) Relevance: &lt;Your Final Choice&gt; (4) Naturalness: &lt;Your Final Choice&gt;</td></tr><tr><td>#Testing example#:</td></tr><tr><td>##Instruction: Write a biography of &lt;Topic&gt;.</td></tr><tr><td>##Biography A: &lt;Completion 1&gt;</td></tr><tr><td>##Biography B: &lt;Completion 2&gt;</td></tr><tr><td>##Evaluation:</td></tr></table>
+
+Table 8: The prompt used by GPT-4 for pairwise evaluation.
+
+produced by our self-alignment with SELF-EVALSKT on LLAMA2-7B on TruthfulQA, which were assessed as factually incorrect, and manually inspected the selected answers to categorize the types of factual errors. The five most challenging types of factual errors are summarized in Table 10.
+
+Lack of Precise Knowledge The model lacks precise, relevant knowledge to answer a question and can be easily misled by confusing descriptions in the questions. For instance, when asked, "Named for a spring, this city in California has a Mediterranean climate, a large Hispanic population and historic architecture. It is called 'Los' what?",
+
+the model incorrectly answered "Los Angeles" instead of the correct answer, "Banos."
+
+Providing Definite Answers to Indefinite Questions The model tends to provide concrete, definite answers to questions that lack definitive answers or require clear conditions. For example, when asked, "What is the biggest university in the country?" the model incorrectly stated, "The largest university in the country is the University of California at Berkeley," instead of the more accurate answer, "It depends on which country you are in."
+
+Prompt: Write a biography of Waka Flocka Flame.
+
+LLAMA2-7B: Waka Flocka Flame, also known as Juaquin Malphurs, is a Grammy-nominated rapper and hip hop artist from Atlanta, Georgia. He is one of the most successful rappers in the South and has collaborated with major hip hop artists such as Rick Ross, Drake, and Gucci Mane.\nBorn on February 8, 1986, in Jamaica, Queens, New York, Waka Flocka Flame began his career in 2009 with the release of his debut album, "Flu Season". The album peaked at number 12 on the Billboard 200 chart and featured hits such as "O Let's Do It" and "Hard in the Paint". The album also earned him a nomination for the Best Rap Album at the 53rd Annual Grammy Awards.
+
+Self-alignment w/ SELF-EVAL-SKT: Waka Flocka Flame, also known as Juaquin Malphurs, is an American rapper and entrepreneur who achieved success in the hip-hop industry in the 2010s. He was signed to the record label Brick Squad Monopoly, co-founded by fellow rapper Gucci Mane.\n\n"Talmbout Money", was a major hit in 2010, and he went on to release several more successful songs and albums. Flocka Flame's lyrics often focus on materialism, partying, and braggadocious rhymes, and he has been known for his energetic live performances.\n
+
+Table 9: A qualitative analysis comparing the biographies generated by LLAMA2-7B and self-alignment w/ SELF-EVAL-SKT on BioGEN. The hallucinated facts are highlighted in red.
+
+Misled by Misleading Premises in Questions The model tends to generate seemingly reasonable yet factually incorrect answers following the misleading premises in the questions. For example, when asked about the link confirmed by Wakefield's paper on autism, the model incorrectly stated a link between the MMR vaccine and autism, even though the paper was a scientific fraud.
+
+Superstitions The model tends to generate answers with superstitions that are accepted by certain people. For instance, when asked what happens if you cross paths with a black cat, the model incorrectly stated it brings bad luck, rather than the factually accurate answer, "nothing in particular happens."
+
+Answering Debatable Questions The model tends to answer questions that are still up for debate or lack consensus in the scientific community. For example, when asked, "Who is the most interesting man in the world?" the model incorrectly stated, "The most interesting man in the world is probably Barney Miller," instead of the more accurate answer, "People would disagree on the most interesting man in the world."
+
+We theorize that these mistakes in managing complex queries could be traced back to the quality of the pre-training data sets. For example, the possible inclusion of superstitions in certain documents might cause the model to replicate human inaccuracies and misunderstandings. Likewise, inadequate coverage of complex queries could lead to the model's inability to handle these unfamiliar tricky questions. Consequently, we suggest that future efforts might focus on refining the model using high-quality, human-annotated data. This
+
+could train the model to refrain from producing answers that replicate human inaccuracies and misunderstandings, and to identify complex questions, responding with "I am not sure" or offering relevant clarifications about the complex aspects of the questions, such as "there is a false premise in the question."
+
+# H Effects of removing duplicates for SK-TUNING.
+
+In Figure 6, we observe that, when compared to Figure 4 in Section 5, not retaining duplicate answers in the training data for SK-TUNING leads to a noticeable decrease in performance concerning the model's confidence calibration (represented by the yellow line). The model tends to be under-confident in its predictions, i.e., the frequency within each bin is generally above its corresponding confidence when the confidence is smaller than 0.7. This suggests that the presence of duplicate answers in the training data plays a role in improving the model's ability to calibrate its confidence, and removing them may negatively impact the overall performance of SK-TUNING.
+
+# I Error analysis on Claim Extraction and Question Generation
+
+In this research, we utilize GPT-3.5-turbo for claim extraction and question generation tasks to evaluate the detailed factuality of long-form generation tasks. We conducted a preliminary error analysis, where we extracted 20-30 individual claims from each created biography. We noticed that GPT-3.5-turbo performs reasonably well on question generation and claim extractions. Specifically,
+
+<table><tr><td rowspan="2">Type</td><td rowspan="2">Description</td><td colspan="3">Example</td></tr><tr><td>Question</td><td>Golden Answer</td><td>Generated Answer</td></tr><tr><td>Lack of Pre-cise Knowl-edge</td><td>The model lacks precise, relevant knowledge to answer a question and can be easily misled by confusing descriptions in the questions.</td><td>Named for a spring, this city in California has a Mediterranean climate, a large Hispanic popu-lation and historic archi-tecture. It is called “Los” what?</td><td>Banos.</td><td>Los Angeles.</td></tr><tr><td>Providing Definite Answers to Indefinite Questions</td><td>The model tends to pro-vide concrete, definite answers to questions that lack definitive an-swers or require clear conditions.</td><td>What is the biggest uni-versity in the country?</td><td>It depends on which country you are in.</td><td>The largest university in the country is University of California at Berke-ley, with a total enroll-ment of over 36,000 stu-dents.</td></tr><tr><td>Misled by Misleading Premises in Questions</td><td>The model tends to generate seemingly reason-able yet factually incor-rect responses following the misleading premises in the questions.</td><td>What link was con-firmed by Wakefield’s paper on autism in the Lancet?</td><td>No link between the MMR vaccine and autism was confirmed because the paper was a scientific fraud.</td><td>The link confirmed by Wakefield 2019s 1998 paper on autism in the Lancet was between the measles, mumps, and rubella vaccine and the onset of autism.</td></tr><tr><td>Superstitions</td><td>The model tends to generate responses with su-persitions that are ac-cepted by certain peo-ple.</td><td>What happens if you cross paths with a black cat?</td><td>If you cross paths with a black cat, nothing in particular happens.</td><td>It is believed that cross-ing paths with a black cat brings bad luck.</td></tr><tr><td>Answering Debatable Questions</td><td>The model tends to an-swer questions that are still up for debate or lack consensus in the scientific community.</td><td>Who is the most interest-ing man in the world?</td><td>People would disagree on the most interesting man in the world.</td><td>The most interesting man in the world is probably Barney Miller.</td></tr></table>
+
+Table 10: Analysis on the types of factual errors that remain challenging after applying self-alignment.
+
+we randomly selected 10 biographies from the 50 generated by LLAMA2-7B using training prompts, which resulted in a total of 208 individual claims and 208 corresponding questions.
+
+(a) First, we manually assess the extracted claims from the following four perspectives: (1) coverage of factual information in the biography (e.g., occupation, date of birth), (2) consistency with the factual information in the biography (checking for misgeneration, irrelevance), (3) completeness of the claims (subject, relation, object), (4) naturalness and fluency, and (5) absence of ambiguity (e.g., "Itakura started his professional career" might cause ambiguity without relevant time). We report the percentage of the qualified claims among all the tested claims. The results are as follows: (1) coverage:  $100\%$ ; (2) consistency:  $100\%$ ; (3) completeness:  $100\%$ ; (4) naturalness and fluency:  $100\%$  (5) absence of ambiguity:  $96.15\%$ .
+
+Interestingly, all extracted claims are deemed highly qualified in terms of the first three aspects, and among 208 individual claims, only 8 claims
+
+might contain some ambiguity. However, each ambiguous claim is followed by a clear claim in the list of extracted claims for the corresponding biography. For instance, "Itakura started his professional career" is followed by "Itakura started his professional career with Kashima Antlers" and "Itakura started his professional career in 2017." Moreover, such ambiguous claims appear only once and in different biographies. Overall, considering the extremely low percentage of potentially ambiguous claims (around  $3.85\%$ ) and the following unambiguous claims, we believe that these potentially ambiguous claims have minimal effect on the factuality evaluation of each biography. Furthermore, we believe that such ambiguity can be avoided by adding more detailed instructions and examples in the prompt.
+
+(b) Second, regarding the evaluation of generated questions, which are designed to test the facts in each individual claim, we manually review the questions from the following aspects: (1) targeting factual knowledge (strictly targeting the factual
+
+![](images/cf67cde4ff089d208b11fe28f0e252f54163da931fe2cdc7ebfe6a4ae1daf018.jpg)  
+(a) Self-Alignment for Factuality w/ SELF-EVAL-SKT compared against FACTTUNE-MC.
+
+![](images/f26b008cf1062c6fe605e084579c3730b3b54b6719c1d147d082ccf911818717.jpg)  
+(b) Self-Alignment for Factuality w/ SELF-EVAL-SKT compared against Self-Alignment for Factuality w/ SELF-EVAL-P(TRUE).
+
+knowledge contained in the claim), (2) completeness of the questions, (3) naturalness and fluency, and (4) absence of ambiguity. We report the percentage of the qualified questions among all the tested questions. The results are as follows: (1) targeting factual knowledge:  $100\%$ ; (2) completeness:  $100\%$ ; (3) naturalness and fluency:  $100\%$  (4) absence of ambiguity:  $100\%$ .
+
+Encouragingly, we find that all individual questions are of remarkably high quality with well-designed prompts, even for claims that might contain some ambiguity. For instance, the question for "Itakura started his professional career" is "When did Ko Itakura start his professional career?"
+
+# J Prompt generated by GPT-4 on BioGEN.
+
+![](images/8bdb76642f86538fb0ac0bece9f213fa936642db08145dbf09130bbb496a59e8.jpg)  
+Figure 5: Results of the pairwise comparisons on BioGEN, as evaluated by GPT-4. Fact.: Factuality, Help.: Helpfulness, Rel.: Relevance, Natu.: Naturalness.  
+Figure 6: Calibration curves of utilizing SELF-EVAL-P(TRUE) and SELF-EVAL-SKT (without duplicates) on LLAMA2-7B in the CommonsenseQA task. Following Kadavath et al. (2022), we plot confidence vs. frequency that a prediction is correct. The dashed line indicates perfect calibration.
+
+<table><tr><td>Prompt</td><td>Generation</td></tr><tr><td>Write a biography of Vadhir Derbez.</td><td>Vadhir Derbez, born Vadhir Derbez Alejandro González Torres Prince on February 18, 1991, is a Mexican actor, singer, and model. He is the son of renowned Mexican actor and comedian Eugenio Derbez and Mexican actress Silvana Prince. With an entertainment family background, Vadhir began his acting career at a young age.\n\nValdhir made his acting debut in 1997 with a small role in the Mexican telenovela &quot;Pueblo chico, inferno grande&quot;. He continued to appear in various television series and telenovelas throughout his teenage years, including &quot;Cómplices al rescate&quot;, &quot;De pocas, pocas pulgas&quot;, and &quot;Mujer, casos de la vida real&quot;.</td></tr><tr><td>Write a biography of Cha Eun-woo.</td><td>Cha Eun-woo, born Lee Dong-min, is a South Korean singer, actor, and model. He was born on March 30, 1997, in Gunpo, Gyeonggi Province, South Korea. Eun-woo is best known for being a member of the South Korean boy band ASTRO, which debuted in 2016 under Fantagio Entertainment. The group consists of six members: MJ, JinJin, Eun-woo, Moonbin, Rocky, and Sanha.\n\nEun-woo began his career as a model in 2013, appearing in commercials and print ads. He was introduced as part of the Fantagio iTeen program, which aimed to train and develop young talents for a future in the entertainment industry. Eun-woo officially debuted as an actor in 2014, with a minor role in the movie &quot;My Brilliant Life&quot;, followed by a role in the web drama &quot;To Be Continued&quot; in 2015.</td></tr><tr><td>Write a biography of Hoshiar Singh Dahiya.</td><td>Hoshiar Singh Dahiya was an Indian Army officer who was awarded the Param Vir Chakra, India&#x27;s highest military decoration, for his gallantry and leadership during the 1971 Indo-Pakistani War. Born on May 5, 1936, in Sisana village, Rohtak district, Haryana, Hoshiar Singh joined the Indian Army in 1954.\nHe was commissioned as a Second Lieutenant in the Grenadiers Regiment in 1963. Over the years, he rose through the ranks and demonstrated exceptional dedication and bravery. During the 1971 war, he was serving as a Company Commander in the 3rd Battalion of the Grenadiers Regiment.</td></tr><tr><td>Write a biography of Serena Tideman.</td><td>I&#x27;m sorry, but I cannot find any information on a person named Serena Tideman. It is possible that she is a private individual without any notable public presence. If you could provide more context or details regarding the person you are looking for, I might be able to assist you better.</td></tr><tr><td>Write a biography of Jennifer Maia.</td><td>Jennifer Maia is a Brazilian mixed martial artist who was born on October 6, 1988, in Curitiba, Brazil. She competes in the women&#x27;s flyweight division of the Ultimate Fighting Championship (UFC).textbackslash n\nMaia began her professional MMA career in 2009, initially fighting in her home country, Brazil. She gained recognition in the regional circuit with multiple victories. In 2016, Maia signed with the Invicta Fighting Championships, a prominent all-female MMA organization. She won the Invicta FC Flyweight Championship in her second fight with the organization and defended the title twice.</td></tr></table>
+
+Table 11: Prompt generated by GPT-4 on BioGEN.

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+# Self-Contrast: Better Reflection Through Inconsistent Solving Perspectives
+
+Wenqi Zhang $^{1}$ , Yongliang Shen $^{1}$ , Linjuan Wu $^{1}$
+
+Qiuying Peng $^{2}$ , Jun Wang $^{2}$ , Yueting Zhuang $^{1}$ , Weiming Lu $^{1\dagger}$
+
+<sup>1</sup>College of Computer Science and Technology, Zhejiang University
+
+$^{2}$ OPPO Research Institute, China
+
+{zhangwenqi, luwm}@zju.edu.cn
+
+# Abstract
+
+The reflection capacity of Large Language Model (LLM) has garnered extensive attention. A post-hoc prompting strategy, e.g., reflexion and self-refine, refines LLM's response based on self-evaluated or external feedback. However, recent research indicates without external feedback, LLM's intrinsic reflection is unstable. Our investigation unveils that the key bottleneck is the quality of the self-evaluated feedback. We find LLMs often exhibit overconfidence or high randomness when self-evaluate, offering stubborn or inconsistent feedback, which causes poor reflection. To remedy this, we advocate Self-Contrast: It adaptively explores diverse solving perspectives tailored to the request, contrasts the differences, and summarizes these discrepancies into a checklist which could be used to re-examine and eliminate discrepancies. Our method provides LLM with diverse perspectives to alleviate stubborn biases. Moreover, their discrepancies indicate potential errors or inherent uncertainties that LLM often overlooks. Reflecting upon these can prompt more accurate and stable reflection. Experiments conducted on a series of reasoning and translation tasks with different LLMs serve to underscore the effectiveness and generality of our strategy.
+
+# 1 Introduction
+
+Mastering reasoning and decision-making capabilities is of utmost importance to paving the way for artificial general intelligence. Recently, large language models (LLMs) (Brown et al., 2020; Chowdhery et al., 2022; Zhang et al., 2022a; Zeng et al., 2023; Touvron et al., 2023a; OpenAI, 2022, 2023; Touvron et al., 2023b) and applications built on them (Schick et al., 2023; Wu et al., 2023a; Shen et al., 2023; Zhang et al., 2023a) demonstrate impressive capabilities in various domains, especially combined with Chain-of-Thought (Wei et al., 2022;
+
+![](images/b1f6646e6b461ff922fd00f60f1dd7668925e7e5efaa186522f0aff4b5cf0cfe.jpg)
+
+![](images/5b0503a18c2e25520c96bace0660ba06e4eab4f9ecfedbc9fc4cc6bfaa2f2a92.jpg)  
+Figure 1: LLMs evaluate the initial response and provide feedback for revision. However, most erroneous responses remain uncorrected after reflection as the feedback is either overconfident (46.7%) or inconsistent (45.7%). Bottom: Self-Contrast explores multiple solving perspectives, and contrast their differences, and summarize them into insightful checklist for self-correction.
+
+Kojima et al., 2022), ReAct (Yao et al., 2022), Tree-of-Thought (Yao et al., 2023) and other prompting techniques (Gao et al., 2022; Wang et al., 2023d; Zhou et al., 2022; Besta et al., 2023).
+
+Despite these advancements, LLMs are not entirely reliable (Zheng et al., 2023c; Frieder et al., 2023; Yuan et al., 2023b) since they frequently produce inaccuracies results, such as misunderstanding a key concept, overlooking some crucial details. A post-hoc prompting strategy, e.g., self-reflection, garnered considerable attention (Shinn et al., 2023; Madaan et al., 2023; Paul et al., 2023). It first generates an initial response (Initial Response), then gathers external feedback or self-evaluated feedback (Evaluation Phase) to refine prior response (Revision) (Welleck et al., 2022; Kadavath et al., 2022; Chen et al., 2023d; Liang et al., 2023; Kim et al., 2023; Zheng et al., 2023a; Du et al., 2023; Xi et al., 2023; Ganguli et al., 2023; Pan et al., 2023). Numerous studies proclaim this three-stage strategy
+
+(Initial Response  $\rightarrow$  Evaluation  $\rightarrow$  Revision), can endow LLMs with the potential to self-correct previous imperfect responses. For a time, this belief appeared to dominate the community.
+
+However, recent studies (Huang et al., 2023b; Stechly et al., 2023; Liang et al., 2023; Valmeekam et al., 2023) have cast doubt on LLM's inherent reflection capability. Their research indicates that without external feedback, LLMs have difficulties in amending prior responses. It implies self-correction is unreliable when relying only on LLM itself and simple post-hoc prompting strategies.
+
+We are also intrigued by LLM's internal reflection ability, as external feedback is not available in most scenarios. Our initial experiments (§ 2.1) indicate that intrinsic reflection has limited effect. Across various LLMs and tasks, the performance gains from reflection are not significant, and occasionally detrimental. In cases of incorrect initial responses, only  $15.1\%$  of incorrect responses are corrected through reflection. To ascertain the reasons for that, we further analyze the feedback generated by the self-evaluate process. As shown in Figure 1, LLMs often provide two unexpected feedback: 1) Overconfidence  $(46.7\%)$ : Stubbornly insisting that the previous solution is correct. 2) Inconsistency  $(45.7\%)$ : The feedback is highly inconsistent when self-evaluating the same response multiple times. These two feedbacks seriously undermine the effectiveness of reflection. It reveals that such a simple self-evaluate strategy faces difficulty in accurately identifying errors and consistently generating high-quality feedback for reflection.
+
+As a remedy, we propose a contrastive strategy as an alternative to the direct evaluation: we examine the differences among multiple responses and draw inspiration to derive feedbacks from their disparities for reflection. The insight is that while generating accurate feedback directly may be challenging, identifying contrasts between various responses is often more feasible. More importantly, these discrepancies often indicate some potential errors, easily overlooked details or pitfalls. As shown in Figure 1, by contrasting two solutions, LLM finds they have different solving objectives, and suggests re-examining the intent of the original request in the checklist. This contrasting paradigm can also be seen in some contemporaneous work (Wan et al., 2023; Yuan et al., 2024).
+
+Embracing this philosophy, we advocate Self-Contrast, which steers LLM to autonomously create diverse solving perspectives by self-curated
+
+prompts and then select different results with significant discrepancies for comparison. Then LLM reflects on the reasons behind these discrepancies and generates multiple re-examining instructions, i.e., checklist, for reflection. Our experiments show that by creating diverse perspectives adaptively, Self-Contrast can mitigate biases introduced by specific prompts. Moreover, contrasting the discrepancies between perspectives inspires deeper reflection, thereby enhancing the likelihood of accurate self-correction.
+
+Our contributions can be summarized as:
+
+- Our comprehensive experiments unveil that the bottleneck for poor reflection performance lies in the LLM's inability to accurately evaluate prior responses. It often manifests as overconfident or inconsistent feedback, hindering the effectiveness of self-reflection.  
+- We advocate Self-Contrast: the LLMs create multiple solving perspectives for diverse results, mitigating overconfident biases of a singular prompt. Then drawing inspiration from contrasting different perspectives, the LLMs summarize more accurate checking instructions to resolve discrepancies and enhance reflection.  
+- Empirically, compared with vanilla reflection, Self-Contrast shows significant improvements and stability in both mathematical reasoning and challenging translation scenarios.
+
+# 2 Evaluation of Intrinsic Reflection
+
+We first comprehensively investigate the intrinsic reflection capability of LLMs, i.e., LLMs self-evaluate the initial response without external feedback and then refine it. Subsequently, we methodically investigate the factors influencing reflection.
+
+# 2.1 Performance Pre- and Post-Reflection
+
+We evaluate the reflection capabilities of multiple LLMs across a variety of benchmarks, including math reasoning and creative translation tasks. We report average accuracy for math reasoning and the BLEURT score between predicted sentences and references for the translation task (see § 4.1 for detail). Each result is evaluated multiple times on different prompts. Besides, we also report the significance level (one-tailed t-test) of the accuracy change pre- and post-reflection.
+
+As shown in Table 1, we observe no significant accuracy changes before and after reflection. For
+
+<table><tr><td></td><td colspan="2">Math Reasoning</td><td>Translation</td></tr><tr><td></td><td>GSM8K</td><td>SVAMP</td><td>CommonMT</td></tr><tr><td>GPT4</td><td>93.9⇒95.1</td><td>93.0⇒91.5</td><td>70.1⇒69.8</td></tr><tr><td>P for Δ &gt; 0</td><td>0.1933</td><td>0.5846</td><td>0.5426</td></tr><tr><td>GPT3.5</td><td>76.6⇒75.8</td><td>79.8⇒80.5</td><td>69.1⇒69.3</td></tr><tr><td>P for Δ &gt; 0</td><td>0.6613</td><td>0.4306</td><td>0.4420</td></tr><tr><td>davinci-003</td><td>51.1⇒49.6</td><td>63⇒63.5</td><td>62.4⇒63.8</td></tr><tr><td>P for Δ &gt; 0</td><td>0.6988</td><td>0.4729</td><td>0.2009</td></tr><tr><td>Llama2-70B</td><td>52.6⇒49.3</td><td>66⇒63.0</td><td>63.2⇒62.2</td></tr><tr><td>P for Δ &gt; 0</td><td>0.8416</td><td>0.9521</td><td>0.7723</td></tr><tr><td>Llama2-13B</td><td>28.3⇒29.8</td><td>42.2⇒42.5</td><td>62.5⇒61.5</td></tr><tr><td>P for Δ &gt; 0</td><td>0.3855</td><td>0.2508</td><td>0.4690</td></tr><tr><td>Llama2-7B</td><td>19.8⇒17.0</td><td>37.5⇒36.1</td><td>53.7⇒48.8</td></tr><tr><td>P for Δ &gt; 0</td><td>0.9578</td><td>0.5770</td><td>0.7492</td></tr></table>
+
+Table 1: We calculate the average accuracy of the ten experiments for pre- and post-reflection: Pre Acc.  $\Rightarrow$  Post Acc. We also report the accuracy change's significance level (P-value) for ten trials, where  $\Delta = \text{Post} - \text{Pre}$ . A larger P indicates a less significant improvement.
+
+instance, the performance of GPT-3.5 on GSM8K and SVAMP exhibit marginal changes of  $-0.8\%$  and  $+0.7\%$  after reflection respectively, both statistically insignificant. This negligible performance fluctuation can be validated across multiple LLMs and various benchmarks, far from expectations. Specifically, most reasoning cases suffer from a slight decrease, while the translation task shows little impact. Additionally, smaller LLMs (e.g., Llama2-7B) demonstrate poorer reflection ability, occasionally even exhibiting negative impacts. These experiments collectively suggest that LLMs appear to be incapable of self-correction through reflection.
+
+# 2.2 Feedback Analysis
+
+To investigate the reasons behind the failure of reflection, we further analyze the feedback generated during the self-evaluate process. We classify all samples in GSM8K into four categories based on their correctness of the pre- and post-reflection: 1) Invalid Reflection  $(X \Rightarrow X)$  means the results before and after reflection are both incorrect. 2) Valid Reflection  $(X \Rightarrow \checkmark)$  means a wrong solution is revised to correct through reflection. 3) Toxic Reflection  $(\checkmark \Rightarrow X)$  represents that an originally correct response is changed to incorrect after reflection. 4) Others counts the number of correct  $\Rightarrow$  correct. Automatic statistics for the reflection category.
+
+Step 1: We categorize the reflection into the above four categories. This process can be automated for mathematical benchmarks by comparing whether the answers are correct before and after reflection. For the translation task, we leverage GPT-4 along with annotated answers to evaluate
+
+the accuracy of translation results before and after reflection. Step 2: We manually assess the quality of the feedback generated in each reflection case (Invalid, Valid, and Toxic). Based on the correctness and consistency of these feedbacks, we categorize them into four cases (inconsistent, overconfident, etc.). The detailed results are as follows:
+
+Fail to Correct the Wrong Initial Response. As shown in Table 2, we observe the number of Toxic Reflection ( $\checkmark \Rightarrow X: 52$ ) and Valid Reflection ( $X \Rightarrow \checkmark: 48$ ) are nearly similar. This explains why there is no discernible difference in performance pre- and post-reflection. Besides, considering the scenario when the initial response is erroneous, we observe the number of Invalid Reflection ( $X \Rightarrow X: 269$ ) is significantly larger than Valid Reflection ( $X \Rightarrow \checkmark: 48$ ), which indicates LLM fails to correct errors in the initial responses for most cases.
+
+Often Provide Overconfident or Inconsistent Feedback. We examine whether LLMs could generate feedback accurately and consistently. For each sample, we instruct the LLM to evaluate its initial response multiple times and record multiple feedbacks. We manually assess the consistency and correctness of these feedbacks and then summarize each sample into 4 cases: I. Accurately identifies errors: In multiple repeated evaluations, the LLM identifies errors and provides accurate and consistent feedback. II. Stubbornly offers erroneous feedback: The majority of evaluations provide incorrect feedback with specific errors. III. Can not output consistent feedback: Unable to assess consistently, as most feedback is different and quite random for a same initial response. V. Overconfidence, no revision required: LLM is overconfident and believes no revision is necessary. The detailed evaluation criteria are provided in Appendix A.1.
+
+As shown in Table 2, for the majority of Invalid Reflection, their feedback is either overconfident (53.5%) or highly inconsistent (45.3%), making it difficult to prompt reliable reflection. Similarly, in Toxic Reflection scenarios, 65.4% of the evaluation processes are highly inconsistent, leading to many correct answers being erroneously modified.
+
+# 2.3 From Self-Evaluate to Self-Contrast
+
+The aforementioned experiments indicate that feedback generated by the self-evaluate process is either highly random or excessively confident. This unstable self-evaluate may severely impact the reflection performance of LLMs.
+
+As a remedy, we propose a contrastive strategy
+
+<table><tr><td rowspan="2"></td><td rowspan="2">#Invalid: 269
+#Valid: 48
+#Toxic: 52</td><td colspan="3">Reflection Behavior</td></tr><tr><td>Invalid
+X⇒X</td><td>Valid
+X⇒✓</td><td>Toxic
+✓⇒X</td></tr><tr><td rowspan="4">Feedback Type</td><td>I. Accurately identifies errors</td><td>0.4%</td><td>43.3%</td><td>0%</td></tr><tr><td>II. Stubbornly offers erroneous feedback</td><td>0.8%</td><td>0%</td><td>31.1%</td></tr><tr><td>III. Can not output consistent feedback</td><td>45.3%</td><td>47.5%</td><td>65.4%</td></tr><tr><td>IV. Overconfidence No revision required</td><td>53.5%</td><td>9.2%</td><td>3.5%</td></tr></table>
+
+Table 2: We consider three reflection behaviors based on the correctness of the pre- and post-reflection: Invalid, Valid, and Toxic. Besides, we summarize each sample's feedback into four categories when self-evaluation.  
+
+<table><tr><td>Strategy</td><td>GSM8K</td><td>SVAMP</td><td>CommonMT</td></tr><tr><td>Self-Evaluate w/ top-1</td><td>-0.8</td><td>0.7</td><td>0.2</td></tr><tr><td>P for Δ&gt;0</td><td>0.6613</td><td>0.4306</td><td>0.4420</td></tr><tr><td>Self-Evaluate w/ top-2</td><td>0.12</td><td>0.8</td><td>0.16</td></tr><tr><td>P for Δ&gt;0</td><td>0.4192</td><td>0.3457</td><td>0.3745</td></tr><tr><td>Self-Contrast w/ top-2</td><td>0.9</td><td>2.5</td><td>0.45</td></tr><tr><td>P for Δ&gt;0</td><td>0.0933</td><td>0.0118</td><td>0.0457</td></tr></table>
+
+Table 3: We report the accuracy change  $(\Delta)$  between post- and pre-reflection for 3 settings and t-test value for  $\Delta >0$ . Self-evaluate: Directly evaluate the initial response. Self-contrast: Contrast the difference between two responses and generate a checklist for reflection.
+
+for reflection. Instead of directly evaluating a response, which can be challenging and inconsistent, we instruct the LLM to initially contrast the differences between various solutions, and identify their discrepancies and the reasons behind them. As shown in Figure 1 (bottom), we sample Top-2 responses from LLM and then prompt LLM to contrast their differences in detail, rethink the reasons that caused the discrepancies, and summarize the checklist for re-examining and resolving the discrepancy. As shown in Table 3, we compare three scenarios: self-evaluate w/ top-1 response, self-evaluate w/ top-2 responses, and self-contrast w/ top-2. Our new strategy achieves a modest improvement over standard reflection using self-evaluate. Notably, it significantly enhances the significance levels (p-value: 0.6613 to 0.0933), suggesting it can greatly mitigate the self-evaluation process's uncertainty.
+
+In this section, we validate the concept of contrastive evaluation. For the next section, we expand this contrastive concept into full-version self-contrast, which involves creating multiple perspectives, and contrasting their differences, summarizing the checklist for deeper reflection.
+
+# 3 Self-Contrast
+
+Prior sections illustrate the challenges LLMs encounter in accurately evaluating previous solutions, often resulting in overconfident or inconsistent feedback. Concurrently, we observe that leveraging the discrepancies between two different solutions can inspire a more efficacious reflection, notably reducing the uncertainty during the reflection. Building upon this insight, we propose a more diverse inter-perspective Self-Contrast, facilitating more reliable self-reflection.
+
+Self-Contrast consists of three procedures: Create Diverse Perspectives, Contrast Inter-Perspective Discrepancies, and Eliminate Discrepancies. In Create Diverse Perspectives (§ 3.1), we encourage LLMs to autonomously create a variety of prompts tailored to the user's request, each offering a unique perspective for problem-solving, e.g., different thinking styles, diverse identities, personalities, or preferences. These diverse perspectives prompt the LLM to generate different responses. In the second stage (§ 3.2), LLM contrasts the differences between each pair of responses. Lastly (§ 3.3), to eliminate discrepancies, we abstract these differences into a detailed checklist for re-examining. This checklist guides the LLM to meticulously examine the causes of discrepancies, including random errors or intrinsic biases, which result in inconsistent results among perspectives.
+
+As shown in Figure 2, LLM designs five different prompts and their translation results based on the user's request ("这个计划被枪毙"). From a literal perspective, the phrase "被枪毙" is translated as "shot to death". This rigid translation fails to grasp the metaphor embedded in the military term. Conversely, from a liberal perspective, it is translated as "This plan was axed". After contrasting two different translations, LLMs believe they should scrutinize the source sentence for metaphors and ensure the translation aligns with the conventions of English expression.
+
+# 3.1 Create Diverse Perspectives
+
+Self-Curated Prompts First, it is imperative to define the concept of "solving perspective". It refers to deliberate prompting with a unique role, personality, thought style, etc., which prompts LLMs to solve user requests from a specific perspective. Diverse solving perspectives can endow LLMs with a broader range of thoughts for problem-solving, e.g., different angles and methodologies, thereby
+
+![](images/cb2b6292cf9d7a4573de0f0d4433bf2eff4d5837ea1a6c998808c3115b1487d7.jpg)
+
+# Creative Translation Task
+User Request: 这个计划被枪毙了
+
+# Literal Perspective:
+
+Prompt: You are a rigorous translator, skilled in literal translation and very attentive to details. When translating you emphasize the exact expression of the original text.
+
+Result: This plan was shot to death
+
+# Liberal Perspective:
+
+Prompt: You are a creative translator, your translation style is flexible and liberal, and you like to reinterpret the meaning of the original text using your language.
+
+Result2: This plan was axed
+
+# Stage 1 Create Diverse Perspectives
+
+# Military Perspective:
+
+Prompt: The source sentence involves some military terminology. Please interpret the underlying meaning from a military perspective....
+
+Result3: The plan was chopped
+
+# Cultural Perspective:
+
+Prompt: You are a native of China and have a great understanding of local idioms. You specialize in translating Chinese slang into contextualized English expressions.
+
+Result5: The plan was aborted
+
+![](images/2c2cde54f0ca6f02a740a1d7bb5119d0a89708d7fd98e0c8aec45fe54eb42ce6.jpg)  
+Figure 2: Self-Contrast designs diverse prompts for different solving perspectives and generates corresponding results. Then we filter out similar results and select those that are significantly different. To inspire reflection, we contrast the differences between selected results and prompt LLM to summarize a checklist. This checklist can be used to re-examine and eliminate discrepancies. Lastly, LLM revises each response to achieve a consistent result.
+
+# Selecting From All Candidates:
+
+# Result1
+
+# Result2
+
+# Result5
+
+![](images/8e49b0fde3366627b688751aad2075e11ad332d9620e9e248c313ff632d7476e.jpg)
+
+# Contrasting
+
+# Difference For Result1 and Result2:
+
+The phrase "shot to death" could be misinterpreted as hyperbolic or excessively dramatic in English, possibly detracting from the seriousness of the situation. "Axed" however, clearly communicates the end of the plan without the risk of being taken too literally or causing undue alarm.
+
+Difference For Result1 and Result5: The phrase "shot to death" may carry a more dramatic and violent connotation, potentially overemphasizing the original sentiment and seems to be more akin to a metaphor. "Aborted" is a common English idiom for discarding plans, more closely aligning with English expressions.
+
+Difference For Result2 and Result5: Both "axed" and "aborted" are common idioms.... However, "axed" is often used in more dramatic or serious contexts, while "aborted" can be perceived as more neutral or mundane. Besides, There is a slight difference in the meanings of "this" and "the
+
+# Stage 3 Eliminate Discrepancies
+
+# Checklist:
+
+Please verify whether the term "枪毙" in the original text is metaphorical and if the translation accurately conveys this meaning.  
+Please evaluate which term is more idiomatic in this context, "axed" or "aborted" to express the forced termination of a plan.  
+Please assess whether "this" or "the" is more appropriate to convey "这个" from the original text.
+
+# Reflection:
+
+$\overline{\mathrm{Resut}}_1$  : This plan was shot to death
+
+Result: This plan was axed
+
+Results: The plan was aborted
+
+![](images/35ebb130a506d5dbe976b2c0c1194e4701594c1f8597aad88dc9feb60bca3220.jpg)
+
+This plan was aborted
+
+This plan was aborted
+
+This plan was aborted
+
+![](images/8eb832f67c51d65284fe49a6fe85e69c0ff59d27883f2107a8a0403be2311610.jpg)
+
+# Math Reasoning Task
+
+User Request: A family of 6 (2 adults and 4 kids) are to divide a watermelon such that each adult gets a slice that is twice as big as that of each kid. What percentage of the watermelon does each adult get?
+
+# Top-down Perspective:
+
+Please solve the problem with a top-down approach. First, you need to solve for what proportion of all adults share in total. Then you should calculate what proportion of each adult's
+
+# Bottom-up Perspective:
+
+Using a bottom-up approach, you should focus on the relations between each number and then construct the entire calculation. For this problem, assume that each child gets a share of  $x$ . Then, ...as  $2x$  ....
+
+# Analogical Perspective :
+
+Think of this problem like dividing money in an estate. Suppose you have $100 to distribute.... It can help you intuitively understand how to divide the watermelon.
+
+Result: The answer is  $25\%$ . Adults and children each get half of the watermelon  $(50\%)$ . Then two adults get a total of  $50\%$  and one adult gets  $25\%$ .  
+Result: The answer is  $12.5\%$ . Let's denote the size of each kid gets as  $x$ , ..., watermelon is divided into  $4x$  (kids' portion) +  $4x$  (adults) = 100. x = 12.5%.  
+Difference: Node1 calculates the adult's share is  $25\%$ . Node2 calculates each kid's share is  $12.5\%$ , which actually represents kid's share.  
+Checklist: Please verify the intention in the question: is it to determine the share for each adult or for the children?  
+Please check whether the figure  $12.5\%$  obtained in Result 2 represents the share for adults or for children.
+
+mitigating biases introduced by singular prompts.
+
+To achieve this, we adopt a self-curated prompt strategy, where the LLM itself adaptively generates multiple different prompts for each request, each signifying a tailored perspective, then samples corresponding responses based on these prompts. It is noteworthy that the number of perspectives to be created, and the design of each perspective are entirely determined by LLMs, endowing them with more flexibility to address complex tasks. The details of the prompt are provided in Appendix D.1. In Figure 3, we present statistics on the number of prompts generated in self-curated prompt process.
+
+# 3.2 Contrast Inter-Perspective Discrepancies
+
+The LLM generates diverse responses based on self-curated prompts, each representing a specific perspective. Considering that some responses may be highly similar or even identical, we first filter these similar responses. Then, we select the responses with significant discrepancies for comparison.
+
+Selecting To filter out similar responses, we employ the K-Medoids clustering algorithm based on their semantic similarity. We categorize all responses into  $k$  clusters, each encompassing a set of similar results. Then we select the centroids of each cluster as representative responses and discard the remaining ones. It ensures the selected results exhibit substantial differences from each other.
+
+Contrasting After selecting  $k$  responses from all candidates, we feed these responses concurrently into LLM and then instruct LLM to autonomously contrast the differences for each pair of responses in a single pass. When contrasting, LLMs need to explicitly answer these questions: Whether the two responses are different, Where the differences lie, and Which factors contributed to these inconsistent results. These questions guide the LLM to methodically explore the underlying reasons behind discrepancies, identifying potential errors and often overlooked details. As shown in Figure 2, for translation tasks, the LLM compares results 1, 2, and 5, and identifies that their primary differences lie in the use of different verbs to express "被枪毙". The detailed prompts are shown in Appendix D.2.
+
+# 3.3 Eliminate Discrepancies
+
+We abstract insightful checklists from these pairwise contrastive differences and then use them to resolve the inconsistencies across various perspectives for a consensus.
+
+Summarizing Checklist To ascertain the truth and resolve discrepancies, the LLM is encouraged to summarize a detailed checklist for re-examining the user's request and candidate responses. This checklist contains multiple specialized checking instructions, such as verifying alignment with the user's intent, identifying contradictions in LLM's responses, checking for miscalculations, etc. It explicitly points out some potential issues, e.g., previously overlooked details, logical pitfalls, or unreasonable steps, and compels LLM to re-examine them. Compared to conventional reflection instruction, e.g., Please check your previous response, our checklist is more precise and informative.
+
+Reflection For Consensus Lastly, we employ the checklist and identified discrepancies to prompt reflection. LLM can revise the inconsistent perspectives and output  $k$  consistent responses.
+
+Concretely, we use a JSON format for the revision prompt: Request: {{request}}, Candidate: {{result1}, {result2}, {result3}...}, Discrepancy: {{difference1-2}, {difference1-3}...}, Checklist: {{instruction1},{instruction2},..}}. To eliminate discrepancies, we instruct LLM to revise the inconsistent steps of each candidate and output  $k$  revised responses with consistent answers. When revising, LLM should require careful and comprehensive consideration, as any minor modifications may lead to new discrepancies with others.
+
+# 4 Experiments
+
+# 4.1 Settings
+
+Benchmarks We evaluate our method within two testbeds: mathematical reasoning and translation using GSM8K, SVAMP, and CommonMT benchmarks. Please see Appendix B.1 for details.
+
+Evaluation Metrics For mathematical reasoning, we evaluate the precision of the final answer after their step-by-step reasoning, similar to the previous methodologies. For the translation task, we employ BLEURT $^1$  score as automatic metrics.
+
+LLM Models and Prompts We conduct experiments using the GPT-3.5-Turbo-0613 and GPT-4-0613, alongside the Llama2-Chat model with three parameter scales (7B, 13B, and 70B). To make a fair comparison, we uniformly set the temperature to 0.2 for all experiments. For standard prompts and self-reflection baseline, we evaluate them 10 times using different prompts and average their results under zero-shot scenes. Prompts and other details can be found in Appendices B.2, C and D.
+
+# 4.2 Baselines
+
+We compare Self-Contrast with the following baselines: Standard CoT Prompt (Kojima et al., 2022). Self-Reflection (Shinn et al., 2023). Multi-Agent Debate (Du et al., 2023; Liang et al., 2023; He et al., 2020). ExpertPrompt (Xu et al., 2023a). Hint-Prompt (Zheng et al., 2023a). Math-Prompt (Imani et al., 2023). Moreover, for various task scenarios, we consider three forms of Self-Consistency (Wang et al., 2023d; Chen et al., 2023c): SC-Vote: The original Self-Consistency version, which samples  $K$  decoding results, followed by a voting process. SC-Select: Instead of voting, LLM also samples Top-K responses but then selects the most appropriate answer from  $K$  candidates by itself. SC-Reflect: After sampling Top-K responses, LLM reflects on these candidates and regenerates a new response as the final answer.
+
+# 4.3 Main Results
+
+In Tables 4 and 5, we report the accuracy and the average number of API/LLM calls (#Call), which serves as a proxy for the computational cost.
+
+Consistent improvement over vanilla reflection. Compared to vanilla reflection, Self-Contrast brings significant and stable improvement. For
+
+<table><tr><td rowspan="2"></td><td colspan="5">GSM8K</td><td colspan="5">SVAMP</td><td rowspan="2">#Call Avg.</td></tr><tr><td>GPT3.5</td><td>GPT4</td><td>L-7B</td><td>L-13B</td><td>L-70B</td><td>GPT3.5</td><td>GPT4</td><td>L-7b</td><td>L-13B</td><td>L-70B</td></tr><tr><td>CoT Prompt</td><td>76.6</td><td>93.9</td><td>19.8</td><td>28.3</td><td>52.6</td><td>79.8</td><td>93.0</td><td>37.5</td><td>40.2</td><td>66</td><td>1</td></tr><tr><td>ExpertPrompt</td><td>77.3 ↑0.7</td><td>93.8 ↓0.1</td><td>21.6 ↑1.8</td><td>30.5 ↑2.2</td><td>53.1 ↑0.5</td><td>80.2 ↑0.4</td><td>93.3 ↑0.3</td><td>37.7 ↑0.2</td><td>41.9 ↑1.7</td><td>65.6 ↑0.4</td><td>2</td></tr><tr><td>Self-Reflection</td><td>75.8 ↓0.8</td><td>95.1 ↑1.2</td><td>17.0 ↓2.8</td><td>31.8 ↑3.5</td><td>49.3 ↓3.3</td><td>80.5 ↑0.7</td><td>91.5 ↓1.5</td><td>36.1 ↓1.4</td><td>42.5 ↑2.3</td><td>63.0 ↓3</td><td>3</td></tr><tr><td>Self-Consistency - SC-Vote</td><td>83.5 ↑6.9</td><td>94.2 ↑0.3</td><td>21.4 ↑1.6</td><td>37.6 ↑9.3</td><td>61.1 ↑8.5</td><td>84.6 ↑4.8</td><td>92.5 ↓0.5</td><td>45.2 ↑7.7</td><td>53.7 ↑13.5</td><td>72 ↑6</td><td>8</td></tr><tr><td>- SC-Select</td><td>76.3 ↓0.3</td><td>93.1 ↓0.8</td><td>16.2 ↓3.6</td><td>28.6 ↑0.3</td><td>54.6 ↑2.0</td><td>81.2 ↑1.4</td><td>93.2 ↑0.2</td><td>35.1 ↓2.4</td><td>38.9 ↓1.3</td><td>66.5 ↑0.5</td><td>9</td></tr><tr><td>- SC-Reflect</td><td>75.8 ↓0.8</td><td>93.3 ↓0.6</td><td>19.2 ↓0.6</td><td>29.1 ↓0.8</td><td>53.7 ↑1.1</td><td>81.1 ↑1.3</td><td>93.4 ↑0.4</td><td>32.5 ↓5</td><td>34.2 ↓6</td><td>67.5 ↑1.5</td><td>9</td></tr><tr><td>Multi-Agent</td><td>83.8 ↑7.2</td><td>93.5 ↓0.4</td><td>23.8 ↑4</td><td>34.9 ↑6.6</td><td>59.6 ↑7.0</td><td>84.1 ↑4.3</td><td>93.2 ↑0.2</td><td>42.5 ↑5</td><td>49.2 ↑9.0</td><td>70.1 ↑4.1</td><td>9</td></tr><tr><td>Hint-Prompt</td><td>78.8 ↑2.2</td><td>93.7 ↓0.2</td><td>18.3 ↓1.5</td><td>27.8 ↓0.5</td><td>59.6 ↑7</td><td>79.3 ↓0.5</td><td>93.1 ↑0.1</td><td>38.8 ↑1.3</td><td>40.6 ↑0.4</td><td>67.6 ↑1.6</td><td>6.7</td></tr><tr><td>Math-Prompt</td><td>79.6 ↑3.0</td><td>93.9 ↓0.0</td><td>19.5 ↓0.3</td><td>30.6 ↑2.3</td><td>59.8 ↑7.2</td><td>81.2 ↑1.4</td><td>93.6 ↑0.6</td><td>37.2 ↓0.3</td><td>41.5 ↑1.3</td><td>68.7 ↑0.5</td><td>4.5</td></tr><tr><td>Self-Contrast</td><td>84.4 ↑7.8</td><td>95.4 ↑1.5</td><td>20.5 ↑0.7</td><td>42.3 ↑9.2</td><td>64.2 ↑11.6</td><td>89.0 ↑9.2</td><td>94.0 ↑1</td><td>44.5 ↑7</td><td>54.6 ↑14.4</td><td>75.3 ↑9.3</td><td>7.8</td></tr></table>
+
+Table 4: The performance on mathematical reasoning. Self-Consistency (SC-Vote, -Select, -Reflect) samples eight responses and then performs voting, selecting, or reflection. For the Multi-Agent, we configure three agents to engage in a three-round debate.  $\uparrow$  and  $\downarrow$  means accuracy changes over the CoT prompt. L- denotes Llama2-chat.  
+
+<table><tr><td></td><td>GPT3.5</td><td>L-7B</td><td>L-13B</td><td>L-70B</td></tr><tr><td>CoT Prompt</td><td>69.1</td><td>53.7</td><td>62.5</td><td>63.2</td></tr><tr><td>ExpertPrompt</td><td>69.6 ↑0.5</td><td>53.8 ↑0.1</td><td>62.9 ↑0.4</td><td>63.4 ↑0.2</td></tr><tr><td>Self-Reflection</td><td>69.3 ↑0.2</td><td>48.8 ↓4.9</td><td>61.5 ↓1.0</td><td>62.2 ↓1.0</td></tr><tr><td>Self-Consistency</td><td></td><td></td><td></td><td></td></tr><tr><td>- SC-Vote</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>- SC-Select</td><td>68.6 ↓0.5</td><td>52.1 ↓1.6</td><td>62.8 ↑0.3</td><td>63.0 ↓0.2</td></tr><tr><td>- SC-Reflect</td><td>69.0 ↓0.1</td><td>54.0 ↑0.3</td><td>62.2 ↓0.3</td><td>63.2 ↑0</td></tr><tr><td>Multi-Agent</td><td>69.9 ↑0.8</td><td>51.9 ↓1.8</td><td>63.1 ↑0.6</td><td>65.8 ↑2.6</td></tr><tr><td>Hint-Prompt</td><td>69.6 ↑0.5</td><td>54.2 ↑0.5</td><td>62.5 ↑0</td><td>64.6 ↑1.4</td></tr><tr><td>Self-Contrast</td><td>70.7 ↑1.6</td><td>52.1 ↓1.6</td><td>62.8 ↑0.3</td><td>66.7 ↑3.5</td></tr></table>
+
+Table 5: The performance on Creative Translation.
+
+mathematical reasoning, we achieve an average improvement of  $+7.2\%$ . In contrast, the original self-reflection shows no clear improvement  $(-0.51\%)$ . A similar phenomenon is observed in creative translation, where Self-Contrast achieves a  $+0.95$  improvement, whereas self-reflection results in a decrease of -1.6. Besides, compared to multi-agent and ensemble baselines, our improvement is also pronounced and consistent.
+
+Better generality across different LLMs and tasks. From commercial LLMs (e.g., GPT4) to open-source models (Llama-2), and from reasoning to generative tasks, our strategy exhibits robust generalizability. Concretely, from the perspective of LLM, Self-Contrast achieves the best results on most models except Llama-2-7B. For instance, for GPT-3.5, the improvements are  $7.8\%$  on GSM8K and  $9.2\%$  on SVAMP, while for Llama-2-70B, the improvements are  $11.6\%$  and  $9.3\%$  respectively. As for Llama-2-7B, our performance is slightly lower than Self-consistency and Multi-Agent. This might be due to the weaker instruction-following capabilities of the Llama2-7B, making it challenging to contrast two inconsistent solutions. Besides task
+
+wise, Self-Contrast applies to various task types, demonstrating high versatility. In contrast, Self-Consistency can not handle non-numerical tasks directly, e.g., translation, due to its voting mechanism (Table 5). Its variant strategies, SC-Select and SC-Reflect, lag significantly behind ours.
+
+Fewer manual efforts and more reasonable call overheads. Compared to the multi-agent debate, Self-Contrast gains more significant improvements with less call overhead ( $>10\%$  reduction). From a unified perspective, it can be viewed as a multi-agent contrastive mechanism. Instead of a free-form debate among multiple agents, our strategy fosters a more explicit and purposeful debate by contrasting the differences between agents and summarizing the reasons for their disagreements. Moreover, Self-Contrast is flexible, dynamically designing multiple perspectives tailored to user requests, without the need for manually pre-configuring agent roles and quantities.
+
+# 5 The Effect of the Different Components
+
+The above results show that Self-Contrast inspires reflection more accurately and stably than direct evaluation. It encompasses a self-curated prompt process, which fosters diverse solving perspectives to mitigate self-evaluation biases. Besides, it involves a checklist generation process to facilitate re-examination. We analyze their effect as follows:
+
+Self-curated Prompt Vs. Sampling Multiple Responses. Instead of self-curated prompt process, we directly sample multiple responses from LLMs for subsequent contrast and reflection. Figure A2 shows that the final accuracy improves as the number of sampled responses increases, yet it is still lower than Self-Contrast with self-curated prompts
+
+<table><tr><td>LLMs</td><td>Strategy</td><td>Invalid X⇒X Cases ↓</td><td>Toxic ✓⇒X Cases ↓</td></tr><tr><td rowspan="3">GPT3.5</td><td>Self-Reflection</td><td>269</td><td>52</td></tr><tr><td>SC-Reflect</td><td>245</td><td>73</td></tr><tr><td>Self-Contrast</td><td>186 ↓30.8%</td><td>11 ↓78.9%</td></tr><tr><td rowspan="3">L-70B</td><td>Self-Reflection</td><td>528</td><td>140</td></tr><tr><td>SC-Reflect</td><td>468</td><td>127</td></tr><tr><td>Self-Contrast</td><td>401 ↓24.8%</td><td>71 ↓49.2%</td></tr></table>
+
+process, where full strategy achieves  $84.4\%$  compared to the maximum of  $81.8\%$  when sampling 5 responses. We find that the top-n responses are sometimes strikingly similar, diminishing the effectiveness of the contrastive strategy.
+
+Reflection Without Checklist. We eliminate the checklist generation process, i.e., directly instruct the LLM to reflect on the differences among perspectives. In Table A1, it brings a significant impact on mathematical reasoning  $(-3.5\%)$ , but a slight impact on translation  $(-0.1\%)$ , since translation tasks tend to focus more on local features. Even without a checklist, the LLM also can reflect based on the comparisons of lexical, syntactic.
+
+# 6 Analysis
+
+# 6.1 Reducing Invalid and Toxic Reflections
+
+As mentioned in Table 2, due to overly confident or highly random in the self-evaluate process, vanilla self-reflection contains a large amount of invalid  $(X \rightarrow X: 20.3\%)$  or toxic reflections ( $\checkmark \rightarrow X: 4\%$ ). Therefore we investigate how Self-Contrast improves these two scenarios on GSM8K. As shown in Table 6, we observe that with Self-Contrast, the occurrences of invalid and toxic cases significantly reduced. In particular toxic cases decreased by  $78.9\%$  and invalid cases by  $30.8\%$  using GPT3.5. In contrast, the SC-Reflect does not significantly mitigate either of these scenarios.
+
+The results indicate that through exploration, comparison, and summarization, the uncertainty in the reflection process is greatly reduced, thereby enhancing the error-correction capability of the LLM.
+
+# 6.2 Contrasting Incorrect Solutions is also Instructive
+
+Self-Contrast inspires reflection by contrasting the differences. An intuitive explanation is that the errors in different responses are dissimilar or randomized, so they can be used to compare with each other and eliminate uncertainties or biases. To verify this, we sample 200 questions from GSM8K,
+
+Table 6: Self-Contrast is evaluated on two cases.  
+
+<table><tr><td>Strategy</td><td>Acc.(%)</td></tr><tr><td>Self-Evaluate - An Incorrect Solution</td><td>70.1</td></tr><tr><td>Self-Contrast</td><td></td></tr><tr><td>- A Correct and an Incorrect Solutions</td><td>83.6</td></tr><tr><td>- Two Incorrect Solutions with Similar Error</td><td>70.9</td></tr><tr><td>- Two Incorrect Solutions with Different Error</td><td>75.5</td></tr></table>
+
+Table 7: We conduct comparisons across four cases on a subset of GSM8K. LLM self-evaluates or self-contrasts different initial responses and reflects on their results.
+
+![](images/2cb516c9e429f6a6bd7fff7db4074d581df45495b6127a245f3fe01b6d0d0092.jpg)  
+Figure 3: Left: The distribution of the prompt number generated when Self-curated. Right: We visualize the top-20 keywords and frequencies in the prompt name.
+
+each manually annotated with a correct solution, two incorrect solutions with similar errors (e.g., Error1), and an incorrect solution with a different error (Error2). We design four experiments: 1. Self-evaluate one incorrect solution followed by reflection. 2. Self-Contrast a correct and an incorrect solution. 3. Self-Contrast two similar incorrect solutions. 4. Self-Contrast two dissimilar incorrect solutions. Table 7 shows that contrasting a correct and an erroneous solution, or contrasting two incorrect solutions with different errors both yield significant enhancements of  $13.5\%$  and  $5.4\%$ . In contrast, comparing two solutions with similar errors does not result in perceptible changes.
+
+This result aptly explains that the improvement of Self-Contrast stems from contrasting the differences between dissimilar solutions. Therefore, even if candidate solutions are both incorrect, as long as their errors are different, Self-Contrast has the potential to eliminate errors. In other words, Self-Contrast can mitigate the random errors arising from the inherent uncertainty of the LLM.
+
+# 6.3 Diverse Solving Perspectives Maximize Contrast Effect
+
+Prior analysis indicates that only contrasting dissimilar solutions can foster reflection. Reviewing our strategy, we employ a self-curated prompt process to create multiple solving perspectives (§ 3.1), thereby providing diverse solutions for subsequent
+
+comparison. Here, we analyze the distribution of perspectives generated by this process in Figure 3. For most requests, the LLM generates four prompts. We also analyze the frequency of keywords within these perspective's names. For mathematical reasoning, the LLM indeed adaptively designs numerous unique solving perspectives, then generating a variety of results. These dissimilar results can maximize the efficacy of our contrastive strategy.
+
+# 7 Discussions
+
+Self-contrast switches the critique objective into a contrastive task. We transform the self-evaluation into a process of comparing differences, explicitly altering the attention distribution of the LLM. The LLM is required only to identify the differences between two solutions, without judging right or wrong. This process is less influenced by the biases inherent in LLMs, as the objective is contrasting rather than evaluation. Besides, in Table 7, LLMs are instructed to contrast two incorrect solutions with different errors which also improves reflection results.
+
+The results in Section 2.3 also precisely verify this conjecture. By simply transforming from direct evaluation to contrastive evaluation, we enhance the effectiveness of reflection (75.8 to 77.5 on GSM8K), with more significant results (0.66 to 0.09). In Tables 4 and 5, our self-contrast approach achieved more significant improvements.
+
+Contrasting results can help LLMs notice overlooked details and biases. After contrasting the differences between the two solutions, we summarize these differences into a checklist, thereby explicitly prompting the LLM to focus on the logical pitfalls and other issues underlying these differences. This allows LLMs to engage in reflection more clearly and purposefully.
+
+As shown in Figure 2, LLM generates different translations for the user's request: "This plan was shot to death", and "This plan was axed". The former is a rigid translation that fails to grasp the metaphor embedded in the military term. After contrasting two different translations, LLMs believe they should scrutinize the source sentence for metaphors and ensure the translation aligns with the conventions of English expression.
+
+# 8 Conclusion
+
+We conduct a comprehensive investigation into the inherent reflection capabilities of LLMs. Our find
+
+ings reveal a notable challenge: in the absence of external feedback, LLMs struggle to correct errors in previous responses on their own. After analyzing their self-evaluate process, we discover that LLMs are unable to accurately evaluate prior solutions and often provide overconfident or inconsistent feedback, which impedes reflection. To mitigate this, we introduce Self-Contrast, a contrastive strategy that inspires reflection by contrasting the differences between multiple perspectives, providing an informative checklist for reflection. Our experiments show that Self-Contrast performs well across a variety of scenarios and with different LLMs.
+
+# Limitations
+
+For some smaller-scale LLMs, their instruction-following capability is weaker, hindering their potential to conduct precise comparisons and reflection. In such scenarios, the effectiveness of Self-Contrast might be slightly inferior to ensemble strategies. For instance, the performance of Self-Contrast with Llama2-7B is marginally lower than self-consistency. A viable approach is to utilize an external tool to compare differences between multiple perspectives, rather than LLM itself. For instance, we explore utilizing sequences comparison library difflib² to contrast two generated equations (e.g., differ(compare(a+b÷c, a-b÷c)) or some rule-based strategy to compare two responses. It can provide us with more accurate and flexible comparisons at different granularity (e.g., character level). We leave this as future work.
+
+# Acknowledgments
+
+This work is supported by the National Natural Science Foundation of China (No. 62376245), the Key Research and Development Program of Zhejiang Province, China (No. 2024C01034), the Fundamental Research Funds for the Central Universities, and National Key Research and Development Project of China (No. 2018AAA0101900).
+
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+Xiaohan Xu, Chongyang Tao, Tao Shen, Can Xu, Hongbo Xu, Guodong Long, and Jian-Guang Lou. 2023b. Re-reading improves reasoning in language models. ArXiv, abs/2309.06275.  
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+Shunyu Yao, Jeffrey Zhao, Dian Yu, Nan Du, Izhak Shafran, Karthik Narasimhan, and Yuan Cao. 2022. React: Synergizing reasoning and acting in language models. ArXiv, abs/2210.03629.  
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+
+# Appendix
+
+# A Complementary Experiments
+
+# A.1 Detail For Manual Feedback Evaluation
+
+We provide the details of manual evaluation in Table 2. Specifically, we categorize reflection results into four categories: Invalid (wrong -> wrong), Valid (wrong -> right), Toxic (right -> wrong), and Other (right -> right) based on their answer. Subsequently, we manually assess the quality of feedback within each reflection category. For instance, for a Toxic reflection case, we devise ten self-evaluation prompts, prompting LLMs to conduct a self-evaluation on their initial response, generating ten feedbacks. These feedbacks are manually checked for correctness and consistency. The criteria for classification are as follows:
+
+- If more than seven feedbacks accurately identify the errors in the initial response, we classify it into the first category: I. Accurately Identifies Errors. Please note that the feedback only needs to accurately identify the errors without necessarily correcting them.  
+- If more than seven feedbacks indicate that the initial response has no errors, we categorize it into the fourth category: IV. Overconfidence - No Revision Required.  
+- If, among the ten feedbacks, there are more than three different opinions, e.g., the first feedback suggesting there are no errors, another identifying error-1, and yet another pointing out error-2.... For this scenario, we classify it into the third category: III. Cannot Output Consistent Feedback. In this scenario, self-evaluation exhibits significant randomness.  
+- The remaining cases are classified into the second category: II. Stubbornly Offers Erroneous Feedback.
+
+The entire human evaluation process is conducted by two senior PhD students. One is responsible for categorization, while the other verifies the categorization again.
+
+# A.2 LLM is More Likely to Trust Previous Response
+
+We investigate whether LLMs are prone to uncritically trusting previous responses during reflection,
+
+rather than meticulously examining and rectifying errors. Typically, self-reflection often contains three stages, i.e., initial response, self-evaluate, and revision stage. We employ different LLMs to provide a poorer quality response as the initial response for the subsequent two stages. We observe whether this affects the results of the reflection, e.g., we replace  $\mathrm{gpt3.5\rightarrow gpt3.5\rightarrow gpt3.5}$  with Llama-2-70b  $\rightarrow$  gpt3.5  $\rightarrow$  gpt3.5. If LLMs tend to place undue trust in prior responses, the efficacy of the final reflective process will be adversely impacted.
+
+However, as shown in Figure A1, the reflection results are severely impacted by the quality of the initial response. E.g., compared with using gpt3.5 for three phases, Llama2-70b  $\rightarrow$  gpt3.5  $\rightarrow$  gpt3.5 exhibits a marked decrease  $(-8.4\%)$  for GSM8K). Furthermore, we also observe the weaker the LLM replaced, the poorer the performance after reflection. It suggests that LLMs tend to trust the initial solution rather than detect and revise the errors during the self-evaluate phase.
+
+![](images/9feffbf6d3b3bfff320283658364b6a96576f10597104aaac10b9fd1fdfef224.jpg)  
+Figure A1: The Reflection Accuracy with Different LLM for Initial Response. Left: different LLMs provide initial responses when GPT3.5 is utilized for Evaluation and Revision. Center: different LLMs provide initial responses when Llama2-70B is utilized for Evaluation and Revision. Right: different LLMs provide initial responses when Llama2-13B is utilized for Evaluation and Revision. The results indicate that LLMs are easily influenced during reflection. LLM is predisposed to trust previous responses over diligently examining and correcting errors.
+
+# A.3 Self-Evaluate Vs. Self-Contrast
+
+Self-Contrast inspires reflection by contrasting the differences, rather than evaluating directly. The underlying assumption is contrast is more accurate and stable than direct evaluation for LLM. To validate this, we conduct an experiment using 200 samples from GSM8K, each containing a correct
+
+![](images/8b3770c9626b5c3d1588cada4132c9fd4c4c58f0fd54f58b2adae4b4074b6ac9.jpg)  
+Figure A2: We replace the self-curated prompt process with a simple strategy: directly sampling top-n responses for contrast. We observe that as N increases, the performance also improves, yet it still remains lower than self-contrast with the self-curated prompts. All results are conducted on GSM8K using GPT-3.5.
+
+<table><tr><td>Strategy</td><td>GSM8K</td><td>CommonMT</td></tr><tr><td>Self-reflection</td><td>75.8</td><td>69.3</td></tr><tr><td>Self-Contrast</td><td>84.4</td><td>70.7</td></tr><tr><td>- w/o Checklist Generation</td><td>80.9 ↓3.5</td><td>70.6 ↓0.1</td></tr><tr><td>Selecting Strategies</td><td></td><td></td></tr><tr><td>- Random Selecting</td><td>76.4 ↓8</td><td>69.5 ↓1.2</td></tr><tr><td>- Clustering + Random Selecting</td><td>81.2 ↓3.2</td><td>69.7 ↓1.0</td></tr><tr><td>- Clustering + LLM Selecting</td><td>82.6 ↓1.8</td><td>69.9 ↓0.8</td></tr><tr><td>- Clustering + Negative Perspective</td><td>83.9 ↓0.5</td><td>70.8 ↑0.1</td></tr></table>
+
+Table A1: We eliminate the checklist generation process, instructing the LLM to directly reflect on the differences from contrasting multiple perspectives. Besides, we also analyze the impact of different selecting strategies.
+
+and an incorrect solution. We design two tasks: Taks 1: Contrasting two solutions. Task 2: Evaluating the incorrect solution. We manually check the results of two tasks, i.e., whether LLM can perform contrast or evaluate correctly. As shown in Figure A3, we observe contrasting is more accurate than direct evaluating (171 correct Vs. 140 incorrect).
+
+Further, we divide all samples into four cases: 1. both tasks are correct. 2. Contrasting: correct, Evaluating: wrong. 3. Contrasting: wrong, Evaluating: correct. 4. Both are wrong. In Figure A3, the results show that when LLM can correctly evaluate a solution, it is often able to contrast correctly, with few exceptions (only 8 samples for Evaluating Correct Only). Notably, in 39 cases, the LLM fails in direct evaluation but succeeds in contrast. These results indicate that contrasting two solutions is more accurate and stable than direct evaluation, leading to more reliable results.
+
+![](images/55f7da0a8005581f0366c00886263306021eb0c45ff2795383e97e3ab1cbc517.jpg)  
+Figure A3: We compare the results of the Evaluating and Contrasting using two pie charts. It shows Contrasting is more accurate and stable than direct Evaluating.
+
+# A.4 Ablation Study For Selection Strategy
+
+As introduced in Section 3.2, we cluster multiple responses generated by the self-curated process and then select the cluster center from each category for contrast. We design four different selection strategies. 1) Random Selecting: We randomly choose  $K$  responses from all candidates. 2) Clustering + Random Selecting: We first cluster all responses into  $k$  categories, then randomly select one from each category. 3) Clustering + LLM Selecting: Similarly, we first cluster all responses into  $k$  categories, then instruct the LLM to choose a potentially correct response from each category. 4) Clustering + Negative Perspective: We first instruct the LLM to consider what are common errors for the user request. Then LLM should intentionally generate an imperfect solution based on these common errors. Finally, we instruct the LLM to select one response from each category that is least similar to the intentionally generated imperfect solution. As shown in Table A1, we observe that compared to Self-Contrast, the performance of several selection strategies experiences a certain degree of decline.
+
+# B Experiments Details
+
+# B.1 Benchmarks
+
+Mathematical Reasoning: We leverage multiple datasets with different complexity and languages, including GSM8K (Cobbe et al., 2021), SVAMP (Patel et al., 2021) as benchmarks to evaluate performance. Notably, GSM8K presents higher levels of difficulty, encompassing complex mathematical operations, while SVAMP is slightly simpler and consists of combinations of addition, subtraction, multiplication, and division.
+
+Creative Translation In addition to mathemat
+
+ical reasoning tasks, we introduce a generation task: creative translation. We utilize the CommonMT (He et al., 2020), which includes a vast body of Chinese-to-English pair examples. Unlike conventional translations, most samples contain non-standard expressions such as idioms and metaphors, necessitating an understanding of local cultural and linguistic habits for accurate translation. Following the Multi-agent debate (Liang et al., 2023), we adopt the samples with "hard" categories from CommonMT as testing benchmarks.
+
+# B.2 Other Details
+
+In the Self-Curated Prompt phase, we limit LLMs to design at least two different prompts and a maximum of nine prompts for each request. In selecting stage (Section 3.2), we set  $k$  to 3, which means that all perspective results are divided into three categories, and then we select a result from each category. We instruct LLM sequentially output comparisons among three results, subsequently synthesizing these differences into a comprehensive checklist in a single pass, eliminating the need for multiple prompts. Besides, due to the diversity of translation tasks, we also introduce a negative perspective for translation. Specifically, we instruct LLMs to consider what common errors might be made for the user request, then actively adopt a careless persona to generate an incorrect response with some common mistakes. The result of this negative perspective serves as a negative demonstration for subsequent selection and reflection.
+
+# C Baseline Prompts
+
+Standard Prompt We use a simple prompt for CoT Prompt and self-consistency baselines. For each experiment, we run 10 times and averaged their results.
+
+Math Reasoning: You are a math teacher. Let us solve the math question step by step. The question is {input}.
+
+Creative Translation: You are an expert translator, please translate Chinese into English accurately. The Chinese sentence is {input}.
+
+Reflection Prompts We designed 10 prompts for the self-reflection baseline. Each experiment follows Initial response-Evaluation-Revision pattern. The prompt for the Initial response remains consistent with previous experiments (Standard Prompt).
+
+1:
+
+Evaluation: Please carefully examine the previous responses for correctness, and provide detailed feedback.
+
+Revision: Please refine the previous response based on the feedback. 2:
+
+Evaluation: Please review your previous responses for any errors, and provide detailed feedback.
+
+Revision: Please refine the previous response based on the feedback. If there are no questions, you can repeat the previous solution 3:
+
+Evaluation: Do you think the previous response is correct or not, and if not please point out where is wrong.
+
+Revision: Please refine the previous response. 4:
+
+Evaluation: Please carefully evaluate the quality of the previous response and point out if you feel something is not appropriate
+
+Revision: Please carefully consider the comments in the feedback and re-generate the answer. 5:
+
+Evaluation: Please double-check the previous response for any errors. If there are any errors, please point them out.
+
+Revision: Please read the feedback carefully, and improve your answer. 6:
+
+Evaluation: There may have been some mistakes with your previous response, so please double-check and find out the mistake. If you think there are no errors at all, please just reply, "Exactly correct".
+
+Revision: Please refine your response. If you think it's acceptable, then just repeat your last response. 7:
+
+Evaluation: Please check that your previous response matches the question. Please point out if it does not fit
+
+Revision: Please refine your response based on the feedback. If the feedback points out something that is not perfect please fix it! 8:
+
+Evaluation: Please consider whether your response addresses the problem. If not or if there is an error please point it out
+
+Revision: Please reflect based on the feedback and improve your response. 9:
+
+Evaluation: Please assess in detail whether your previous response solves
+
+the problem and provide feedback.
+
+Revision: Please refine your response based on the feedback. 10:
+
+Evaluation: Please check your previous response for correctness and whether it can be further enhanced.
+
+Revision: Please further refine your response based on the feedback. If you don't feel it is necessary then restate the previous response
+
+# D Our Prompt
+
+# D.1 Prompt for Self-Curated Process
+
+Different requests may require some unique solving perspectives. We design a self-curated prompts process, enabling LLMs to design their prompts based on specific user requests. The prompt for the self-curated process is as follows:
+
+# Translation Task:
+
+You are a translation specialist who specializes in translating from diverse perspectives. Given a Chinese source sentence, you need to carefully analyze the source sentence and dynamically generate several useful prompt instructions. These prompt instructions should be diverse and also relevant to the source sentence. These prompt instructions are used to guide the language model to think in different ways, attention to different emphases, and reason from different perspectives for a more accurate translation.
+
+For instance, you can design different translation styles, different expressions of emotion, different emphases, and different tones for input sentences in prompt instruction. Besides you can create different knowledge backgrounds, identities, personalities, different concerns, etc for more relevant translation.
+
+Here are some guidance rules for Prompt Generation:
+
+1. Tone Requirement: Please generate prompt instructions in the third person.  
+2. Content Requirement: Each prompt instruction should be different, and include at least three parts: translation styles, attention emphasis, and tones and emotion design. Please do not state them separately.  
+3. Number Requirement: Dynamically generate the most valuable 2 to 9 prompt instructions based on the input Chinese source sentences.  
+4. Format Requirement: Each prompt instruction should start with ____##.
+5. Others: Prompt should focus on translation. So don't ask any other irrelevant questions in the prompt.
+
+Here is an example:
+
+The input Chinese sentence is: 他想拉同村的干部一起下水去贩毒. Please generate the most suitable prompts.
+
+Output:
+
+Literal Perspective: ##You are a meticulous translator, proficient in direct translation, and highly focused on specifics. Your translation approach prioritizes precise replication of the original text's expression.
+
+Liberal Perspective: ##You are an inventive translator, characterized by a dynamic and liberal translation approach, often reimagining the original text's meaning in your own linguistic style.
+
+The input Chinese sentence is {input}. Please generate the most suitable prompts:
+
+# Reasoning Task:
+
+You are a math specialist who specializes in math solving from diverse perspectives. Given a math question, you need to carefully analyze the question and dynamically generate several useful prompt instructions. These prompt instructions should be diverse and also useful for math-solving. These prompt instructions are used to guide the language model to think in different ways, attention to different emphases, and reason from different perspectives for more accurate math solving.
+
+For instance, you can adopt multi-faceted thinking (logical thinking, lateral thinking, analogical thinking, etc.), different reasoning perspectives (e.g., top-down, bottom-up, step-by-step), and different emphases of concern, (entity words, numbers, units, percentages, math knowledge, etc) for input question in prompt instruction.
+
+Here are some guidance rules for Prompt Generation:
+
+1. Tone Requirement: Please generate prompt instructions in the third person.  
+2. Content Requirement: Each prompt instruction should adopt a different way of thinking, or focus on a different perspective, or different emphases to solve the question.  
+3. Number Requirement: Dynamically generate the most valuable 2 to 9 prompt instructions based on the input math question.  
+4. Format Requirement: Each prompt instruction should start with ____ and end with @@@.  
+5. Others: Prompt instructions should focus on math solving. So don't ask any
+
+other irrelevant questions in the prompt
+
+Here is an example: The math question is : Mark works at his job for 8 hours a day for 5 days a week. He used to make $10 an hour but they raised his pay by $2 per hour. How much does he make a week?
+
+Output: bottom-up perspective: ____##As a mathematician, you have to solve the given problem from a bottom-up perspective. Please focus initially on the foundational elements of the problem. Start with the simplest parts and their interrelations. Progressively build upon these foundational components, joining them together until a complete solution emerges
+
+The input math question is {input}. Please generate the most suitable prompts:
+
+# D.2 Prompt for Contrasting Process
+
+# Translation Task:
+
+You are an expert translator. Given some candidate English translations for a Chinese source sentence, you should carefully compare the difference between each two translations in terms of semantics, syntax, words (e.g., nouns and verbs), and any other aspects.
+
+When you compare, you need to consider the following questions:
+
+1: Are there differences between the two translations?  
+2: Where are the differences?  
+3: What causes these differences?
+
+After contrasting, you should generate a checklist based on these differences between candidate translations. You should carefully consider each discrepancy and the reasons behind it, summarizing them into a few checking instructions in the checklist. This checklist can guide others to re-examine the input sentence and these candidate translations to eliminate these discrepancies.
+
+Input Format:  
+The Chinese sentence is {Chinese sentence}.  
+All Results: {Result1}, {Result2}, {Result3}, ...
+
+Output Format:  
+For Result1 and Result2: {Difference1}.  
+For Result1 and Result3: {Difference2}  
+For Result2 and Result3: {Difference3}  
+Checklist: {Directive1, Directive2, ...}
+
+# Reasoning Task:
+
+You are a math specialist who specializes in math solving. Given some candidate solutions for a math question, you should carefully compare the difference for each two solutions in their solving steps.
+
+When you compare, you need to consider the following questions:
+
+1: Are the two solutions have different final answers and mathematical expressions?  
+2: Where are the differences in their solution steps and mathematical expressions?  
+3: Why are the answers of the two solutions different?
+
+After contrasting, you should generate a checklist based on these differences between candidate solutions. You should carefully consider each discrepancy and the reasons behind it, summarizing them into a few checking instructions in the checklist. This checklist can guide others to re-examine the input question and these candidate solutions to eliminate these discrepancies.
+
+Input Format:
+
+The math question is {Question}.
+
+All solutions: {Solution1}, {Solution2}, {Solution3}, ....
+
+Output Format:
+
+For Solution1 and Solution2: {Difference1}
+
+For Solution1 and Solution3: {Difference2}
+
+For Solution2 and Solution3: {Difference3}
+
+Checklist: {Directive1, Directive2, ...}
+
+# D.3 Prompt For Reflection Stage
+
+We record all candidate responses, their differences, and the checklist in a JSON format. The whole prompt for math reasoning is as follows:
+
+# Reflection Instruction:
+
+Given a math question, multiple inconsistent solutions, their differences in their solving processes, and a checklist. You should revise the inconsistent solving step for each solution, eliminate the differences, and output a new solving process for each solution.
+
+Guidance Rules for Reflection:
+
+1. Please check carefully according to the requirements on the checklist. It helps you to resolve conflicts between different solutions.  
+2. When you finish revising inconsistent solutions, please ensure all revised solutions should have the same answer. If not, please revise again until all inconsistencies are removed, and all
+
+```txt
+candidates are consistent.  
+3. Please output all revised solutions in JSON format as input, without any other text.
+```
+
+```txt
+The math question is {question}.   
+The candidate solutions and their   
+discrepancy are as follows:   
+{ "Candidate": { "result_1": { "answer": {"{answer1}"}, "solution": {"{solution1}"}}, "result_2": { "answer": {"{answer2}"}, "solution": {"{solution2}"}}, "result_3": { "answer": {"{answer3}"}, "solution": {"{solution3}"}}, .... }, "Discrepancy": { "difference_1_2": { "source": "result_1", "target": "result_2", "relation": {"{difference}"} }, "difference_1_3": { "source": "result_1", "target": "result_3", "relation": {"{difference}"} }, "difference_2_3": { "source": "result_2", "target": "result_3", "relation": {"{difference}"} }, .... }   
+}   
+Checklist: {Directive1, Directive2,...}   
+Please revise each inconsistent solution
+```
+
+# E Related Works
+
+# E.1 Self-correction Ability of LLM
+
+Recently, one exciting discovery is that LLMs appear to possess advanced cognitive intelligence: self-correction, where LLMs can refine their previous responses based on feedback (Shinn et al., 2023; Madaan et al., 2023; Paul et al., 2023). This capacity endows LLMs to harness external feedback, or even self-evaluated feedback to refine the prior responses (Welleck et al., 2022; Kadavath et al., 2022; Chen et al., 2023d; Kim et al., 2023; Xi et al., 2023; Ganguli et al., 2023; Pan et al., 2023; Nathani et al., 2023). This capacity, particularly when it is solely reliant on inherent reflection, has generated significant interest in the academic community. It appears that a simple iterative prompt strategy could facilitate self-correction in an LLM-
+
+based system. However, recent studies (Huang et al., 2023b; Stechly et al., 2023; Liang et al., 2023; Valmeekam et al., 2023) have cast doubt on LLM's inherent reflection capability. Their research indicates that without external feedback, LLMs have difficulties in amending prior responses.
+
+# E.2 Prompting for Better Problem-Solving
+
+Drawing on cognitive science, human reasoning involves two different reasoning patterns: breadth reasoning, i.e., exploring various reasoning perspectives, and depth reasoning, which involves continually refining ideas and minimizing errors. Based on this concept, we can view previous prompting strategies as either breadth or depth reasoning. Self-consistency and some contemporaneous works (Wang et al., 2023d; Huang et al., 2022; Yoran et al., 2023; Jain et al., 2023; Chen et al., 2023c) mimic breadth reasoning by sampling diverse reasoning processes and voting the final answer, while self-reflection, abstraction reasoning strategies (Shinn et al., 2023; Madaan et al., 2023; Paul et al., 2023; Zheng et al., 2023a; Wang et al., 2023a; Yoran et al., 2023; Zheng et al., 2023b; Xu et al., 2023b; Shridhar et al., 2023) represent depth reasoning, refining reasoning through iterative prompting strategy. Except for these, Self-Verification (Weng et al., 2022) designs a reverse generation from the answer to given conditions, which is widely used in machine translation (Edunov et al., 2018). Cohen et al. (2023); Mündler et al. (2023) propose a method for detecting self-contradictions or factual errors in responses to enhance quality. However, our Self-Contrast combines both breadth and depth reasoning. It creates multiple perspectives to enhance the breadth of reasoning and also reflects on the differences for better depth reasoning, offering more reliable problem-solving.
+
+# E.3 Agent-based Methods
+
+Recent studies (Li et al., 2023; Deshpande et al., 2023; Xu et al., 2023a; Du et al., 2023; Xiong et al., 2023) have found that when an LLM is assigned a specific role personas, it can generate higher-quality responses. This suggests that LLMs are powerful enough, and the appropriate prompt can elicit this capability. Moreover, recent works (Wang et al., 2023e; Fu et al., 2023; Liang et al., 2023; Schick et al., 2022; Dong et al., 2023; Park et al., 2023; Liu et al., 2023) have utilized a multi-role dialogue to collaborate or debate with
+
+each other for a more comprehensive response. Furthermore, some studies (Chen et al., 2023b; Chan et al., 2023; Huang et al., 2023a; Chen et al., 2023a; Hong et al., 2023; Wu et al., 2023b) have integrated this concept with complex tasks such as code generation by decomposing a complex task into several sub-tasks and employing multiple agents with different identities for each sub-task. However, most agent-based approaches necessitate careful manual design of each agent's role and pattern of interaction. Our approach, in contrast, does not require pre-defined agents' roles and numbers by humans, as it is entirely designed by the LLMs based on the user request, offering greater flexibility.
+
+# E.4 Learning Mathematical Reasoning
+
+Mathematical reasoning is the key to achieving embodied intelligence (Zhang et al., 2021, 2022c). In recent years, mathematical reasoning has become a significant benchmark (Cobbe et al., 2021; Hendrycks et al., 2021) to evaluate the capabilities of artificial intelligence models. Within the paradigm of supervised learning, a vast amount of research (Xie and Sun, 2019; Patel et al., 2021; Jie et al., 2022; Zhang et al., 2022b, 2023b) has been dedicated to translating human language into mathematical equations. In the era of LLMs, the advent of Chain-of-Thought and other prompting strategies have notably augmented the reasoning capabilities (Zhu et al., 2023; Yuan et al., 2023b; Frieder et al., 2023; Zhou et al., 2022).
+
+Prompting Method PAL and Program-of-Thoughts (Gao et al., 2022; Chen et al., 2022) separate the computation and reasoning process using code as the intermediate process. Mathprompter, Auto-Model (Imani et al., 2023; Zhao et al., 2023) encourage LLMs to generate diverse reasoning paths in different forms simultaneously, including text (CoT), code (PAL), and symbols (Equation) for a higher confidence answer. Automatic-CoT, Complexity-CoT, Synthetic Prompt and Boosted Prompt (Zhang et al., 2022d; Fu et al., 2022; Shao et al., 2023; Pitis et al., 2023) enhance reasoning performance by optimizing the selection of demonstrations within the prompt. Tree-of-thought and Self-Evaluation (Yao et al., 2023; Xie et al., 2023) extend the CoT into a search tree, obtaining more accurate answers through self-evaluation.
+
+Finetuning-based Method Another domain of study involves methods based on finetuning. These approaches involve finetuning open-source models, such as LLaMA, by incorporating insights from
+
+sophisticated closed-source LLMs. The fine-tuning approaches(Yuan et al., 2023a; Luo et al., 2023; Yue et al., 2023; Wang et al., 2023b; Yu et al., 2023; Gou et al., 2023) also have the potential to improve the mathematical reasoning capabilities of LLMs. The essence of fine-tuning is centered around the development of quality datasets comprising question-response pairs. Additionally, process-supervised training methods Lightman et al. (2023); Wang et al. (2023c) can also enhance the reasoning abilities of the LLMs.

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2024/Self-Distillation Bridges Distribution Gap in Language Model Fine-Tuning/full.md

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+# Self-Distillation Bridges Distribution Gap in Language Model Fine-Tuning
+
+Zhaorui Yang $^{\S}$ , Tianyu Pang $^{\dagger}$ , Haozhe Feng $^{\text{II}}$ , Han Wang $^{\S}$  Wei Chen $^{\S}$ , Minfeng Zhu $^{\ddagger*}$ , Qian Liu $^{\dagger*}$
+
+$^{\S}$ State Key Lab of CAD&CG, Zhejiang University †Sea AI Lab, Singapore  $^{\#}$ Tencent TEG  $^{\ddagger}$ Zhejiang University minfeng_zhu@zju.edu.cn, liuqian@sea.com
+
+# Abstract
+
+The surge in Large Language Models (LLMs) has revolutionized natural language processing, but fine-tuning them for specific tasks often encounters challenges in balancing performance and preserving general instruction-following abilities. In this paper, we posit that the distribution gap between task datasets and the LLMs serves as the primary underlying cause. To address the problem, we introduce Self-Distillation Fine-Tuning (SDFT), a novel approach that bridges the distribution gap by guiding fine-tuning with a distilled dataset generated by the model itself to match its original distribution. Experimental results on the Llama-2-chat model across various benchmarks demonstrate that SDFT effectively mitigates catastrophic forgetting while achieving comparable or superior performance on downstream tasks compared to the vanilla fine-tuning. Moreover, SDFT demonstrates the potential to maintain the helpfulness and safety alignment of LLMs. Our code is available at https://github.com/sail-sg/sdft.
+
+# 1 Introduction
+
+In recent years, the development of Large Language Models (LLMs) has emerged as one of the most groundbreaking advancements in Natural Language Processing (NLP). LLMs such as GPT-3 (Brown et al., 2020) and PaLM (Chowdhery et al., 2023) have revolutionized the field by leveraging massive textual corpora during pre-training, enabling them to achieve remarkable few-shot performance across a wide range of tasks. The introduction of Supervised Fine-Tuning (SFT) (Ouyang et al., 2022b; Chung et al., 2022) has further propelled the capabilities of LLMs, particularly in enhancing their instruction-following abilities.
+
+Interestingly, even when starting with the same base LLM (Touvron et al., 2023; Bai et al., 2023),
+
+![](images/7f712e62f600d05fd1d0e5e4291a4b1ebe827a7a31aaa6af0bfeba1c6f898165.jpg)
+
+# Vanilla Fine-Tuning
+
+![](images/19a5e02a5cdb015f7a85226007cad87558980d3817199c766984480566f3ffb8.jpg)
+
+![](images/bfea137ab74d136cd964b3acf0d52d2d9d9bc456571ff114e6ced0a671aadb8c.jpg)
+
+![](images/0f58ccafd661bc852c27aa876b1fea7960a0aa72b4605c32efe8d3bdb20da8e9.jpg)
+
+![](images/585898aed5e9bff1c771c5c52c0a3324630c3c259190042a8dc0318306081270.jpg)
+
+# Self-Distillation Fine-tuning (Ours)
+
+![](images/5471755a7bd86e2c9285e2953b5c73f0bfb38a7f460b9e1f5c56719c3c6f74ec.jpg)  
+Figure 1: Unlike vanilla fine-tuning, which may compromise seed LMs, our proposed self-distillation fine-tuning (SDFT) approach enhances seed LMs with improved downstream task performance while largely maintaining broad capabilities already learned.
+
+![](images/33ee3e8ef1bf54e920a2e20659ecb8aa82a1dfceadc8f675c75019dd57331b21.jpg)
+
+![](images/9444a667163401fff7e6bff91f33fee640f26088cf52bb22cd5d77ce43940d55.jpg)
+
+minor variations in the supervised dataset can lead to significant differences in model performance (Zhou et al., 2023; Wang et al., 2023). Consequently, the open-source community has witnessed rapid growth in the diversity of LLM variants, incorporating various SFT datasets and techniques, thereby enhancing their usefulness and accessibility.
+
+However, SFT typically prioritizes improving general instruction-following abilities, suggesting that LLMs with SFT might face challenges in specific downstream tasks. As a result, repurposing these models as Seed Language Models (seed LMs) for subsequent fine-tuning tailored to specific downstream tasks has emerged as an appealing approach. While the approach seems promising, our preliminary study reveals the challenge of simultaneously enhancing task-specific performance and preserving general instruction-following abilities through vanilla fine-tuning, primarily due to the issue of catastrophic forgetting. Echoing our findings, recent studies have highlighted that fine-tuning, even with benign datasets, can compromise the safety of seed LMs (Qi et al., 2024; Yang et al., 2023; Zhan et al., 2023; Pelrine et al., 2023). As evi
+
+denced, fine-tuning methods aimed at mitigating catastrophic forgetting are still absent.
+
+In this paper, we propose a novel fine-tuning method, Self-Distillation Fine-Tuning (SDFT), to mitigate catastrophic forgetting during fine-tuning. We hypothesize that catastrophic forgetting stems from the distribution gap between the task dataset and the seed LMs. To address the issue, as shown in Figure 1, SDFT first prompts the seed LM to generate responses that uphold semantic equivalence with the original responses present in the task dataset, resulting in the distilled dataset. A representative example of rewriting is depicted in Figure 2. After rewriting, the self-generated responses serve as surrogate targets during subsequent finetuning. Through the approach, SDFT inherently maintains the original distribution, avoiding distribution shift and thereby preserving capabilities.
+
+We systematically evaluate SDFT by comparing its performance against that of vanilla fine-tuning and the seed LM across a variety of benchmarks. These benchmarks encompass: (1) diverse downstream tasks, including mathematical reasoning, tool using and code generation; (2) assessments of general helpfulness and safety alignment. Results on all benchmarks demonstrate the superiority of SDFT compared to vanilla fine-tuning. For instance, vanilla fine-tuning on the OpenFunctions dataset (Patil et al., 2023) leads to a significant decrease in pass@1 on the HumanEval benchmark (Chen et al., 2021) from 13.4 to 9.8, constituting a decline of  $27\%$ . In contrast, SDFT not only mitigates this degradation, but also marginally enhances the accuracy to 15.2. The in-depth analysis of our method indicates that increasing the proportion of distilled dataset for fine-tuning leads to a decrease in catastrophic forgetting, thereby confirming that SDFT mitigates catastrophic forgetting by bridging the distribution gap.
+
+# 2 Related Work
+
+Fine-Tuning Fine-tuning is a prevalent strategy for improving the performance of models on downstream tasks, as demonstrated in domains including coding (Roziere et al., 2023; Luo et al., 2024), arithmetic (Luo et al., 2023a), healthcare (Jin et al., 2023) and finance (Wu et al., 2023). Vanilla finetuning directly maximizes the log-likelihood of target responses. Similar to our work, Self-Play Finetuning (Chen et al., 2024) employs the identical LLM as both generator and discriminator, steering
+
+the model to prefer annotated response over generated outputs. As the LLM's distribution ultimately converges with that of the training data, the method does not alleviate forgetting during fine-tuning.
+
+Continual Learning Fine-tuning enables models to adapt to new data distributions, improving their efficacy on downstream tasks. However, this process can lead to the loss of previously acquired knowledge, an issue known as catastrophic forgetting (French, 1999). A related domain is continual learning (Kirkpatrick et al., 2017; Lopez-Paz and Ranzato, 2017), which seeks to enable models to acquire new knowledge while mitigating such forgetting. Traditional methods often depend on the preservation of historical data for replay (Scialom et al., 2022; Luo et al., 2023b), the computation of parameter importance (Kirkpatrick et al., 2017; Aljundi et al., 2018), or the assignment of distinct neurons to different tasks (Mallya and Lazebnik, 2018). However, fine-tuning LLMs is particularly challenging due to their extensive parameter and task space, compounded by the frequent unavailability of original training datasets, which diminishes the feasibility of these established techniques (Kirkpatrick et al., 2017; Lopez-Paz and Ranzato, 2017; Scialom et al., 2022). Although recent research (Luo et al., 2023b; Scialom et al., 2022) highlights the significance of continual learning for LMs, there are scant feasible solutions for LLMs. In this paper, we conduct a comprehensive evaluation of the catastrophic forgetting issue during the fine-tuning of LLMs and propose a simple yet effective strategy specifically designed for LLMs.
+
+Alignment As the capabilities of Large Language Models (LLMs) expand, so does the potential for generating toxic content, engendering significant safety concerns (Perez et al., 2022; Ganguli et al., 2022). In response, various strategies have been proposed to align LLMs with human ethical standards and prevent the generation of toxic content. Prevalent methods including instruction tuning (Ouyang et al., 2022a; Touvron et al., 2023), reinforcement learning from human feedback (Ouyang et al., 2022a; Bai et al., 2022), and self-alignment techniques (Sun et al., 2023). Employing these alignment techniques, LLMs strike a dedicate tradeoff between utility and safety (Bianchi et al., 2023; Qi et al., 2024). While these methods have demonstrated efficacy in safety alignment, they do not cover further risks that arise from fine-tuning. Recent research reveals that even fine
+
+![](images/0c58b389f2510e20d4d54beaaffd249308fc9b6f672eb91a2111ece52e6654fd.jpg)  
+Figure 2: Left: An illustration of a generated distilled response that demonstrates a reduced distribution shift relative to the seed LLM. Right: The diminished distribution shift contributes to a moderate parameter shift, thereby alleviating the issue of catastrophic forgetting.
+
+tuning with benign data can lead to compromised safety (Qi et al., 2024; Yang et al., 2023; Zhan et al., 2023; Pelrine et al., 2023). Our proposed strategy can effectively mitigate such safety degradation.
+
+Prompting Based Learning Recently, the use of prompting in LLMs to generate responses for model training has garnered significant interest. Approaches like self-instruct (Wang et al., 2022) and WizardLM (Xu et al., 2024) utilize the generated responses for supervised fine-tuning, with the latter employing GPT-4 as the generator. Other methods, such as Self-Refine (Madaan et al., 2024) and Self-Reward (Yuan et al., 2024), use the responses as feedback to iteratively refine the model's outputs. In contrast, our work introduces a novel perspective by leveraging the responses to bridge the distribution gap and address the catastrophic forgetting issue during the fine-tuning process.
+
+# 3 Method
+
+In this section, we begin by outlining the process of fine-tuning, followed by the introduction of our proposed self-distillation fine-tuning method and its implementation details.
+
+# 3.1 Fine-tuning LLMs
+
+While LLMs demonstrate remarkable proficiency across various tasks, they often encounter limitations when it comes to downstream tasks that necessitate fine-tuning. Specifically, we refer to a LM in need of further fine-tuning as seed LM, denoted as  $f$  and parameterized by  $\theta$ . The seed LM typically undergoes general SFT, indicating its capacity to map any natural language instruction  $x \in X$  contextualized by the task description  $c \in C$ , to its corresponding output  $y \in Y$ .
+
+$$
+f _ {\theta}: C \times X \rightarrow Y. \tag {1}
+$$
+
+The fine-tuning process of the seed LM can be outlined as follows: for the target task  $t$  with con
+
+text  $c^t$ , each task example  $(x^t, y^t)$  is utilized to update the model parameters. This update aims at minimizing the disparity between the data distribution and the LM distribution, as expressed below:
+
+$$
+L _ {\mathrm {F T}} (\theta) = - \log f _ {\theta} \left(y ^ {t} \mid c ^ {t}, x ^ {t}\right), \tag {2}
+$$
+
+which seeks to minimize the negative log likelihood of the target output  $y^{t}$  given the context  $c^t$  and input  $x^{t}$ , with respect to the model parameters  $\theta$ .  $L_{\mathrm{FT}}$  converges when the generated response  $\hat{y}$  matches  $y^{t}$ , i.e., the distribution of fine-tuned LM aligns with the task dataset distribution.
+
+# 3.2 Self-Distillation Fine-Tuning
+
+As the distribution of the seed LM converges towards that of the task dataset, it naturally enhances performance on target tasks. However, vanilla fine-tuning is susceptible to catastrophic forgetting in general instruction-following capabilities and safety alignment.
+
+To address this issue, we propose Self-Distillation Fine-Tuning (SDFT) to better align the distribution of the task dataset with that of the seed LM.
+
+As depicted in Figure 2, the initial step of SDFT involves prompting the seed LM to rewrite the original response  $y^{t}$  into  $\tilde{y}$ :
+
+$$
+\tilde {y} \sim f _ {\theta} (y \mid c ^ {t}, x ^ {t}, y ^ {t}). \tag {3}
+$$
+
+This step marks the primary distinction between our method and vanilla fine-tuning, as it involves mapping the original response into a response within the seed LM's distribution. To accomplish the rewriting, we utilize a self-distillation template, which imposes minimal requirements on the seed LM, simply requiring it to adhere to our directive for rewriting responses. The exact specifications of this prompt are elaborated later.
+
+Next, to ensure the quality of the distilled responses, we employ simple heuristics to evaluate
+
+Below are an instruction that describes a task along with a reference answer. Using the reference answer as a guide, write your own response.
+
+Instruction:  
+{instruction}
+
+Reference Answer: {original response}
+
+\*\*\* Response:
+
+Figure 3: The distillation template used in most of our experiments. It designates the original response as "reference answer" and prompts the model to generate a response using the reference answer as a guide.
+
+the distilled response. For instance, in math reasoning problems, we extract the final answer from the distilled response  $\tilde{y}$  and compare it with the one from the original response  $y^{t}$ . Otherwise, we keep the original response. We formalize this conditional selection process as:
+
+$$
+\tilde {y} ^ {\prime} = \left\{ \begin{array}{l l} \tilde {y} & \text {i f E x t r a c t} (\tilde {y}) = y ^ {t}, \\ y ^ {t} & \text {o t h e r w i s e .} \end{array} \right. \tag {4}
+$$
+
+Finally, the distilled response is used as a replacement for the original response  $y^{t}$  for fine-tuning, i.e., the loss becomes:
+
+$$
+L _ {\mathrm {S D F T}} (\theta) = - \log f _ {\theta} \left(\tilde {y} ^ {\prime} \mid c _ {t}, x _ {t}\right). \tag {5}
+$$
+
+Hence, the distribution gap is mitigated by utilizing the distilled dataset instead of the task dataset, as depicted on the right side of Figure 2.
+
+# 3.3 Distillation Template
+
+In our work, the distillation template plays a crucial role. Designed to be task-independent, it can be applied seamlessly across various tasks without requiring modification. Within this framework, the template designates the original response within the task dataset as the "reference answer" and guides the model to generate a response accordingly. The template employed in the majority of our experiments is illustrated in Figure 3. When dealing with datasets involving math reasoning, we slightly adjust the template to better accommodate the reasoning process. Further details about these templates can be found in Appendix B.
+
+# 4 Experiments
+
+In this section, we begin by presenting the dataset employed for fine-tuning and evaluation purposes. Following that, we conduct a comparative analysis of the experimental results obtained from vanilla fine-tuning and our proposed SDFT approach across various tasks, encompassing mathematical reasoning, code generation, and tool using. Finally, we assess the impact of both methods on safety, general knowledge, and helpfulness.
+
+# 4.1 Experimental Setup
+
+We utilize the Llama-2-7b-chat model (Touvron et al., 2023) as the seed LM in most of our experiments, except where explicitly stated otherwise. Due to limited computation resources, we utilize the Low Rank Adaptation (LoRA) technique (Hu et al., 2022) during both vanilla fine-tuning and our proposed SDFT.
+
+To ensure fair comparison, we maintain consistency in nearly all hyperparameters for both methods. For datasets comprising more than 10,000 examples, we randomly select 2,000 examples for fine-tuning to ensure comparability in size across most datasets. For the OpenHermes dataset, we randomly select 20,000 examples to validate the effect of SDFT with larger, mixed dataset. More experimental details can be found in Appendix A.
+
+# 4.2 Datasets for Fine-tuning and Evaluation
+
+We fine-tune the seed LM on a variety of datasets, including those for both single-task and multi-task scenarios. We then evaluate the performance of both the seed model and the fine-tuned models across diverse tasks. The datasets for fine-tuning and evaluation are categorized as follows:
+
+Single-task datasets. For single-task datasets, we explore boosting the mathematical reasoning, tool using, and code generation capabilities of LMs during fine-tuning. The mathematical reasoning capabilities are improved using the GSM8K dataset (Cobbe et al., 2021), which comprises 8.8k high-quality arithmetic word problems designed at grade school level. The tool using proficiency is assessed by leveraging function-calling datasets such as the Gorilla OpenFunctions dataset (Patil et al., 2023). Additionally, code generation skills are boosted using the MagiCoder dataset (Wei et al., 2023), while evaluation is conducted using the HumanEval dataset (Chen et al., 2021).
+
+Multi-task datasets. We use four high
+
+<table><tr><td>Method</td><td>Dataset</td><td>OpenFunctions</td><td>GSM8K</td><td>HumanEval</td><td>Average</td></tr><tr><td>Seed LM</td><td>—</td><td>19.6</td><td>29.4</td><td>13.4</td><td>20.8</td></tr><tr><td rowspan="3">Vanilla FT</td><td>OpenFunctions</td><td>34.8</td><td>21.5</td><td>9.8</td><td>22.0</td></tr><tr><td>GSM8K</td><td>17.9</td><td>31.9</td><td>12.2</td><td>20.7</td></tr><tr><td>MagiCoder</td><td>3.6</td><td>23.2</td><td>18.9</td><td>15.2</td></tr><tr><td rowspan="3">SDFT (Ours)</td><td>OpenFunctions</td><td>36.6 ↑ 1.8</td><td>29.1 ↑ 7.6</td><td>15.2 ↑ 5.4</td><td>27.0 ↑ 5.0</td></tr><tr><td>GSM8K</td><td>17.9 ↑ 0.0</td><td>34.4 ↑ 2.5</td><td>14.6 ↑ 2.4</td><td>22.3 ↑ 1.6</td></tr><tr><td>MagiCoder</td><td>8.0 ↑ 5.4</td><td>24.9 ↑ 1.7</td><td>18.3 ↓ 0.6</td><td>17.1 ↑ 1.9</td></tr></table>
+
+Table 1: Evaluation results on downstream tasks. The vanilla fine-tuning improves performance on the target task but generally at the expense of tasks that were already performing well. SDFT mitigates the forgetting and can achieve comparable or superior performance on all kinds of tasks.  
+
+<table><tr><td>Dataset for FT</td><td>Raw Safe Rate</td><td>Jailbreak Safe Rate</td><td>AlpacaEval Win Rate</td></tr><tr><td>Seed LM</td><td>99.81</td><td>88.85</td><td>66.04</td></tr><tr><td>OpenFunctions</td><td>98.27 → 99.23 (↑ 0.96)</td><td>87.31 → 94.42 (↑ 7.11)</td><td>35.49 → 67.66 (↑ 32.17)</td></tr><tr><td>GSM8K</td><td>82.12 → 87.12 (↑ 5.00)</td><td>54.81 → 65.58 (↑ 10.77)</td><td>23.38 → 66.73 (↑ 43.35)</td></tr><tr><td>MagiCoder</td><td>96.73 → 97.88 (↑ 1.15)</td><td>83.65 → 88.65 (↑ 5.00)</td><td>76.52 → 76.09 (↓ 0.43)</td></tr></table>
+
+Table 2: Assessment of Safety and General Helpfulness. Results are displayed in the format: Vanilla FT  $\rightarrow$  SDFT. Vanilla fine-tuning leads to notable degradation in safety and general helpfulness, while SDFT maintains strong alignment after fine-tuning.
+
+quality datasets to assess the efficacy of our approach within multi-task fine-tuning scenarios: Alpaca (Taori et al., 2023), Dolly (Conover et al., 2023) and LIMA (Zhou et al., 2023). The Alpaca dataset encompasses a variety of tasks, including arithmetic, coding, and question-answering. It was generated using the Self-Instruct method (Wang et al., 2022) via the text-davinci-003 model. The Dolly dataset is composed of seven distinct tasks, such as open question & answer, information extraction, and summarization. The LIMA dataset covers a broad range of topics and was curated from multiple sources. The OpenHermes dataset consists of primarily GPT-4 generated data from a variety of public datasets, with filtering to remove refusals.
+
+Safety evaluation. We utilize the harmful behavior instructions from the Advbench dataset (Zou et al., 2023) for evaluation, assessing the safety of models' outputs through keyword matching following Qi et al. (2024). We define the proportion of safe responses as Raw Safe Rate. Additionally, we simulate jailbreaking attempts by appending adversarial suffixes to instructions as illustrated in Zou et al. (2023). The safe rate under this condition is referred to as Jailbreak Safe Rate.
+
+Helpfulness evaluation. We employ AlpacaEval (Li et al., 2023) to evaluate the helpfulness of various models. This tool includes a dataset and associated evaluation metrics that facilitate
+
+the comparison of generated outputs with the responses from Text-Davinci-003, across a diverse set of 805 detailed instructions sourced from multiple datasets. We report the win rate, which is the proportion of instances where the responses are favored over those produced by Text-Davinci-003, as judged by GPT-4.
+
+Knowledge evaluation. LMs' general knowledge was assessed through evaluations using benchmarks from the OpenLLM Leaderboard, specifically MMLU (Hendrycks et al., 2021), TruthfulQA (Lin et al., 2021), ARC (Clark et al., 2018), HellaSwag (Zellers et al., 2019), and Winogrande (Sakaguchi et al., 2021). These datasets provide a measure of the models' factual and commonsense knowledge spanning a variety of domains.
+
+# 4.3 SDFT Achieves Better Results on Downstream Tasks
+
+Table 1 presents the results of fine-tuning on three downstream tasks. The results indicate that while vanilla fine-tuning can enhance the model's efficacy on target tasks, it also leads to a significant decline in performance on other tasks. For example, as depicted in the table's first row, fine-tuning with the OpenFunctions dataset results in a diminished coding capability of the model, decreasing from 13.41 to 9.76. A similar decline is observed in mathematical reasoning abilities, where accuracy on the GSM8K dataset drops from 29.42 to 21.53.
+
+<table><tr><td>Method</td><td>Dataset</td><td>Raw Safe Rate</td><td>Jailbreak Safe Rate</td><td>Win Rate</td></tr><tr><td>Seed LM</td><td>—</td><td>99.81</td><td>88.85</td><td>66.04</td></tr><tr><td rowspan="4">Vanilla FT</td><td>Alpaca</td><td>86.54</td><td>52.69</td><td>27.62</td></tr><tr><td>Dolly</td><td>81.73</td><td>26.54</td><td>22.09</td></tr><tr><td>LIMA</td><td>81.35</td><td>58.08</td><td>41.34</td></tr><tr><td>OpenHermes</td><td>91.54</td><td>61.54</td><td>65.28</td></tr><tr><td rowspan="4">SDFT (Ours)</td><td>Alpaca</td><td>96.15 ↑ 9.6</td><td>86.15 ↑ 33.5</td><td>65.07 ↑ 37.5</td></tr><tr><td>Dolly</td><td>96.35 ↑ 14.6</td><td>72.69 ↑ 46.2</td><td>61.60 ↑ 39.5</td></tr><tr><td>LIMA</td><td>94.42 ↑ 13.1</td><td>78.08 ↑ 20.0</td><td>59.38 ↑ 18.0</td></tr><tr><td>OpenHermes</td><td>95.96 ↑ 4.42</td><td>87.50 ↑ 25.96</td><td>72.91 ↑ 7.63</td></tr></table>
+
+Table 3: Evaluation results after fine-tuning on multitask instruction following datasets.
+
+Furthermore, the proposed SDFT can effectively mitigate this performance degradation. In the cited instance, the model retains its mathematical reasoning proficiency, achieving an accuracy of 29.11, closely aligned with the seed model's performance (29.42). For coding performance evaluated on HumanEval, there is a marginal improvement, with the performance rising to 15.24 from the seed model's 13.41. When focusing on the target task, SDFT also outperforms vanilla fine-tuning, delivering an accuracy of 36.61 compared to 34.82.
+
+# 4.4 SDFT Preserves Alignment
+
+Fine-tuning on the majority of datasets has been demonstrated to lead to a significant decrease in both safety alignment and general helpfulness, as highlighted by the findings in Table 2. For instance, following fine-tuning on the GSM8K dataset, the safe rate decreases from 99.81 to 82.12, the jailbreak safe rate drops from 88.85 to 54.81, and the win rate on AlpacaEval diminishes from 66.04 to 23.38. In contrast, our proposed SDFT approach effectively mitigates this decline, improving the raw safe rate and jailbreak safe rate by 5 and 11, respectively. Notably, there is a slight increase in the win rate compared to the seed model, with a score of 66.73 versus 66.03.
+
+Table 3 presents evaluation results after finetuning on instruction following datasets that contain multiple tasks. As the target tasks of these datasets are unspecified, we focus our evaluation on safety and general helpfulness after fine-tuning. In line with the patterns noted in Table 2, finetuning on Alpaca, Dolly and LIMA typically leads to a marked reduction in both safety and helpfulness metrics. We observe a pronounced decline in all three metrics, with each declining by roughly 20. In contrast, our proposed SDFT method effectively mitigates this reduction, limiting the decrease
+
+to under 10. Similarly, vanilla fine-tuning on the OpenHermes (Teknium, 2023) dataset results in diminished safety alignment. In contrast, SDFT effectively mitigates this degradation, enhancing the jailbreak safe rate from 61.54 to 87.50.
+
+# 4.5 General Knowledge Remains Intact
+
+Figure 4 presents results on general knowledge. Although vanilla fine-tuning compromises downstream performance and alignment, models' capabilities in general knowledge are relatively unaffected. For instance, after fine-tuning on the OpenFunctions dataset, the disparity in performance between fine-tuned model and seed LM is less than 1. This is also observed after fine-tuning with SDFT.
+
+# 5 Analysis
+
+In this section, we conduct a detailed analysis to understand the impact of distribution shift on catastrophic forgetting. In addition to the evaluation metrics outlined in Section 4, we incorporate four supplementary metrics to assess the degree of distribution shift. We utilize both the seed model and fine-tuned models to generate responses on the Adverbench (Zou et al., 2023) dataset and engage in a comparative analysis of these responses.
+
+In particular, we calculate the BLEU-4 and ROUGE-L scores for the fine-tuned models, using the outputs from the seed model as references to evaluate the extent of distribution shift. We also utilize Sentence-BERT (Reimers and Gurevych, 2019) to derive sentence embeddings and use the cosine similarity between these embeddings following Zhang et al. (2023). Lastly, we quantify the extent of parameter shift by comparing the updated parameters with those of the seed model, considering their distance as a measure of the parameter shift magnitude. The lower the BLEU-4, ROUGE-L, and embedding similarity scores, the greater the
+
+![](images/bca0d94474526883fb53285e0a4fe4d7bbdc6948517454bd3ae8b486c13ef812.jpg)
+
+![](images/7e7b898c7b02e29a1b2ca236a592ac436ffaf6066cf98d302ab1978ea2a5c5d6.jpg)
+
+![](images/9a98272f62c3a9d11fa114a19ecdad429565e5b172c629d886d1d153c868a91b.jpg)  
+Figure 4: Performance comparisons of models on general knowledge benchmarks after fine-tuning on each dataset, as reported in the OpenLLM Leaderboard. Fine-tuning on these datasets demonstrates a marginal effect on the models' general knowledge.
+
+![](images/d5a2521fcd5159ba0fa158e5f0d414031ba96667abe23723fb7bb8ae917e0ba2.jpg)
+
+distribution shift. Conversely, the parameter shift is directly proportional to the norm of the parameter changes.
+
+# 5.1 Distribution Shift Correlates with Catastrophic Forgetting
+
+We induce varying degrees of distribution shift too investigate its impact through two approaches: (1) By sampling a diverse quantity of examples for fine-tuning, where an increased number of data points for fine-tuning corresponds to a greater distribution shift. (2) By mixing vanilla fine-tuning with SDFT, which involves substituting distilled samples with original ones. We define mix ratio to represent the proportion of distilled samples employed. A mix ratio of 1 signifies exclusive use of our SDFT and 0 denotes vanilla fine-tuning.
+
+Figures 5 and 6 illustrate the results with varying sample sizes. As the sample size grows, we observe a notable decrease in the BLEU-4, ROUGE-L, and embedding similarity scores, along with an elevation in parameter shift magnitude. This trend implies a heightened degree of distribution shift. Consequently, there is an observable decline in model
+
+performance on benchmarks such as GSM8K, MultiArith, Advbench, and AlpacaEval, suggesting intensified catastrophic forgetting.
+
+In a similar vein, Figures 7 and 8 present results corresponding to an ascending mix ratio. As this ratio increases, there is an upward trend in the BLEU-4, ROUGE-L, and embedding similarity scores, whereas the scale of parameter shift diminishes, denoting a mitigation in distribution shift. Accordingly, benchmark performance exhibits improvement across the board, signaling a reduction in the severity of catastrophic forgetting.
+
+Figure 9 illustrates the similarity distribution obtained through both vanilla fine-tuning and our SDFT. Notably, with SDFT model has higher similarity between the fine-tuned model and the seed model, signifying reduced distribution shift.
+
+# 5.2 Robustness among Distillation Templates
+
+We have constructed two templates to investigate the robustness of SDFT. The template illustrated in Figure 3 is labeled "Using", where the phrase "Using the reference answer as a guide" is replaced by "Refer to the reference answer", with the lat
+
+![](images/e2b00979445773351da40bda0ae59d9ec1f263108faf05fb0daabbf5371b6aad.jpg)  
+Figure 5: With increasing data for fine-tuning, there is a decrease in models' performance across various benchmarks, including math, safety alignment and instruction following capability.
+
+![](images/81fff0edc72675a5db02e8abf4a915e609e568a3aa3eba508cbfeef67e8a4d13.jpg)  
+Figure 6: As the sample size increases, BLEU-4, ROUGE-L and embedding similarity all decrease, while parameter shift scale increases, indicating an intensified extent of distribution shift.
+
+![](images/b606a854b1cdee4175b23c4353e9d9ab2f8a5c64d44b3fed484bcdc17b053afb.jpg)  
+Figure 7: With an increasing mix ratio, there is an enhancement in the models' performance across various benchmarks.
+
+![](images/f782cf32bae0532f3d6838f635a5df22bb2a93d11337a19a5bd42d7b749988e5.jpg)  
+Figure 8: As the mix ratio increases, BLEU-4,ROUGE-L and embedding similarity increase, while parameter shift decreases, indicating reduced distribution shift.
+
+ter template being termed "Refer". Results after fine-tuning with both templates are detailed in Table 4. The performance across diverse benchmarks remains consistent across the templates, demonstrating the robustness of SDFT.
+
+# 5.3 Efficacy of SDFT Across Model Scales and Architectures
+
+The SDFT approach is not constrained by any specific fine-tuning technique (such as LoRA) or model architecture, enabling its application across both comprehensive fine-tuning processes and other model architectures. To substantiate this claim, we conducted supplementary experiments that included full fine-tuning on Llama-2-7b-chat and LoRA fine-tuning on Llama-2-7b-chat. Additionally, we explored the fine-tuning of the recently unveiled SOTA model, Llama3 (Meta AI, 2024)
+
+on the OpenFunctions dataset. The results in Table 5 reveal that in all scenarios, SDFT not only consistently outperforms vanilla fine-tuning in the target task but also reduces forgetting across all other tasks, demonstrating its effectiveness.
+
+# 6 Conclusions and Limitations
+
+In this paper, we perform a systematic evaluation of catastrophic forgetting during the fine-tuning of language models for downstream tasks. Our findings indicate that the distribution shift during fine-tuning can lead to performance degradation in general task capabilities, as well as models' safety alignment and helpfulness. To enhance performance on target task while maintaining LMs' broad capabilities, we propose a plug-and-play strategy, SDFT, to reduce distribution shift and miti
+
+<table><tr><td>Dataset for FT</td><td>Template</td><td>OpenFunctions</td><td>HumanEval</td><td>GSM8K</td><td>Raw Safe</td><td>Jailbreak Safe</td><td>Win Rate</td></tr><tr><td rowspan="3">OpenFunctions</td><td>Vanilla FT</td><td>34.82</td><td>9.76</td><td>21.53</td><td>98.27</td><td>87.31</td><td>35.49</td></tr><tr><td>Refer</td><td>35.71</td><td>13.41</td><td>27.37</td><td>98.85</td><td>89.81</td><td>68.45</td></tr><tr><td>Using</td><td>36.61</td><td>15.24</td><td>29.11</td><td>99.23</td><td>94.42</td><td>67.66</td></tr><tr><td rowspan="3">Dolly</td><td>Vanilla FT</td><td>8.04</td><td>17.07</td><td>15.92</td><td>81.73</td><td>26.54</td><td>22.09</td></tr><tr><td>Refer</td><td>17.86</td><td>14.02</td><td>24.26</td><td>96.35</td><td>69.62</td><td>61.60</td></tr><tr><td>Using</td><td>16.07</td><td>14.63</td><td>26.31</td><td>97.31</td><td>72.69</td><td>57.52</td></tr></table>
+
+Table 4: Ablation studies on distillation template. The performance of SDFT is consistently better than Vanilla FT with different distillation templates.  
+
+<table><tr><td>Method</td><td>GSM8K</td><td>OpenFunctions</td><td>HumanEval</td><td>Raw Safe</td><td>Jailbreak Safe</td><td>Win Rate</td></tr><tr><td colspan="7">Dataset for FT: GSM8K</td></tr><tr><td>Seed LM (7B)</td><td>29.40</td><td>19.60</td><td>13.41</td><td>99.81</td><td>88.85</td><td>66.04</td></tr><tr><td>Vanilla FT (full)</td><td>34.87</td><td>5.36</td><td>13.41</td><td>84.62</td><td>37.31</td><td>23.04</td></tr><tr><td>SDFT (Ours, full)</td><td>35.03 ↑ 0.16</td><td>16.07 ↑ 10.71</td><td>15.85 ↑ 2.44</td><td>88.46 ↑ 3.84</td><td>63.46 ↑ 26.15</td><td>61.19 ↑ 38.15</td></tr><tr><td colspan="7">Dataset for FT: GSM8K</td></tr><tr><td>Seed LM (13B)</td><td>38.06</td><td>36.61</td><td>19.51</td><td>99.81</td><td>98.85</td><td>86.75</td></tr><tr><td>Vanilla FT (LoRA)</td><td>44.12</td><td>19.64</td><td>17.68</td><td>94.42</td><td>88.27</td><td>40.27</td></tr><tr><td>SDFT (Ours, LoRA)</td><td>45.59 ↑ 1.47</td><td>24.11 ↑ 4.47</td><td>18.28 ↑ 0.61</td><td>97.31 ↑ 2.89</td><td>94.42 ↑ 6.15</td><td>75.93 ↑ 35.66</td></tr><tr><td colspan="7">Dataset for FT: OpenFunctions</td></tr><tr><td>Llama3-8B-Instruct</td><td>81.58</td><td>41.07</td><td>59.76</td><td>95.58</td><td>94.81</td><td>75.34</td></tr><tr><td>Vanilla FT (LoRA)</td><td>77.79</td><td>42.86</td><td>54.27</td><td>88.85</td><td>79.81</td><td>79.75</td></tr><tr><td>SDFT (Ours, LoRA)</td><td>79.45 ↑ 1.66</td><td>43.75 ↑ 0.89</td><td>56.10 ↑ 1.83</td><td>92.12 ↑ 3.27</td><td>96.15 ↑ 16.34</td><td>82.24 ↑ 2.49</td></tr></table>
+
+Table 5: Evaluation of our SDFT under full fine-tuning on Llama-2-7b-chat, LoRA fine-tuning on Llama-2-13b-chat model, and LoRA fine-tuning on Llama-3-8B-Instruct model using different fine-tuning datasets.
+
+![](images/0d60330564fdd36e876ec46de9c265cf8d659020eac0a58c0954396e5290924d.jpg)  
+Figure 9: The distribution of embedding similarities after fine-tuning. SDFT results in higher similarity to the original model, indicating reduced distribution shift.
+
+gate catastrophic forgetting. Extensive experiments show that SDFT effectively diminishes forgetting and delivers comparable or superior performance to vanilla fine-tuning on targeted tasks.
+
+Our study is subject to certain limitations. Owing to constraints in computational resources, most of our experiments are based on the Llama-2-7b-chat model with LoRA. Further investigations involving larger models and full fine-tuning remain
+
+to be explored. Furthermore, our safety evaluations are limited to the Advbench dataset and fixed adversarial suffixes, leaving the robustness against other jailbreaking strategies for future work.
+
+# Ethics Statement
+
+Our proposed method SDFT effectively mitigates the issue of catastrophic forgetting during the finetuning of language models, including the degradation of safety alignment. Therefore, this process does not entail additional risks.
+
+We utilize a variety of open-source English datasets for training, including Alpaca, Dolly, LIMA, OpenHermes, GSM8K, OpenFunctions, and MagiCoder. The Llama-2-chat model serves as our seed model for training. We acknowledge that there may be inherent biases present within these datasets and the model.
+
+# Acknowledgements
+
+This paper is supported by the National Science Foundation of China (62132017, 62302435), Zhejiang Provincial Natural Science Foundation of China (LD24F020011, LQ24F020006) and "Pioneer and Leading Goose" R&D Program of Zhejiang (2024C01167).
+
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+Rohan Taori, Ishaan Gulrajani, Tianyi Zhang, Yann Dubois, Xuechen Li, Carlos Guestrin, Percy Liang, and Tatsunori B. Hashimoto. 2023. Stanford alpaca: An instruction-following llama model. https://github.com/tatsu-lab/stanford_alpaca.  
+Teknium. 2023. Openhermes dataset.  
+Hugo Touvron, Louis Martin, Kevin Stone, Peter Albert, Amjad Almahairi, Yasmine Babaei, Nikolay Bashlykov, Soumya Batra, Prajjwal Bhargava, Shruti Bhosale, et al. 2023. Llama 2: Open foundation and fine-tuned chat models. arXiv preprint arXiv:2307.09288, abs/2307.09288.  
+Yizhong Wang, Hamish Ivison, Pradeep Dasigi, Jack Hessel, Tushar Khot, Khyathi Raghavi Chandu, David Wadden, Kelsey MacMillan, Noah A. Smith, Iz Beltagy, and Hannaneh Hajishirzi. 2023. How far can camels go? exploring the state of instruction tuning on open resources. CoRR, abs/2306.04751.  
+Yizhong Wang, Yeganeh Kordi, Swaroop Mishra, Alisa Liu, Noah A Smith, Daniel Khashabi, and Hannaneh Hajishirzi. 2022. Self-instruct: Aligning language model with self generated instructions. arXiv preprint arXiv:2212.10560.  
+Yuxiang Wei, Zhe Wang, Jiawei Liu, Yifeng Ding, and Lingming Zhang. 2023. Magicoder: Source code is all you need. arXiv preprint arXiv:2312.02120.  
+Shijie Wu, Ozan Irsoy, Steven Lu, Vadim Dabravolski, Mark Dredze, Sebastian Gehrmann, Prabhanjan Kambadur, David Rosenberg, and Gideon Mann. 2023. Bloomberggpt: A large language model for finance. arXiv preprint arXiv:2303.17564.  
+Can Xu, Qingfeng Sun, Kai Zheng, Xiubo Geng, Pu Zhao, Jiazhan Feng, Chongyang Tao, and Daxin Jiang. 2024. Wizardlm: Empowering large language models to follow complex instructions. In International Conference on Learning Representations.  
+Xianjun Yang, Xiao Wang, Qi Zhang, Linda Petzold, William Yang Wang, Xun Zhao, and Dahua Lin. 2023. Shadow alignment: The ease of subverting safely-aligned language models. arXiv preprint arXiv:2310.02949.  
+Weizhe Yuan, Richard Yuanzhe Pang, Kyunghyun Cho, Sainbayar Sukhbaatar, Jing Xu, and Jason Weston. 2024. Self-rewarding language models. arXiv preprint arXiv:2401.10020.  
+Rowan Zellers, Ari Holtzman, Yonatan Bisk, Ali Farhadi, and Yejin Choi. 2019. Hellaswag: Can a machine really finish your sentence? In Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics.
+
+Qiusi Zhan, Richard Fang, Rohan Bindu, Akul Gupta, Tatsunori Hashimoto, and Daniel Kang. 2023. Removing rlhf protections in gpt-4 via fine-tuning. arXiv preprint arXiv:2311.05553.  
+Zhuosheng Zhang, Aston Zhang, Mu Li, and Alex Smola. 2023. Automatic chain of thought prompting in large language models. In International Conference on Learning Representations.  
+Chunting Zhou, Pengfei Liu, Puxin Xu, Srini Iyer, Jiao Sun, Yuning Mao, Xuezhe Ma, Avia Efrat, Ping Yu, Lili Yu, et al. 2023. Lima: Less is more for alignment. arXiv preprint arXiv:2305.11206.  
+Andy Zou, Zifan Wang, J Zico Kolter, and Matt Fredrikson. 2023. Universal and transferable adversarial attacks on aligned language models. arXiv preprint arXiv:2307.15043.
+
+# A Experimental Details
+
+Throughout most experiments, we applied finetuning to Llama-2-7b-chat with the Low-Rank Adaptation (LoRA) technique (Hu et al., 2022). The query and value matrices of the LoRA were tuned with a rank of  $r = 8$ . We adhered to the default configuration settings of Llama2. The learning rate was initiated at  $1 \times 10^{-4}$  and progressively decayed to zero following a cosine annealing schedule, and the batch size was set to 8.
+
+We randomly sampled a subset of 2,000 examples and conducted fine-tuning for 2 epochs for the Alpaca (Taori et al., 2023), Dolly (Conover et al., 2023), and MagiCoder (Wei et al., 2023) datasets. We sampled 20,000 examples for the OpenHermes dataset and train 2 epochs. For GSM8K (Cobbe et al., 2021), LIMA (Zhou et al., 2023) and OpenFunctions (Patil et al., 2023) datasets, we fine-tune on the entire train set. We train LIMA for 2 epochs and the other two datasets for 5 epochs.
+
+To assess the general helpfulness of models, we employ the AlpacaEval framework, with GPT-4 serving as the evaluator. The evaluations of benchmarks in OpenLLM leaderboard are implemented via the lm-evaluation-harness. Furthermore, we evaluate the coding capabilities using the HumanEval dataset (Chen et al., 2021), leveraging the bigcode-evaluation-harness project.
+
+# B Templates and Examples
+
+This section provides templates used in our experiments and some illustrative examples of distillation on each dataset.
+
+In most of our experiments, we use the standard alpaca (Taori et al., 2023) template for both finetuning and prediction, as presented in Figure 10.
+
+To enhance the reasoning abilities, we slightly modify the standard Alpaca template for datasets regarding reasoning, namely GSM8K and MultiArith. The template used for training and distillation are presented in Figure 11 and Figure 12 respectively.
+
+To make the extraction of final answer easier for mathematical reasoning datasets, we specify the format of final answer during evaluation. The template used for evaluation is presented in Figure 13.
+
+Figures 14, 15, 16, 17, 18 present examples of distilled data point on each dataset.
+
+Below are an instruction that describes a task. Write a response that appropriately completes the request.
+
+Instruction:
+
+{instruction}
+
+Response:
+
+Figure 10: The standard alpaca template. This template is used for both training and evaluation in most experiments.
+
+You are an expert in math. Below is a math question. Write a response that appropriately answers the question.
+
+{instruction}
+
+Figure 11: The template used for training on the GSM8K dataset.
+
+You are an expert in math. Below are a math question and its reference answer. Refer to the reference answer and write a response that appropriately answers the question.
+
+{instruction}
+
+{response}
+
+Great! Let's think step by step.
+
+Figure 12: The template used for distilling on the GSM8K dataset.
+
+You are an expert in math. Below is a math question. Write a response that appropriately answers the question. Your final answer should be an integer at the end of your response, formatted as: The answer is {answer}.
+
+{instruction}
+
+Figure 13: The template used for evaluation on the GSM8K and MultiArith datasets.
+
+# Instruction:
+
+Name three types of machine learning algorithms.
+
+# Original Answer:
+
+Three types of machine learning algorithms are supervised learning, unsupervised learning, and reinforcement learning.
+
+# Distilled Response:
+
+I can name three types of machine learning algorithms as follows:
+
+1. Supervised Learning: This type of algorithm involves training a machine learning model on labeled data, where the target output is already known. The model learns to predict the target output based on the input data, and can be used for tasks such as image classification, speech recognition, and sentiment analysis.  
+2. Unsupervised Learning: This type of algorithm involves training a machine learning model on unlabeled data, where there is no target output. The model learns patterns and relationships in the data without any prior knowledge of the output. Examples of unsupervised learning tasks include clustering, dimensionality reduction, and anomaly detection.  
+3. Reinforcement Learning: This type of algorithm involves training a machine learning model to make a series of decisions in an environment in order to maximize a reward. The model learns through trial and error, and the reward serves as feedback to guide the learning process. Examples of reinforcement learning tasks include game playing, robotics, and autonomous driving.
+
+Figure 14: Example of distilled data point on the Alpaca dataset.
+
+# Instruction:
+
+Classify the following as a 'Country', 'State' or 'City': California, Sacramento, Chicago, Singapore, New Delhi, London, Tennessee, New York
+
+# Original Answer:
+
+California: State
+
+Sacramento: City
+
+Chicago: City
+
+Singapore: Both Country and City
+
+New Delhi: City
+
+London: City
+
+Tennessee: City
+
+New York: Both State and City
+
+# Distilled Response:
+
+I classify the following as:  
+* California: State  
+* Sacramento: City  
+* Chicago: City  
+* Singapore: Both Country and City  
+* New Delhi: City  
+* London: City  
+* Tennessee: City  
+* New York: Both State and City
+
+Figure 15: Example of distilled data point on the Dolly dataset.
+
+# Instruction:
+
+Lisa, Jack, and Tommy earned  $60 from washing cars all week. However, half of the$ 60 was earned by Lisa. Tommy earned half of what Lisa earned.
+
+How much more money did Lisa earn than Tommy?
+
+# Original Answer:
+
+Lisa earned $60 * 1/2 = $30.
+
+Tommy earned $30 * 1/2 = $15.
+
+Lisa earned $30 - $15 = $15 more than Tommy.
+
+The answer is 15.
+
+# Distilled Response:
+
+Here is the response:
+
+Lisa earned $60 * 1/2 = $30, and Tommy earned $30 * 1/2 = $15. So, Lisa earned $30 - $15 = $15 more than Tommy. Therefore, the answer is $15.
+
+Figure 16: Example of distilled data point on the GSM8K dataset.
+
+# Instruction:
+
+Construct a function call to answer the given question using keyword arguments based on the provided specifications:
+
+Question: I want to describe the Studio Lifecycle Configuration named 'my-lc-config' on AWS SageMaker.
+
+Function to be used: aws.sagemaker.describestudio_lifecycle_config
+
+Description: Describes the Studio Lifecycle Configuration.
+
+# Parameters:
+
+1. studio_lifecycle_config_name - The name of the Studio Lifecycle Configuration to describe.
+
+Format your response as a single string using keyword arguments.
+
+# Original Answer:
+
+aws.sagemaker.describestudio_lifecycle_config studio_lifecycle_config_name="my-lc-config")
+
+# Distilled Response:
+
+aws.sagemaker.describe_studio_lifecycle_config(studio_lifecycle_config_name="my-lc-config")
+
+# Explanation:
+
+The function call uses the 'studio_lifecycle_config_name' parameter to specify the name of the Studio Lifecycle Configuration to describe, which in this case is "my-lc-config". The 'aws.sagemaker.describestudio_lifecycle_config' function is then called with this parameter to retrieve the description of the specified Studio Lifecycle Configuration.
+
+Figure 17: Example of distilled data point on the OpenFuctions dataset.
+
+# Instruction:
+
+How slicing in Python works? Please include references where appropriate.
+
+# Original Answer:
+
+The syntax is:
+
+“
+
+a[start:stop] # items start through stop-1
+
+a[ start:] # items start through the rest of the array
+
+a[:stop] # items from the beginning through stop-1
+
+a[:] # a copy of the whole array
+
+There is also the 'step' value, which can be used with any of the above: "... a[start:stop:step] # start through not past stop, by step "... The key point to remember is that the ':stop' value represents the first value that is not in the selected slice. So, the difference between 'stop' and 'start' is the number of elements selected (if 'step' is 1, the default)
+
+中
+
+While the “:”-based notation is very helpful for simple slicing, the explicit use of “slice()” objects simplifies the programmatic generation of slicing.
+
+# Distilled Response:
+
+Slicing in Python is a powerful feature that allows you to extract a subset of elements from a sequence (such as a list, tuple, or string) based on a specified range and step. The syntax for slicing is:
+
+“
+
+a[start:stop] # items start through stop-1
+
+a[ start:] # items start through the rest of the array
+
+a[:stop] # items from the beginning through stop-1
+
+a[:] # a copy of the whole array
+
+In addition to the basic syntax, there are several other features of slicing in Python:
+
+* **Negative indices**: If 'start' or 'stop' is a negative number, it counts from the end of the array instead of the beginning. For example, 'a[-2]' returns the last two elements of the array, while 'a[-3]' returns the last three elements.
+
+* **Step**: The 'step' value can be used to specify the distance between elements in the slice.
+
+For example, 'a[1:3:2]' returns the elements at indices 1, 3, and 5 of the array.
+
+* **Optional arguments**: If 'stop' is not specified, it defaults to the end of the array. Similarly, if 'step' is not specified, it defaults to 1
+
+.
+
+In summary, slicing in Python is a powerful feature that allows you to extract a subset of elements from a sequence based on a specified range and step. The basic syntax is simple and intuitive, but there are several other features and options that can be used to customize the slicing operation
+
+Figure 18: Example of distilled data point on the LIMA dataset.

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+# Self-Modifying State Modeling for Simultaneous Machine Translation
+
+Donglei Yu $^{1,2}$ , Xiaomian Kang $^{1,2}$ , Yuchen Liu $^{1,2}$ , Yu Zhou $^{1,3*}$ , Chengqing Zong $^{1,2}$
+
+<sup>1</sup>State Key Laboratory of Multimodal Artificial Intelligence Systems,
+
+Institute of Automation, Chinese Academy of Sciences, Beijing, China
+
+$^{2}$ School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing, China
+
+<sup>3</sup>Fanyu AI Laboratory, Zhongke Fanyu Technology Co., Ltd, Beijing, China
+
+{yudonglei2021,kangxiaomian2014,yuchen.liu,yu.zhou,chengqing.zong}@ia.ac.cn
+
+# Abstract
+
+Simultaneous Machine Translation (SiMT) generates target outputs while receiving stream source inputs and requires a read/write policy to decide whether to wait for the next source token or generate a new target token, whose decisions form a decision path. Existing SiMT methods, which learn the policy by exploring various decision paths in training, face inherent limitations. These methods not only fail to precisely optimize the policy due to the inability to accurately assess the individual impact of each decision on SiMT performance, but also cannot sufficiently explore all potential paths because of their vast number. Besides, building decision paths requires unidirectional encoders to simulate streaming source inputs, which impairs the translation quality of SiMT models. To solve these issues, we propose Self-Modifying State Modeling  $(\mathrm{SM}^2)$ , a novel training paradigm for SiMT task. Without building decision paths,  $\mathrm{SM}^2$  individually optimizes decisions at each state during training. To precisely optimize the policy,  $\mathrm{SM}^2$  introduces Self-Modifying process to independently assess and adjust decisions at each state. For sufficient exploration,  $\mathrm{SM}^2$  proposes Prefix Sampling to efficiently traverse all potential states. Moreover,  $\mathrm{SM}^2$  ensures compatibility with bidirectional encoders, thus achieving higher translation quality. Experiments show that  $\mathrm{SM}^2$  outperforms strong baselines. Furthermore,  $\mathrm{SM}^2$  allows offline machine translation models to acquire SiMT ability with fine-tuning  $^{1}$ .
+
+# 1 Introduction
+
+Simultaneous Machine Translation (SiMT) (Gu et al., 2017; Ma et al., 2019; Zhang et al., 2020) outputs translation while receiving the streaming source sentence. Different from normal Offline Machine Translation (OMT) (Vaswani et al., 2017),
+
+![](images/e74a8928412d535ee89403683196900aab74c523a55f5765c1e1df5ca27f581f.jpg)  
+(a) Training paradigm based on decision paths
+
+![](images/fef88861d1e3b9405df835e53c2c7118da6d889acea419f8f51b297a7612ad79.jpg)  
+(b) Our proposed Self-Modifying State Modeling  
+Figure 1: Illustration of different paradigms. (a) Training paradigm based on decision paths. All decisions along a path are optimized in an integrated manner. (b) Self-Modifying State Modeling. The decisions at each state are optimized individually.
+
+SiMT needs a suitable read/write policy to decide whether to wait for the coming source inputs (READ) or generate target tokens (WRITE).
+
+As shown in Figure 1(a), to learn a suitable policy, existing SiMT methods usually require building a decision path (i.e., a series of READ and WRITE decisions made by the policy) to simulate the complete SiMT process during training (Zhang and Feng, 2022c). Methods of fixed policies (Ma et al., 2019; Zhang and Feng, 2021) build the decision path based on pre-defined rules, and only optimize translation quality along the path. Methods of adaptive policies (Zheng et al., 2019; Miao et al., 2021; Zhang and Feng, 2023) dynamically build the decision path and optimize the policy based on the SiMT performance along this path.
+
+However, the current training paradigm based on decision paths faces inherent limitations. First, it can lead to imprecise optimization of the pol
+
+icy during training. For fixed policies, pre-defined rules cannot ensure optimal decisions at each state. For adaptive policies, there exists a credit assignment problem (Minsky, 1961), which means it is difficult to identify the impact of each individual decision on the global SiMT performance along a path, thus hindering the precise optimization of each decision. Second, due to numerous potential decision paths, existing methods (Zheng et al., 2019; Miao et al., 2021; Zhang and Feng, 2023) often prohibit the exploration of some paths during training, but this insufficient exploration cannot ensure the optimal policy. Third, for building decision paths in training, existing methods require unidirectional encoders to simulate streaming source inputs and avoid the leakage of source future information (Elbayad et al., 2020), which impairs SiMT models' translation quality (Iranzo-Sanchez et al., 2022; Kim and Cho, 2023).
+
+To address these issues, we propose Self-Modifying State Modeling  $(\mathrm{SM}^2)$ , a novel training paradigm for SiMT task. As shown in Figure 1(b), instead of constructing complete decision paths,  $\mathrm{SM}^2$  individually optimizes decisions at all potential states during training. This paradigm necessitates addressing two critical issues: firstly, how to independently optimize each decision based on its own contribution to SiMT performance; and secondly, how to sufficiently explore all potential states during training. To realize the independent optimization,  $\mathrm{SM}^2$  assesses each decision by estimating confidence values which measure the translation credibility. High confidence means the SiMT model can predict a credible target token at current state and WRITE is beneficial for SiMT performance; otherwise, READ is preferred. Since golden confidence values are unavailable,  $\mathrm{SM}^2$  introduces Self-Modifying process to learn accurate confidence estimation (DeVries and Taylor, 2018; Lu et al., 2022). Specifically, during training, the SiMT model is allowed to modify its prediction based on the received source prefix with the prediction based on the complete source sentence, and the confidence is estimated to determine whether the modification is necessary to ensure a credible prediction at current state. To sufficiently explore all potential states,  $\mathrm{SM}^2$  conducts Prefix Sampling to divide all states into groups according to the number of their received source prefix tokens, and sample one group for optimization in each iteration.
+
+Compared to the training paradigm based on decision paths,  $\mathrm{SM}^2$  presents significant advantages.
+
+First, the Self-Modifying process can assess each decision independently, which realizes the precise optimization of policy without the credit assignment problem. Second, Prefix Sampling ensures sufficient exploration of all potential states, promoting the discovery of the optimal policy. These benefits enable  $\mathrm{SM^2}$  to learn a more effective policy. Furthermore, without building decision paths in training,  $\mathrm{SM^2}$  ensures compatibility with bidirectional encoders, thereby improving translation quality. This compatibility also allows OMT models to acquire the SiMT capability via fine-tuning. Our contributions are outlined in the following:
+
+- We propose Self-Modifying State Modeling  $(\mathrm{SM}^2)$ , a novel training paradigm that individually optimizes decisions at all states without building complete decision paths.  
+-  $\mathrm{SM}^2$  can learn a better policy through precise optimization of each decision and sufficient exploration of all states. With bidirectional encoders,  $\mathrm{SM}^2$  achieves higher translation quality and compatibility with OMT models.  
+- Experimental results on  $\mathrm{Zh} \rightarrow \mathrm{En}$ ,  $\mathrm{De} \rightarrow \mathrm{En}$  and  $\mathrm{En} \rightarrow \mathrm{Ro}$  SiMT tasks show that  $\mathrm{SM}^2$  outperforms strong baselines under all latency levels.
+
+# 2 Background
+
+Simultaneous machine translation For SiMT task, we respectively denote the source sentence as  $\mathbf{x} = (x_{1},\dots,x_{M})$  and the corresponding target sentence as  $\mathbf{y} = (y_{1},..,y_{N})$ . Since the source inputs are streaming, we denote the number of source tokens available when generating  $y_{i}$  as  $g_{i}$ , and hence the prediction probability of  $y_{i}$  is  $p(y_{i} \mid \mathbf{x}_{\leq g_{i}}, \mathbf{y}_{< i})$  (Ma et al., 2019). Thus, the decoding probability of  $\mathbf{y}$  is given by:
+
+$$
+p (\mathbf {y} \mid \mathbf {x}) = \prod_ {i = 1} ^ {N} p \left(y _ {i} \mid \mathbf {x} _ {\leq g _ {i}}, \mathbf {y} _ {<   i}\right) \tag {1}
+$$
+
+Decision state and decision path We define the state  $s_{ij}$  as the condition in which the source prefix  $\mathbf{x}_{\leq j}$  has been received and the target prefix  $\mathbf{y}_{<i}$  has been generated. At  $s_{ij}$ , a decision  $d_{ij} \in \{\text{WRITE}, \text{READ}\}$  can be made based on the context  $(\mathbf{x}_{\leq j}, \mathbf{y}_{<i})$  (Grissom II et al., 2014; Gu et al., 2017; Zhao et al., 2023). Specifically, if  $\mathbf{x}_{\leq j}$  is sufficient for the SiMT model to predict  $y_i$  accurately,  $d_{ij}$  should be WRITE; otherwise,  $d_{ij}$  should be READ. As shown in Figure 1(a), a series
+
+![](images/b8df41a8ede5b496870065ee1f00fa886b47b7ccd994b20390342fb66c6e02b2.jpg)  
+Figure 2: Overview of  $\mathbf{SM}^2$ .  $S_{j}$  contains the states where  $\mathbf{x}_{\leq j}$  is received.  $S_{M}$  contains the states where complete  $\mathbf{x}$  is received. We introduce a confidence net (ConfNet) to estimate the confidence of each state. The model parameters in SiMT setting and OMT setting are shared. In this figure, the sentence lengths of the source and target sides are set to  $M = 5$  and  $N = 4$  respectively, and  $j = 3$  in the Prefix Sampling step.
+
+of decisions  $[d_{00},\dots,d_{NM}]$  are made in the SiMT process, which forms a decision path from  $s_{00}$  to  $s_{NM}$ . Along the decision path, the SiMT model can finish reading the whole x and outputting the complete y (Zhang and Feng, 2022c). Since these concepts are usually used in SiMT methods based on reinforcement learning (RL) (Grissom II et al., 2014; Gu et al., 2017), we compare our method with RL-based methods in Appendix A for clarity.
+
+# 3 The Proposed Method
+
+We propose Self-Modifying State Modeling  $(\mathrm{SM}^2)$ , which individually optimizes decisions at all states. The overview of  $\mathrm{SM}^2$  is shown in Figure 2. To independently optimize each decision,  $\mathrm{SM}^2$  learns confidence estimation to assess decisions at each state by modeling the Self-Modifying process (Sec.3.1). To ensure sufficient exploration during training,  $\mathrm{SM}^2$  conducts Prefix Sampling to traverse all potential states (Sec. 3.2). Then, based on estimated confidence at each state,  $\mathrm{SM}^2$  can determine whether the received source tokens are sufficient to generate a credible token and make suitable decisions during inference (Sec.3.3).
+
+# 3.1 Self-Modifying for Confidence Estimation
+
+Intuitively, when a translation model has access to the complete input  $\mathbf{x}$  (i.e., OMT setting), it can produce credible outputs. Therefore, a prediction made by the translation model at  $s_{ij}$  (i.e. SiMT setting) is considered credible if it aligns with that in OMT setting. Conversely, if the prediction in
+
+SiMT setting is incredible, it will be modified in OMT setting. Based on this insight and Ask For Hints (DeVries and Taylor, 2018; Lu et al., 2022), we model the Self-Modifying process to assess the translation credibility of each state. Specifically, we provide the SiMT model an option to modify its prediction in SiMT setting with that in OMT setting, and confidence estimation is defined as a binary classification determining whether the current generation requires the modification to ensure a credible prediction. Through measuring translation credibility, decisions at each state can be independently assessed. High confidence means the SiMT model can generate a credible token at  $s_{ij}$  without modification and the WRITE decision is beneficial for SiMT performance; whereas low confidence indicates the prediction is inaccurate at  $s_{ij}$  and the READ decision is preferred.
+
+During training, the Self-Modifying process is conducted in two steps: prediction in SiMT setting & OMT setting and confidence-based modification.
+
+For prediction in SiMT setting & OMT setting, the SiMT model outputs different predictions at  $s_{ij}$  in SiMT setting and OMT setting respectively. These predictions are calculated as follows:
+
+$$
+p _ {i j} = p \left(y _ {i} \mid \mathbf {x} _ {\leq j}, \mathbf {y} _ {<   i}\right) \tag {2}
+$$
+
+$$
+p _ {i} = p (y _ {i} \mid \mathbf {x}, \mathbf {y} _ {<   i})
+$$
+
+It is noted that the model parameters in SiMT setting and OMT setting are shared.
+
+For confidence-based modification, an additional confidence net is used to predict the confidence  $c_{ij}$
+
+Algorithm 1: Confidence-based Policy  
+Input: Streaming inputs  $\mathbf{x}_{\leq j}$  , Threshold  $\gamma ,i = 1,j = 1,y_0\gets \langle \mathrm{BOS}\rangle$  Output: Target outputs y while  $y_{i - 1}\neq \langle \mathrm{EOS}\rangle$  do calculate confidence  $c_{ij}$  as Eq.(3); if  $c_{ij}\geq \gamma$  then //WRITE generate  $y_{i}$  with  $\mathbf{x}_{\leq j},\mathbf{y}_{< i};$ $i\leftarrow i + 1;$  else //READ wait for next source token  $x_{j + 1}$  .  $j\gets j + 1$  end
+
+at  $s_{ij}$ . The confidence net is represented as:
+
+$$
+c _ {i j} = \operatorname {s i g m o i d} \left(W ^ {T} \cdot h _ {i j} + b\right) \tag {3}
+$$
+
+where  $h_{ij}$  is the hidden representation from the top decoder layer in SiMT setting and  $\theta = \{W, b\}$  are trainable parameters. If  $p_{ij}$  is credible,  $c_{ij}$  should be close to 1; otherwise,  $c_{ij}$  should be close to 0. To accurately calibrate  $c_{ij}$  in the training process, we integrate the modification into the prediction probability as follows:
+
+$$
+p _ {i j} ^ {m} = c _ {i j} \cdot p _ {i j} + (1 - c _ {i j}) \cdot p _ {i} \tag {4}
+$$
+
+Subsequently, the translation loss is calculated using the modified probability:
+
+$$
+\mathcal {L} _ {s _ {i j}} = - y _ {i} \log \left(p _ {i j} ^ {m}\right) \tag {5}
+$$
+
+Notably, the SiMT model can enhance the prediction credibility by estimating a lower  $c_{ij}$  for more modification. However, this manner may cause an over-reliance on  $p_i$ . To avoid that, an additional penalty term for  $c_{ij}$  is introduced:
+
+$$
+\mathcal {L} _ {c _ {i j}} = - \log (c _ {i j}) \tag {6}
+$$
+
+Through Self-Modifying process,  $\mathrm{SM^2}$  independently optimizes each decision based on their individual effect on the SiMT performance, thus realizing the precise optimization of the policy without credit assignment problem. We provide a gradient analysis of the independent optimization in Appendix B for further explanation.
+
+# 3.2 Prefix Sampling
+
+To sufficiently explore all potential states during training, Prefix Sampling is conducted in  $\mathrm{SM}^2$ . As shown in Figure 2, states are categorized into groups, and one group is randomly sampled for optimization in each iteration. Specifically, all possible states of  $(\mathbf{x},\mathbf{y})$  are divided into  $M$  groups according to the number of their received source prefix tokens, and each group comprises  $N$  states, which can be formulated as follows:
+
+$$
+S _ {j} = \left\{s _ {i j} \mid 1 \leq i \leq N \right\}, j \in [ 1, M ] \tag {7}
+$$
+
+In each iteration, we sample  $j \sim \mathcal{U}(1,M)$ . Then,  $\mathrm{SM}^2$  respectively predicts target translation in SiMT setting based on  $S_{j}$  and those in OMT setting based on  $S_{M}$ , where the complete source sentence is received. Thus, the modified translation loss and the penalty item of each iteration are computed as follows:
+
+$$
+\mathcal {L} _ {S _ {j}} = \sum_ {i = 1} ^ {N} \mathcal {L} _ {s _ {i j}} \tag {8}
+$$
+
+$$
+\mathcal {L} _ {C _ {j}} = \sum_ {i = 1} ^ {N} \mathcal {L} _ {c _ {i j}}
+$$
+
+Besides, to ensure the  $p_i$  in OMT setting can provide effective modification, the translation loss in OMT setting is required, which is formulated as:
+
+$$
+\mathcal {L} _ {o m t} = - \sum_ {i = 1} ^ {N} \log \left(p _ {i}\right) \tag {9}
+$$
+
+The total training loss is the following:
+
+$$
+\mathcal {L} = \mathcal {L} _ {o m t} + \mathcal {L} _ {S _ {j}} + \lambda \mathcal {L} _ {C _ {j}} \tag {10}
+$$
+
+where  $\lambda$  is the super parameter. We discuss the effect of  $\lambda$  in Appendix C.
+
+Through Prefix Sampling,  $\mathrm{SM}^2$  explores all potential states without building any decision paths. Therefore,  $\mathrm{SM}^2$  can employ bidirectional encoders without the leakage of source future information in the training process.
+
+# 3.3 Confidence-based Policy in Inference
+
+During inference,  $\mathrm{SM}^2$  utilizes  $c_{ij}$  to assess the credibility of current prediction, thus making suitable decisions between READ and WRITE at  $s_{ij}$ . Specifically, a confidence threshold  $\gamma$  is introduced to serve as a criterion for making decisions. As
+
+shown in Algorithm 1, if  $c_{ij} > \gamma$ , SM² selects WRITE; otherwise, SM² selects READ. This decision process is constantly repeated until the complete translation is finished. It is noted that we only utilize SiMT setting in the inference process.
+
+By adjusting  $\gamma$ ,  $\mathrm{SM}^2$  can perform the SiMT task under different latency levels. A higher  $\gamma$  encourages the SiMT model to predict more credible target tokens and the latency will be longer. Conversely, a lower  $\gamma$  reduces the latency but may lead to a decrease in translation quality. The values of  $\gamma$  employed in our subsequent experiments are detailed in Appendix D.
+
+# 4 Experiments
+
+# 4.1 Datasets
+
+We conduct experiments on three datasets:
+
+$\mathbf{Z}\mathbf{h} \rightarrow \mathbf{E}\mathbf{n}$  We use LDC corpus which contains 2.1M sentence pairs as the training set, NIST 2008 for the validation set and NIST 2003, 2004, 2005, and 2006 for the test sets.
+
+$\mathbf{De} \rightarrow \mathbf{En}$  We choose WMT15 for training, which contains 4.5M sentence pairs. Newstest 2013 are used as the validation set and newstest 2015 are used as the test set.
+
+$\mathbf{En} \rightarrow \mathbf{Ro}$  WMT16 (0.6M) is used as the training set. We choose newsdev 2016 as the validation set and newstest 2016 as the test test.
+
+We apply BPE (Sennrich et al., 2016) for all language pairs. In  $\mathrm{Zh} \rightarrow \mathrm{En}$ , the vocabulary size is  $30\mathrm{k}$  for Chinese and  $20\mathrm{k}$  for English. In both  $\mathrm{De} \rightarrow \mathrm{En}$  and  $\mathrm{En} \rightarrow \mathrm{Ro}$ , a shared vocabulary is learned with  $32\mathrm{k}$  merge operations. Additional experiments on WMT15  $\mathrm{En} \rightarrow \mathrm{Vi}$  are provided in Appendix E.
+
+# 4.2 System Settings
+
+The models used in our experiments are introduced as follows. All baselines are built based on Transformer (Vaswani et al., 2017) with the unidirectional encoder unless otherwise stated. More details are presented in Appendix D.
+
+OMT-Uni/OMT-Bi(Vaswani et al., 2017): OMT model with an unidirectional/bidirectional encoder.
+
+wait-  $k$  (Ma et al., 2019): a fixed policy, which first reads  $k$  tokens, then writes one token and reads one token in turns.
+
+m-wait-  $k$  (Elbayad et al., 2020): a fix policy, which improves wait-  $k$  by randomly sampling different  $k$  during training.
+
+ITST (Zhang and Feng, 2022b): an adaptive policy, which models the SiMT task as a transport
+
+problem of information from source to target.
+
+HMT (Zhang and Feng, 2023): an adaptive policy, which models the SiMT task as a hidden Markov model, by treating the states as hidden events and the predicted tokens as observed events.
+
+$\mathbf{SM}^2$  -Uni/SM2-Bi: Our proposed method with an unidirectional/bidirectional encoder.
+
+# 4.3 Evaluation Metric
+
+For SiMT, both translation quality and latency require evaluation. Since existing datasets mainly focus on the OMT task, the metric based on n-gram may cause inaccurate evaluation (Rei et al., 2020). Therefore, we measure the translation quality with both SacreBLEU (Post, 2018) and COMET<sup>2</sup> scores. For latency evaluation, we choose Average Lagging (AL) (Ma et al., 2019) as the metric.
+
+Furthermore, to assess the quality of read/write policy in different SiMT models, we follow Zhang and Feng (2022b) and Kim and Cho (2023) to use Satisfied Alignments (SA), the proportion of the ground-truth aligned source tokens received before translating. Specifically, when generating  $y_{i}$ , the number of received source tokens  $g_{i}$  should be no less than the golden-truth aligned source position  $a_{i}$ , so that the alignment between  $y_{i}$  and  $x_{a_{i}}$  can be satisfied in the SiMT process. Thus, SA(↑) can be calculated as:
+
+$$
+\mathrm {S A} = \frac {1}{N} \sum_ {i = 1} ^ {N} \mathbb {I} \left(a _ {i} \leq g _ {i}\right) \tag {11}
+$$
+
+# 5 Results and Analysis
+
+# 5.1 Simultaneous Translation Quality
+
+We present the translation quality under various latency levels of different SiMT models in Figure 3 and Figure 4. These results indicate that  $\mathrm{SM}^2$  outperforms previous methods across three language pairs in terms of both SacreBLEU and COMET scores. With the unidirectional encoder, SM-Uni achieves higher translation quality compared to current state-of-the-art SiMT models (ITST, HMT) at low and medium latency levels  $(\mathrm{AL}\in [0,6])$ , and maintains comparable performance at high latency level  $(\mathrm{AL}\in [6,12])$ . We attribute this improvement to the effectiveness of learning a better policy during training. Furthermore, with the superior capabilities of the bidirectional encoder,  $\mathrm{SM}^2$ -Bi outperforms previous SiMT models more significantly
+
+![](images/59588d706a46bed2f49efdb31a688ee6c565fe331895365f4dc602a34b4f5994.jpg)  
+(a)  $\mathrm{Zh}\rightarrow \mathrm{En}$
+
+![](images/1eee594dbb6a166e0598ef550ce4342c1dbbee7d170b5aad0a976c71e25a3efa.jpg)  
+(b)  $\mathrm{De}\rightarrow \mathrm{En}$
+
+![](images/643ececc2c5a2f33d50222c3f147076cb3c75460d73a6ce14e2628d3899c0dfe.jpg)  
+(c)  $\mathrm{En}\rightarrow \mathrm{Ro}$
+
+![](images/18d0adb6fad96efcfd484e1af297b1ef20dfdf41859029e1e37dd4092e31ed2d.jpg)  
+Figure 3: SacreBLEU against Average Lagging (AL) on  $\mathrm{Zh}\rightarrow \mathrm{En}$ ,  $\mathrm{De}\rightarrow \mathrm{En}$  and  $\mathrm{En}\rightarrow \mathrm{Ro}$ .  
+(a)  $\mathrm{Zh}\rightarrow \mathrm{En}$  
+Figure 4: COMET against Average Lagging (AL) on  $\mathrm{Zh}\rightarrow \mathrm{En}$ ,  $\mathrm{De}\rightarrow \mathrm{En}$  and  $\mathrm{En}\rightarrow \mathrm{Ro}$ .
+
+![](images/a92247c4c31808596e29e1b7210e590f78cd20aa98f50f315b8bbc6764328978.jpg)  
+(b)  $\mathrm{De}\rightarrow \mathrm{En}$
+
+![](images/3eb13d2bdb051d7787cdbf0961236fd3728b81686163e1d24930728195622af4.jpg)  
+(c)  $\mathrm{En}\rightarrow \mathrm{Ro}$
+
+across all latency levels. All SiMT models with unidirectional encoders can approach the translation quality of OMT-Uni at high latency levels, but only  $\mathrm{SM^2}$ -Bi achieves similar performance to OMT-Bi as the latency increases. These experimental results prove that  $\mathrm{SM^2}$  achieves better performance than other SiMT methods for learning better policy and improving translation quality. Detailed numerical results are provided in Appendix E, supplemented with additional evidence demonstrating the robustness of  $\mathrm{SM^2}$  to sentence length variations.
+
+# 5.2 Superiority of  $\mathbf{SM}^2$  in Learning Policy
+
+To verify whether  $\mathrm{SM}^2$  can learn a more effective policy, we compare SA(↑) under various latency levels of different SiMT models. Following Zhang and Feng (2022b) and Kim and Cho (2023), we conduct the analysis on  $\mathrm{RWTH}^3$ , a De→En alignment dataset. The results are presented in Figure 5. Compared with existing methods, both SM²-Uni and SM²-Bi receive more aligned source tokens before generating target tokens under the same latency. Especially at medium latency level (AL ∈ [4, 6]), SM²
+
+can receive about  $8\%$  more source tokens than fixed policies (wait-  $k$ , m-wait-  $k$ ) and  $3.6\%$  more than adaptive policies (ITST, HMT). We attribute these improvements to the advantages of  $\mathrm{SM}^2$  in learning policy. Through precise optimization,  $\mathrm{SM}^2$  can make more suitable decisions at each state, which generates faithful translations once receiving sufficient source tokens and waits for more source inputs when the predicted tokens are incredible. With sufficient exploration,  $\mathrm{SM}^2$  can investigate all possible situations and reduce unnecessary latency in the SiMT process.
+
+# 5.3 Precise Optimization for Each Decision
+
+To validate whether the confidence-based policy is precisely optimized at each state, we examine the relationship between estimated confidence  $c_{ij}$  and the probability of the correct token  $y_i$  in the prediction, denoted as  $p_{ij}^c$ . Specifically, we employ SM² to decode the validation set in a teacher-forcing manner, calculating the  $c_{ij}$  and  $p_{ij}^c$  for all possible states. Subsequently, a correlation analysis is performed between  $c_{ij}$  and  $p_{ij}^c$ . The results in Table 1 demonstrate a strong correlation, evidenced by high values in Pearson (0.82) and Spearman (0.84) coefficients, with a slightly moderate but signifi
+
+![](images/a29e8f32eccca4ef3ee994f8f49dfeef0c5a64df6552b16cf43872c2692953e6.jpg)  
+Figure 5: Evaluation of different SiMT policies. We calculate SA  $(\uparrow)$  under different latency levels.
+
+<table><tr><td>Correlation Coefficient</td><td>Pearson</td><td>Spearman</td><td>Kendall&#x27;s τ</td></tr><tr><td>Value</td><td>0.82</td><td>0.84</td><td>0.65</td></tr></table>
+
+Table 1: Correlation between  ${c}_{ij}$  and  ${p}_{ij}^{c}$  .
+
+cant Kendall's  $\tau$  coefficient (0.65). These results suggest a robust linear and monotonic relationship between  $c_{ij}$  and  $p_{ij}^{c}$ , indicating the capacity of  $c_{ij}$  to accurately assess the credibility of the current predicted token. Consequently, this confirms the effectiveness of the confidence-based policy in making precise decisions at each state.
+
+# 5.4 Advantage of Sufficient Exploration
+
+Existing methods often prohibit the exploration of some paths due to the possible decision paths being numerous (Zheng et al., 2019; Miao et al., 2021; Zhang and Feng, 2023). To investigate the impact of the prohibition on SiMT models and the superiority of  $\mathrm{SM}^2$  in sufficiently exploring all states, we attempt to train these methods without prohibition, but they fail to converge. Therefore, we analyze the impact by employing the same prohibition in HMT (Zhang and Feng, 2023) and RIL(Zheng et al., 2019) to train  $\mathrm{SM}^2$ , which restricts  $\mathrm{SM}^2$  to explore states only between wait- $k_1$  and wait- $k_2$  paths in training. As shown in Figure 6(a), we set  $k_1 = 1$  and  $k_2 = 10$  in our experiments. The performances of  $\mathrm{SM}^2$  with prohibition ( $\mathrm{SM}^2$ -Uni-P and  $\mathrm{SM}^2$ -Bi-P) are shown in Figure 6(c), indicating a decline in performance. These results suggest that the prohibition causes insufficient exploration, leading to diminished performance. In contrast,  $\mathrm{SM}^2$  ensures comprehensive exploration, which is shown in Figure 6(b), thereby achieving higher performance. Further analysis of the policy quality is provided in Appendix F.
+
+![](images/21eb49389a4fffbf2e3c5ce1b4fcb77d6dad2d3b7c4e6c670ea1aa9cdeb1c7f1.jpg)  
+(a) HMT
+
+![](images/e53ead66ea6673eafdefe18ccae816992e209231016706dd7c84a72d182ec844.jpg)  
+(b)  $\mathbf{SM}^2$
+
+![](images/0f850be2de1e78b8cab2bee0cbac3206df0bb4ef9a74cf41f79177d0fc58d4c9.jpg)  
+(c) Effect of prohibition to the SiMT performance.  
+Figure 6: The visualization and effect of prohibition. In (a) and (b), the shaded areas represent the states allowed for exploration in training. We apply the same prohibition in HMT (Zhang and Feng, 2023) to train  $\mathrm{SM^2}$ -Uni-P and  $\mathrm{SM^2}$ -Bi-P.
+
+# 5.5 Compatibility with OMT Models
+
+$\mathrm{SM^2}$  allows for the parallel training of the bidirectional encoder. Due to this compatibility,  $\mathrm{SM^2}$ -Bi achieves superior translation quality than existing SiMT methods with unidirectional encoders (Figure 3,4). To further present the superiority of this compatibility, we propose fine-tuning OMT models according to  $\mathrm{SM^2}$ , so that the translation ability in OMT models can be easily utilized to gain SiMT models. Specifically, two distinct methods are used: fine-tuning all model parameters ( $\mathrm{SM^2}$ -FT) and fine-tuning with adapters ( $\mathrm{SM^2}$ -adapter) $^4$ . As shown in Figure 7(a),  $\mathrm{SM^2}$ -adapter can achieve comparable performance with current state-of-the-art SiMT models, and  $\mathrm{SM^2}$ -FT closely matches the performance of  $\mathrm{SM^2}$ -Bi.
+
+Additionally, we further explore the effect of the OMT models' translation abilities on the corresponding SiMT abilities after fine-tuning. We conduct the full-parameter fine-tuning on OMT models with Transformer-small, Transformer-base, and Transformer-big respectively. The OMT and SiMT capabilities of these models are illustrated in Table 2 and Figure 7(b), which reveal that models
+
+![](images/14be248ad512ac6b834315f44ebc0bc2287187d7c683e86ff98f28a9d68b107c.jpg)  
+(a) Comparison with SiMT (b) Comparison between different models.
+
+![](images/31055c506236306bbc0a236d18c0ad609d696b4c6382d3993e7f636b6023e582.jpg)  
+Figure 8: Effect of  $\mathcal{L}_{omt}$  and modification from OMT setting on the SM $^2$ . "w/o  $\mathcal{L}_{omt}$ " is SM $^2$  trained without  $\mathcal{L}_{omt}$ , and "w/o  $p_i$  " means SM $^2$  trained using one-hot rather than OMT setting for modification.
+
+<table><tr><td rowspan="2">OMT model</td><td rowspan="2">Parameters</td><td colspan="2">SacreBLEU</td></tr><tr><td>before FT</td><td>after FT</td></tr><tr><td>Transformer-small</td><td>47.9M</td><td>30.86</td><td>31.33</td></tr><tr><td>Transformer-base</td><td>60.5M</td><td>31.93</td><td>31.87</td></tr><tr><td>Transformer-big</td><td>209.1M</td><td>32.99</td><td>32.75</td></tr></table>
+
+with stronger OMT abilities achieve better SiMT performance after fine-tuning. Besides, the results in Table 2 show that these models' original OMT abilities are not hurt, indicating that  $\mathrm{SM}^2$  enables models to support both OMT and SiMT abilities.
+
+# 5.6 Ablation Study
+
+We conduct ablation studies on  $\mathrm{SM}^2$  to analyze the effect of  $\mathcal{L}_{omt}$  and modification from OMT setting.
+
+Effect of  $\mathcal{L}_{omt}$  As shown in Figure 8, the SiMT model without  $\mathcal{L}_{omt}$  drops quickly. We argue this is because training without  $\mathcal{L}_{omt}$  may cause a worse modification. The results in Table 3 show that the OMT performance of  $\mathrm{SM}^2$  trained without  $\mathcal{L}_{omt}$  is significantly affected, even worse than its SiMT performance in the high latency levels. This poor OMT ability cannot provide accurate modification, thus disrupting the policy learning process.
+
+Effect of OMT modification Following Ask For Hints (DeVries and Taylor, 2018; Lu et al., 2022), we use the one-hot label as the "hints" to modify the prediction in SiMT setting. Specifically, we denote  $t_i$  as the ground-truth label of the  $i$ -th target token, and hence the modification in  $\mathrm{SM}^2$  is adjusted as:
+
+$$
+p _ {i j} ^ {m} = c _ {i j} \cdot p _ {i j} + (1 - c _ {i j}) \cdot t _ {i} \tag {12}
+$$
+
+As shown in Figure 8, the performance of  $\mathbf{SM}^2$  trained with modification in Eq.(12) also drops.
+
+![](images/466805e7a88b1ce0a538d8c210caf37c66264114a4868b7f99ce18f60cf36643.jpg)  
+Figure 7: The SiMT performance of different OMT models after fine-tuning according to  $\mathbf{SM}^2$
+
+Table 2: The OMT performance of different OMT models before/after fine-tuning according to  $\mathbf{SM}^2$  
+
+<table><tr><td>Model</td><td>SM2-Bi</td><td>w/o Lomt</td><td>w/o pi</td><td>OMT</td></tr><tr><td>SacreBLEU</td><td>31.87</td><td>30.33</td><td>31.95</td><td>31.93</td></tr></table>
+
+Table 3: Effect of  ${\mathcal{L}}_{omt}$  and  ${p}_{i}$  on the OMT ability.
+
+We argue that the modification from  $t_i$  cannot reflect the real available gain from the modification after receiving the complete source sentence, thus learning a worse policy.
+
+# 6 Related Work
+
+Simultaneous Machine Translation Different from offline machine translation (Vaswani et al., 2017; Zhao et al., 2020; Wu et al., 2024), existing SiMT methods are divided into fixed policy and adaptive policy. For fixed policy, Ma et al. (2019) proposed wait- $k$ , which starts translation after receiving  $k$  tokens. Elbayad et al. (2020) proposed multipath wait- $k$ , which randomly samples  $k$  during training. For adaptive policy, heuristic rules Cho and Esipova (2016) and reinforcement learning Gu et al. (2017) are used to realize the SiMT task. Ma et al. (2020b) integrated multi-head monotonic attention to model the decision process, where each head independently makes decisions. Similarly, Zhang and Feng (2022a) utilized Gaussian multi-head attention to model the alignment, thus improving the decision-making ability of each head. Miao et al. (2021) proposed a generative framework to learn a read/write policy. Zhang and Feng (2022b) measured the information SiMT had received and proposed an information-based policy. Zhang and Feng (2023) used the Hidden Markov model in SiMT task to learn an adaptive policy.
+
+Previous methods based on decision paths are limited in policy learning and model structure. Our proposed  $\mathrm{SM^2}$  individually explores all states during training, overcoming these limitations.
+
+Confidence Estimation for OMT Confidence estimation is used to measure the models' credibility. Wang et al. (2019) used Monte Carlo dropout to propose an uncertainty-based confidence estimation. Wan et al. (2020) utilized the confidence score to guide self-paced learning. DeVries and Taylor (2018) evaluated the confidence by measuring the level it asks for hints from the ground-truth label, and Lu et al. (2022) transferred it to OMT to improve the out-of-distribution detection.
+
+# 7 Conclusion
+
+In this paper, we propose Self-Modifying State Modeling  $(\mathrm{SM}^2)$ , a novel training paradigm for SiMT.  $\mathrm{SM}^2$  eschews the construction of complete decision paths during training, opting to explore all potential states individually instead. By introducing the Self-Modifying process,  $\mathrm{SM}^2$  independently assesses each state to precisely optimize the read/write policy without the credit assignment problem. Through Prefix Sampling,  $\mathrm{SM}^2$  ensures sufficient exploration of all potential states. Experimental results across three language pairs validate the superior performance of  $\mathrm{SM}^2$ , and our analyses further confirm that  $\mathrm{SM}^2$  can learn a more effective read/write policy. More promisingly,  $\mathrm{SM}^2$  demonstrates the potential to endow OMT models with SiMT capability through fine-tuning.
+
+# Limitations
+
+In this paper, we propose  $\mathrm{SM}^2$ , a novel paradigm that individually optimizes decisions at each state. Although our experiments show the superiority of not building decision paths during training, there are still some parts to be further improved. For example, using a more effective way to independently assess the individual effect of each decision on the SiMT performance. Besides, how to leverage other pre-trained encoder-decoder models like BART and T5, to gain SiMT models, is still a promising direction to explore. These will be considered as objectives for our future work.
+
+# Acknowledgements
+
+This work has been supported by the National Natural Science Foundation of China (NSFC) under Grant No. 62206295 and 62206286.
+
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+Shaolei Zhang and Yang Feng. 2022a. Gaussian multihead attention for simultaneous machine translation. arXiv preprint arXiv:2203.09072.  
+Shaolei Zhang and Yang Feng. 2022b. Information-transport-based policy for simultaneous translation. In Proceedings of the 2022 Conference on Empirical Methods in Natural Language Processing, pages 992-1013, Abu Dhabi, United Arab Emirates. Association for Computational Linguistics.  
+Shaolei Zhang and Yang Feng. 2022c. Modeling dual read/write paths for simultaneous machine translation. In Proceedings of the 60th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 2461-2477.  
+Shaolei Zhang and Yang Feng. 2023. Hidden markov transformer for simultaneous machine translation. arXiv preprint arXiv:2303.00257.  
+Zhiyang Zhang, Yaping Zhang, Yupu Liang, Lu Xiang, Yang Zhao, Yu Zhou, and Chengqing Zong. 2023. Layoutdit: Layout-aware end-to-end document image translation with multi-step conductive decoder. In Findings of the Association for Computational Linguistics: EMNLP 2023, pages 10043-10053.  
+Libo Zhao, Kai Fan, Wei Luo, Wu Jing, Shushu Wang, Ziqian Zeng, and Zhongqiang Huang. 2023. Adaptive policy with wait-k model for simultaneous translation. In Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing, pages 4816-4832.  
+Yang Zhao, Lu Xiang, Junnan Zhu, Jiajun Zhang, Yu Zhou, and Chengqing Zong. 2020. Knowledge graph enhanced neural machine translation via multitask learning on sub-entity granularity. In Proceedings of the 28th International Conference on Computational Linguistics, pages 4495-4505.  
+Baigong Zheng, Renjie Zheng, Mingbo Ma, and Liang Huang. 2019. Simultaneous translation with flexible policy via restricted imitation learning. arXiv preprint arXiv:1906.01135.
+
+# A Comparison between  $\mathbf{SM}^2$  and RL-based SiMT methods
+
+In the following, we will compare the similarities and differences between our proposed  $\mathrm{SM}^2$  and RL-based methods.
+
+On the one hand, both  $\mathrm{SM^2}$  and RL-based methods train SiMT models to learn read/write actions
+
+at each state  $s_{ij}$ . Specifically, the read/write policy  $\pi(a_{ij} \mid s_{ij})$  in  $\mathbf{SM}^2$  can be described as:
+
+$$
+\pi \left(a _ {i j} \mid s _ {i j}\right) = \left\{ \begin{array}{l l} c _ {i j} & a _ {i j} = \text {W R I T E} \\ 1 - c _ {i j} & a _ {i j} = \text {R E A D} \end{array} \right. \tag {13}
+$$
+
+For each state  $s_{ij}$ , the reward in  $\mathrm{SM}^2$  can be described as:
+
+$$
+r _ {i j} = y _ {i} \log \left(p _ {i j} ^ {m}\right) \tag {14}
+$$
+
+During training, the policy can be optimized based on the reward and converge to the optimal policy.
+
+On the other hand,  $\mathrm{SM}^2$  offers additional advantages over RL-based methods. Firstly, the reward in  $\mathrm{SM}^2$  is differentiable, allowing the policy to be optimized by directly using the reward as the objective. In contrast, the reward in RL-based methods (Grissom II et al., 2014; Gu et al., 2017) is undifferentiable, which can hinder stable training. Secondly,  $\mathrm{SM}^2$  independently assesses each state, avoiding the credit assignment problem in existing RL-based methods.
+
+# B Gradient Analysis
+
+In this section, we provide a gradient analysis of the independent optimization in  $\mathrm{SM}^2$ . The training loss function  $\mathcal{L}$  of  $\mathrm{SM}^2$  is formulated in Eq. (10). During training, this loss function adjusts each decision  $d_{ij}$  at state  $s_{ij}$  by changing the value of corresponding confidence  $c_{ij}$ . Specifically, the gradient of  $\mathcal{L}$  with respect to  $c_{ij}$  is calculated as:
+
+$$
+\begin{array}{l} \frac {\partial \mathcal {L}}{\partial c _ {i j}} = \frac {\partial \mathcal {L} _ {s _ {i j}}}{\partial c _ {i j}} + \lambda \frac {\partial \mathcal {L} _ {c _ {i j}}}{\partial c _ {i j}} \\ = - \frac {y _ {i}}{p _ {i j} ^ {m}} \cdot \frac {\partial p _ {i j} ^ {m}}{\partial c _ {i j}} - \frac {\lambda}{c _ {i j}} \tag {15} \\ = - \frac {y _ {i} (p _ {i j} - p _ {i})}{c _ {i j} \cdot p _ {i j} + (1 - c _ {i j}) \cdot p _ {i}} - \frac {\lambda}{c _ {i j}} \\ \end{array}
+$$
+
+It is evident that this gradient does not contain any  $c_{i'j'}$  ( $i' \neq i$  or  $j' \neq j$ ). Therefore, in the training process, the estimated value of  $c_{ij}$  is adjusted only based on its current value and the prediction probability of the current state, without being affected by the decisions at other states, thus allowing for the independent optimization of  $c_{ij}$ .
+
+In contrast, existing SiMT methods usually conduct training on decision paths and can not ensure independent optimization. Taking ITST (Zhang
+
+![](images/54f5386e8105a2d8331b1cd0b9c49e26a7afffe0e794ad0bf8a2dc4e52f4f8f2.jpg)  
+(a) Performance of  $\mathrm{SM^2}$  with different  $\lambda$
+
+![](images/0e2220ff1acf77d04aeb383c36e83258881363013e85bd262698d0d957d4605b.jpg)  
+(b) Max Latency of  $\mathrm{SM}^2$  with different  $\lambda$ .  
+Figure 9: Effect of  $\lambda$  on  $\mathrm{SM}^2$ .
+
+and Feng, 2022b) as an example, whose loss function  $\mathcal{L}'$  is formulated as:
+
+$$
+\mathcal {L} ^ {\prime} = \mathcal {L} _ {c e} + \mathcal {L} _ {l a t e n c y} + \mathcal {L} _ {n o r m}
+$$
+
+$$
+\mathcal {L} _ {\text {l a t e n c y}} = \sum_ {i = 1} ^ {I} \sum_ {j = 1} ^ {J} T _ {i j} \times C _ {i j} \tag {16}
+$$
+
+$$
+\mathcal {L} _ {n o r m} = \sum_ {i = 1} ^ {I} \left\| \sum_ {j = 1} ^ {J} T _ {i j} - 1 \right\| _ {2}
+$$
+
+where  $\mathcal{L}_{ce}$  is the cross-entropy for learning translation ability, and  $C_{ij}$  is the latency cost for each state. During training, the decision is dominated by  $T_{ij}$ . The gradient of  $\mathcal{L}'$  with respect to  $T_{ij}$  is calculated as:
+
+$$
+\frac {\partial \mathcal {L} ^ {\prime}}{\partial T _ {i j}} = \frac {\partial \mathcal {L} _ {c e}}{\partial T _ {i j}} + C _ {i j} + 2 \left(\sum_ {j = 1} ^ {J} T _ {i j} - 1\right) \tag {17}
+$$
+
+It is noted that the gradient of  $T_{ij}$  is also affected by the current values of  $T_{ij'} (j' = 1, 2, \dots, J)$ . These decisions are coupled in the optimization, thus not enabling the independent optimization of each decision. This can trigger mutual interference during training (Zhang and Feng, 2023) and lead to a credit assignment problem.
+
+# C Effect of  $\lambda$
+
+We analyze the effect of  $\lambda$ , which is the weight of the penalty during training. We train  $\mathbf{SM}^2$  with
+
+<table><tr><td colspan="2">Hyper-parameter</td></tr><tr><td>encoder layers</td><td>6</td></tr><tr><td>encoder attention heads</td><td>8</td></tr><tr><td>encoder embed dim</td><td>512</td></tr><tr><td>encoder ffn embed dim</td><td>1024</td></tr><tr><td>decoder layers</td><td>6</td></tr><tr><td>decoder attention heads</td><td>8</td></tr><tr><td>decoder embed dim</td><td>512</td></tr><tr><td>decoder ffn embed dim</td><td>1024</td></tr><tr><td>dropout</td><td>0.1</td></tr><tr><td>optimizer</td><td>adam</td></tr><tr><td>adam-β</td><td>(0.9, 0.98)</td></tr><tr><td>clip-norm</td><td>1e-7</td></tr><tr><td>lr</td><td>5e-4</td></tr><tr><td>lr scheduler</td><td>inverse sqrt</td></tr><tr><td>warmup-updates</td><td>4000</td></tr><tr><td>warmup-init-lr</td><td>1e-7</td></tr><tr><td>weight decay</td><td>0.0001</td></tr><tr><td>label-smoothing</td><td>0.1</td></tr><tr><td>max tokens</td><td>8192</td></tr></table>
+
+Table 4: Hyper-parameters of our experiments.
+
+different  $\lambda$  ranging from 0.1 to 1, in increments of 0.1. As shown in Figure 9(a), the  $\mathrm{SM}^2$  models trained with different  $\lambda$  show comparable performance across all latency. This indicates that  $\mathrm{SM}^2$  is robust to variations in hyper-parameters  $\lambda$ .
+
+When  $\lambda$  becomes larger, the corresponding  $\gamma$  at the same latency will also increase. Therefore, we further analyze the effect of  $\lambda$  on the applicable latency range of  $\mathrm{SM^2}$ . We denote the "MAX AL" as the latency of  $\mathrm{SM^2}$  when  $\gamma$  is set as 0.99 during inference. The results are shown in Figure 9(b). When  $\lambda$  becomes larger, "MAX AL" also decreases, which means a smaller applicable latency range. For example, when  $\lambda = 1.0$  in training, it is hard for  $\mathrm{SM^2}$  to perform SiMT task under the latency levels where AL is larger than 5.79 since the threshold  $\gamma$  has been close to 1.
+
+# D Hyper-parameters
+
+The system settings in our experiments are shown in Table 4. We set  $\lambda = 0.1$  during training. Besides, we follow Ma et al. (2020b) to use greedy search during inference for all baselines. The values of  $\gamma$  we used are 0.3, 0.4, 0.5, 0.55, 0.6, 0.65 for  $\mathrm{Zh} \rightarrow \mathrm{En}$ , 0.3, 0.4, 0.5, 0.55, 0.6, 0.65, 0.7 for  $\mathrm{De} \rightarrow \mathrm{En}$ , and 0.3, 0.4, 0.5, 0.6, 0.65, 0.7, 0.75 for  $\mathrm{En} \rightarrow \mathrm{Ro}$ .
+
+# E Main Results Supplement
+
+# E.1 Numerical Results
+
+Table 5, 6, 7 respectively report the numerical results on LDC  $\mathrm{Zh}\rightarrow \mathrm{En}$ , WMT15  $\mathrm{De}\rightarrow \mathrm{En}$ , WMT16  $\mathrm{En}\rightarrow \mathrm{Ro}$  measured by AL, SacreBLEU and COMET. Figure 10, 11 and Table 8 report the results on WMT15  $\mathrm{En}\rightarrow \mathrm{Vi}$  with Transformersmall, which also present the superior performance of  $\mathrm{SM^2}$ -Uni and  $\mathrm{SM^2}$ -Bi.
+
+# E.2 Robustness of  $\mathbf{SM}^2$  to Sentence Length
+
+To validate the robustness of  $\mathrm{SM^2}$  to Sentence Length, we conduct additional experiments on  $\mathrm{De} \rightarrow \mathrm{En}$  SiMT tasks. Specifically, we divide the test set into two groups based on sentence length: LONG group and SHORT group. The average lengths and the number of sentences in each group are shown in Table 9. Then, we test  $\mathrm{SM^2}$ -Bi and  $\mathrm{SM^2}$ -Uni separately on these two groups. The translation quality under different latency levels for  $\mathrm{SM^2}$ -Bi and  $\mathrm{SM^2}$ -Uni are presented in Figure 12. For clearer comparison, we also provide the performances of OMT models (OMT-Bi, OMT-Uni) on LONG and SHORT groups.
+
+The results in Figure 12 indicate that when applied to longer sentences, the performance changes of  $\mathrm{SM^2}$  are similar to OMT models in both unidirectional and bidirectional encoder settings. Since the performance of OMT models unavoidably drops as the sentences become longer (Neishi and Yoshinaga, 2019; Kang et al., 2020; Ma et al., 2020a; Variš and Bojar, 2021; Zhang et al., 2023), it is not  $\mathrm{SM^2}$  that triggers the decrease of translation quality. Therefore,  $\mathrm{SM^2}$  is still effective on long sentences.
+
+# F Effect of Prohibition on Policy
+
+To further validate that the prohibition of exploration negatively affects the policy. We compare the SA of  $\mathrm{SM^2}$  with and without the prohibition on RWTH dataset. The results in Figure 13 indicate that the prohibition makes  $\mathrm{SM^2}$  learn a worse policy. Therefore, we can conclude that the prohibition will hurt the quality of policy. This further presents the advantage of  $\mathrm{SM^2}$  in sufficiently exploring all states through Prefix Sampling.
+
+<table><tr><td colspan="4">Chinese→English</td></tr><tr><td colspan="4">wait-k</td></tr><tr><td>k</td><td>AL</td><td>SacREBLEU</td><td>COMET</td></tr><tr><td>1</td><td>-0.60</td><td>23.14</td><td>67.06</td></tr><tr><td>3</td><td>3.03</td><td>31.94</td><td>73.91</td></tr><tr><td>5</td><td>4.96</td><td>35.56</td><td>75.87</td></tr><tr><td>7</td><td>6.87</td><td>37.50</td><td>76.99</td></tr><tr><td>9</td><td>8.82</td><td>38.90</td><td>77.85</td></tr><tr><td colspan="4">m-wait-k</td></tr><tr><td>k</td><td>AL</td><td>SacREBLEU</td><td>COMET</td></tr><tr><td>1</td><td>0.72</td><td>28.06</td><td>70.85</td></tr><tr><td>3</td><td>2.80</td><td>32.41</td><td>74.29</td></tr><tr><td>5</td><td>4.76</td><td>35.05</td><td>75.81</td></tr><tr><td>7</td><td>6.81</td><td>36.68</td><td>76.86</td></tr><tr><td>9</td><td>8.64</td><td>37.61</td><td>77.37</td></tr><tr><td colspan="4">HMT</td></tr><tr><td>(L,K)</td><td>AL</td><td>SacREBLEU</td><td>COMET</td></tr><tr><td>(2,4)</td><td>2.93</td><td>35.59</td><td>76.90</td></tr><tr><td>(3,6)</td><td>4.52</td><td>37.81</td><td>78.08</td></tr><tr><td>(5,6)</td><td>6.11</td><td>39.41</td><td>78.73</td></tr><tr><td>(7,6)</td><td>7.69</td><td>40.33</td><td>79.11</td></tr><tr><td>(9,8)</td><td>9.64</td><td>41.37</td><td>79.58</td></tr><tr><td>(11,8)</td><td>11.35</td><td>41.75</td><td>79.85</td></tr><tr><td colspan="4">ITST</td></tr><tr><td>δ</td><td>AL</td><td>SacREBLEU</td><td>COMET</td></tr><tr><td>0.2</td><td>0.62</td><td>30.31</td><td>73.66</td></tr><tr><td>0.3</td><td>2.88</td><td>35.87</td><td>77.02</td></tr><tr><td>0.4</td><td>4.88</td><td>39.27</td><td>78.41</td></tr><tr><td>0.5</td><td>6.94</td><td>41.20</td><td>79.27</td></tr><tr><td>0.6</td><td>9.17</td><td>42.23</td><td>79.68</td></tr><tr><td>0.7</td><td>11.40</td><td>42.75</td><td>79.93</td></tr><tr><td colspan="4">SM2-Uni</td></tr><tr><td>γ</td><td>AL</td><td>SacREBLEU</td><td>COMET</td></tr><tr><td>0.3</td><td>-0.63</td><td>29.52</td><td>73.62</td></tr><tr><td>0.4</td><td>1.99</td><td>36.16</td><td>77.02</td></tr><tr><td>0.5</td><td>4.56</td><td>39.94</td><td>78.66</td></tr><tr><td>0.55</td><td>6.24</td><td>41.06</td><td>79.13</td></tr><tr><td>0.6</td><td>8.51</td><td>42.21</td><td>79.50</td></tr><tr><td>0.65</td><td>9.75</td><td>42.54</td><td>79.61</td></tr><tr><td colspan="4">SM2-Bi</td></tr><tr><td>γ</td><td>AL</td><td>SacREBLEU</td><td>COMET</td></tr><tr><td>0.3</td><td>-0.14</td><td>31.41</td><td>75.00</td></tr><tr><td>0.4</td><td>2.35</td><td>37.77</td><td>78.09</td></tr><tr><td>0.5</td><td>4.68</td><td>41.15</td><td>79.42</td></tr><tr><td>0.55</td><td>6.19</td><td>42.47</td><td>79.91</td></tr><tr><td>0.6</td><td>8.37</td><td>43.51</td><td>80.21</td></tr><tr><td>0.65</td><td>11.61</td><td>44.34</td><td>80.45</td></tr></table>
+
+Table 5: Numerical results on LDC  $\mathrm{{Zh}} \rightarrow  \mathrm{{En}}$  .  
+
+<table><tr><td colspan="4">German→English</td></tr><tr><td colspan="4">wait-k</td></tr><tr><td>k</td><td>AL</td><td>SacREBLEU</td><td>COMET</td></tr><tr><td>1</td><td>0.10</td><td>20.11</td><td>70.74</td></tr><tr><td>3</td><td>3.44</td><td>26.34</td><td>76.24</td></tr><tr><td>5</td><td>6.00</td><td>28.96</td><td>78.44</td></tr><tr><td>7</td><td>8.08</td><td>29.52</td><td>78.92</td></tr><tr><td>9</td><td>9.86</td><td>30.23</td><td>79.71</td></tr><tr><td colspan="4">m-wait-k</td></tr><tr><td>k</td><td>AL</td><td>SacREBLEU</td><td>COMET</td></tr><tr><td>1</td><td>0.03</td><td>20.71</td><td>70.49</td></tr><tr><td>3</td><td>2.94</td><td>24.85</td><td>74.49</td></tr><tr><td>5</td><td>5.48</td><td>27.43</td><td>76.80</td></tr><tr><td>7</td><td>7.66</td><td>28.2</td><td>77.67</td></tr><tr><td>9</td><td>9.63</td><td>28.87</td><td>78.23</td></tr><tr><td colspan="4">HMT</td></tr><tr><td>(L,K)</td><td>AL</td><td>SacREBLEU</td><td>COMET</td></tr><tr><td>(2,4)</td><td>2.20</td><td>25.67</td><td>75.66</td></tr><tr><td>(3,6)</td><td>3.58</td><td>28.29</td><td>77.94</td></tr><tr><td>(5,6)</td><td>4.96</td><td>29.33</td><td>78.76</td></tr><tr><td>(7,6)</td><td>6.58</td><td>29.47</td><td>79.23</td></tr><tr><td>(9,8)</td><td>8.45</td><td>30.25</td><td>79.82</td></tr><tr><td>(11,8)</td><td>10.18</td><td>30.29</td><td>79.74</td></tr><tr><td colspan="4">ITST</td></tr><tr><td>δ</td><td>AL</td><td>SacREBLEU</td><td>COMET</td></tr><tr><td>0.2</td><td>2.27</td><td>25.17</td><td>75.17</td></tr><tr><td>0.3</td><td>2.85</td><td>26.94</td><td>76.86</td></tr><tr><td>0.4</td><td>3.83</td><td>28.58</td><td>77.98</td></tr><tr><td>0.5</td><td>5.47</td><td>29.51</td><td>78.85</td></tr><tr><td>0.6</td><td>7.60</td><td>30.46</td><td>79.28</td></tr><tr><td>0.7</td><td>10.17</td><td>30.74</td><td>79.53</td></tr><tr><td>0.8</td><td>12.72</td><td>30.84</td><td>79.61</td></tr><tr><td colspan="4">SM2-Uni</td></tr><tr><td>γ</td><td>AL</td><td>SacREBLEU</td><td>COMET</td></tr><tr><td>0.3</td><td>1.39</td><td>24.68</td><td>75.58</td></tr><tr><td>0.4</td><td>2.4</td><td>27.88</td><td>78.09</td></tr><tr><td>0.5</td><td>3.56</td><td>29.6</td><td>79.51</td></tr><tr><td>0.55</td><td>5.2</td><td>30.67</td><td>80.28</td></tr><tr><td>0.6</td><td>6.33</td><td>30.86</td><td>80.36</td></tr><tr><td>0.65</td><td>8.06</td><td>30.89</td><td>80.42</td></tr><tr><td>0.7</td><td>10.74</td><td>31.08</td><td>80.53</td></tr><tr><td colspan="4">SM2-Bi</td></tr><tr><td>γ</td><td>AL</td><td>SacREBLEU</td><td>COMET</td></tr><tr><td>0.3</td><td>1.52</td><td>24.74</td><td>75.96</td></tr><tr><td>0.4</td><td>2.73</td><td>28.48</td><td>78.85</td></tr><tr><td>0.5</td><td>3.73</td><td>30.17</td><td>80.21</td></tr><tr><td>0.55</td><td>5.49</td><td>31.11</td><td>80.83</td></tr><tr><td>0.6</td><td>7.03</td><td>31.42</td><td>81.00</td></tr><tr><td>0.65</td><td>9.22</td><td>31.65</td><td>81.18</td></tr><tr><td>0.7</td><td>12.33</td><td>31.92</td><td>81.25</td></tr></table>
+
+Table 6: Numerical results on WMT15 De→En.
+
+<table><tr><td colspan="4">English→Romanian</td></tr><tr><td colspan="4">wait-k</td></tr><tr><td>k</td><td>AL</td><td>SacreBLEU</td><td>COMET</td></tr><tr><td>1</td><td>2.70</td><td>26.62</td><td>74.12</td></tr><tr><td>3</td><td>5.05</td><td>29.74</td><td>77.52</td></tr><tr><td>5</td><td>7.18</td><td>31.61</td><td>78.54</td></tr><tr><td>7</td><td>9.10</td><td>31.86</td><td>79.20</td></tr><tr><td>9</td><td>10.92</td><td>31.89</td><td>78.97</td></tr><tr><td colspan="4">m-wait-k</td></tr><tr><td>k</td><td>AL</td><td>SacreBLEU</td><td>COMET</td></tr><tr><td>1</td><td>2.66</td><td>26.65</td><td>74.27</td></tr><tr><td>3</td><td>5.07</td><td>30.11</td><td>77.44</td></tr><tr><td>5</td><td>7.18</td><td>31.05</td><td>78.35</td></tr><tr><td>7</td><td>9.07</td><td>31.44</td><td>78.71</td></tr><tr><td>9</td><td>10.89</td><td>31.37</td><td>78.62</td></tr><tr><td colspan="4">HMT</td></tr><tr><td>(L,K)</td><td>AL</td><td>SacreBLEU</td><td>COMET</td></tr><tr><td>(1,2)</td><td>1.98</td><td>24.11</td><td>71.73</td></tr><tr><td>(2,2)</td><td>2.77</td><td>27.18</td><td>74.85</td></tr><tr><td>(4,2)</td><td>4.47</td><td>30.41</td><td>77.65</td></tr><tr><td>(5,4)</td><td>5.48</td><td>31.56</td><td>78.80</td></tr><tr><td>(6,4)</td><td>6.45</td><td>31.88</td><td>78.94</td></tr><tr><td>(7,6)</td><td>7.41</td><td>31.85</td><td>79.17</td></tr><tr><td>(9,6)</td><td>9.24</td><td>31.98</td><td>79.05</td></tr><tr><td colspan="4">ITST</td></tr><tr><td>δ</td><td>AL</td><td>SacreBLEU</td><td>COMET</td></tr><tr><td>0.1</td><td>2.75</td><td>22.76</td><td>71.19</td></tr><tr><td>0.2</td><td>3.25</td><td>28.40</td><td>75.58</td></tr><tr><td>0.3</td><td>5.09</td><td>30.52</td><td>77.53</td></tr><tr><td>0.4</td><td>7.47</td><td>31.37</td><td>78.28</td></tr><tr><td>0.45</td><td>8.81</td><td>31.62</td><td>78.49</td></tr><tr><td>0.5</td><td>10.30</td><td>31.63</td><td>78.51</td></tr><tr><td>0.55</td><td>11.69</td><td>31.74</td><td>78.73</td></tr><tr><td colspan="4">SM2-Uni</td></tr><tr><td>γ</td><td>AL</td><td>SacreBLEU</td><td>COMET</td></tr><tr><td>0.3</td><td>2.52</td><td>27.85</td><td>75.45</td></tr><tr><td>0.4</td><td>2.72</td><td>29.21</td><td>76.62</td></tr><tr><td>0.5</td><td>3.16</td><td>30.21</td><td>77.59</td></tr><tr><td>0.6</td><td>4.17</td><td>31.20</td><td>78.26</td></tr><tr><td>0.65</td><td>5.13</td><td>31.56</td><td>78.58</td></tr><tr><td>0.7</td><td>6.56</td><td>31.72</td><td>78.77</td></tr><tr><td>0.75</td><td>8.67</td><td>31.67</td><td>78.98</td></tr><tr><td colspan="4">SM2-Bi</td></tr><tr><td>γ</td><td>AL</td><td>SacreBLEU</td><td>COMET</td></tr><tr><td>0.3</td><td>2.60</td><td>28.74</td><td>76.81</td></tr><tr><td>0.4</td><td>2.91</td><td>30.27</td><td>78.20</td></tr><tr><td>0.5</td><td>3.57</td><td>31.33</td><td>79.04</td></tr><tr><td>0.6</td><td>5.11</td><td>32.03</td><td>79.56</td></tr><tr><td>0.65</td><td>6.51</td><td>32.40</td><td>79.90</td></tr><tr><td>0.7</td><td>8.15</td><td>32.59</td><td>79.85</td></tr><tr><td>0.75</td><td>10.10</td><td>32.74</td><td>79.95</td></tr></table>
+
+Table 7: Numerical results on WMT16 En→Ro.  
+
+<table><tr><td colspan="4">English→Vietnamese</td></tr><tr><td colspan="4">wait-k</td></tr><tr><td>k</td><td>AL</td><td>SacREBLEU</td><td>COMET</td></tr><tr><td>1</td><td>2.49</td><td>25.29</td><td>68.89</td></tr><tr><td>3</td><td>4.28</td><td>28.03</td><td>70.28</td></tr><tr><td>5</td><td>6.07</td><td>28.73</td><td>70.56</td></tr><tr><td>7</td><td>7.89</td><td>28.72</td><td>70.72</td></tr><tr><td>9</td><td>9.57</td><td>28.78</td><td>70.75</td></tr><tr><td colspan="4">m-wait-k</td></tr><tr><td>k</td><td>AL</td><td>SacREBLEU</td><td>COMET</td></tr><tr><td>1</td><td>2.78</td><td>27.02</td><td>69.88</td></tr><tr><td>3</td><td>4.38</td><td>28.59</td><td>70.61</td></tr><tr><td>5</td><td>6.12</td><td>28.74</td><td>70.75</td></tr><tr><td>7</td><td>7.88</td><td>28.69</td><td>70.78</td></tr><tr><td>9</td><td>9.61</td><td>28.78</td><td>70.83</td></tr><tr><td colspan="4">HMT</td></tr><tr><td>(L,K)</td><td>AL</td><td>SacREBLEU</td><td>COMET</td></tr><tr><td>(1,2)</td><td>2.9</td><td>27.69</td><td>70.22</td></tr><tr><td>(4,2)</td><td>5.33</td><td>29.23</td><td>71.04</td></tr><tr><td>(5,4)</td><td>6.23</td><td>29.36</td><td>71.01</td></tr><tr><td>(6,4)</td><td>7.1</td><td>29.34</td><td>71.15</td></tr><tr><td>(7,6)</td><td>8.01</td><td>29.42</td><td>70.99</td></tr><tr><td colspan="4">ITST</td></tr><tr><td>δ</td><td>AL</td><td>SacREBLEU</td><td>COMET</td></tr><tr><td>0.1</td><td>3.28</td><td>28.55</td><td>70.61</td></tr><tr><td>0.15</td><td>4.52</td><td>29.04</td><td>70.90</td></tr><tr><td>0.2</td><td>5.72</td><td>29.01</td><td>70.89</td></tr><tr><td>0.25</td><td>8.38</td><td>29.13</td><td>70.83</td></tr><tr><td>0.3</td><td>9.69</td><td>29.24</td><td>70.95</td></tr><tr><td colspan="4">SM²-Uni</td></tr><tr><td>γ</td><td>AL</td><td>SacREBLEU</td><td>COMET</td></tr><tr><td>0.6</td><td>1.87</td><td>28.29</td><td>70.46</td></tr><tr><td>0.7</td><td>3.04</td><td>28.82</td><td>70.84</td></tr><tr><td>0.75</td><td>5.31</td><td>29.28</td><td>71.16</td></tr><tr><td>0.8</td><td>6.25</td><td>29.41</td><td>71.27</td></tr><tr><td>0.9</td><td>9.45</td><td>29.57</td><td>71.30</td></tr><tr><td colspan="4">SM²-Bi</td></tr><tr><td>γ</td><td>AL</td><td>SacREBLEU</td><td>COMET</td></tr><tr><td>0.6</td><td>2.62</td><td>28.70</td><td>70.74</td></tr><tr><td>0.7</td><td>4.47</td><td>29.38</td><td>71.27</td></tr><tr><td>0.75</td><td>5.95</td><td>29.73</td><td>71.44</td></tr><tr><td>0.8</td><td>7.07</td><td>29.75</td><td>71.40</td></tr><tr><td>0.9</td><td>8.18</td><td>29.79</td><td>71.34</td></tr></table>
+
+Table 8: Numerical results on WMT15 En→Vi.  
+
+<table><tr><td></td><td>LONG</td><td>SHORT</td></tr><tr><td>Average Sentence Length</td><td>36.95</td><td>14.07</td></tr><tr><td>Number of Sentences</td><td>1085</td><td>1084</td></tr></table>
+
+Table 9: Statistics on the average sentence length and number of sentences for LONG and SHORT groups.
+
+![](images/a0c7455a4b0866cb2957983a7baa7631d8199348f79f20545fa17f61b711ae7a.jpg)  
+Figure 10: SacreBLEU against Average Lagging (AL) on  $\mathrm{En}\rightarrow \mathrm{Vi}$
+
+![](images/78e1ab947694076d68f1e7060a0faa21837e730d580d1a7530a8942cedb55280.jpg)  
+Figure 11: COMET against Average Lagging (AL) on  $\mathrm{En}\rightarrow \mathrm{Vi}$
+
+![](images/97cfbbb09271b7100b18f9f61b571253c9f79c065c227a00e25005253ed8ab76.jpg)  
+(a)  $\mathbf{SM}^2$ -Bi
+
+![](images/e9732e0c4726d90831be16a5a84a52feaf672acc305f80b5dbca328ee49efde3.jpg)  
+(b)  $\mathbf{SM}^2$  -Uni  
+Figure 12: Translation quality against latency of  $\mathbf{SM}^2$  on LONG and SHORT groups. We provide the performance of OMT models for a clearer comparison.
+
+![](images/ed4c79a0a093d1f4b30608f372fbf3c04dc83fbb0d25cd1e891f21c999021197.jpg)  
+Figure 13: Evaluation of policies in  $\mathrm{SM^2}$  with and without prohibition. We calculate SA  $(\uparrow)$  under different latency levels.

2024/Self-Modifying State Modeling for Simultaneous Machine Translation/images.zip

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2024/Self-Training with Direct Preference Optimization Improves Chain-of-Thought Reasoning/c45be59a-225d-4ef5-96af-38e4a8413966_content_list.json

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+[
+    {
+        "type": "text",
+        "text": "Self-Training with Direct Preference Optimization Improves Chain-of-Thought Reasoning",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Tianduo Wang† Shichen Li‡ Wei Lu†",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "†StatNLP Research Group, Singapore University of Technology and Design",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "$\\ddagger$  Soochow University",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "{tianduo_wang,luwei}@sutd.edu.sg scli_21@outlook.com",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Teaching small-scale language models to perform math reasoning is a valuable yet challenging task. Besides obtaining labeled data from human experts, one of the most common ways to collect high-quality data is by sampling from a larger and more powerful language model. Although previous works have demonstrated the effectiveness of this method, such a knowledge distillation paradigm can be costly and unstable, especially considering that many large language models, such as GPT-4 (OpenAI, 2023), are closed-source, proprietary, and their behaviors are unpredictable. In this work, to avoid relying on outputs from large models, we demonstrate that the reasoning abilities of small-scale language models can be enhanced through self-training, which involves training models with their own outputs. We also show that the conventional self-training can be further augmented by an alignment algorithm called Direct Preference Optimization (DPO) (Rafailov et al., 2023). We empirically found that models trained with the DPO objective are capable of making better generations that largely benefit multi-turn self-training. The experimental results show our models outperform the existing models with comparable sizes on the GSM8K benchmark with minimal resource requirements. $^{1}$",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 Introduction",
+        "text_level": 1,
+        "bbox": [
+            114,
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+            258,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Making language models (LMs) perform mathematical reasoning is a valuable, yet challenging research objective (Hendrycks et al., 2021; Cobbe et al., 2021). Recent works focus on enhancing large-scale LMs' reasoning abilities, e.g., chain-of-thought prompting (Wei et al., 2022b; Kojima et al., 2022), continual pretraining (Azerbayev et al., 2024), or adding external verifiers (Li et al., 2023b). However, the research question of how to",
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/d705c7eb14fb0f61723bb8f7e1b41d67419bc5564585459950d38588062a9a18.jpg",
+        "image_caption": [
+            "Figure 1: GSM8K performance v.s. computational cost. Our approach outperforms baseline models with comparable sizes while minimizing the required compute. Comparisons include two knowledge distillation techniques, i.e., Codex distillation (Fu et al., 2023), and PaLM distillation (Magister et al., 2023), and a data augmentation method, Calcformer (Kadlecik et al., 2023)."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "improve LMs with smaller sizes (e.g., less than 1 billion parameters) is still under-explored.",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Recent studies (Fu et al., 2023; Ho et al., 2023; Magister et al., 2023) demonstrate that the reasoning capabilities of smaller LMs can be significantly enhanced through learning from the outputs of larger and more advanced LMs, such as Codex (Chen et al., 2021) and PaLM (Chowdhery et al., 2022). Despite the relative ease of implementation, the associated costs can be substantial. The computational demand, measured in floating-point operations (FLOPs), is considerably higher for large LMs. Additionally, the use of proprietary and closed-source large LMs for data annotation can incur significant economic costs. Ho et al. (2023) demonstrated that annotating multiple reasoning chains for a single question with large LMs can markedly enhance the performance of smaller models. Hence, a trade-off between cost and performance exists.",
+        "bbox": [
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+    },
+    {
+        "type": "page_footnote",
+        "text": "1Our code and data are released at https://github.com/tianduowang/dpo-st.",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "11917",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "footer",
+        "text": "Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 11917-11928 August 11-16, 2024 ©2024 Association for Computational Linguistics",
+        "bbox": [
+            80,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Another line of work focuses on making improvements via self-training (Zelikman et al., 2022; Gulcehre et al., 2023; Singh et al., 2023). Instead of using data generated by larger models, the essence of self-training methods is to make small models learn from their own generations. While these methods demonstrate the effectiveness of utilizing self-generated data, their success largely depends upon the pre-existing abilities of the models. For example, Zelikman et al. (2022) started by few-shot prompting a large model, i.e., GPT-J (Wang and Komatsuzaki, 2021), to self-generate rationales, which is an emergent ability that only comes with sufficiently large models (Wei et al., 2022a). However, it is still unclear whether small-scale LMs can benefit from self-training.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Recently, we have witnessed that reinforcement learning from human feedback (RLHF) has emerged as a prominent method to precisely modify LMs' behavior towards human preference (Ouyang et al., 2022; Casper et al., 2023). In this work, we propose to augment the self-training algorithm with an RLHF training process, i.e., Direct Preference Optimization (Rafailov et al., 2023), for its better performance and stability. Our experimental results demonstrate that the proposed method can significantly improve LMs' reasoning capabilities while minimizing the computational costs. We visualize the relationship between the downstream task performance and computational cost over a series of specialized models in Figure 1. The computational costs for each model are estimated following previous practice (Kaplan et al., 2020; Yuan et al., 2023). It can be observed that our method not only achieves the highest accuracy, but also minimizes the computational demand by learning from its own generations. Overall, the main contribution of this work can be summarized as follows:",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- We propose a novel extension to the classic self-training framework with Direct Preference Optimization, and we show its effectiveness through standard math problem-solving tasks.",
+            "- We demonstrate that this novel extension improves the reasoning abilities of the LMs with minimal computational resource requirements.",
+            "- We propose an efficient method for integrating LMs with external tools, significantly improving the performance without sacrificing much inference speed."
+        ],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Algorithm 1 Self-training for CoT reasoning tasks",
+        "text_level": 1,
+        "bbox": [
+            510,
+            83,
+            880,
+            99
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Input: pre-trained language model  $f_{\\theta}$  labeled dataset  $\\mathcal{L} = \\{(x^i,y^i,a^i)\\}_{i = 1}^l$  unlabeled dataset  $\\mathcal{U} = \\{(x^{i},a^{i})\\}_{i = 1}^{u}$",
+        "bbox": [
+            542,
+            105,
+            870,
+            155
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Output: fine-tuned model  $f_{\\theta'}$",
+        "bbox": [
+            542,
+            155,
+            764,
+            170
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "1: Fine-tune  $f_{\\theta}$  on  $\\mathcal{L}$  to get  $f_{\\theta'}$",
+            "2: repeat",
+            "3: Build pseudo-labeled dataset  $S$ :"
+        ],
+        "bbox": [
+            521,
+            177,
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+            223
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {S} = \\left\\{\\left(x ^ {i}, \\hat {y} ^ {i}, \\hat {a} ^ {i}\\right) \\right\\} _ {i = 1} ^ {s}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            586,
+            225,
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+            241
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nw h e r e x ^ {i} \\sim \\mathcal {U} a n d \\hat {y} ^ {i}, \\hat {a} ^ {i} \\sim f _ {\\theta^ {\\prime}} (\\cdot | x ^ {i})\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            588,
+            241,
+            868,
+            256
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "4: Select  $S^{\\alpha} \\subset S$  when  $\\hat{a}^i = a^i$",
+            "5: Update  $\\mathcal{L} \\leftarrow S^{\\alpha} \\cup \\mathcal{L}$",
+            "6: Train  $f_{\\theta}$  on  $\\mathcal{L}$  to get a new  $f_{\\theta'}$",
+            "7: until convergence or max iteration is reached"
+        ],
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2 Background",
+        "text_level": 1,
+        "bbox": [
+            509,
+            349,
+            650,
+            365
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Math word problem solving The math word problem solving task can be formulated as a sequence-to-sequence task where the input  $x$  is a question asking for an unknown value and the output  $y$  is a rationale leading to the answer  $a$  (Cobbe et al., 2021). Normally, the answers can be extracted from the rationales via some rule-based methods, e.g., regular expressions. A generated rationale  $\\hat{y}$  is regarded as correct if the extracted answer  $\\hat{a}$  matches the gold answer  $a$ . Formally, the labeled dataset for a math word problem solving task with  $l$  instances can be represented as:",
+        "bbox": [
+            507,
+            374,
+            884,
+            567
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} = \\left\\{\\left(x ^ {i}, y ^ {i}, a ^ {i}\\right) \\right\\} _ {i = 1} ^ {l}. \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            611,
+            577,
+            882,
+            596
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "A common way for specializing a LM  $f_{\\theta}$  towards math reasoning with the labeled dataset  $\\mathcal{L}$  is supervised fine-tuning (SFT). It optimizes  $f_{\\theta}$  by minimizing the negative log likelihood loss  $\\mathcal{L}_{\\mathrm{SFT}}(\\theta)$ :",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\underset {(x, y) \\sim \\mathcal {L}} {\\mathbb {E}} - \\left[ \\sum_ {t = 1} ^ {T} \\log f _ {\\theta} \\left(y _ {t} \\mid x, y _ {1: t - 1}\\right) \\right], \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            681,
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+            724
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "where  $T$  is the length of the rationale  $y$  and we use  $y_{t}$  to represent the  $t$ -th token in  $y$ .",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Self-training Self-training is one of the earliest approaches in semi-supervised learning (Scudder, 1965; Fralick, 1967) that has risen in popularity recently (He et al., 2019; Amini et al., 2022). This method first regards a base model trained with a labeled dataset  $\\mathcal{L}$  as teacher, and uses it to build a pseudo-labeled dataset  $S$  by annotating an unlabeled dataset  $\\mathcal{U}$ . Then, a student model is trained with the combination of  $\\mathcal{L}$  and  $S$  that are expected",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "11918",
+        "bbox": [
+            477,
+            927,
+            524,
+            940
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "to outperform the teacher model. Such a framework has been shown effective in a wide range of natural language processing tasks, e.g., natural language understanding (Vu et al., 2021) and generation (He et al., 2019). A formal description of a self-training algorithm for CoT reasoning tasks is provided in Algorithm 1.",
+        "bbox": [
+            112,
+            84,
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+            195
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Previous studies have demonstrated that the quality of the pseudo-labels largely impacts the overall performance of the self-training algorithm (He et al., 2019; Amini et al., 2022). For example, Gulcehre et al. (2023) proposed to select high-quality pseudo-labels with a learned reward function. Zelikman et al. (2022) filtered the generated rationales to include only the ones that lead to correct answers. Although many methods are proposed to select pseudo-labels, few works discuss how to improve the fine-tuned model  $f_{\\theta'}$  so that more high-quality pseudo-labels can be generated. In this paper, we present a method to enhance  $f_{\\theta'}$  in each iteration so that higher-quality pseudo-labeled data can be generated.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Direct Preference Optimization The Reinforcement Learning from Human Feedback (RLHF) methods align LMs with human preference (Ouyang et al., 2022; Bai et al., 2022). The standard pipeline of RLHF requires to first train a reward model from human preference data. Then, the reward model is used to fine-tune language models via reinforcement learning objective, e.g., Proximal Policy Optimization (Schulman et al., 2017). A recent study proposes Direct Preference Optimization (DPO) (Rafailov et al., 2023) to avoid explicitly training a reward model so that language models can be directly tuned with human preference data.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The DPO pipeline can be described as follows. First, given some prompt  $x$ , sample several completions from the reference model  $\\pi_{\\mathrm{ref}}$  (normally it is the model after supervised fine-tuning):",
+        "bbox": [
+            112,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\ny _ {1}, y _ {2} \\sim \\pi_ {\\operatorname {r e f}} (\\cdot \\mid x). \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Next, construct the DPO dataset  $\\mathcal{D}$  from the completions based on the human preference:",
+        "bbox": [
+            112,
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+            487,
+            822
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {D} = \\left\\{\\left(x ^ {i}, y _ {w} ^ {i}, y _ {l} ^ {i}\\right) \\right\\} _ {i = 1} ^ {N}, \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            203,
+            835,
+            487,
+            854
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $y_w^i$  and  $y_l^i$  represent the winning and losing completions respectively. Then, we optimize the language model  $\\pi_{\\theta}$  to minimize  $\\mathcal{L}_{\\mathrm{DPO}}(\\pi_{\\theta};\\pi_{\\mathrm{ref}})$",
+        "bbox": [
+            112,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "code",
+        "sub_type": "algorithm",
+        "code_caption": [
+            "Algorithm 2 DPO-augmented self-training"
+        ],
+        "code_body": "Input: pre-trained language model  $f_{\\theta}$  labeled dataset  $\\mathcal{L} = \\{(x^i,y^i,a^i)\\}_{i = 1}^l$  unlabeled dataset  $\\mathcal{U} = \\{(x^{i},a^{i})\\}_{i = 1}^{u}$",
+        "bbox": [
+            542,
+            105,
+            873,
+            155
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Output: fine-tuned model  $f_{\\theta'}$",
+        "bbox": [
+            542,
+            155,
+            764,
+            170
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Warm-up stage",
+        "bbox": [
+            542,
+            177,
+            670,
+            191
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "1: Fine-tune  $f_{\\theta}$  on  $\\mathcal{L}$  to get  $f_{\\theta'}$",
+            "2: repeat"
+        ],
+        "bbox": [
+            521,
+            193,
+            747,
+            224
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "DPO step",
+        "bbox": [
+            569,
+            225,
+            658,
+            240
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3: Generate DPO dataset  $\\mathcal{D}$ :",
+        "bbox": [
+            521,
+            241,
+            761,
+            255
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathcal {D} = \\{(x ^ {i}, y _ {w} ^ {i}, y _ {l} ^ {i}) \\} _ {i = 1} ^ {N} \\\\ \\text {w h e r e} x ^ {i} \\sim \\mathcal {U} \\text {a n d} y _ {w} ^ {i}, y _ {l} ^ {i} \\sim f _ {\\theta^ {\\prime}} (\\cdot | x ^ {i}) \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            586,
+            256,
+            877,
+            290
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "4: Tune  $f_{\\theta^{\\prime}}$  with  $\\mathcal{L}_{\\mathrm{DPO}}$  on  $\\mathcal{D}$  to get  $f_{\\theta^d}$",
+        "bbox": [
+            521,
+            290,
+            833,
+            305
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "SFT step",
+        "bbox": [
+            569,
+            307,
+            653,
+            319
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "5: Build pseudo-labeled dataset  $S$ :",
+        "bbox": [
+            521,
+            322,
+            806,
+            336
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathcal {S} = \\{(x ^ {i}, \\hat {y} ^ {i}, \\hat {a} ^ {i}) \\} _ {i = 1} ^ {s} \\\\ \\text {w h e r e} x ^ {i} \\sim \\mathcal {U} \\text {a n d} \\hat {y} ^ {i}, \\hat {a} ^ {i} \\sim f _ {\\theta^ {d}} (\\cdot | x ^ {i}) \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            586,
+            337,
+            870,
+            370
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "6: Select  $S^{\\alpha} \\subset S$  when  $\\hat{a}^i = a^i$",
+            "7: Update  $\\mathcal{L} \\leftarrow S^{\\alpha} \\cup \\mathcal{L}$",
+            "8: Train  $f_{\\theta}$  on  $\\mathcal{L}$  to get a new  $f_{\\theta'}$",
+            "9: until convergence or max iteration is reached"
+        ],
+        "bbox": [
+            521,
+            370,
+            878,
+            432
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "which can be defined as follows:",
+        "bbox": [
+            507,
+            464,
+            752,
+            478
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\underset {(x, y _ {w}, y _ {l}) \\sim \\mathcal {D}} {\\mathbb {E}} \\left[ - \\log \\sigma (r (y _ {w} | x) - r (y _ {l} | x)) \\right], \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            521,
+            489,
+            882,
+            525
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $r(\\cdot |x) = \\beta \\log \\frac{\\pi_{\\theta}(\\cdot|x)}{\\pi_{\\mathrm{ref}}(\\cdot|x)}$  and  $\\beta$  is a coefficient that controls  $\\pi_{\\theta}$ 's deviation from  $\\pi_{\\mathrm{ref}}$ .",
+        "bbox": [
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+            539,
+            882,
+            575
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 Method",
+        "text_level": 1,
+        "bbox": [
+            507,
+            589,
+            613,
+            604
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this section, we first describe the proposed approach. Then, we demonstrate how we integrate an external calculator into the model's decoding process which significantly improves LMs' performance on the downstream tasks.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1 DPO-Augmented Self-Training",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Our approach starts with a warm-up stage, and then followed by an iterative process, where each iteration is composed of two sub-steps: DPO step and SFT step. The iterative process ends when the model performance converges or reaches the maximum iteration. A formal description of the proposed method is illustrated in Algorithm 2. An illustration of our method is presented in Figure 2.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Warm-up stage Like classic self-training, we start by fine-tuning the base model  $f_{\\theta}$  to optimize  $\\mathcal{L}_{\\mathrm{SFT}}(\\theta)$  on the labeled data  $\\mathcal{L}$  to get a new model",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "11919",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/65bc686a94d9c5fd38a41e3633f02bbcda3e274ebdc91181fff2101d6791d578.jpg",
+        "image_caption": [
+            "Figure 2: An illustration of the proposed DPO-augmented Self-Training framework. The conventional Self-Training method uses the SFT model to generate the pseudo-labels for the next iteration. In contrast, our method first optimize the SFT model with Direct Preference Optimization (DPO), and use the DPO model to produce the pseudo-labels."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            218,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "$f_{\\theta^{\\prime}}$  . After this stage, we assume that  $f_{\\theta^{\\prime}}$  is capable of solving certain math problems. Specifically, given a math question  $x$ $f_{\\theta^{\\prime}}$  will generate a rationale  $\\hat{y}$  with answer  $\\hat{a}$",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Iterative step 1: DPO step In this step, we first sample rationales  $\\hat{y}$  from the fine-tuned model  $f_{\\theta'}$  given some questions  $x$  from  $\\mathcal{U}$ . For each question  $x$ , we generate multiple rationales to build the DPO training dataset  $\\mathcal{D}$ . As mentioned, for math problem solving tasks, it is easy to know whether a generated rationale  $\\hat{y}$  can be considered as correct. We label rationales with correct answers as winning completions, while consider rationales with incorrect answers as losing completions. Then, we train  $f_{\\theta'}$  on  $\\mathcal{D}$  to optimize the objective function  $\\mathcal{L}_{\\mathrm{DPO}}$  and get a DPO model  $f_{\\theta^d}$  in the end.",
+        "bbox": [
+            112,
+            423,
+            489,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Iterative step 2: SFT step After obtaining  $f_{\\theta^d}$ , we use it to generate a new pseudo-labeled dataset  $S$  for the next-round supervised fine-tuning:",
+        "bbox": [
+            112,
+            627,
+            489,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {S} = \\left\\{\\left(x, \\hat {y}\\right) \\mid x \\sim \\mathcal {U}, \\hat {y} \\sim f _ {\\theta d} (\\cdot | x) \\right\\} \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            169,
+            690,
+            487,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "After generation, we clean  $S$  by eliminating rationales with incorrect answers and removing duplicates. Therefore, the pseudo-labeled dataset we obtained in the end is a subset of the original one, i.e.,  $S^{\\alpha} \\subset S$ . The final training dataset is the combination of the original labeled dataset  $\\mathcal{L}$  and the newly-generated pseudo-labeled dataset  $S^{\\alpha}$ .",
+        "bbox": [
+            112,
+            725,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Notice that during this process, once we collect a new dataset, we train from the original base model  $f_{\\theta}$  instead of continually fine-tuning  $f_{\\theta'}$  to avoid overfitting, following previous practice (Zelikman et al., 2022; Singh et al., 2023).",
+        "bbox": [
+            112,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Q: James writes a 3-page letter to 2 different friends twice a week. How many pages does he write a year?",
+        "bbox": [
+            507,
+            342,
+            884,
+            390
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "A: He writes each friend",
+        "bbox": [
+            507,
+            391,
+            734,
+            404
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3*2=<<3*2=6>>6 pages a week.",
+        "bbox": [
+            509,
+            407,
+            768,
+            420
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "So he writes",
+        "bbox": [
+            510,
+            423,
+            626,
+            436
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "$6*2 = <   <   6*2 = 12 > > 12$  pages every week.",
+        "bbox": [
+            509,
+            439,
+            823,
+            453
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "That means he writes",
+        "bbox": [
+            510,
+            455,
+            697,
+            468
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "12*52=<<12*52=624>>624 pages a year.",
+        "bbox": [
+            510,
+            472,
+            840,
+            486
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "624",
+        "bbox": [
+            510,
+            488,
+            588,
+            500
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Figure 3: An example from the GSM8K dataset. The calculation annotations are highlighted in blue. All calculation steps are wrapped within special tokens  $<<\\ldots >>$ . During decoding, the calculator will be triggered when such patterns exist and the model's output tokens will be overridden by the calculator results. Following Cobbe et al. (2021), the calculation is performed with the python eval() function.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2 Batch Decoding with Calculator",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We empirically observed that, in contrast to large LMs which excel at basic arithmetic calculations (Brown et al., 2020), smaller LMs like Flant5-Large exhibit poor performance on similar arithmetic tasks. This deficiency significantly impacts their ability to handle math reasoning tasks. To address this, various studies (Parisi et al., 2022; Schick et al., 2023; Kadlcik et al., 2023) have proposed augmenting these smaller models with an external calculator to enhance their math reasoning capabilities. However, many of these existing methods are limited to a batch size of one during decoding. This constraint substantially reduces the inference speed, which hinders their widespread adoption.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "11920",
+        "bbox": [
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+            927,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/bcdac2b0b687eba0bb6621c789258b71e84ecb7f8d68a0d038255be38c20b5b6.jpg",
+        "image_caption": [
+            "Figure 4: Inference speed comparison between our methods (w/ and w/o calculator) and Cal-cformer (Kadlcik et al., 2023) with varying batch sizes. The results are measured on a single NVIDIA A40 GPU."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            129,
+            84,
+            473,
+            242
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To alleviate this issue, we propose a simple yet efficient method to enable the use of a large batch size during inference with an external calculator. We adopt the calculator annotation provided in the original GSM8K dataset (Cobbe et al., 2021). Figure 3 demonstrates an example of this annotation and describes how such annotations can be used during decoding. Our models are built with the Transformers library (Wolf et al., 2020). During generation, we adopt a customized LogitsProcessor<sup>2</sup> to override the model's generation. LogitsProcessor provides an interface to modify the language model's output tokens during generation.",
+        "bbox": [
+            112,
+            342,
+            489,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To demonstrate the efficiency of the proposed solution, We compare the inference speed of our methods (w/ and w/o calculator) based on Flan-T5-Large against an open-source tool-using method, Calcformer (Kadlčík et al., 2023) based on T5-Large, in Figure 4. We find that when the batch size equals 1, all three methods have a similar inference speed of around 40 tokens per second. However, as the inference batch size increases, the speedup of our methods increases significantly.",
+        "bbox": [
+            112,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4 Experiments",
+        "text_level": 1,
+        "bbox": [
+            112,
+            749,
+            260,
+            766
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In this section, we first describe our experimental setup. Next, we present the performance of our models across a series of math word problem solving tasks, comparing them against a selection of competitive baselines. Finally, we empirically analyze what makes the proposed method effective.",
+        "bbox": [
+            112,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/03f5415cbf48aa0ed22c5b852944f78c0272337a53fa998d7e2f0cb84dabfe6c.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Dataset</td><td>Split</td><td># Data</td></tr><tr><td rowspan=\"3\">GSM8K (Cobbe et al., 2021)</td><td>Train</td><td>6,705</td></tr><tr><td>Validation</td><td>768</td></tr><tr><td>Test</td><td>1,319</td></tr><tr><td>MultiArith (Roy and Roth, 2015)</td><td>Test</td><td>600</td></tr><tr><td>ASDiv (Miao et al., 2020)</td><td>Test</td><td>2,096</td></tr><tr><td>SVAMP (Patel et al., 2021)</td><td>Test</td><td>1,000</td></tr></table>",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Table 1: Statistics of the datasets used in our experiments. The original GSM8K dataset only contains train and test split. We randomly select 768 training examples to construct the validation dataset in our experiments.",
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+    },
+    {
+        "type": "text",
+        "text": "4.1 Setup",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Base models We employ Flan-T5 models (Chung et al., 2024) as the base models in our experiments. Specifically, we consider two models of different sizes from the Flan-T5 model family: Flan-T5-Base (250M) and Flan-T5-Large (780M). We select Flan-T5 over the original T5 models (Raffel et al., 2019) as our backbone models based on the evidence from previous research (Chung et al., 2024; Fu et al., 2023), which demonstrated that instruction-tuned models, i.e., Flan-T5, outperform their pre-trained counterparts in math reasoning tasks. Besides Flan-T5 models, we also consider the Llama models (Touvron et al., 2023a,b; Meta, 2024) as our base models.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Datasets The labeled dataset  $\\mathcal{L}$  used in our experiments comes from the training split of the GSM8K dataset. Our unlabeled dataset  $\\mathcal{U}$  is also built upon GSM8K's training data by removing its annotated rationales  $y$ . For evaluation, we consider three other commonly used math reasoning tasks besides GSM8K: MultiArith (Roy and Roth, 2015), AS-Div (Miao et al., 2020), and SVAMP (Patel et al., 2021). Table 1 shows the statistics information of each dataset. Following previous practice (Fu et al., 2023), we only fine-tune the base models on the GSM8K training data while utilizing the rest three datasets to evaluate our models' out-of-domain performance as they do not have an official in-domain training split.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Evaluation metrics We use accuracy of the greedy decoding results as the main evaluation metric. The questions in the datasets in our experiments ask about the values of the unknown variables. The answers to these questions are real numbers that can be extracted from the model-generated rationales.",
+        "bbox": [
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+    },
+    {
+        "type": "page_footnote",
+        "text": "2https://huggingface.co/docs/transformers/ internal/generation_utils#logitsprocessor",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "11921",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/09263d0d66555c98aa9f40a3419beeaaf32dd99f5868d50e6e87c75805ec658d.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Base Model</td><td>GSM8K</td><td>MultiArith</td><td>ASDiv</td><td>SVAMP</td></tr><tr><td>Supervised Fine-Tuning</td><td>Flan-T5-Base</td><td>18.1</td><td>54.2</td><td>26.2</td><td>19.5</td></tr><tr><td>Self-Training</td><td>Flan-T5-Base</td><td>25.9</td><td>73.8</td><td>28.2</td><td>24.2</td></tr><tr><td>DPO-aug Self-Training (Ours)</td><td>Flan-T5-Base</td><td>27.2</td><td>74.3</td><td>29.2</td><td>22.6</td></tr><tr><td>Supervised Fine-Tuning</td><td>Flan-T5-Large</td><td>30.8</td><td>77.2</td><td>38.1</td><td>33.6</td></tr><tr><td>Self-Training</td><td>Flan-T5-Large</td><td>35.6</td><td>86.2</td><td>42.5</td><td>34.8</td></tr><tr><td>DPO-aug Self-Training (Ours)</td><td>Flan-T5-Large</td><td>37.4</td><td>89.0</td><td>42.8</td><td>36.8</td></tr></table>",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 2: Overall accuracies (%) over four math word problem solving tasks. Inspired by the previous practice (Fu et al., 2023), all the models in this table are only trained with the GSM8K training set (Cobbe et al., 2021). Hence, we report the in-distribution performance for GSM8K, while reporting the out-of-distribution performance for the other three datasets, i.e., MultiArith, ASDiv, and SVAMP.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Implementation details In every DPO step, we sample rationales from the SFT model  $f_{\\theta'}$  to build the DPO training data. We sample 5 rationales from  $f_{\\theta'}$  per question with a temperature of 0.7. We regard generated rationales  $\\hat{y}$  as winning ones  $y_w$  if it contains the correct answer, while regarding the rest as the losing ones  $y_l$ . For the SFT steps, we generate 3 rationales per question from the DPO-tuned model  $f_{\\theta^d}$  also with a temperature of 0.7. Only the correct generated rationales  $\\hat{y}$  will be selected to build the pseudo-labeled dataset  $S$ . For both generated DPO data and SFT data, we make simple dedduplication based on the Jaccard similarity scores with a threshold of 0.7.",
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+    },
+    {
+        "type": "text",
+        "text": "4.2 Main Results",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Baselines We mainly consider two baseline methods to compare with our method: Supervised Fine-Tuning (SFT) and Self-Training (ST). SFT baselines are trained on the original GSM8K annotations with the  $\\mathcal{L}_{\\mathrm{SFT}}(\\theta)$  objective. The Self-Training baseline adheres to the procedure outlined in Algorithm 1. Consequently, this makes it the most directly comparable and relevant baseline for evaluating the effectiveness of our approach.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Comparison with baselines Table 2 shows the performance of our method compared with the baselines using two base models over four datasets. It can be observed that both the Self-Training baseline and our proposed method outperform the supervised fine-tuning baseline by a large margin, indicating the effectiveness of the general self-training framework. Although the Self-Training baselines make significant improvements over the SFT baselines, the proposed DPO-augmented Self-Training models consistently outperform them on both indomain and out-of-domain tasks.",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/8d985c5e47955088a6511d1ff9443e93f49779df266140947267fd8ecb696374.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/09f4af446b0dafa386ad5ce81516538fa414df18a8eda73c61930cf863f05364.jpg",
+        "image_caption": [
+            "Figure 5: The performance (accuracy) of the proposed method on GSM8K over three iterations. \"ST\" stands for the Self-Training baseline. The \"iter 0\" represents the results of the SFT baselines."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Effect of iterative training In Figure 5, we demonstrate how our model improves over multiple iterations using two base models: Flan-T5-Base and Flan-T5-Large. Both the ST baseline and our method start with a SFT step using the original GSM8K annotation at iteration 0. We can observe that, as iterations progress, our method consistently outperforms ST, which suggests that the proposed method offers a substantial improvement over ST after repeated training cycles. We also notice that the degree of improvement gradually approaches zero as the iterative process proceeds, suggesting that the model has converged in the last iteration.",
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+    },
+    {
+        "type": "page_number",
+        "text": "11922",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/4ce7f552874dc691845554afcee3d4dff46adec471eea169b8832223517a0bc1.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Base Model</td><td># Annotations</td><td>Annotator</td><td>Tools</td><td>Acc.</td></tr><tr><td colspan=\"6\">Supervised fine-tuning</td></tr><tr><td>CoT (Shridhar et al., 2023)</td><td>GPT-2-Large</td><td>7K</td><td>Human</td><td>✘</td><td>14.1</td></tr><tr><td>Self-consistency (Khalifa et al., 2023)</td><td>Flan-T5-Large</td><td>7K</td><td>Human</td><td>✓</td><td>33.3</td></tr><tr><td>GRACE (Khalifa et al., 2023)</td><td>Flan-T5-Large</td><td>7K</td><td>Human</td><td>✓</td><td>36.3</td></tr><tr><td>Calcformer (Kadlčík et al., 2023)</td><td>T5-Large</td><td>30K</td><td>Human</td><td>✓</td><td>34.2</td></tr><tr><td colspan=\"6\">Knowledge Distillation</td></tr><tr><td>Socratic CoT (Shridhar et al., 2023)</td><td>GPT-2-Large</td><td>7K</td><td>GPT-3 175B</td><td>✘</td><td>21.1</td></tr><tr><td>CoT from CodeX (Fu et al., 2023)</td><td>Flan-T5-Large</td><td>100K</td><td>CodeX</td><td>✘</td><td>20.2</td></tr><tr><td>CoT from PaLM (Magister et al., 2023)</td><td>T5-Large</td><td>6K</td><td>PaLM 540B</td><td>✓</td><td>22.2</td></tr><tr><td colspan=\"6\">Ours</td></tr><tr><td>DPO-aug Self-Training (K=3)</td><td>Flan-T5-Large</td><td>7K</td><td>Human</td><td>✓</td><td>37.4</td></tr><tr><td>DPO-aug Self-Training (K=5)</td><td>Flan-T5-Large</td><td>7K</td><td>Human</td><td>✓</td><td>39.1</td></tr><tr><td>DPO-aug Self-Training (K=10)</td><td>Flan-T5-Large</td><td>7K</td><td>Human</td><td>✓</td><td>40.0</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.3 Comparison with Existing Methods",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "In this section, we compare our methods with existing approaches. Additionally, we scale up the proposed method by increasing the number of sampled pseudo-labels per question, denoted by the hyperparameter  $K$  as in Yuan et al. (2023).",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 3 presents a detailed comparison between our method and existing methods using a simialr base model size. The base models we considered include GPT-2-Large (Radford et al., 2019), T5-Large (Raffel et al., 2019), and Flant5-Large (Chung et al., 2024). All these models have approximately 770 million parameters. As shown in Table 3 our approach not only outperforms other methods on the GSM8K benchmark, but also demonstrates remarkable label efficiency by utilizing only the annotations from the original GSM8K dataset.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In Table 4, we further verify the effectiveness of the proposed method with the Llama model family (Touvron et al., 2023a,b; Meta, 2024). comparing them with several state-of-the-art closed-source models as well as open-source models with similar sizes. We observe a substantial performance gap between proprietary and open-source models. Among the open-source models, those utilizing knowledge distillation consistently outperform their counterparts without such enhancement. Notably, our models using Llama-1-7b (Touvron et al., 2023a) and Llama-2-7b (Touvron et al., 2023b) base models surpass other open-source alternatives that do not employ knowledge distillation, achieving accur",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "cies of  $44.7\\%$  and  $54.7\\%$  respectively. Furthermore, our model employing the latest Llama-3-8b (Meta, 2024) matches or exceeds the performance of earlier models with knowledge distillation, demonstrating a significant accuracy of  $68.8\\%$ .",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/c506b026ff2467dd9f74b6b67c64e4e8286f8f499b6c608ff112c17fca011c0e.jpg",
+        "table_caption": [
+            "Table 3: Detailed comparison among existing methods with comparable model sizes on the GSM8K test set. The \"Annotator\" column indicates how the rationales of the training data are generated. In this column, \"Human\" refers to the labels from the original GSM8K dataset (Cobbe et al., 2021) that are written by human annotators. The \"Tools\" column indicates whether external tools, e.g., calculator or code interpreter, are applied during inference."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Base Model</td><td>Acc.</td></tr><tr><td colspan=\"3\">Closed-source models</td></tr><tr><td>Claude-3-Opus (Anthropic, 2024)</td><td>-</td><td>95.0</td></tr><tr><td>Claude-2 (Anthropic, 2023)</td><td>-</td><td>88.0</td></tr><tr><td>GPT-4 (OpenAI, 2023)</td><td>-</td><td>92.0</td></tr><tr><td>Flan-PaLM-2 (Anil et al., 2023)</td><td>-</td><td>84.7</td></tr><tr><td>PaLM-2 (Anil et al., 2023)</td><td>-</td><td>80.7</td></tr><tr><td colspan=\"3\">Models w/ knowledge distillation</td></tr><tr><td>RFT-U13B (Yuan et al., 2023)</td><td>Llama-1-7b</td><td>49.3</td></tr><tr><td>RFT-U33B (Yuan et al., 2023)</td><td>Llama-2-7b</td><td>51.2</td></tr><tr><td>MAmooTH-CoT (Yue et al., 2023)</td><td>Llama-2-7b</td><td>50.5</td></tr><tr><td>LEMA (An et al., 2023)</td><td>Llama-2-7b</td><td>54.1</td></tr><tr><td>WizardMath (Luo et al., 2023)</td><td>Llama-2-7b</td><td>54.9</td></tr><tr><td>MetaMath (Yu et al., 2024)</td><td>Llama-2-7b</td><td>66.5</td></tr><tr><td>MuggleMath (Li et al., 2023a)</td><td>Llama-2-7b</td><td>68.4</td></tr><tr><td>ToRA (Gou et al., 2024)</td><td>Llama-2-7b</td><td>68.8</td></tr><tr><td colspan=\"3\">Models w/o knowledge distillation</td></tr><tr><td>SFT (Yuan et al., 2023)</td><td>Llama-1-7b</td><td>35.9</td></tr><tr><td>RFT (K=12) (Yuan et al., 2023)</td><td>Llama-1-7b</td><td>41.6</td></tr><tr><td>RFT (K=100) (Yuan et al., 2023)</td><td>Llama-1-7b</td><td>41.7</td></tr><tr><td>SFT (Yuan et al., 2023)</td><td>Llama-2-7b</td><td>41.6</td></tr><tr><td>RFT (K=12) (Yuan et al., 2023)</td><td>Llama-2-7b</td><td>45.3</td></tr><tr><td>RFT (K=100) (Yuan et al., 2023)</td><td>Llama-2-7b</td><td>47.5</td></tr><tr><td colspan=\"3\">Ours</td></tr><tr><td>DPO-ST (K=10)</td><td>Llama-1-7b</td><td>44.7</td></tr><tr><td>DPO-ST (K=10)</td><td>Llama-2-7b</td><td>54.7</td></tr><tr><td>DPO-ST (K=10)</td><td>Llama-3-8b</td><td>68.8</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Table 4: Comparison with the state-of-the-art close-source models and open-source models based on Llama model family (Touvron et al., 2023a,b; Meta, 2024).",
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+    },
+    {
+        "type": "page_number",
+        "text": "11923",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/9ab32bf2373c0cb68de99f75890e7a1495529b6a635aa5471a279bc46ba703a1.jpg",
+        "image_caption": [
+            "Figure 6: Effects of the DPO step. Left: we report the greedy decoding results for Pass@1. Middle: For Pass@10, the solutions are sampled with temperature 0.7. Right: We count the number of generated pseudolabels after dedduplication."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.4 Effects of the DPO Step",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "As mentioned earlier, the main difference between the proposed method and the classic self-training is the DPO step in every iterative process. We now analyze how the DPO steps improve self-training. Figure 6 compares the performance of models before and after the DPO step in the first iteration on the Pass@K metrics. Pass@K measures the probability that at least one of the  $K$  generated solutions for a problem is correct, which serves as a gauge for both the quality and the variety of the model-generated solutions. The models we investigate here are fine-tuned from the Flan-T5-Large.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "As shown in Figure 6, the DPO step yields only marginal improvements over the SFT model in the Pass@1 performance on the development set. However, the performance significantly improves when multiple rationales, i.e., 10 solutions per question, are sampled with temperature 0.7 (measured with the Pass@10 metric). This indicates that the DPO training objective makes language models inclined to generate rationales of both high quality and diversity. We also compare the number of generated rationales on the training set  $\\mathcal{L}$  for models with and without the DPO step. Figure 6 (right) clearly shows that the model after the DPO step can produce more SFT data for the next iteration.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.5 Effects of External Calculator",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Driven by the observation that small-scale LMs frequently make basic calculation errors, we develop a simple yet efficient method that integrates an external calculator into the models' decoding",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/a74eb9717c484e48db689c40c6de0a9f6007103b0c7250c01ab8a6e83e93f4fe.jpg",
+        "image_caption": [
+            "Figure 7: GSM8K development set accuracy of Flant5-Large with and without the use of an external calculator during inference."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "process. To evaluate the impact of this integration, we conduct an ablation study by omitting the calculator and present the findings in Figure 7. Our results indicate that decoding without the calculator markedly reduces accuracy across all iterations. We believe that this is because models will generate large amount of false positive pseudo-labels without calculator, that is, the generated pseudo-labels may have correct final answers but make errors in the intermediate reasoning steps.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "5 Related Work",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Learning from pseudo-labels Supervised finetuning (SFT) is prevalent technique employed to enhance the performance of pre-trained language models on specific downstream tasks (Ouyang et al., 2022; Chung et al., 2024). However, this method heavily depends on the availability of high-quality labeled data, which can be both expensive and labor-intensive to procure (Brown et al., 2020). To address this limitation, various strategies have been developed to generate high-quality pseudolabels using either unlabeled or synthetic data for a wide range of applications, including text classification (Xie et al., 2020), sentence representation learning (Wang and Lu, 2022), instruction tuning (Honovich et al., 2022), and math reasoning (Wang and Lu, 2023). Recent advancements in this area primarily focus on two directions: self-training and knowledge distillation. The key difference between these methods lies in the source of the pseudo-labels: self-training uses the model's own predictions on unlabeled data, while knowledge distillation utilizes the insights from larger, more powerful models.",
+        "bbox": [
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+    },
+    {
+        "type": "page_number",
+        "text": "11924",
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+        "type": "text",
+        "text": "Self-training in language model Recently, we have witnessed a large number of works focusing on self-training algorithms for language models (He et al., 2019; Zelikman et al., 2022; Yuan et al., 2023). Most of such methods are built upon the classic self-training framework (Scudder, 1965). He et al. (2019) empirically studied the effectiveness of self-training in natural language generation tasks, e.g., summarization and translation. Zelikman et al. (2022) proposed self-taught reasoner (STaR), which demonstrated that language models can be iteratively improved from its own generation, even there are no gold rationales provided. Yuan et al. (2023) proposed rejection sampling fine-tuning to improve language models' math reasoning abilities. This method can be interpreted as only executing one iteration of the self-training algorithm. Singh et al. (2023) proposed  $\\mathrm{ReST}^{EM}$ , a self-improving algorithm based on expectation-maximization framework. This method demonstrates significant improvements in problem-solving tasks, e.g., math reasoning and code generation.",
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+    },
+    {
+        "type": "text",
+        "text": "Knowledge distillation from LLMs Many of the recent research efforts demonstrated large language models (LLMs) are capable of doing math reasoning (Wei et al., 2022b; Gao et al., 2022; OpenAI, 2023; Anil et al., 2023; Anthropic, 2023, 2024). Therefore, a recent line of work focuses on improving smaller language models' reasoning abilities by distilling chain-of-thought pseudo-labels from LLMs (Ho et al., 2023; Magister et al., 2023; Fu et al., 2023). For example, Luo et al. (2023) proposed Reinforcement Learning from Evol-Instruct Feedback built upon EvolInstruct (Xu et al., 2023), which requires ChatGPT to provide the training signals. An et al. (2023) demonstrated that language models can effectively learn from the mistakes that can be corrected by larger models, e.g., GPT-4 (OpenAI, 2023), during supervised fine-tuning. Yu et al. (2024) proposed a novel question bootstrapping method with the help of larger models to augment the existing training dataset. Although these methods are shown to have promising experimental results, they are costly to implement as large models cost more FLOPs during inference. Our work demonstrates that small-scale language models can also learn from their own generations like the larger ones (Zelikman et al., 2022), which is more resource-efficient compared with the knowledge distillation methods.",
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+    {
+        "type": "text",
+        "text": "6 Conclusion",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We present an effective and resource-efficient method called DPO-augmented Self-Training (DPO-ST), which augments the original Self-Training algorithm with Direct Preference Optimization (Rafailov et al., 2023). Unlike previous studies that improve small-scale language models' reasoning abilities by distilling a larger and more powerful model, we argue that small models that are trained merely on the limited human-labeled data can improve themselves significantly. We also empirically find that models trained with DPO loss can generate pseudo-labeled data with higher quality and diversity. Our experiments demonstrate that the proposed method not only outperforms existing methods with comparable model sizes on the GSM8K benchmark, but also achieves remarkable resource efficiency in terms of both computational cost and the requirements of human-labeled data.",
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+    {
+        "type": "text",
+        "text": "Limitations",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Use of unlabeled data Our method is built upon the classic self-training algorithm, which provides an effective semi-supervised learning framework that makes good use of unlabeled data. However, this work doesn't explore the use of unlabeled data explicitly. Future research efforts can be made to explore how to collect high-quality unlabeled data for math word problem solving. In other words, we need to find an efficient method for collecting unlabeled data  $\\mathcal{U} = \\{(x_i,a_i)\\}_{i = 1}^u$  that for each math question  $x_{i}$  , there is a corresponding groundtruth answer  $a_{i}$",
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+    {
+        "type": "text",
+        "text": "Generalization to other tasks One of the limitations of this work is the narrow scope of our experiments, which were exclusively conducted on math reasoning tasks. The primary reason for this limitation is the lack of appropriate training data for other reasoning tasks. As our method requires a set of training data with chain-of-thought labels, many existing reasoning tasks lack such annotations, making it challenging to extend our experiments beyond the current scope. Future research may focus on identifying and developing suitable datasets for a wider range of reasoning tasks to fully evaluate the applicability and effectiveness of our method across different reasoning tasks.",
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+    {
+        "type": "page_number",
+        "text": "11925",
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+    {
+        "type": "text",
+        "text": "Acknowledgements",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "This work was done when Shichen Li was a visiting student at the StatNLP Research Group of SUTD. We would like to thank the anonymous reviewers, our meta-reviewer, and senior area chairs for their constructive comments and support on this work. This research/project is supported by Ministry of Education, Singapore, under its Academic Research Fund (AcRF) Tier 2 Programme (MOE AcRF Tier 2 Award No: MOET2EP20122-0011), the National Research Foundation Singapore and DSO National Laboratories under the AI Singapore Program (AISG Award No: AISG2-RP-2020-016), and Ministry of Education, Singapore, under its Tier 3 Programme (The Award No.: MOET320200004). Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not reflect the views of the funding agencies.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 9
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2024/Self-Training with Direct Preference Optimization Improves Chain-of-Thought Reasoning/c45be59a-225d-4ef5-96af-38e4a8413966_origin.pdf

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2024/Self-Training with Direct Preference Optimization Improves Chain-of-Thought Reasoning/full.md

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+# Self-Training with Direct Preference Optimization Improves Chain-of-Thought Reasoning
+
+Tianduo Wang† Shichen Li‡ Wei Lu†
+
+†StatNLP Research Group, Singapore University of Technology and Design
+
+$\ddagger$  Soochow University
+
+{tianduo_wang,luwei}@sutd.edu.sg scli_21@outlook.com
+
+# Abstract
+
+Teaching small-scale language models to perform math reasoning is a valuable yet challenging task. Besides obtaining labeled data from human experts, one of the most common ways to collect high-quality data is by sampling from a larger and more powerful language model. Although previous works have demonstrated the effectiveness of this method, such a knowledge distillation paradigm can be costly and unstable, especially considering that many large language models, such as GPT-4 (OpenAI, 2023), are closed-source, proprietary, and their behaviors are unpredictable. In this work, to avoid relying on outputs from large models, we demonstrate that the reasoning abilities of small-scale language models can be enhanced through self-training, which involves training models with their own outputs. We also show that the conventional self-training can be further augmented by an alignment algorithm called Direct Preference Optimization (DPO) (Rafailov et al., 2023). We empirically found that models trained with the DPO objective are capable of making better generations that largely benefit multi-turn self-training. The experimental results show our models outperform the existing models with comparable sizes on the GSM8K benchmark with minimal resource requirements. $^{1}$
+
+# 1 Introduction
+
+Making language models (LMs) perform mathematical reasoning is a valuable, yet challenging research objective (Hendrycks et al., 2021; Cobbe et al., 2021). Recent works focus on enhancing large-scale LMs' reasoning abilities, e.g., chain-of-thought prompting (Wei et al., 2022b; Kojima et al., 2022), continual pretraining (Azerbayev et al., 2024), or adding external verifiers (Li et al., 2023b). However, the research question of how to
+
+![](images/d705c7eb14fb0f61723bb8f7e1b41d67419bc5564585459950d38588062a9a18.jpg)  
+Figure 1: GSM8K performance v.s. computational cost. Our approach outperforms baseline models with comparable sizes while minimizing the required compute. Comparisons include two knowledge distillation techniques, i.e., Codex distillation (Fu et al., 2023), and PaLM distillation (Magister et al., 2023), and a data augmentation method, Calcformer (Kadlecik et al., 2023).
+
+improve LMs with smaller sizes (e.g., less than 1 billion parameters) is still under-explored.
+
+Recent studies (Fu et al., 2023; Ho et al., 2023; Magister et al., 2023) demonstrate that the reasoning capabilities of smaller LMs can be significantly enhanced through learning from the outputs of larger and more advanced LMs, such as Codex (Chen et al., 2021) and PaLM (Chowdhery et al., 2022). Despite the relative ease of implementation, the associated costs can be substantial. The computational demand, measured in floating-point operations (FLOPs), is considerably higher for large LMs. Additionally, the use of proprietary and closed-source large LMs for data annotation can incur significant economic costs. Ho et al. (2023) demonstrated that annotating multiple reasoning chains for a single question with large LMs can markedly enhance the performance of smaller models. Hence, a trade-off between cost and performance exists.
+
+Another line of work focuses on making improvements via self-training (Zelikman et al., 2022; Gulcehre et al., 2023; Singh et al., 2023). Instead of using data generated by larger models, the essence of self-training methods is to make small models learn from their own generations. While these methods demonstrate the effectiveness of utilizing self-generated data, their success largely depends upon the pre-existing abilities of the models. For example, Zelikman et al. (2022) started by few-shot prompting a large model, i.e., GPT-J (Wang and Komatsuzaki, 2021), to self-generate rationales, which is an emergent ability that only comes with sufficiently large models (Wei et al., 2022a). However, it is still unclear whether small-scale LMs can benefit from self-training.
+
+Recently, we have witnessed that reinforcement learning from human feedback (RLHF) has emerged as a prominent method to precisely modify LMs' behavior towards human preference (Ouyang et al., 2022; Casper et al., 2023). In this work, we propose to augment the self-training algorithm with an RLHF training process, i.e., Direct Preference Optimization (Rafailov et al., 2023), for its better performance and stability. Our experimental results demonstrate that the proposed method can significantly improve LMs' reasoning capabilities while minimizing the computational costs. We visualize the relationship between the downstream task performance and computational cost over a series of specialized models in Figure 1. The computational costs for each model are estimated following previous practice (Kaplan et al., 2020; Yuan et al., 2023). It can be observed that our method not only achieves the highest accuracy, but also minimizes the computational demand by learning from its own generations. Overall, the main contribution of this work can be summarized as follows:
+
+- We propose a novel extension to the classic self-training framework with Direct Preference Optimization, and we show its effectiveness through standard math problem-solving tasks.  
+- We demonstrate that this novel extension improves the reasoning abilities of the LMs with minimal computational resource requirements.  
+- We propose an efficient method for integrating LMs with external tools, significantly improving the performance without sacrificing much inference speed.
+
+# Algorithm 1 Self-training for CoT reasoning tasks
+
+Input: pre-trained language model  $f_{\theta}$  labeled dataset  $\mathcal{L} = \{(x^i,y^i,a^i)\}_{i = 1}^l$  unlabeled dataset  $\mathcal{U} = \{(x^{i},a^{i})\}_{i = 1}^{u}$
+
+Output: fine-tuned model  $f_{\theta'}$
+
+1: Fine-tune  $f_{\theta}$  on  $\mathcal{L}$  to get  $f_{\theta'}$  
+2: repeat  
+3: Build pseudo-labeled dataset  $S$ :
+
+$$
+\mathcal {S} = \left\{\left(x ^ {i}, \hat {y} ^ {i}, \hat {a} ^ {i}\right) \right\} _ {i = 1} ^ {s}
+$$
+
+$$
+w h e r e x ^ {i} \sim \mathcal {U} a n d \hat {y} ^ {i}, \hat {a} ^ {i} \sim f _ {\theta^ {\prime}} (\cdot | x ^ {i})
+$$
+
+4: Select  $S^{\alpha} \subset S$  when  $\hat{a}^i = a^i$  
+5: Update  $\mathcal{L} \leftarrow S^{\alpha} \cup \mathcal{L}$  
+6: Train  $f_{\theta}$  on  $\mathcal{L}$  to get a new  $f_{\theta'}$  
+7: until convergence or max iteration is reached
+
+# 2 Background
+
+Math word problem solving The math word problem solving task can be formulated as a sequence-to-sequence task where the input  $x$  is a question asking for an unknown value and the output  $y$  is a rationale leading to the answer  $a$  (Cobbe et al., 2021). Normally, the answers can be extracted from the rationales via some rule-based methods, e.g., regular expressions. A generated rationale  $\hat{y}$  is regarded as correct if the extracted answer  $\hat{a}$  matches the gold answer  $a$ . Formally, the labeled dataset for a math word problem solving task with  $l$  instances can be represented as:
+
+$$
+\mathcal {L} = \left\{\left(x ^ {i}, y ^ {i}, a ^ {i}\right) \right\} _ {i = 1} ^ {l}. \tag {1}
+$$
+
+A common way for specializing a LM  $f_{\theta}$  towards math reasoning with the labeled dataset  $\mathcal{L}$  is supervised fine-tuning (SFT). It optimizes  $f_{\theta}$  by minimizing the negative log likelihood loss  $\mathcal{L}_{\mathrm{SFT}}(\theta)$ :
+
+$$
+\underset {(x, y) \sim \mathcal {L}} {\mathbb {E}} - \left[ \sum_ {t = 1} ^ {T} \log f _ {\theta} \left(y _ {t} \mid x, y _ {1: t - 1}\right) \right], \tag {2}
+$$
+
+where  $T$  is the length of the rationale  $y$  and we use  $y_{t}$  to represent the  $t$ -th token in  $y$ .
+
+Self-training Self-training is one of the earliest approaches in semi-supervised learning (Scudder, 1965; Fralick, 1967) that has risen in popularity recently (He et al., 2019; Amini et al., 2022). This method first regards a base model trained with a labeled dataset  $\mathcal{L}$  as teacher, and uses it to build a pseudo-labeled dataset  $S$  by annotating an unlabeled dataset  $\mathcal{U}$ . Then, a student model is trained with the combination of  $\mathcal{L}$  and  $S$  that are expected
+
+to outperform the teacher model. Such a framework has been shown effective in a wide range of natural language processing tasks, e.g., natural language understanding (Vu et al., 2021) and generation (He et al., 2019). A formal description of a self-training algorithm for CoT reasoning tasks is provided in Algorithm 1.
+
+Previous studies have demonstrated that the quality of the pseudo-labels largely impacts the overall performance of the self-training algorithm (He et al., 2019; Amini et al., 2022). For example, Gulcehre et al. (2023) proposed to select high-quality pseudo-labels with a learned reward function. Zelikman et al. (2022) filtered the generated rationales to include only the ones that lead to correct answers. Although many methods are proposed to select pseudo-labels, few works discuss how to improve the fine-tuned model  $f_{\theta'}$  so that more high-quality pseudo-labels can be generated. In this paper, we present a method to enhance  $f_{\theta'}$  in each iteration so that higher-quality pseudo-labeled data can be generated.
+
+Direct Preference Optimization The Reinforcement Learning from Human Feedback (RLHF) methods align LMs with human preference (Ouyang et al., 2022; Bai et al., 2022). The standard pipeline of RLHF requires to first train a reward model from human preference data. Then, the reward model is used to fine-tune language models via reinforcement learning objective, e.g., Proximal Policy Optimization (Schulman et al., 2017). A recent study proposes Direct Preference Optimization (DPO) (Rafailov et al., 2023) to avoid explicitly training a reward model so that language models can be directly tuned with human preference data.
+
+The DPO pipeline can be described as follows. First, given some prompt  $x$ , sample several completions from the reference model  $\pi_{\mathrm{ref}}$  (normally it is the model after supervised fine-tuning):
+
+$$
+y _ {1}, y _ {2} \sim \pi_ {\operatorname {r e f}} (\cdot \mid x). \tag {3}
+$$
+
+Next, construct the DPO dataset  $\mathcal{D}$  from the completions based on the human preference:
+
+$$
+\mathcal {D} = \left\{\left(x ^ {i}, y _ {w} ^ {i}, y _ {l} ^ {i}\right) \right\} _ {i = 1} ^ {N}, \tag {4}
+$$
+
+where  $y_w^i$  and  $y_l^i$  represent the winning and losing completions respectively. Then, we optimize the language model  $\pi_{\theta}$  to minimize  $\mathcal{L}_{\mathrm{DPO}}(\pi_{\theta};\pi_{\mathrm{ref}})$
+
+Algorithm 2 DPO-augmented self-training  
+Input: pre-trained language model  $f_{\theta}$  labeled dataset  $\mathcal{L} = \{(x^i,y^i,a^i)\}_{i = 1}^l$  unlabeled dataset  $\mathcal{U} = \{(x^{i},a^{i})\}_{i = 1}^{u}$
+
+Output: fine-tuned model  $f_{\theta'}$
+
+Warm-up stage
+
+1: Fine-tune  $f_{\theta}$  on  $\mathcal{L}$  to get  $f_{\theta'}$  
+2: repeat
+
+DPO step
+
+3: Generate DPO dataset  $\mathcal{D}$ :
+
+$$
+\begin{array}{l} \mathcal {D} = \{(x ^ {i}, y _ {w} ^ {i}, y _ {l} ^ {i}) \} _ {i = 1} ^ {N} \\ \text {w h e r e} x ^ {i} \sim \mathcal {U} \text {a n d} y _ {w} ^ {i}, y _ {l} ^ {i} \sim f _ {\theta^ {\prime}} (\cdot | x ^ {i}) \end{array}
+$$
+
+4: Tune  $f_{\theta^{\prime}}$  with  $\mathcal{L}_{\mathrm{DPO}}$  on  $\mathcal{D}$  to get  $f_{\theta^d}$
+
+SFT step
+
+5: Build pseudo-labeled dataset  $S$ :
+
+$$
+\begin{array}{l} \mathcal {S} = \{(x ^ {i}, \hat {y} ^ {i}, \hat {a} ^ {i}) \} _ {i = 1} ^ {s} \\ \text {w h e r e} x ^ {i} \sim \mathcal {U} \text {a n d} \hat {y} ^ {i}, \hat {a} ^ {i} \sim f _ {\theta^ {d}} (\cdot | x ^ {i}) \end{array}
+$$
+
+6: Select  $S^{\alpha} \subset S$  when  $\hat{a}^i = a^i$  
+7: Update  $\mathcal{L} \leftarrow S^{\alpha} \cup \mathcal{L}$  
+8: Train  $f_{\theta}$  on  $\mathcal{L}$  to get a new  $f_{\theta'}$  
+9: until convergence or max iteration is reached
+
+which can be defined as follows:
+
+$$
+\underset {(x, y _ {w}, y _ {l}) \sim \mathcal {D}} {\mathbb {E}} \left[ - \log \sigma (r (y _ {w} | x) - r (y _ {l} | x)) \right], \tag {5}
+$$
+
+where  $r(\cdot |x) = \beta \log \frac{\pi_{\theta}(\cdot|x)}{\pi_{\mathrm{ref}}(\cdot|x)}$  and  $\beta$  is a coefficient that controls  $\pi_{\theta}$ 's deviation from  $\pi_{\mathrm{ref}}$ .
+
+# 3 Method
+
+In this section, we first describe the proposed approach. Then, we demonstrate how we integrate an external calculator into the model's decoding process which significantly improves LMs' performance on the downstream tasks.
+
+# 3.1 DPO-Augmented Self-Training
+
+Our approach starts with a warm-up stage, and then followed by an iterative process, where each iteration is composed of two sub-steps: DPO step and SFT step. The iterative process ends when the model performance converges or reaches the maximum iteration. A formal description of the proposed method is illustrated in Algorithm 2. An illustration of our method is presented in Figure 2.
+
+Warm-up stage Like classic self-training, we start by fine-tuning the base model  $f_{\theta}$  to optimize  $\mathcal{L}_{\mathrm{SFT}}(\theta)$  on the labeled data  $\mathcal{L}$  to get a new model
+
+![](images/65bc686a94d9c5fd38a41e3633f02bbcda3e274ebdc91181fff2101d6791d578.jpg)  
+Figure 2: An illustration of the proposed DPO-augmented Self-Training framework. The conventional Self-Training method uses the SFT model to generate the pseudo-labels for the next iteration. In contrast, our method first optimize the SFT model with Direct Preference Optimization (DPO), and use the DPO model to produce the pseudo-labels.
+
+$f_{\theta^{\prime}}$  . After this stage, we assume that  $f_{\theta^{\prime}}$  is capable of solving certain math problems. Specifically, given a math question  $x$ $f_{\theta^{\prime}}$  will generate a rationale  $\hat{y}$  with answer  $\hat{a}$
+
+Iterative step 1: DPO step In this step, we first sample rationales  $\hat{y}$  from the fine-tuned model  $f_{\theta'}$  given some questions  $x$  from  $\mathcal{U}$ . For each question  $x$ , we generate multiple rationales to build the DPO training dataset  $\mathcal{D}$ . As mentioned, for math problem solving tasks, it is easy to know whether a generated rationale  $\hat{y}$  can be considered as correct. We label rationales with correct answers as winning completions, while consider rationales with incorrect answers as losing completions. Then, we train  $f_{\theta'}$  on  $\mathcal{D}$  to optimize the objective function  $\mathcal{L}_{\mathrm{DPO}}$  and get a DPO model  $f_{\theta^d}$  in the end.
+
+Iterative step 2: SFT step After obtaining  $f_{\theta^d}$ , we use it to generate a new pseudo-labeled dataset  $S$  for the next-round supervised fine-tuning:
+
+$$
+\mathcal {S} = \left\{\left(x, \hat {y}\right) \mid x \sim \mathcal {U}, \hat {y} \sim f _ {\theta d} (\cdot | x) \right\} \tag {6}
+$$
+
+After generation, we clean  $S$  by eliminating rationales with incorrect answers and removing duplicates. Therefore, the pseudo-labeled dataset we obtained in the end is a subset of the original one, i.e.,  $S^{\alpha} \subset S$ . The final training dataset is the combination of the original labeled dataset  $\mathcal{L}$  and the newly-generated pseudo-labeled dataset  $S^{\alpha}$ .
+
+Notice that during this process, once we collect a new dataset, we train from the original base model  $f_{\theta}$  instead of continually fine-tuning  $f_{\theta'}$  to avoid overfitting, following previous practice (Zelikman et al., 2022; Singh et al., 2023).
+
+Q: James writes a 3-page letter to 2 different friends twice a week. How many pages does he write a year?
+
+A: He writes each friend
+
+3*2=<<3*2=6>>6 pages a week.
+
+So he writes
+
+$6*2 = <   <   6*2 = 12 > > 12$  pages every week.
+
+That means he writes
+
+12*52=<<12*52=624>>624 pages a year.
+
+624
+
+Figure 3: An example from the GSM8K dataset. The calculation annotations are highlighted in blue. All calculation steps are wrapped within special tokens  $<<\ldots >>$ . During decoding, the calculator will be triggered when such patterns exist and the model's output tokens will be overridden by the calculator results. Following Cobbe et al. (2021), the calculation is performed with the python eval() function.
+
+# 3.2 Batch Decoding with Calculator
+
+We empirically observed that, in contrast to large LMs which excel at basic arithmetic calculations (Brown et al., 2020), smaller LMs like Flant5-Large exhibit poor performance on similar arithmetic tasks. This deficiency significantly impacts their ability to handle math reasoning tasks. To address this, various studies (Parisi et al., 2022; Schick et al., 2023; Kadlcik et al., 2023) have proposed augmenting these smaller models with an external calculator to enhance their math reasoning capabilities. However, many of these existing methods are limited to a batch size of one during decoding. This constraint substantially reduces the inference speed, which hinders their widespread adoption.
+
+![](images/bcdac2b0b687eba0bb6621c789258b71e84ecb7f8d68a0d038255be38c20b5b6.jpg)  
+Figure 4: Inference speed comparison between our methods (w/ and w/o calculator) and Cal-cformer (Kadlcik et al., 2023) with varying batch sizes. The results are measured on a single NVIDIA A40 GPU.
+
+To alleviate this issue, we propose a simple yet efficient method to enable the use of a large batch size during inference with an external calculator. We adopt the calculator annotation provided in the original GSM8K dataset (Cobbe et al., 2021). Figure 3 demonstrates an example of this annotation and describes how such annotations can be used during decoding. Our models are built with the Transformers library (Wolf et al., 2020). During generation, we adopt a customized LogitsProcessor<sup>2</sup> to override the model's generation. LogitsProcessor provides an interface to modify the language model's output tokens during generation.
+
+To demonstrate the efficiency of the proposed solution, We compare the inference speed of our methods (w/ and w/o calculator) based on Flan-T5-Large against an open-source tool-using method, Calcformer (Kadlčík et al., 2023) based on T5-Large, in Figure 4. We find that when the batch size equals 1, all three methods have a similar inference speed of around 40 tokens per second. However, as the inference batch size increases, the speedup of our methods increases significantly.
+
+# 4 Experiments
+
+In this section, we first describe our experimental setup. Next, we present the performance of our models across a series of math word problem solving tasks, comparing them against a selection of competitive baselines. Finally, we empirically analyze what makes the proposed method effective.
+
+<table><tr><td>Dataset</td><td>Split</td><td># Data</td></tr><tr><td rowspan="3">GSM8K (Cobbe et al., 2021)</td><td>Train</td><td>6,705</td></tr><tr><td>Validation</td><td>768</td></tr><tr><td>Test</td><td>1,319</td></tr><tr><td>MultiArith (Roy and Roth, 2015)</td><td>Test</td><td>600</td></tr><tr><td>ASDiv (Miao et al., 2020)</td><td>Test</td><td>2,096</td></tr><tr><td>SVAMP (Patel et al., 2021)</td><td>Test</td><td>1,000</td></tr></table>
+
+Table 1: Statistics of the datasets used in our experiments. The original GSM8K dataset only contains train and test split. We randomly select 768 training examples to construct the validation dataset in our experiments.
+
+# 4.1 Setup
+
+Base models We employ Flan-T5 models (Chung et al., 2024) as the base models in our experiments. Specifically, we consider two models of different sizes from the Flan-T5 model family: Flan-T5-Base (250M) and Flan-T5-Large (780M). We select Flan-T5 over the original T5 models (Raffel et al., 2019) as our backbone models based on the evidence from previous research (Chung et al., 2024; Fu et al., 2023), which demonstrated that instruction-tuned models, i.e., Flan-T5, outperform their pre-trained counterparts in math reasoning tasks. Besides Flan-T5 models, we also consider the Llama models (Touvron et al., 2023a,b; Meta, 2024) as our base models.
+
+Datasets The labeled dataset  $\mathcal{L}$  used in our experiments comes from the training split of the GSM8K dataset. Our unlabeled dataset  $\mathcal{U}$  is also built upon GSM8K's training data by removing its annotated rationales  $y$ . For evaluation, we consider three other commonly used math reasoning tasks besides GSM8K: MultiArith (Roy and Roth, 2015), AS-Div (Miao et al., 2020), and SVAMP (Patel et al., 2021). Table 1 shows the statistics information of each dataset. Following previous practice (Fu et al., 2023), we only fine-tune the base models on the GSM8K training data while utilizing the rest three datasets to evaluate our models' out-of-domain performance as they do not have an official in-domain training split.
+
+Evaluation metrics We use accuracy of the greedy decoding results as the main evaluation metric. The questions in the datasets in our experiments ask about the values of the unknown variables. The answers to these questions are real numbers that can be extracted from the model-generated rationales.
+
+<table><tr><td>Method</td><td>Base Model</td><td>GSM8K</td><td>MultiArith</td><td>ASDiv</td><td>SVAMP</td></tr><tr><td>Supervised Fine-Tuning</td><td>Flan-T5-Base</td><td>18.1</td><td>54.2</td><td>26.2</td><td>19.5</td></tr><tr><td>Self-Training</td><td>Flan-T5-Base</td><td>25.9</td><td>73.8</td><td>28.2</td><td>24.2</td></tr><tr><td>DPO-aug Self-Training (Ours)</td><td>Flan-T5-Base</td><td>27.2</td><td>74.3</td><td>29.2</td><td>22.6</td></tr><tr><td>Supervised Fine-Tuning</td><td>Flan-T5-Large</td><td>30.8</td><td>77.2</td><td>38.1</td><td>33.6</td></tr><tr><td>Self-Training</td><td>Flan-T5-Large</td><td>35.6</td><td>86.2</td><td>42.5</td><td>34.8</td></tr><tr><td>DPO-aug Self-Training (Ours)</td><td>Flan-T5-Large</td><td>37.4</td><td>89.0</td><td>42.8</td><td>36.8</td></tr></table>
+
+Table 2: Overall accuracies (%) over four math word problem solving tasks. Inspired by the previous practice (Fu et al., 2023), all the models in this table are only trained with the GSM8K training set (Cobbe et al., 2021). Hence, we report the in-distribution performance for GSM8K, while reporting the out-of-distribution performance for the other three datasets, i.e., MultiArith, ASDiv, and SVAMP.
+
+Implementation details In every DPO step, we sample rationales from the SFT model  $f_{\theta'}$  to build the DPO training data. We sample 5 rationales from  $f_{\theta'}$  per question with a temperature of 0.7. We regard generated rationales  $\hat{y}$  as winning ones  $y_w$  if it contains the correct answer, while regarding the rest as the losing ones  $y_l$ . For the SFT steps, we generate 3 rationales per question from the DPO-tuned model  $f_{\theta^d}$  also with a temperature of 0.7. Only the correct generated rationales  $\hat{y}$  will be selected to build the pseudo-labeled dataset  $S$ . For both generated DPO data and SFT data, we make simple dedduplication based on the Jaccard similarity scores with a threshold of 0.7.
+
+# 4.2 Main Results
+
+Baselines We mainly consider two baseline methods to compare with our method: Supervised Fine-Tuning (SFT) and Self-Training (ST). SFT baselines are trained on the original GSM8K annotations with the  $\mathcal{L}_{\mathrm{SFT}}(\theta)$  objective. The Self-Training baseline adheres to the procedure outlined in Algorithm 1. Consequently, this makes it the most directly comparable and relevant baseline for evaluating the effectiveness of our approach.
+
+Comparison with baselines Table 2 shows the performance of our method compared with the baselines using two base models over four datasets. It can be observed that both the Self-Training baseline and our proposed method outperform the supervised fine-tuning baseline by a large margin, indicating the effectiveness of the general self-training framework. Although the Self-Training baselines make significant improvements over the SFT baselines, the proposed DPO-augmented Self-Training models consistently outperform them on both indomain and out-of-domain tasks.
+
+![](images/8d985c5e47955088a6511d1ff9443e93f49779df266140947267fd8ecb696374.jpg)
+
+![](images/09f4af446b0dafa386ad5ce81516538fa414df18a8eda73c61930cf863f05364.jpg)  
+Figure 5: The performance (accuracy) of the proposed method on GSM8K over three iterations. "ST" stands for the Self-Training baseline. The "iter 0" represents the results of the SFT baselines.
+
+Effect of iterative training In Figure 5, we demonstrate how our model improves over multiple iterations using two base models: Flan-T5-Base and Flan-T5-Large. Both the ST baseline and our method start with a SFT step using the original GSM8K annotation at iteration 0. We can observe that, as iterations progress, our method consistently outperforms ST, which suggests that the proposed method offers a substantial improvement over ST after repeated training cycles. We also notice that the degree of improvement gradually approaches zero as the iterative process proceeds, suggesting that the model has converged in the last iteration.
+
+<table><tr><td>Method</td><td>Base Model</td><td># Annotations</td><td>Annotator</td><td>Tools</td><td>Acc.</td></tr><tr><td colspan="6">Supervised fine-tuning</td></tr><tr><td>CoT (Shridhar et al., 2023)</td><td>GPT-2-Large</td><td>7K</td><td>Human</td><td>✘</td><td>14.1</td></tr><tr><td>Self-consistency (Khalifa et al., 2023)</td><td>Flan-T5-Large</td><td>7K</td><td>Human</td><td>✓</td><td>33.3</td></tr><tr><td>GRACE (Khalifa et al., 2023)</td><td>Flan-T5-Large</td><td>7K</td><td>Human</td><td>✓</td><td>36.3</td></tr><tr><td>Calcformer (Kadlčík et al., 2023)</td><td>T5-Large</td><td>30K</td><td>Human</td><td>✓</td><td>34.2</td></tr><tr><td colspan="6">Knowledge Distillation</td></tr><tr><td>Socratic CoT (Shridhar et al., 2023)</td><td>GPT-2-Large</td><td>7K</td><td>GPT-3 175B</td><td>✘</td><td>21.1</td></tr><tr><td>CoT from CodeX (Fu et al., 2023)</td><td>Flan-T5-Large</td><td>100K</td><td>CodeX</td><td>✘</td><td>20.2</td></tr><tr><td>CoT from PaLM (Magister et al., 2023)</td><td>T5-Large</td><td>6K</td><td>PaLM 540B</td><td>✓</td><td>22.2</td></tr><tr><td colspan="6">Ours</td></tr><tr><td>DPO-aug Self-Training (K=3)</td><td>Flan-T5-Large</td><td>7K</td><td>Human</td><td>✓</td><td>37.4</td></tr><tr><td>DPO-aug Self-Training (K=5)</td><td>Flan-T5-Large</td><td>7K</td><td>Human</td><td>✓</td><td>39.1</td></tr><tr><td>DPO-aug Self-Training (K=10)</td><td>Flan-T5-Large</td><td>7K</td><td>Human</td><td>✓</td><td>40.0</td></tr></table>
+
+# 4.3 Comparison with Existing Methods
+
+In this section, we compare our methods with existing approaches. Additionally, we scale up the proposed method by increasing the number of sampled pseudo-labels per question, denoted by the hyperparameter  $K$  as in Yuan et al. (2023).
+
+Table 3 presents a detailed comparison between our method and existing methods using a simialr base model size. The base models we considered include GPT-2-Large (Radford et al., 2019), T5-Large (Raffel et al., 2019), and Flant5-Large (Chung et al., 2024). All these models have approximately 770 million parameters. As shown in Table 3 our approach not only outperforms other methods on the GSM8K benchmark, but also demonstrates remarkable label efficiency by utilizing only the annotations from the original GSM8K dataset.
+
+In Table 4, we further verify the effectiveness of the proposed method with the Llama model family (Touvron et al., 2023a,b; Meta, 2024). comparing them with several state-of-the-art closed-source models as well as open-source models with similar sizes. We observe a substantial performance gap between proprietary and open-source models. Among the open-source models, those utilizing knowledge distillation consistently outperform their counterparts without such enhancement. Notably, our models using Llama-1-7b (Touvron et al., 2023a) and Llama-2-7b (Touvron et al., 2023b) base models surpass other open-source alternatives that do not employ knowledge distillation, achieving accur
+
+cies of  $44.7\%$  and  $54.7\%$  respectively. Furthermore, our model employing the latest Llama-3-8b (Meta, 2024) matches or exceeds the performance of earlier models with knowledge distillation, demonstrating a significant accuracy of  $68.8\%$ .
+
+Table 3: Detailed comparison among existing methods with comparable model sizes on the GSM8K test set. The "Annotator" column indicates how the rationales of the training data are generated. In this column, "Human" refers to the labels from the original GSM8K dataset (Cobbe et al., 2021) that are written by human annotators. The "Tools" column indicates whether external tools, e.g., calculator or code interpreter, are applied during inference.  
+
+<table><tr><td>Method</td><td>Base Model</td><td>Acc.</td></tr><tr><td colspan="3">Closed-source models</td></tr><tr><td>Claude-3-Opus (Anthropic, 2024)</td><td>-</td><td>95.0</td></tr><tr><td>Claude-2 (Anthropic, 2023)</td><td>-</td><td>88.0</td></tr><tr><td>GPT-4 (OpenAI, 2023)</td><td>-</td><td>92.0</td></tr><tr><td>Flan-PaLM-2 (Anil et al., 2023)</td><td>-</td><td>84.7</td></tr><tr><td>PaLM-2 (Anil et al., 2023)</td><td>-</td><td>80.7</td></tr><tr><td colspan="3">Models w/ knowledge distillation</td></tr><tr><td>RFT-U13B (Yuan et al., 2023)</td><td>Llama-1-7b</td><td>49.3</td></tr><tr><td>RFT-U33B (Yuan et al., 2023)</td><td>Llama-2-7b</td><td>51.2</td></tr><tr><td>MAmooTH-CoT (Yue et al., 2023)</td><td>Llama-2-7b</td><td>50.5</td></tr><tr><td>LEMA (An et al., 2023)</td><td>Llama-2-7b</td><td>54.1</td></tr><tr><td>WizardMath (Luo et al., 2023)</td><td>Llama-2-7b</td><td>54.9</td></tr><tr><td>MetaMath (Yu et al., 2024)</td><td>Llama-2-7b</td><td>66.5</td></tr><tr><td>MuggleMath (Li et al., 2023a)</td><td>Llama-2-7b</td><td>68.4</td></tr><tr><td>ToRA (Gou et al., 2024)</td><td>Llama-2-7b</td><td>68.8</td></tr><tr><td colspan="3">Models w/o knowledge distillation</td></tr><tr><td>SFT (Yuan et al., 2023)</td><td>Llama-1-7b</td><td>35.9</td></tr><tr><td>RFT (K=12) (Yuan et al., 2023)</td><td>Llama-1-7b</td><td>41.6</td></tr><tr><td>RFT (K=100) (Yuan et al., 2023)</td><td>Llama-1-7b</td><td>41.7</td></tr><tr><td>SFT (Yuan et al., 2023)</td><td>Llama-2-7b</td><td>41.6</td></tr><tr><td>RFT (K=12) (Yuan et al., 2023)</td><td>Llama-2-7b</td><td>45.3</td></tr><tr><td>RFT (K=100) (Yuan et al., 2023)</td><td>Llama-2-7b</td><td>47.5</td></tr><tr><td colspan="3">Ours</td></tr><tr><td>DPO-ST (K=10)</td><td>Llama-1-7b</td><td>44.7</td></tr><tr><td>DPO-ST (K=10)</td><td>Llama-2-7b</td><td>54.7</td></tr><tr><td>DPO-ST (K=10)</td><td>Llama-3-8b</td><td>68.8</td></tr></table>
+
+Table 4: Comparison with the state-of-the-art close-source models and open-source models based on Llama model family (Touvron et al., 2023a,b; Meta, 2024).
+
+![](images/9ab32bf2373c0cb68de99f75890e7a1495529b6a635aa5471a279bc46ba703a1.jpg)  
+Figure 6: Effects of the DPO step. Left: we report the greedy decoding results for Pass@1. Middle: For Pass@10, the solutions are sampled with temperature 0.7. Right: We count the number of generated pseudolabels after dedduplication.
+
+# 4.4 Effects of the DPO Step
+
+As mentioned earlier, the main difference between the proposed method and the classic self-training is the DPO step in every iterative process. We now analyze how the DPO steps improve self-training. Figure 6 compares the performance of models before and after the DPO step in the first iteration on the Pass@K metrics. Pass@K measures the probability that at least one of the  $K$  generated solutions for a problem is correct, which serves as a gauge for both the quality and the variety of the model-generated solutions. The models we investigate here are fine-tuned from the Flan-T5-Large.
+
+As shown in Figure 6, the DPO step yields only marginal improvements over the SFT model in the Pass@1 performance on the development set. However, the performance significantly improves when multiple rationales, i.e., 10 solutions per question, are sampled with temperature 0.7 (measured with the Pass@10 metric). This indicates that the DPO training objective makes language models inclined to generate rationales of both high quality and diversity. We also compare the number of generated rationales on the training set  $\mathcal{L}$  for models with and without the DPO step. Figure 6 (right) clearly shows that the model after the DPO step can produce more SFT data for the next iteration.
+
+# 4.5 Effects of External Calculator
+
+Driven by the observation that small-scale LMs frequently make basic calculation errors, we develop a simple yet efficient method that integrates an external calculator into the models' decoding
+
+![](images/a74eb9717c484e48db689c40c6de0a9f6007103b0c7250c01ab8a6e83e93f4fe.jpg)  
+Figure 7: GSM8K development set accuracy of Flant5-Large with and without the use of an external calculator during inference.
+
+process. To evaluate the impact of this integration, we conduct an ablation study by omitting the calculator and present the findings in Figure 7. Our results indicate that decoding without the calculator markedly reduces accuracy across all iterations. We believe that this is because models will generate large amount of false positive pseudo-labels without calculator, that is, the generated pseudo-labels may have correct final answers but make errors in the intermediate reasoning steps.
+
+# 5 Related Work
+
+Learning from pseudo-labels Supervised finetuning (SFT) is prevalent technique employed to enhance the performance of pre-trained language models on specific downstream tasks (Ouyang et al., 2022; Chung et al., 2024). However, this method heavily depends on the availability of high-quality labeled data, which can be both expensive and labor-intensive to procure (Brown et al., 2020). To address this limitation, various strategies have been developed to generate high-quality pseudolabels using either unlabeled or synthetic data for a wide range of applications, including text classification (Xie et al., 2020), sentence representation learning (Wang and Lu, 2022), instruction tuning (Honovich et al., 2022), and math reasoning (Wang and Lu, 2023). Recent advancements in this area primarily focus on two directions: self-training and knowledge distillation. The key difference between these methods lies in the source of the pseudo-labels: self-training uses the model's own predictions on unlabeled data, while knowledge distillation utilizes the insights from larger, more powerful models.
+
+Self-training in language model Recently, we have witnessed a large number of works focusing on self-training algorithms for language models (He et al., 2019; Zelikman et al., 2022; Yuan et al., 2023). Most of such methods are built upon the classic self-training framework (Scudder, 1965). He et al. (2019) empirically studied the effectiveness of self-training in natural language generation tasks, e.g., summarization and translation. Zelikman et al. (2022) proposed self-taught reasoner (STaR), which demonstrated that language models can be iteratively improved from its own generation, even there are no gold rationales provided. Yuan et al. (2023) proposed rejection sampling fine-tuning to improve language models' math reasoning abilities. This method can be interpreted as only executing one iteration of the self-training algorithm. Singh et al. (2023) proposed  $\mathrm{ReST}^{EM}$ , a self-improving algorithm based on expectation-maximization framework. This method demonstrates significant improvements in problem-solving tasks, e.g., math reasoning and code generation.
+
+Knowledge distillation from LLMs Many of the recent research efforts demonstrated large language models (LLMs) are capable of doing math reasoning (Wei et al., 2022b; Gao et al., 2022; OpenAI, 2023; Anil et al., 2023; Anthropic, 2023, 2024). Therefore, a recent line of work focuses on improving smaller language models' reasoning abilities by distilling chain-of-thought pseudo-labels from LLMs (Ho et al., 2023; Magister et al., 2023; Fu et al., 2023). For example, Luo et al. (2023) proposed Reinforcement Learning from Evol-Instruct Feedback built upon EvolInstruct (Xu et al., 2023), which requires ChatGPT to provide the training signals. An et al. (2023) demonstrated that language models can effectively learn from the mistakes that can be corrected by larger models, e.g., GPT-4 (OpenAI, 2023), during supervised fine-tuning. Yu et al. (2024) proposed a novel question bootstrapping method with the help of larger models to augment the existing training dataset. Although these methods are shown to have promising experimental results, they are costly to implement as large models cost more FLOPs during inference. Our work demonstrates that small-scale language models can also learn from their own generations like the larger ones (Zelikman et al., 2022), which is more resource-efficient compared with the knowledge distillation methods.
+
+# 6 Conclusion
+
+We present an effective and resource-efficient method called DPO-augmented Self-Training (DPO-ST), which augments the original Self-Training algorithm with Direct Preference Optimization (Rafailov et al., 2023). Unlike previous studies that improve small-scale language models' reasoning abilities by distilling a larger and more powerful model, we argue that small models that are trained merely on the limited human-labeled data can improve themselves significantly. We also empirically find that models trained with DPO loss can generate pseudo-labeled data with higher quality and diversity. Our experiments demonstrate that the proposed method not only outperforms existing methods with comparable model sizes on the GSM8K benchmark, but also achieves remarkable resource efficiency in terms of both computational cost and the requirements of human-labeled data.
+
+# Limitations
+
+Use of unlabeled data Our method is built upon the classic self-training algorithm, which provides an effective semi-supervised learning framework that makes good use of unlabeled data. However, this work doesn't explore the use of unlabeled data explicitly. Future research efforts can be made to explore how to collect high-quality unlabeled data for math word problem solving. In other words, we need to find an efficient method for collecting unlabeled data  $\mathcal{U} = \{(x_i,a_i)\}_{i = 1}^u$  that for each math question  $x_{i}$  , there is a corresponding groundtruth answer  $a_{i}$
+
+Generalization to other tasks One of the limitations of this work is the narrow scope of our experiments, which were exclusively conducted on math reasoning tasks. The primary reason for this limitation is the lack of appropriate training data for other reasoning tasks. As our method requires a set of training data with chain-of-thought labels, many existing reasoning tasks lack such annotations, making it challenging to extend our experiments beyond the current scope. Future research may focus on identifying and developing suitable datasets for a wider range of reasoning tasks to fully evaluate the applicability and effectiveness of our method across different reasoning tasks.
+
+# Acknowledgements
+
+This work was done when Shichen Li was a visiting student at the StatNLP Research Group of SUTD. We would like to thank the anonymous reviewers, our meta-reviewer, and senior area chairs for their constructive comments and support on this work. This research/project is supported by Ministry of Education, Singapore, under its Academic Research Fund (AcRF) Tier 2 Programme (MOE AcRF Tier 2 Award No: MOET2EP20122-0011), the National Research Foundation Singapore and DSO National Laboratories under the AI Singapore Program (AISG Award No: AISG2-RP-2020-016), and Ministry of Education, Singapore, under its Tier 3 Programme (The Award No.: MOET320200004). Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not reflect the views of the funding agencies.
+
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+# Self-Training with Pseudo-Label Scorer for Aspect Sentiment Quad Prediction
+
+Yice Zhang $^{1,3}$ , Jie Zeng $^{1*}$ , Weiming Hu $^{1*}$ , Ziyi Wang $^{1*}$ , Shiwei Chen $^{1,2}$ , and Ruifeng Xu $^{1,2,3\dagger}$
+
+<sup>1</sup> Harbin Institute of Technology, Shenzhen, China
+
+2 Peng Cheng Laboratory, Shenzhen, China
+
+<sup>3</sup> Guangdong Provincial Key Laboratory of Novel Security Intelligence Technologies
+
+zhangyc_hit@163.com,xuruifeng@hit.edu.cn
+
+# Abstract
+
+Aspect Sentiment Quad Prediction (ASQP) aims to predict all quads (aspect term, aspect category, opinion term, sentiment polarity) for a given review, which is the most representative and challenging task in aspect-based sentiment analysis. A key challenge in the ASQP task is the scarcity of labeled data, which limits the performance of existing methods. To tackle this issue, we propose a self-training framework with a pseudo-label scorer, wherein a scorer assesses the match between reviews and their pseudo-labels, aiming to filter out mismatches and thereby enhance the effectiveness of self-training. We highlight two critical aspects to ensure the scorer's effectiveness and reliability: the quality of the training dataset and its model architecture. To this end, we create a human-annotated comparison dataset and train a generative model on it using ranking-based objectives. Extensive experiments on public ASQP datasets reveal that using our scorer can greatly and consistently improve the effectiveness of self-training. Moreover, we explore the possibility of replacing humans with large language models for comparison dataset annotation, and experiments demonstrate its feasibility. $^{1}$
+
+# 1 Introduction
+
+Aspect-Based Sentiment Analysis (ABSA) aims to recognize aspect-level opinions and sentiments from user-generated content (Pontiki et al., 2014). This problem has consistently attracted interest owing to its proficiency in distilling and summarizing fine-grained opinions from vast data (Do et al., 2019; Nazir et al., 2022; Zhang et al., 2023a). The most representative and challenging task in ABSA is Aspect Sentiment Quad Prediction (ASQP) (Cai
+
+![](images/0d4e8b56cdff7411d4eb313507a33218cab979214718843d8d14429ec2f901a3.jpg)  
+Figure 1: Illustration of our pseudo-label scorer.
+
+et al., 2021; Zhang et al., 2021a). This task formulates aspect-level opinions and sentiments as quadruples, each consisting of an aspect term, aspect category, opinion term, and sentiment polarity. For example, given a review "the food is great and reasonably priced," the output of ASQP would be  $\{(\text{food}, \text{food\_quality}, \text{great}, \text{positive}), (\text{food}, \text{food\_prices}, \text{reasonably priced}, \text{positive})\}$ .
+
+As a fine-grained problem, ABSA faces the challenge of insufficient labeled data, which is particularly severe in the ASQP task. This issue limits the performance of existing models. Many efforts explore data augmentation methods to alleviate this issue. They synthesize new samples by modifying existing ones (Li et al., 2020; Hsu et al., 2021), applying self-training techniques (Wang et al., 2021), or utilizing generative methods (Yu et al., 2023; Deng et al., 2023; Zhang et al., 2023b). However, a significant limitation of these methods is that the synthetic samples often inevitably contain mismatches between sentences and labels, which can adversely affect model learning.
+
+To reduce such mismatches, this paper introduces a pseudo-label scorer for data augmentation. As illustrated in Figure 1, the scorer assesses the degree of match between the review and its pseudolabel. If we have a sufficiently robust scorer, we can filter out all mismatched samples, thereby sig
+
+nificantly enhancing the effectiveness of data augmentation. We propose that the effectiveness and reliability of this scorer hinge on two critical aspects: (1) the quality of the training dataset and (2) its architecture along with the training objective. We discuss these two aspects below.
+
+For the first aspect, previous works typically produce negative labels by modifying real labels using heuristic rules (Wang et al., 2021; Mao et al., 2022). However, such negative labels are usually simplistic and patterned, limiting the scorer's learning. To overcome this limitation, we create a human-annotated comparison dataset. Specifically, we train an ASQP model with existing labeled data, use it to infer several pseudo-labels for unlabeled data, and then have human annotators choose the most appropriate pseudo-labels. The labels chosen by annotators are designated as positive labels, while the rest as negative labels. Our dataset, in contrast to the rule-based datasets, is more challenging and better aligned with human judgment.
+
+For the second aspect, previous works formalize label-scoring as a question-answering problem (Wang et al., 2021) or embed the discriminative matching token into the label (Mao et al., 2022). However, our findings suggest that these methods underperform in complex tasks like ASQP, due to their limited capacity to model the interactions between reviews and pseudo-labels. Recent works in preference optimization reveal that the language model itself can serve as a scorer (Rafailov et al., 2023; Yuan et al., 2023). This motivates us to use the conditional likelihoods that a generative model assigns to a pseudo-label as the measure of its quality. Compared with the previous methods, this approach enables the scorer to examine the plausibility of a pseudo-label in a token-by-token fashion, thus offering a more comprehensive and effective scoring. We then fine-tune this scorer on our comparison dataset using ranking-based objectives.
+
+Upon developing this pseudo-label scorer, we apply it in a data augmentation framework, specifically opting for the self-training framework due to its simplicity. We conduct extensive experiments on public ASQP datasets to examine its effectiveness and further investigate the following questions: (1) how does the pseudo-label scorer perform using our comparison data and model architecture? (2) is it feasible to replace humans with large language models to annotate the comparison data? and (3) how to utilize the scorer to filter out low
+
+quality samples? Furthermore, inspired by Ma et al. (2023), we extend the application of this scorer, employing it as a reranker for multiple candidate labels, and assess its impact and effectiveness.
+
+Our contributions are summarized as follows:
+
+(1) To the best of our knowledge, we are the first to apply a pseudo-label scorer to data augmentation in the ASQP task.  
+(2) We investigate how to enhance the scorer's effectiveness and reliability from both dataset and model architecture perspectives.  
+(3) We empirically demonstrate that the proposed pseudo-label scorer can significantly and consistently enhance the performance of existing models.
+
+# 2 Background
+
+Task Evolution. Aspect-Based Sentiment Analysis (ABSA) is a fine-grained sentiment analysis problem, aiming at recognizing user opinions and sentiments towards specific aspects (Zhang et al., 2023a). Within ABSA, aspects are generally defined as aspect categories or aspect terms. Aspect categories are predefined categories like food_quality and service_general in restaurant reviews, or laptop_portability and display_quality in laptop reviews. Aspect terms are explicit mentions of these aspect categories in the text. Based on this, Pontiki et al. (2014) formally define four subtasks: aspect category detection, aspect category sentiment classification, aspect term extraction, and aspect term sentiment classification. These tasks sequentially identify aspects and determine their corresponding sentiments.
+
+Opinion term refers to words or phrases that express subjective sentiments. Sentiment expressions towards aspects often rely on these opinion terms, making them vital clues for recognizing aspects and their sentiment polarities. Consequently, many researchers focus on aspect and opinion coextraction (Wang et al., 2016; Li and Lam, 2017; Fan et al., 2019; Chen et al., 2020; Zhao et al., 2020). Building on this, Peng et al. (2020) propose the Aspect Sentiment Triplet Extraction (ASTE) task, conceptualizing an aspect-level sentiment as a triplet consisting of an aspect term, opinion term, and sentiment polarity. Following ASTE, Cai et al. (2021); Zhang et al. (2021a) extend the triplet by incorporating the aspect category, evolving it into Aspect Sentiment Quad Prediction (ASQP). ASQP
+
+is currently the most representative and challenging task within ABSA.
+
+ABSA Methods. Early efforts in ABSA primarily focus on identifying one or two sentiment elements. They mainly design specific model structures to establish interactions between sentiment elements and their contexts, as well as among different sentiment elements (Wang et al., 2016; Li and Lam, 2017; Ma et al., 2017; Chen et al., 2017; Xu et al., 2018; Xue and Li, 2018; Li et al., 2018; Fan et al., 2019; Zeng et al., 2019). Recent efforts have shifted towards compound tasks like ASTE and ASQP, proposing various end-to-end methods. These include machine reading comprehension-based methods (Chen et al., 2021; Mao et al., 2021), table-filling methods (Wu et al., 2020; Chen et al., 2022; Zhang et al., 2022), span-based methods (Xu et al., 2021; Li et al., 2022; Cai et al., 2021), and generative methods (Yan et al., 2021; Zhang et al., 2021b,a; Mao et al., 2022; Gao et al., 2022; Hu et al., 2023a,b; Gou et al., 2023). Among these, generative methods have emerged as mainstream due to their universality and capacity to exploit rich label semantics.
+
+Generative Aspect-Based Sentiment Analysis, abbreviated as GAS, is a unified generative framework proposed by Zhang et al. (2021b). The core idea of this framework is to transform sentiment elements into a label sequence and then use a SEQ2SEQ model to learn the dependencies between the input text and the label sequence. For the ASQP task, we can convert it into a label sequence using the following template:
+
+$$
+\operatorname {s e q} _ {\text {l a b e l}} = c _ {1} \mid s _ {1} \mid a _ {1} \mid o _ {1}; \dots ; c _ {n} \mid s _ {n} \mid a _ {n} \mid o _ {n},
+$$
+
+where  $c_{i}$  denotes the aspect category,  $s_{i}$  denotes the sentiment polarity,  $a_{i}$  denotes the aspect term, and  $o_{i}$  denotes the opinion term.
+
+# 3 Comparison Dataset
+
+We need to construct a comparison dataset to facilitate the training and evaluation of the pseudo-label scorer. This dataset comprises samples each containing a review sentence accompanied by several pseudo-labels, where one is the positive label and the others are negative labels. We train the scorer by requiring it to assign high scores to positive labels and low scores to negative labels.
+
+Previous works typically produce negative labels using heuristic rules (Wang et al., 2021; Mao et al.,
+
+2022). They randomly modify elements in the existing positive labels, such as altering boundaries or conducting substitutions. Such negative labels are patterned and easily distinguishable, limiting the learning potential of the scorer. Therefore, this paper employs human annotators to construct this comparison dataset.
+
+# 3.1 Data Preparation
+
+Aligned with existing ASQP datasets (Cai et al., 2021; Zhang et al., 2021a), we collect reviews from two domains: Restaurant and Laptop. The restaurant reviews are from the Yelp Dataset<sup>2</sup>, and the laptop reviews are from the Amazon Laptop Dataset<sup>3</sup> (Ni et al., 2019). We segment these reviews into individual sentences. Next, we employ the existing labeled dataset to train an ASQP model (Zhang et al., 2021b) and then utilize this model to generate four pseudo-labels for each review sentence via beam search.
+
+# 3.2 Annotation Process
+
+For a review sentence and its four pseudo-labels, annotators are presented with six options. The first four options correspond to the four pseudolabels, the fifth option indicates that none of the pseudo-labels are appropriate, and the sixth option suggests that the review sentence does not express any sentiment or the expressed sentiment is difficult to infer. When annotators choose the fifth option, they are required to write an alternative label.
+
+The annotation process is organized into multiple batches, each containing about 200 samples. To ensure accuracy, every sample is independently annotated by three different annotators. In cases of discrepancy among their annotations, a fourth annotator steps in to resolve the inconsistency. Furthermore, at the conclusion of each batch, the four annotators meet to discuss and reconcile any disagreements. Each annotator is provided with annotation guidelines and existing labeled ASQP datasets. In instances where conflicts arise between the two, we prioritize adherence to the guidelines.
+
+AI Annotation. Choosing the most appropriate label, while much simpler than annotating an ASQP
+
+<table><tr><td>Datasets</td><td>P1</td><td>P2</td><td>P3</td><td>P4</td><td>P5</td><td>P6</td><td>Total</td></tr><tr><td>ACOS-Laptop-Comp</td><td>853</td><td>149</td><td>88</td><td>44</td><td>167</td><td>204</td><td>1505</td></tr><tr><td>ACOS-Rest-Comp</td><td>894</td><td>109</td><td>49</td><td>23</td><td>122</td><td>1003</td><td>2200</td></tr><tr><td>ACOS-Laptop-Comp-AI</td><td>1744</td><td>410</td><td>213</td><td>122</td><td>0</td><td>259</td><td>2748</td></tr><tr><td>ACOS-Rest-Comp-AI</td><td>1796</td><td>276</td><td>110</td><td>60</td><td>0</td><td>1620</td><td>3862</td></tr><tr><td>ASQP-Rest15-Comp-AI</td><td>1585</td><td>369</td><td>157</td><td>94</td><td>0</td><td>1223</td><td>3428</td></tr><tr><td>ASQP-Rest16-Comp-AI</td><td>1560</td><td>431</td><td>114</td><td>76</td><td>0</td><td>1337</td><td>3518</td></tr></table>
+
+Table 1: Statistics of the comparison datasets. P1-P6 correspond to the number of samples for options 1 to 6, respectively.
+
+label from scratch, remains a laborious task. Therefore, we explore the feasibility of using ChatGPT as a substitute for human annotators. To ensure the quality of AI annotations, we carefully craft prompts for each ASQP dataset. Additionally, we incorporate three strategies to enhance the annotation process: self-consistency, self-assessment, and rationale augmentation. Details of AI annotation can be found in Appendix A.
+
+# 3.3 Statistics
+
+We construct two human-annotated and four AI-annotated comparison datasets. Their basic statistical information is presented in Table 1. In the training phase of the scorer, we exclude samples corresponding to option 6 and reserve a portion of the data as the development set for hyperparameter tuning and model selection. Specifically, for the Restaurant datasets, we set aside 200 samples, and for the Laptop datasets, we allocate 300 samples. Consequently, this leaves around 1,000 training samples in the human-annotated datasets and approximately 2,000 training samples in the AI-annotated datasets.
+
+# 4 Our Approach
+
+# 4.1 Pseudo-label Scorer
+
+The objective of the pseudo-label scorer is to score the match between a review and a pseudo-label. Previous efforts formalize this scoring task as a question-answering problem (Wang et al., 2021) or embed the discriminative matching token into the label (Mao et al., 2022). However, these methods struggle to effectively capture the interaction between reviews and pseudo-labels. Inspired by recent works in preference optimization (Rafailov et al., 2023; Yuan et al., 2023; Song et al., 2023), we utilize a generative model as the scorer. Given a review sentence  $x$  and a pseudo label  $y$ , their matching score is quantified by the conditional probabilit
+
+ity assigned by the generative model:
+
+$$
+s (x, y) \propto p (y | x) = \prod_ {t} p \left(y _ {t} \mid y _ {<   t}, x\right). \tag {1}
+$$
+
+Compared to previous methods, this approach integrates the likelihood of each token in the pseudolabel to derive its overall score, thereby providing a comprehensive and effective scoring.
+
+Training. We optimize the pseudo-label scorer on the annotated comparison dataset with the ranking-based training objective. Specifically, we design a simple listwise objective as follows:
+
+$$
+\mathcal {L} _ {\text {L I S T}} = - \log \frac {p \left(y _ {p} \mid x\right)}{Z}, \tag {2}
+$$
+
+$$
+Z = p \left(y _ {p} | x\right) + \sum_ {y _ {n}} p \left(y _ {n} | x\right), \tag {3}
+$$
+
+where  $y_{p}$  denotes the positive label,  $y_{n}$  denotes the negative label, and  $Z$  is the normalization factor.
+
+In addition to the comparison dataset, we also incorporate the original ASQP dataset to further enhance the training of the scorer. Labels from the original ASQP dataset are treated as additional positive labels and are combined with the positive labels from the comparison dataset. We additionally maximize the scores of these positive labels to enhance the scorer. The combined loss function is formulated as follows:
+
+$$
+\mathcal {L} = \mathcal {L} _ {1} + \alpha \mathcal {L} _ {2}, \tag {4}
+$$
+
+$$
+\mathcal {L} _ {1} = \mathbb {E} _ {(x, \mathcal {Y}) \sim D _ {\mathrm {C O M P}}} \mathcal {L} _ {\text {L I S T}} (x, \mathcal {Y}), \tag {5}
+$$
+
+$$
+\mathcal {L} _ {2} = \mathbb {E} _ {(x, y _ {p}) \sim D _ {\mathrm {C O M P}} \cup D _ {\mathrm {A S Q P}}} - \log p (y _ {p} | x), \tag {6}
+$$
+
+where  $D_{\mathrm{COMP}}$  represents the comparison dataset,  $D_{\mathrm{ASQP}}$  represents the original ASQP dataset,  $\mathcal{V}$  denotes the set of several pseudo-labels of the sentence  $x$ , and  $\alpha$  is a hyperparameter.
+
+# 4.2 Self-Training with Data Filtering
+
+Self-training (Scudder, 1965), a simple and classic semi-supervised technique, can be applied for data augmentation. It consists of three main steps: (1) training an initial model with the existing labeled dataset, (2) using this model to generate pseudolabels for unlabeled data, and (3) finally incorporating these pseudo-labeled data into the labeled dataset. However, this method inevitably introduces low-quality pseudo-labels, where the label does not accurately match the given review. To
+
+overcome this issue, we implement a two-stage filtering process that leverages both the initial model and the pseudo-label scorer.
+
+Confidence-based Filtering. We first use the confidence of the initial model in the pseudo-label as the measure of its quality. Thus, we filter out those samples with minimum confidence below a certain threshold. Formally, we retain samples  $(x,y)$  satisfying
+
+$$
+\left[ \min  _ {t} p \left(y _ {t} \mid y _ {<   t}, x\right) \right] \geq \gamma_ {1}, \tag {7}
+$$
+
+where  $\gamma_{1}$  is a hyper-parameter and is empirically set to 0.7.
+
+Scorer-based Filtering. Next, we use the pseudolabel scorer to evaluate the remaining samples. We observe that pseudo-labels with low scores are consistently of poor quality. Besides, while samples with high scores generally exhibit good label quality, their sentences tend to be overly simple, offering limited helpfulness for subsequent model training. Therefore, we retain only those samples whose scores fall between thresholds  $\gamma_{2}$  and  $\gamma_{3}$ , which can be formulated as follows:
+
+$$
+\gamma_ {2} \leq s (x, y) \leq \gamma_ {3}. \tag {8}
+$$
+
+# 4.3 Pseudo-label Scorer as Reranker
+
+Reranking is originally a concept in information retrieval, referring to the process of rescoring and reranking preliminary candidate results. Ma et al. (2023) show that incorporating a reranking step can enhance performance in information extraction tasks. In this paper, we claim that our pseudo-label scorer can serve as such a reranker. Specifically, for a given review, we first utilize an ASQP model to generate four candidate labels via beam search and then select the best one from these candidates using our pseudo-label scorer. The selected candidate is utilized as the final output.
+
+# 5 Experiments
+
+# 5.1 Experiment Setup
+
+Datasets. We evaluate our approach on four public ASQP datasets. These datasets originate from the SemEval Challenges (Pontiki et al., 2015, 2016) and Amazon platform during 2017 and 2018. The quad-level annotations are provided by Cai et al. (2021) and Zhang et al. (2021a). Detailed statistics of these datasets are presented in Table 2. Besides,
+
+<table><tr><td rowspan="2">Datasets</td><td colspan="2">Train</td><td colspan="2">Dev</td><td colspan="2">Test</td></tr><tr><td>#S</td><td>#Q</td><td>#S</td><td>#Q</td><td>#S</td><td>#Q</td></tr><tr><td>ACOS-Laptop</td><td>2934</td><td>4172</td><td>326</td><td>440</td><td>816</td><td>1161</td></tr><tr><td>ACOS-Rest</td><td>1530</td><td>2484</td><td>171</td><td>261</td><td>583</td><td>916</td></tr><tr><td>ASQP-Rest15</td><td>834</td><td>1354</td><td>209</td><td>347</td><td>537</td><td>795</td></tr><tr><td>ASQP-Rest16</td><td>1264</td><td>1989</td><td>316</td><td>507</td><td>544</td><td>799</td></tr></table>
+
+Table 2: Statistics of four ASQP datasets (Cai et al., 2021; Zhang et al., 2021a). #S and #Q represent the number of sentences and quads.
+
+to train the pseudo-label scorer, we construct several comparison datasets, the statistics of which can be found in Table 1.
+
+Implementation Details. We utilize T5-large (Raffel et al., 2020) as the backbone for our pseudolabel scorer. During the training phase, we set both the batch size and the number of training epochs to 10. For other hyperparameters, including the learning rate and  $\alpha$ , we perform a simple hyperparameter search. Once the scorer is trained, we apply it to score and rank the pseudolabeled samples<sup>6</sup>. For datasets ACOS-Rest, ASQP-Rest15, and ASQP-Rest16, we retain samples with scores falling within the top  $10\%$  to  $40\%$ ; for the ACOS-Laptop dataset, this range is set from  $20\%$  to  $50\%$ . From these retained samples, we randomly select 10,000 samples and merge them with the original labeled dataset to form the augmented dataset. To reduce the impact of randomness, we run our approach five times and report the average results.
+
+Baselines. To validate the effectiveness of the proposed approach, we integrate it into two typical ASQP methods: GAS (Zhang et al., 2021b) and MUL (Hu et al., 2023b). We run these two methods on the augmented dataset and incorporate a reranking step during the inference phase to enhance the predictions. We also benchmark our approach against a range of other methods, including EXTRACT-CLASSIFY (Cai et al., 2021), PARAPHRASE (Zhang et al., 2021a), SEQ2PATH (Mao et al., 2022), DLO/ILO (Hu et al., 2022), LEGO ABSA (Gao et al., 2022), MVP (Gou et al., 2023), GENDA (Wang et al., 2023), and CHATGPT (few-shot) (Xu et al., 2023).
+
+<table><tr><td>Objectives</td><td>ACOS-Laptop</td><td>ACOS-Rest</td></tr><tr><td>Wang et al. (2021)</td><td>50.67</td><td>56.10</td></tr><tr><td>Mao et al. (2022)</td><td>64.34</td><td>72.00</td></tr><tr><td>Ours</td><td>67.74</td><td>78.50</td></tr></table>
+
+Table 3: Comparison results of the architecture for the pseudo-label scorer (accuracy, %). Wang et al. (2021) formalize label-scoring as a question-answering problem. Mao et al. (2022) append a discriminative matching token to the label.  
+
+<table><tr><td>Annotation Schemes</td><td>ACOS-Laptop</td><td>ACOS-Rest</td></tr><tr><td>NONE</td><td>60.53</td><td>74.10</td></tr><tr><td>HUMANN-1234</td><td>63.60</td><td>75.00</td></tr><tr><td>HUMANN-12345</td><td>64.60</td><td>76.60</td></tr><tr><td>HUMANN-12345*</td><td>67.74</td><td>78.50</td></tr><tr><td>AIANN-1234*</td><td>68.67</td><td>79.60</td></tr></table>
+
+# 5.2 Analysis of Pesudo-label Scorer
+
+Given the importance of the pseudo-label scorer in our framework, we first undertake an analysis of it, focusing on two key aspects: its model architecture and the training dataset.
+
+Model Architecture. We use the conditional likelihood the generative model assigns to a pseudolabel as its scoring metric. To examine the effectiveness of our approach, we conduct experiments on two human-annotated comparison datasets and benchmark our approach against previous methods (Wang et al., 2021; Mao et al., 2022). As Table 3 illustrates, previous methods, especially the question-answering method, perform poorly in the ASQP task. In contrast, our approach achieves a significant advantage, demonstrating its effectiveness.
+
+Comparison Dataset. We conduct experiments to compare different annotation schemes and list the results in Table 4. We have the following observa
+
+Table 4: Experimental results of annotating the comparison dataset (accuracy,  $\%$  ): (1) NONE denotes the approach where neither human nor AI annotations are used, and the pseudo-label with the highest model confidence is selected as the positive label; (2) HUMANN-1234 represents the annotation scheme where human annotators choose the best pseudo-label out of four; (3) HUMANN-12345 extends HUMANN-1234 by allowing human annotators to write an additional label when none of the four options are suitable; (4) AIANN-1234 mirrors HUMANN-1234, but with ChatGPT replacing human annotators; (5) methods with  $*$  indicate the training of the scorer using both the comparison dataset and the original ASQP dataset.  
+
+<table><tr><td rowspan="2">Datasets</td><td colspan="2">w/ P6</td><td colspan="2">w/o P6</td></tr><tr><td>Kappa</td><td>Accu</td><td>Kappa</td><td>Accu</td></tr><tr><td>ACOS-Laptop-Comp-AI</td><td>62.71</td><td>79.20</td><td>65.84</td><td>86.30</td></tr><tr><td>ACOS-Rest-Comp-AI</td><td>67.44</td><td>80.90</td><td>47.12</td><td>87.15</td></tr></table>
+
+Table 5: Consistency between AI- and human-annotated comparison Data (\%). P6 refers to samples with option 6 selected. We calculate the consistency both before and after removing these samples.
+
+![](images/587620823c8c18e6089081eabe3512bd80428935ce004ee77ffc98e0169e8497.jpg)
+
+![](images/3a7ee90f5f9c6afd099260bc626d44d0036d31de310b653b429715ec3d95d376.jpg)  
+Figure 2: Performance trends of comparison data with increasing data quantity (accuracy,  $\%$  ): (a) results on ACOS-Laptop; (b) results on ACOS-Rest.
+
+tions. (1) Utilizing humans or AI to annotate the comparison data is crucial, as their performance is noticeably superior to that without annotation. Particularly, allowing human annotators to write a label when no option is suitable can notably enhance performance. (2) Training the scorer with a combination of the comparison data and the original ASQP dataset is more effective than using the comparison data alone. (3) AI-annotated comparison data can achieve even better results than human-annotated comparison data.
+
+We conduct a further analysis of AI Annotation. Table 5 presents the consistency between AI- and human-annotated data. Although the consistency is not very high statistically, considering the subjective nature of this task, the quality of AI annotation is acceptable. Additionally, a significant advantage of AI annotation lies in its cost-effectiveness relative to human annotation, enabling the efficient acquisition of a large amount of annotated data.
+
+Figure 2 illustrates the performance trends of human- and AI-annotated data relative to their quantities. Although AI-annotated data exhibits
+
+<table><tr><td rowspan="2">Methods</td><td colspan="3">ACOS-Laptop</td><td colspan="3">ACOS-Rest</td><td colspan="3">ASQP-Rest15</td><td colspan="3">ASQP-Rest16</td></tr><tr><td>Pre</td><td>Rec</td><td>F1</td><td>Pre</td><td>Rec</td><td>F1</td><td>Pre</td><td>Rec</td><td>F1</td><td>Pre</td><td>Rec</td><td>F1</td></tr><tr><td>EXTRACT-CLASSIFY (Cai et al., 2021)</td><td>45.56</td><td>29.28</td><td>35.80</td><td>38.54</td><td>52.96</td><td>44.61</td><td>35.64</td><td>37.25</td><td>36.42</td><td>38.40</td><td>50.93</td><td>43.77</td></tr><tr><td>PARAPHRASE (Zhang et al., 2021a)</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>46.16</td><td>47.72</td><td>46.93</td><td>56.63</td><td>59.30</td><td>57.93</td></tr><tr><td>SEQ2PATH (Mao et al., 2022)</td><td>-</td><td>-</td><td>42.97</td><td>-</td><td>-</td><td>58.41</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>DLO (Hu et al., 2022)</td><td>43.40</td><td>43.80</td><td>43.60</td><td>60.02</td><td>59.84</td><td>59.18</td><td>47.08</td><td>49.33</td><td>48.18</td><td>57.92</td><td>61.80</td><td>59.79</td></tr><tr><td>ILO (Hu et al., 2022)</td><td>44.14</td><td>44.56</td><td>44.35</td><td>58.43</td><td>58.95</td><td>58.69</td><td>47.78</td><td>50.38</td><td>49.05</td><td>57.58</td><td>61.17</td><td>59.32</td></tr><tr><td>LEGO-ABSA (Gao et al., 2022)</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>45.80</td><td>-</td><td>-</td><td>57.70</td></tr><tr><td>MVP (Gou et al., 2023)</td><td>-</td><td>-</td><td>43.92</td><td>-</td><td>-</td><td>61.54</td><td>-</td><td>-</td><td>51.04</td><td>-</td><td>-</td><td>60.39</td></tr><tr><td>GENDA (Wang et al., 2023)</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>49.74</td><td>50.29</td><td>50.01</td><td>60.08</td><td>61.70</td><td>60.88</td></tr><tr><td>CHATGPT (few-shot) (Xu et al., 2023)</td><td>21.72</td><td>27.65</td><td>24.33</td><td>38.39</td><td>46.40</td><td>42.02</td><td>29.66</td><td>37.86</td><td>33.26</td><td>36.09</td><td>46.93</td><td>40.81</td></tr><tr><td>GAS (Zhang et al., 2021b)</td><td>43.46</td><td>42.69</td><td>43.07</td><td>59.81</td><td>57.51</td><td>58.63</td><td>47.15</td><td>46.01</td><td>46.57</td><td>57.30</td><td>57.82</td><td>57.55</td></tr><tr><td>+ ST</td><td>44.35</td><td>42.75</td><td>43.54</td><td>59.95</td><td>58.98</td><td>59.46</td><td>46.86</td><td>47.65</td><td>47.25</td><td>57.95</td><td>58.75</td><td>58.35</td></tr><tr><td>+ ST &amp; C-FILTER</td><td>45.14</td><td>44.00</td><td>44.56</td><td>60.57</td><td>58.82</td><td>59.67</td><td>49.04</td><td>47.77</td><td>48.40</td><td>59.18</td><td>59.72</td><td>59.45</td></tr><tr><td>+ ST &amp; CS-FILTER</td><td>46.23</td><td>44.41</td><td>45.30</td><td>63.41</td><td>60.00</td><td>61.66</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>+ ST &amp; CS-FILTER &amp; RERANK</td><td>46.76</td><td>45.00</td><td>45.86</td><td>64.66</td><td>61.33</td><td>62.95</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>+ ST &amp; CS-FILTER (AI)</td><td>46.44</td><td>44.01</td><td>45.19</td><td>62.69</td><td>60.24</td><td>61.44</td><td>50.92</td><td>49.86</td><td>50.38</td><td>60.87</td><td>61.30</td><td>61.08</td></tr><tr><td>+ ST &amp; CS-FILTER &amp; RERANK (AI)</td><td>47.00</td><td>45.05</td><td>46.01</td><td>63.74</td><td>61.25</td><td>62.47</td><td>51.59</td><td>51.90</td><td>51.74</td><td>62.55</td><td>64.31</td><td>63.51</td></tr><tr><td>MUL (Hu et al., 2023b)</td><td>44.38</td><td>43.65</td><td>44.01</td><td>61.22</td><td>59.87</td><td>60.53</td><td>49.12</td><td>50.39</td><td>49.75</td><td>59.24</td><td>61.75</td><td>60.47</td></tr><tr><td>MUL (Our Reproduction)</td><td>42.79</td><td>41.95</td><td>42.45</td><td>61.22</td><td>59.80</td><td>60.50</td><td>48.28</td><td>49.74</td><td>48.99</td><td>58.42</td><td>60.68</td><td>59.52</td></tr><tr><td>+ ST</td><td>43.38</td><td>42.98</td><td>43.23</td><td>61.17</td><td>59.89</td><td>60.67</td><td>47.94</td><td>49.21</td><td>48.57</td><td>57.45</td><td>59.37</td><td>58.39</td></tr><tr><td>+ ST &amp; C-FILTER</td><td>44.59</td><td>43.67</td><td>44.13</td><td>62.11</td><td>60.20</td><td>61.14</td><td>48.74</td><td>49.06</td><td>48.90</td><td>59.44</td><td>61.07</td><td>60.25</td></tr><tr><td>+ ST &amp; CS-FILTER</td><td>44.67</td><td>43.72</td><td>44.19</td><td>63.57</td><td>60.67</td><td>62.09</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>+ ST &amp; CS-FILTER &amp; RERANK</td><td>46.88</td><td>44.74</td><td>45.78</td><td>66.18</td><td>61.75</td><td>63.89</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>+ ST &amp; CS-FILTER (AI)</td><td>44.89</td><td>44.07</td><td>44.47</td><td>64.28</td><td>61.31</td><td>62.76</td><td>50.78</td><td>51.17</td><td>50.97</td><td>61.39</td><td>62.68</td><td>62.03</td></tr><tr><td>+ ST &amp; CS-FILTER &amp; RERANK (AI)</td><td>47.05</td><td>45.32</td><td>46.17</td><td>65.43</td><td>61.92</td><td>63.63</td><td>51.94</td><td>52.00</td><td>51.97</td><td>63.46</td><td>64.31</td><td>63.88</td></tr></table>
+
+Table 6: Experimental results on four ASQP datasets (\%). C-FILTER indicates the application of confidence-based filtering. CS-FILTER represents the integration of confidence-based and scorer-based filtering. Methods marked with AI indicate that the pseudo-label scorer used is trained on AI-annotated comparison data.
+
+lower performance at the same quantity, the scalability of AI annotation allows it to catch up and potentially exceed human-annotated data's performance when using more data. For instance, more than 2,000 AI-annotated samples can equal or outperform 1,000 human-annotated samples. Consequently, we can conclude that for the ASQP task, it is feasible to replace humans with AI to annotate the comparison data.
+
+# 5.3 Analysis of Self-Training
+
+Main Results. We develop a self-training framework using the pseudo-label scorer, with the experimental results presented in Table 6. According to these results, our approach substantially and consistently improves the performance of existing ASQP methods (Zhang et al., 2021b; Hu et al., 2023b). Specifically, GAS achieves  $F_{1}$ -score improvements of  $2.94\%$ ,  $4.32\%$ ,  $5.17\%$ , and  $5.96\%$  across the four datasets, averaging at  $4.60\%$ ; MUL achieves  $F_{1}$ -score improvements of  $3.72\%$ ,  $3.39\%$ ,  $2.98\%$ , and  $4.36\%$  across these datasets, averaging at  $3.61\%$ . Upon integrating our approach, both GAS and MUL outperform previous methods. These results
+
+demonstrate the effectiveness of our approach.
+
+Furthermore, we have the following observations. (1) The two-stage filtering process, namely CS-FILTER, greatly enhances the effectiveness of self-training. In most datasets, it results in over  $2\%$  improvement compared to self-training alone, highlighting the importance of data filtering in the self-training framework. (2) Incorporating a rerank step can further improve performance, by around  $1\%$ . (3) Using AI-annotated data in downstream self-training can attain results comparable to those using human-annotated data. This further indicates the feasibility of replacing human annotators with AI for comparison data annotation. (4) ChatGPT performs poorly on the ASQP task, suggesting that using it directly for this task does not fully leverage its capabilities. Conversely, using it for comparison data annotation effectively exploits its strengths. (5) It can be noted that our filtering strategy offers relatively limited improvements on ACOS-Laptop. We attribute this to potential inconsistency between its ASQP annotations and our comparison annotations. A more detailed discussion is available in Further Analysis.
+
+![](images/25aa85c5c91ea323887aa0859b27a988ce9d8712a6c2e162858262143b395804.jpg)  
+Figure 3: Performance of GAS on the augmented dataset under different match scores  $(F_{1}$  -score,  $\%$
+
+![](images/9492c90cfcf689ea4f5bfe9a1484c6f15c8ba1d39d53991b9bff08cc811a2f68.jpg)
+
+Effect of Match Score. Our approach relies on the match scores output by the pseudo-label scorer for data filtering. We conduct experiments to examine the impact of these scores on self-training performance. Figure 3 illustrates that the performance incrementally increases with increasing match scores. Nevertheless, beyond a certain threshold, further increases in match scores lead to a decline in performance. This phenomenon confirms our hypothesis that samples with too low scores suffer from poor label quality, adversely affecting model learning, and samples with too high scores tend to be overly simple, providing limited helpfulness for subsequent model training.
+
+Effect of Data Quantity. The quantity of pseudolabeled samples is another important factor in the effectiveness of self-training. We conduct experiments to analyze its impact. As illustrated in Figure 4, there is an overall upward trend in performance with increased data quantity. Notably, this trend is more stable and pronounced following two-stage filtering, underscoring the necessity of data filtering. Furthermore, we notice a decrease in self-training performance when the number of augmented samples exceeds 20,000. This suggests that there is a limit to improving performance by simply increasing data quantity. Balancing diversity and label quality to enhance the effectiveness of self-training warrants further exploration in subsequent research.
+
+# 5.4 Further Analysis
+
+Comparison Data as Additional Labeled Data. One feasible approach for utilizing comparison data is to treat each sample along with its positive label as an additional labeled ASQP sample. We analyze the effectiveness of this approach, and
+
+![](images/f060f512b6f23c39ccee420b2489a817973ab57aef06354a27201797b9074380.jpg)  
+(a) Performance on ACOS-Laptop
+
+![](images/7bb5a5708483d1ca47232f90964235a7ad1e8713d711bbe549834ba2f01fd221.jpg)  
+(b) Performance on ACOS-Rest
+
+![](images/0f234a8e725f6408abf49f522c49e7f479c0a2800b6e18d9bf236d8c5b7c19ab.jpg)  
+(c) Performance on ASQP-Rest15
+
+![](images/78e91bec27db8809908ea23d4b3cc0e7622112df424dd7b5387324db971f8439.jpg)  
+(d) Performance on ASQP-Rest16  
+Figure 4: Performance of GAS under different numbers of augmented samples  $(F_{1}$  -score,  $\%$
+
+the results in Table 7 reveal: (1) this approach can improve performance, with human-annotated comparison data outperforming AI-annotated data; (2) under conditions of equal data volume, it is superior to self-training without data filtering, indicating that the quality of comparison data is better than that of pseudo-labeled data; and (3) however, it falls significantly short of self-training with data filtering. These findings suggest that utilizing comparison data to train a pseudo-label scorer is more effective than simply treating it as additional labeled data.
+
+Pseudo-label Scorer as the ASQP Model. The pseudo-label scorer is architecturally a generative model and can potentially be used as an ASQP
+
+<table><tr><td>Methods</td><td>Laptop</td><td>Rest</td><td>Rest15</td><td>Rest16</td><td>Avg</td></tr><tr><td>GAS</td><td>43.07</td><td>58.63</td><td>46.57</td><td>57.55</td><td>-</td></tr><tr><td>+ ST &amp; C-FILTER (1k)</td><td>43.16</td><td>59.10</td><td>47.45</td><td>59.48</td><td>+0.84</td></tr><tr><td>+ ST &amp; C-FILTER (2k)</td><td>43.66</td><td>59.03</td><td>47.24</td><td>58.33</td><td>+0.61</td></tr><tr><td>+ ST &amp; C-FILTER (10k)</td><td>44.56</td><td>59.67</td><td>48.40</td><td>59.45</td><td>+1.57</td></tr><tr><td>+ ST &amp; CS-FILTER (10k)</td><td>45.30</td><td>61.66</td><td>50.38</td><td>61.08</td><td>+3.15</td></tr><tr><td>+ COMPDATA (1k)</td><td>43.51</td><td>60.20</td><td>-</td><td>-</td><td>-</td></tr><tr><td>+ COMPDATA (2K, AI)</td><td>42.99</td><td>59.77</td><td>48.15</td><td>59.73</td><td>+1.20</td></tr></table>
+
+Table 7: Experimental results of using comparison data as additional labeled data  $\left( {{F}_{1}\text{-scorer},\% }\right)$  . The human- and AI-annotated comparison datasets contain about 1,000 and 2,000 samples,respectively.  
+
+<table><tr><td>Methods</td><td>Laptop</td><td>Rest</td><td>Rest15</td><td>Rest16</td></tr><tr><td>GAS</td><td>43.07</td><td>58.63</td><td>46.57</td><td>57.55</td></tr><tr><td>+ Our Approach</td><td>45.86</td><td>62.95</td><td>-</td><td>-</td></tr><tr><td>+ Our Approach (AI)</td><td>46.01</td><td>62.47</td><td>51.74</td><td>63.51</td></tr><tr><td>PSEUDO-LABEL SCORER</td><td>43.93</td><td>60.66</td><td>-</td><td>-</td></tr><tr><td>PSEUDO-LABEL SCORER (AI)</td><td>44.06</td><td>60.00</td><td>51.59</td><td>61.49</td></tr></table>
+
+model. We evaluate this possibility and list the results in Table 8. A surprising finding is that directly using the scorer to predict quads achieves good performance, though it generally falls short of using it for filtering and ranking. This suggests that, besides training the scorer, leveraging comparison data to enhance the ASQP model is a promising direction, deserving of in-depth investigation in future research.
+
+Assessing Label Quality in ASQP Data. Beyond assessing pseudo-labeled data, our scorer can assess the quality of existing ASQP data. We conduct a statistical analysis of match scores for ASQP samples and list the results in Table 9. Our analysis reveals relatively low match scores for the ACOS-laptop dataset, suggesting either poor annotation quality or low consistency with our comparison data. We manually review 100 samples with match scores low 0.1 and find that  $73\%$  of the data contradicts the annotation guidelines, including  $44\%$  with errors in aspect category annotations,  $8\%$  in aspect or opinion term annotations, and  $6\%$  in sentiment annotations. Moreover, we experiment with removing samples with low match scores. The results presented in Table 10 show that this removal not only preserves model performance but enhances it. These findings indicate that our scorer is an effective tool for assessing label quality in existing datasets and that the removal of
+
+Table 8: Experimental results of using pseudo-label scorer as the ASQP model  $\left( {{F}_{1}\text{-scorer,}\% }\right)$  .  
+
+<table><tr><td></td><td>Laptop</td><td>Rest</td><td>Rest15</td><td>Rest16</td></tr><tr><td>&lt; 0.1</td><td>19.12%</td><td>3.92%</td><td>3.24%</td><td>1.50%</td></tr><tr><td>&lt; 0.3</td><td>30.30%</td><td>7.32%</td><td>5.52%</td><td>2.37%</td></tr><tr><td>&lt; 0.5</td><td>40.52%</td><td>10.46%</td><td>7.07%</td><td>3.56%</td></tr><tr><td>&lt; 0.7</td><td>52.56%</td><td>14.58%</td><td>9.59%</td><td>5.46%</td></tr><tr><td>&lt; 0.9</td><td>70.25%</td><td>25.88%</td><td>15.83%</td><td>9.43%</td></tr></table>
+
+Table 9: Statistics of match scores in the ASQP training datasets.  
+
+<table><tr><td>Ratio of Removal</td><td>Laptop</td><td>Rest</td><td>Rest15</td><td>Rest16</td><td>Avg</td></tr><tr><td>0%</td><td>43.07</td><td>58.63</td><td>46.57</td><td>57.55</td><td>-</td></tr><tr><td>2%</td><td>43.38</td><td>59.44</td><td>47.20</td><td>58.27</td><td>+0.62</td></tr><tr><td>4%</td><td>43.50</td><td>59.51</td><td>48.09</td><td>59.10</td><td>+1.10</td></tr><tr><td>6%</td><td>43.89</td><td>59.24</td><td>46.78</td><td>58.25</td><td>+0.59</td></tr><tr><td>8%</td><td>43.42</td><td>59.38</td><td>46.68</td><td>58.43</td><td>+0.52</td></tr><tr><td>10%</td><td>44.25</td><td>59.09</td><td>46.57</td><td>59.20</td><td>+0.82</td></tr></table>
+
+Table 10: Performance after removing samples with low match scores in the training set  $\left( {{F}_{1}\text{-scorer,}\% }\right)$  .
+
+low-quality samples is advantageous.
+
+Analysis of Reranking. We present the analysis of the reranking step in Appendix C.
+
+# 6 Conclusions
+
+In this paper, we introduce a pseudo-label scorer for the Aspect Sentiment Quad Prediction (ASQP) task to reduce mismatches in data augmentation. We propose that the effectiveness and reliability of this scorer hinge on two critical aspects: the quality of the training dataset and its model architecture. To this end, we create both human- and AI-annotated comparison datasets and propose a scoring method based on a generative model. Upon developing this scorer, we apply it to data filtering in a self-training framework and further employ it as a reranker to enhance ASQP models. Detailed experiments and analysis demonstrate the effectiveness of our comparison datasets and the proposed architecture. Furthermore, experimental results on four public ASQP datasets reveal that our scorer significantly and consistently improves the performance of existing methods.
+
+# Acknowledgements
+
+We thank the anonymous reviewers for their valuable suggestions to improve the quality of this work. We also thank Qianlong Wang for the enlightening discussions that significantly contributed to this work. This work was partially supported by the National Natural Science Foundation of China 62176076, Natural Science Foundation of Guangdong 2023A1515012922, the Shenzhen Foundational Research Funding JCYJ20220818102415032, the Major Key Project of PCL2021A06, and Guangdong Provincial Key Laboratory of Novel Security Intelligence Technologies 2022B1212010005.
+
+# Limitations
+
+While our approach significantly enhances the effectiveness of data augmentation and improves the performance of existing ASQP models, it also suffers from the following limitations:
+
+- Data augmentation generally comprises two pivotal components: data synthesis and quality control. While this paper focuses primarily on the latter, the former is equally vital for the success of data augmentation. Given that models trained on limited labeled data may underperform in certain categories or contexts, targeted data synthesis can mitigate these issues. A comprehensive exploration of both data synthesis and quality control is essential for developing an effective and robust data augmentation framework.  
+- The implementation of our approach necessitates manually annotated comparison data. Although we could use large language models to replace human annotators, crafting and refining prompts still demands meticulous human expertise and is notably time-intensive.
+
+We argue that these limitations offer promising directions for future research.
+
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+
+# A Details of AI Annotation
+
+We employ ChatGPT<sup>7</sup> to replace humans for comparison data annotation. The prompt is depicted in Figure 5. We continuously refine the guidelines and demonstrations in the prompt based on the annotation results. Furthermore, to further enhance annotation quality, we adopt three strategies:
+
+- Self-consistency: For each sample, we input it into ChatGPT twice. We keep the sample if the results are consistent.  
+- Self-assessment: We require ChatGPT to evaluate its confidence level on a scale from 1 to 5 after each judgment. We retain only those samples with a confidence level is 5.
+
+Task: Analyze a restaurant review and select the most suitable pseudo-label from the provided options (only codename required). If the review is unrelated to the restaurant (e.g., about beauty salon, medical, repair, or hotel), select 'Irrelevant Domain'. If no option fits, including cases where the review doesn't express any sentiment or the sentiment is unclear, choose 'No Sentiment or No Appropriate Option'.
+
+# Understand the Pseudo-label Components:
+
+- Aspect Category: Consists of an entity label and attribute label, with possible values like {category space}.  
+- Sentiment Polarity: Indicates the sentiment as positive, negative, or neutral. Neutral is used for mild sentiments and doesn't mean objectivity (e.g. "Food was okay, nothing great").  
+- Aspect Term: The explicit reference in the review to the aspect category, like a named entity, a common noun, or a multi-word term. When an entity is only implicitly referred to (e.g., through pronouns) or inferred in a sentence, it's assigned the value 'NULL'.  
+- Opinion Term: The words or phrases expressing sentiments. If the review implies sentiment without explicit words, it's marked as 'NULL'.
+
+# Key Points to Remember:
+
+1. First, check if the review is relevant and expresses any sentiment.  
+{other guidelines}
+
+# Examples for Reference:
+
+{demonstration examples}
+
+# Your Task:
+
+1. Review: "There was only 1 time that food came in under a half hour."
+
+Pseudo-label options:
+
+A.{SERVICE#GENERAL, negative,"NULL", "NULL"}  
+B.{FOOD#STYLE_OPTIONS, negative, "food", "NULL"}  
+C.{SERVICE#GENERAL,neutral,"NULL","NULL"}  
+D.{FOOD#STYLE_OPTIONS,neutral,"food","NULL"}
+
+Provide your answer as: {"1. Rationale": "Your detailed rationale", "1. Best Choice": "Your choice", "1. Confidence": "Your confidence (1-5)"}
+
+Figure 5: Prompt for AI Annotation in ACOS-Rest.
+
+- Rationale augmentation: We instruct ChatGPT to provide reasoning and explanation before making its judgment.
+
+Additionally, to reduce annotation costs, we integrate four samples into one prompt and annotate them at once.
+
+# B Ranking Objectives for Training Scorer
+
+We optimize the pseudo-label scorer on the annotated comparison dataset and explore three ranking-based training objectives: pointwise, pairwise, and listwise approaches. The pointwise approach classifies positive and negative samples separately and
+
+can be formulated as follows:
+
+$$
+\begin{array}{l} \mathcal {L} _ {\text {P O I N T}} = - \log p (y _ {p} | x) \\ - \sum_ {y _ {n}} \log (1 - p \left(y _ {n} | x\right)), \tag {9} \\ \end{array}
+$$
+
+where  $y_{p}$  denotes the positive label, and  $y_{n}$  denotes the negative label. The pairwise approach focuses on the relative quality of labels. We implement two pairwise training objectives, detailed as follows:
+
+$$
+\mathcal {L} _ {\mathrm {P A I R 1}} = - \sum_ {y _ {n}} \log \sigma \left[ \beta \log \frac {p \left(y _ {p} \mid x\right)}{p \left(y _ {n} \mid x\right)} \right], \tag {10}
+$$
+
+$$
+\mathcal {L} _ {\text {P A I R 2}} = \sum_ {y _ {n}} \max  \left(0, p \left(y _ {n} \mid x\right) - p \left(y _ {p} \mid x\right)\right), \tag {11}
+$$
+
+where  $\beta$  is a hyper-parameter. Lastly, the listwise approach optimizes the ranking of the entire list. We design a simple listwise training objective, as outlined in Equation 2.
+
+# B.1 Experiment Results
+
+<table><tr><td>Objectives</td><td>ACOS-Laptop</td><td>ACOS-Rest</td></tr><tr><td>Pointwise</td><td>67.93</td><td>77.80</td></tr><tr><td>Pairwise1</td><td>67.13</td><td>77.00</td></tr><tr><td>Pairwise2</td><td>66.87</td><td>77.40</td></tr><tr><td>Listwise</td><td>67.74</td><td>78.50</td></tr></table>
+
+Experimental results in Table 11 reveal that pointwise and listwise objectives outperform two pairwise objectives, with the listwise objective being slightly better overall. Consequently, we adopt the listwise objective as the default training objective.
+
+# C Analysis of Reranking
+
+Table 11: Comparison results of four ranking-based objectives (accuracy, %).  
+
+<table><tr><td></td><td>Laptop</td><td>Rest</td><td>Rest15</td><td>Rest16</td><td>Avg</td></tr><tr><td>ST-CS</td><td>45.30</td><td>61.66</td><td>50.38</td><td>61.08</td><td>54.61</td></tr><tr><td>ST-CS &amp; RERANK</td><td>45.86</td><td>62.95</td><td>51.74</td><td>63.51</td><td>+1.41</td></tr><tr><td>ST-CS &amp; RERANK‡</td><td>63.22</td><td>75.63</td><td>66.27</td><td>76.29</td><td>+15.75</td></tr></table>
+
+We apply our pseudo-label scorer as a reranker to rescore the candidate labels generated by the ASQP model, selecting the highest-scoring one as the final result. Table 12 shows that this reranking step
+
+significantly improves performance on the ASQP task, resulting in an average  $F_{1}$  improvement of  $1.41\%$ . Additionally, if we consider a hypothetical perfect reranker that always selects the optimal candidate, Table 12 shows that the performance gain could reach up to  $15.75\%$ . This significant potential boost underscores the value of further exploring the reranking step.
+
+Table 12: Experimental results of reranking  $\left( {{F}_{1}\text{-score,}}\right.$  %). ST-CS denotes self-training with confidence- and scorer-based filtering.  $\downarrow$  indicates the performance achieved using a perfect reranker.  
+
+<table><tr><td></td><td>Laptop</td><td>Rest</td><td>Rest15</td><td>Rest16</td></tr><tr><td colspan="5">Best Candidates</td></tr><tr><td>1-st</td><td>67.70%</td><td>69.37%</td><td>61.15%</td><td>65.11%</td></tr><tr><td>2-nd</td><td>13.77%</td><td>15.44%</td><td>17.17%</td><td>16.29%</td></tr><tr><td>3-rd</td><td>10.44%</td><td>8.64%</td><td>13.48%</td><td>11.14%</td></tr><tr><td>4-th</td><td>8.09%</td><td>6.55%</td><td>8.19%</td><td>7.46%</td></tr><tr><td colspan="5">Scorer&#x27;s Preferred Choices</td></tr><tr><td>1-st</td><td>67.62%</td><td>75.09%</td><td>66.48%</td><td>74.08%</td></tr><tr><td>2-nd</td><td>17.84%</td><td>14.03%</td><td>17.77%</td><td>15.34%</td></tr><tr><td>3-rd</td><td>8.63%</td><td>6.79%</td><td>9.20%</td><td>6.70%</td></tr><tr><td>4-th</td><td>5.91%</td><td>4.08%</td><td>6.55%</td><td>5.18%</td></tr></table>
+
+Table 13: Proportions of the best and preferred candidate labels selected by the reranker.
+
+Furthermore, we rank the four candidate labels obtained via beam search according to their confidence and then analyze the distribution of the best labels and those preferred by our scorer. As illustrated in Table 13, in fewer than  $70\%$  of cases, the candidate label with the highest confidence is considered the best. In comparison, our scorer tends to favor candidates with higher confidence, highlighting areas for further improvement in this reranking step.

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