Add Batch 483dcb5d-2630-4bdd-b609-9e7181dbd4e5 data

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@@ -4073,3 +4073,67 @@ saved_model/**/* filter=lfs diff=lfs merge=lfs -text
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2024/COLLIE_ Systematic Construction of Constrained Text Generation Tasks/a385f7c5-58d0-4428-b174-3123a2838efe_content_list.json

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+        "text": "COLLIE: SYSTEMATIC CONSTRUCTION OF CONSTRAINED TEXT GENERATION TASKS",
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+        "text": "Shunyu Yao* Howard Chen* Austin W. Hanjie* Runzhe Yang* Karthik Narasimhan",
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+        "text": "Department of Computer Science, Princeton University",
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+        "type": "text",
+        "text": "{shunyuy, hc22, hjwang, runzhey, karthikn}@princeton.edu",
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+        "text": "ABSTRACT",
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+        "text": "With the rapid improvement of large language models capabilities, there has been increasing interest in challenging constrained text generation problems. However, existing benchmarks for constrained generation usually focus on fixed constraint types (e.g. generate a sentence containing certain words) that have proved to be easy for state-of-the-art models like GPT-4. We present COLLIE, a grammar-based framework that allows the specification of rich, compositional constraints with diverse generation levels (word, sentence, paragraph, passage) and modeling challenges (e.g. language understanding, logical reasoning, counting, semantic planning). We also develop tools for automatic extraction of task instances given a constraint structure and a raw text corpus. Using COLLIE, we compile the COLLIEv1 dataset with 2,080 instances comprising 13 constraint structures. We perform systematic experiments across five state-of-the-art instruction-tuned language models and analyze their performances to reveal shortcomings. COLLIE is designed to be extensible and lightweight, and we hope the community finds it useful to develop more complex constraints and evaluations in the future.",
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+        "text": "1 INTRODUCTION",
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+        "text": "Large language models (LLMs) are increasingly capable of generating coherent and fluent text when provided with high-level prompts (OpenAI 2023a). Such capabilities have raised the bar for automated text generation, allowing us to explore more nuanced ways of utilizing LMs. One such line of inquiry is constrained text generation, whereby the LM is asked to adhere to a particular topic (Keskar et al., 2019; Dathathri et al., 2020), or avoid using certain words (Lu et al., 2021; 2022). However, these works scratch the surface of a broader phenomenon — LMs do not just generate text, as evidenced by their use in more structured tasks like problem solving (Yao et al., 2022), code generation (Chen et al., 2022b) and even tool use through API calls (Schick et al., 2023).",
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+        "text": "This raises a natural question — 'what is the next iteration of text generation benchmarks that can evaluate these advanced capabilities in LLMs'? We posit that one direction is incorporating logical and compositional challenges via constrained text generation. Existing benchmarks for constrained generation, however, focus only on particular constraint types, require tailored pipelines to collect data and annotations, and/or can only evaluate a specific aspect of LM strengths (Lin et al., 2020; Chen et al., 2022a). They also suffer from challenges in scalable dataset construction.",
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+        "text": "In this paper, we propose COLLIE, a grammar-based framework that enables systematic construction of compositional constraints over diverse generation levels (e.g., words, sentences, paragraphs) and semantic requirements (e.g., language understanding, logical reasoning, counting). Operationally, COLLIE allows researchers to 1) easily specify constraint templates, and then automatically 2) extract constraint values from language corpora, 3) render them into natural language instructions, and 4) evaluate model generations against the constraint instructions.",
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+        "text": "Existing benchmarks for constrained generation focus only on particular constraint types and formats (e.g., \"generate a sentence with words...\"). These limitations mean that benchmarks become quickly obsolete as LLMs progress. In contrast, the modular and extensible design of COLLIE allows the",
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+        "type": "header",
+        "text": "Published as a conference paper at ICLR 2024",
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+        "type": "page_footnote",
+        "text": "*Equal contribution. Project site with code and data: https://collie-benchmark.github.io/Collie is a herding dog that can help guide domesticated animals like llamas and alpacas.",
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+    {
+        "type": "page_number",
+        "text": "1",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/ba2dd8c8fe7730e2a5c11bddb24304f879a9eb8165b6082d9cbac8f8b2496501.jpg",
+        "image_caption": [
+            "Figure 1: Our COLLIE framework for constraint structure specification, ground truth extraction, instruction rendering, and evaluation. First, the user specifies the constraint structure without a specific target value (expressed in  $*$ ). Second, the constraint structure is used to extract ground truth examples from text corpora that contain the target values. Third, the constraint structure and target values are rendered into a natural language instruction. Finally, the model's generation is evaluated against the constraint and the ground truth. The model (gpt-3.5-turbo) violates the constraints by exceeding word limits and leaving the word 'mankind' at the end instead of the specified position."
+        ],
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+        "type": "text",
+        "text": "broader NLP community to contribute additional constraints that can co-evolve with LLM capabilities over time, while also providing a convenient endpoint for users that only want to evaluate their model without developing their own constraints. The flexibility of such a grammar-based framework may not only be useful for evaluation, but also in practice (e.g. word constraints, words blacklist, etc.).",
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+        "text": "We construct the dataset COLLIE-v1 with 2,080 constraint instances across 13 different types, using three different corpora: Wikipedia (Foundation 2022), CC-News (Hamborg et al., 2017), and Project Gutenberg (Brooke et al., 2015). We perform zero-shot evaluations of five state-of-the-art LLMs of varying sizes including GPT-4 (OpenAI 2023a) and PaLM (Anil et al., 2023). While GPT-4 comparatively performs the best, it still achieves an average constraint satisfaction rate of only  $50.9\\%$ . We find that challenges correlate with position – for instance, instructing models to begin a sentence with a specific word leads to a  $100\\%$  success rate for GPT-4, while asking models to end a sentence with a particular word results in a success rate of  $40\\% -60\\%$ . These insights can help us diagnose LLMs, which in turn can improve LLM capabilities, and further advance the benchmark itself.",
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+        "text": "To summarize, we make the following contributions: (1) We introduce COLLIE, a framework for systematic generation of compositional constraints, that is flexible and extensible. (2) We use COLLIE to curate a new dataset COLLIE-v1 comprising of 13 constraint structures. (3) We perform a comprehensive evaluation of five state-of-the-art LLMs of varying sizes and provide useful insights for both model and benchmark development in the future.",
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+    {
+        "type": "text",
+        "text": "2 RELATED WORK",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Constrained text generation (CTG). Early work in controllable text generation used control codes to steer the generation towards desired topics or to reduce undesirable content, by controlling for broad attributes such as sentiment or toxicity (Hu et al., 2017; Keskar et al., 2019; Dathathri et al., 2020; Krause et al., 2021). Other work on constrained decoding provides to the language model a collection of lexical items as constraints to be included or excluded in the final generated text (Hokamp and Liu, 2017; Hasler et al., 2018; Dinu et al., 2019; Hu et al., 2019; Lin et al., 2020; Lu et al., 2021; Li et al., 2022b). Recent advances in instruction tuning LLMs (Ouyang et al., 2022) have brought major improvements to controllability. These advancements have made it challenging to use existing controllable generation datasets to fully assess the capabilities of modern LLMs. InstructCTG (Zhou et al., 2023) is a concurrent work that also constructed a dataset with text constraints. However, it mainly focuses on synthesizing 5 types of simple CTG instructions for tuning small language models such as T5-11B (Raffel et al., 2020), whereas COLLIE serves to construct much more challenging and open-ended CTG tasks to evaluate and diagnose start-of-the-art LLMs like GPT-4 (OpenAI, 2023b). Lastly, there is a line of work that sets up CTG in more practical downstream applications, such as controllable summarization (Zhang et al., 2023). The flexibility of COLLIE allows these \"functional constraints\" to be incorporated for more usefulness, which we leave for future work.",
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+    {
+        "type": "header",
+        "text": "Published as a conference paper at ICLR 2024",
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+    },
+    {
+        "type": "page_number",
+        "text": "2",
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+    {
+        "type": "text",
+        "text": "Grammar-based compositional tests. Building benchmarks with data synthesized from grammars has been explored previously in the context of question answering (Weston et al., 2015), instruction following (Chevalier-Boisvert et al., 2019; Ruis et al., 2020)) and visual reasoning (Johnson et al., 2017). These benchmarks showcased the utility of grammars to systematically generate a comprehensive set of test cases or to specify some fixed constraints. In contrast, COLLIE aims to enable flexible, and dynamic constraint construction that can co-evolve with models. Furthermore, previous datasets were synthetic with limited linguistic diversity and practical applicability to real-world scenarios. In contrast, since our COLLIE framework extracts values and examples from natural language corpora to construct the constraints, it represents a more realistic challenge for modern LLMs.",
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+    {
+        "type": "text",
+        "text": "Systematic and scalable language benchmarks. The emergence of increasingly powerful general-purpose language models has created a need for scalable benchmarks that can systematically and comprehensively evaluate them. A few recent examples include HELM (Liang et al., 2022), BIG-Bench (Srivastava et al., 2022), MMLU (Hendrycks et al., 2020), TaskBench500 (Li et al., 2022a), and Natural Instructions (Wang et al., 2022). However, building such benchmarks require considerable human effort, and may become obsolete when stronger models enter the arena. We provide a new perspective in this race between model capabilities and challenging benchmarks: leverage compositionality to construct automatic and scalable benchmarks with minimal human effort that can co-evolve with model capabilities to remain challenging and relevant.",
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+        "type": "text",
+        "text": "3 COLLIE FRAMEWORK TO CONSTRUCT CONSTRAINED TEXT GENERATION",
+        "text_level": 1,
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+        "type": "text",
+        "text": "COLLIE allows researchers to easily 1) specify textual constraint structures via a grammar, then automatically 2) extract constraint values from text corpora, 3) render constraints into natural language instructions, and 4) evaluate generations with respect to constraints.",
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+        "text": "Grammar. Two observations about text constraints motivate a grammar characterization: 1) they involve different levels of text, e.g. character, word, sentence, or paragraph; and 2) many of them specify either the count or position at a certain text level (existence is equivalent to count  $>0$ ).",
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+        "text": "Let capitalized letters  $(S,M,C,T)$  denote non-terminal variables, and other symbols  $(\\ell ,\\circ ,\\oplus ,v)$  denote terminals. A full constraint specification within our grammar  $S$  (Eq. 1) consists of two parts: a generation level  $(\\mathrm{level}(\\xi) = \\ell)$  specifying whether the generated text  $\\xi$  should be a word, a sentence, a paragraph, or a document, and a multi-constraint  $M$  (Eq. 2), which is a logical composition of one or more base-constraints  $C$ . A text  $T$  (Eq. 4) within these constraints can either be the full generated text  $\\xi$ , or a part of it when qualified with a pos( $\\cdot$ ). For example, pos(pos( $\\xi$ , paragraph, 3), sentence, -1) means \"the last sentence of the 3rd paragraph of the generated text\". For terminal variables, we define a level  $\\ell$  of a text (Eq. 5), a string or number relation  $\\circ$  or  $\\oplus$  (Eq. 6), and a string or number value  $v_{\\mathrm{str}}$  or  $v_{\\mathrm{num}}$  (Eq. 7).  $\\wedge$  represents the logical 'and' operator, and  $\\vee$  represents the logical 'or'. With these definitions, we construct the following grammar:",
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+        "text": "\n$$\nS \\rightarrow (\\text {l e v e l} (\\xi) = \\ell) \\wedge M \\quad (\\text {c o n s t r a i n t s p e c i f i c a t i o n}) \\tag {1}\n$$\n",
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+        "text": "\n$$\nM \\rightarrow C \\mid C \\wedge M \\mid C \\vee M \\quad (\\text {m u l t i - c o n s t r a i n t}) \\tag {2}\n$$\n",
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+        "text": "\n$$\nC \\rightarrow \\operatorname {c o u n t} (T, \\ell , v _ {\\mathrm {s t r}} \\mid \\ell^ {\\prime}) \\oplus v _ {\\mathrm {n u m}} \\mid \\operatorname {p o s} (T, \\ell , v _ {\\mathrm {n u m}}) \\circ v _ {\\mathrm {s t r}} \\quad (\\text {b a s e - c o n s t r a i n t}) \\tag {3}\n$$\n",
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+        "text": "\n$$\nT \\rightarrow \\xi \\mid \\operatorname {p o s} (T, \\ell , v _ {\\text {n u m}}) \\tag {4}\n$$\n",
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+        "type": "equation",
+        "text": "\n$$\n\\ell \\rightarrow \\text {c h a r} | \\text {w o r d} | \\text {s e n t e n c e} | \\text {p a r a g r a p h} | \\text {p a s s a g e} \\tag {5}\n$$\n",
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+        "text": "\n$$\n\\circ \\rightarrow = | \\neq \\quad \\oplus \\rightarrow = | \\neq | > | <   | \\leq | \\geq \\tag {6}\n$$\n",
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+        "text": "\n$$\nv _ {\\mathrm {s t r}} \\in \\Sigma^ {*} \\quad v _ {\\mathrm {n u m}} \\in \\mathbb {Z} \\tag {7}\n$$\n",
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+        "text": "At the core of our grammar, we consider two (symmetrical) types of base-constraints  $C$  (Eq. 3):",
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+        "list_items": [
+            "1. Count constraints. count  $(T,\\ell ,v_{\\mathrm{str}})\\oplus v_{\\mathrm{num}}$  constrains the occurrences of a particular level-  $\\ell$  string  $v_{\\mathrm{str}}$ . For example, count  $(T,$  word, happy')  $\\leq 3$  means \"T should contain the word happy' no more than 3 times\". In contrast, count  $(T,\\ell ,\\ell^{\\prime})\\oplus v_{\\mathrm{num}}$  constrains the occurrences of level-  $\\ell$  strings in each level-  $\\ell^{\\prime}$  unit of text T. For example, count  $(T,$  char, sentence)  $= 50$  means \"each sentence of text T should have exactly 50 characters\".",
+            "2. Position constraints.  $\\text{pos}(T, \\ell, v_{\\text{num}}) \\circ v_{\\text{str}}$  specifies that a particular part of the text  $T$  should equal (or not equal) the given string  $v_{\\text{str}}$ . For example,  $\\text{pos}(T, \\text{word}, 3) = \\text{'happy'}$  means \"the 3rd word should be 'happy' in text  $T$ \". We also allow negative indices for reverse counting, e.g.  $\\text{pos}(T, \\text{char}, -1) \\neq x$  means \"the last letter should not be 'x' in text  $T$ \"."
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+    {
+        "type": "header",
+        "text": "Published as a conference paper at ICLR 2024",
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+        "page_idx": 2
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+    {
+        "type": "page_number",
+        "text": "3",
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+    {
+        "type": "text",
+        "text": "Note that the grammar above can easily be extended to accommodate more types of base-constraints (e.g. part of speech, sentiment) by implementing the corresponding semantic checks — we leave this to future work. Also for convenience, we use constraint structure to refer to a family of constraint specifications that only differ in their values (e.g. generate a sentence with exactly  $x$  words,  $x \\in \\mathbb{N}$ ), and constraint to refer to a particular constraint specification with concrete values (e.g. generate a sentence with exactly 5 words).",
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+    {
+        "type": "text",
+        "text": "Examples and conceptual challenges. Our grammar can express a wide range of constraints through logical compositions of base-constraints across different text levels. Table II illustrates some structures across generation levels, identified by names such as para01 for paragraph generation, etc.",
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+    {
+        "type": "text",
+        "text": "In addition to the generation levels, count and pos across different levels introduce a variety of challenges. For example, word01 and sent01 challenge token-based language models to count characters; pass01 requires high-level semantic planning for models to generate a coherent passage under constraints; sent04 and para02 challenge models to generate text with presence or absence of particular words; sent03, para03, and para04 require counting at multiple levels; and word02, word03, sent02, para05, and pass01 combine counting and positional challenges at different levels, which can be considered most demanding conceptually. We empirically assess the difficulty of constraint structures in Section 5. Example COLLIE usage is presented in Figure 2",
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+    {
+        "type": "code",
+        "sub_type": "code",
+        "code_caption": [],
+        "code_body": "from collieconstraints import ( Constraint, TargetLevel, Count, Relation   \n）   \nc  $=$  Constraint( target_level  $\\equiv$  TargetLevel('word'), transformation  $\\equiv$  Count(), relation  $\\equiv$  Relation('==')，   \n）   \ntext  $=$  'This is a good sentence.'   \nprint(c.check(text,5)) # True",
+        "guess_lang": "python",
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+    {
+        "type": "text",
+        "text": "Figure 2: Example COLLIE code for a simple number of words constraint.",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/e2ef9be83a2cd6b619270a5dd3406807cc0d31a107026703229f9c3c58029fda.jpg",
+        "table_caption": [
+            "Table 1: List of all constraint structures used in COLLIE-v1, with (simplified) example values."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>ID</td><td>Example instruction</td><td>Multi-constraint M</td></tr><tr><td>word01</td><td>Generate a word with at least 15 letters.</td><td>count(ξ, char, word) ≥ 15</td></tr><tr><td>word02</td><td>Generate a word with 10 letters, where letter 1 is &#x27;s&#x27;, letter 3 is &#x27;r&#x27;, letter 9 is &#x27;e&#x27;.</td><td>count(ξ, char, word) = 10 ∧ pos(ξ, char, 1) = &#x27;s&#x27; ∧ pos(ξ, char, 3) = &#x27;r&#x27; ∧ pos(ξ, char, 9) = &#x27;e&#x27;</td></tr><tr><td>word03</td><td>Generate a word with at most 10 letters and ends with &quot;r&quot;.</td><td>count(ξ, char, word) ≤ 10 ∧ pos(ξ, char, -1) = &#x27;r&#x27;</td></tr><tr><td>sent01</td><td>Please generate a sentence with exactly 82 characters. Include whitespace into your character count.</td><td>count(ξ, char, sentence) = 82</td></tr><tr><td>sent02</td><td>Generate a sentence with 10 words, where word 3 is &quot;soft&quot; and word 7 is &quot;beach&quot; and word 10 is &quot;math&quot;.</td><td>count(ξ, word, sentence) = 10 ∧ pos(ξ, word, 3) = &quot;soft&quot; ∧ pos(ξ, word, 7) = &quot;beach&quot; ∧ pos(ξ, word, 10) = &quot;math&quot;</td></tr><tr><td>sent03</td><td>Generate a sentence with at least 20 words, and each word less than six characters.</td><td>count(ξ, word, sentence) ≥ 20 ∧ count(ξ, char, word) ≤ 6</td></tr><tr><td>sent04</td><td>Generate a sentence but be sure to include the words &quot;soft&quot;, &quot;beach&quot; and &quot;math&quot;.</td><td>count(ξ, word, &#x27;soft&#x27;) &gt; 0 ∧ count(ξ, word, &#x27;beach&#x27;) &gt; 0 ∧ count(ξ, word, &#x27;math&#x27;) &gt; 0</td></tr><tr><td>para01</td><td>Generate a paragraph where each sentence begins with the word &quot;soft&quot;.</td><td>pos(pos(ξ, sentence, 1), word, 1) = &#x27;soft&#x27; ∧ pos(pos(ξ, sentence, 2), word, 1) = &#x27;soft&#x27; ∧ ...</td></tr><tr><td>para02</td><td>Generate a paragraph with at least 4 sentences, but do not use the words &quot;the&quot;, &quot;and&quot; or &quot;of&quot;.</td><td>count(ξ, sentence, paragraph) ≥ 4 ∧ count(ξ, word, &#x27;the&#x27;) = 0 ∧ count(ξ, word, &#x27;and&#x27;) = 0 ∧ count(ξ, word, &#x27;of&#x27;) = 0</td></tr><tr><td>para03</td><td>Generate a paragraph with exactly 4 sentences, each with between 10 and 15 words.</td><td>count(ξ, sentence, paragraph) = 4 ∧ count(ξ, word, sentence) ≥ 10 ∧ count(ξ, word, sentence) ≤ 15</td></tr><tr><td>para04</td><td>Generate a paragraph with at least 3 sentences, each with at least 15 words.</td><td>count(ξ, sentence, paragraph) ≥ 3 ∧ count(ξ, word, sentence) ≥ 15</td></tr><tr><td>para05</td><td>Generate a paragraph with 2 sentences that end in &quot;math&quot; and &quot;rock&quot; respectively.</td><td>count(ξ, sentence, paragraph) = 2 ∧ pos(pos(ξ, sentence, 1), word, -1) = &quot;math&quot; ∧ pos(pos(ξ, sentence, 2), word, -1) = &quot;rock&quot;</td></tr><tr><td>pass01</td><td>Generate a passage with 2 paragraphs, each ending in &quot;I sit.&quot; and &quot;I cry.&quot; respectively.</td><td>count(ξ, paragraph, passage) = 2 ∧ pos(pos(ξ, paragraph, 1), sentence, -1) = &quot;I sit.&quot; ∧ pos(pos(ξ, paragraph, 2), sentence, -1) = &quot;I cry.&quot;</td></tr></table>",
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+        "text": "Published as a conference paper at ICLR 2024",
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+        "text": "4",
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+        "type": "text",
+        "text": "In conjunction with the grammar, we develop a set of compiling tools to help construct datasets with minimal human efforts. Concretely, the pipeline of dataset construction involves 4 stages (Figure 1):",
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+        "list_items": [
+            "1. Specify constraint structures. Researchers can specify constraint structures (e.g. Table [1]), and optionally with a value range (e.g. \"generate a sentence with  $x$  words\", and  $5 \\leq x \\leq 10$ ). This is the only stage that involves manual effort.",
+            "2. Extract constraint values from corpora. We design an automatic extraction algorithm that runs through a given text corpus to find strings that fit a constraint structure with some value ranges. For example, given the constraint structure count( $\\xi$ , word,  $\\emptyset$ ) =  $x$  with value range  $5 \\leq x \\leq 10$ , the extraction algorithm returns sentences in the corpus that have 5-10 words, with associated word counts. This ensures each constraint has at least one natural solution. More details are in Section 4.1.",
+            "3. Render natural language instructions. Each constraint can be rendered into a natural language instruction (Table I) via ruled-based translation, thanks to the compositionality grammar of COLLIE. For example, a constraint count  $(\\xi ,\\mathrm{char},\\mathrm{'v'}) = 2\\land \\mathrm{count}(\\xi ,\\mathrm{char},\\mathrm{'i'}) = 3$  can be synthetically rendered into the instruction \"Please generate a word with exactly 2 character 'v' and exactly 3 character 'i'\". It is also possible to improve the instruction fluency or naturalness by adding additional rules to the synthetic translation, or use LLMs to polish instructions. More details are in Section A.1",
+            "4. Evaluate generations. Given text  $\\xi$  generated by a model, we use a parser to evaluate it against a constraint specification  $S$  and derive a True/False value, indicating if  $\\xi$  satisfies  $S$ . We use an average success rate as the main metric to evaluate constraint conformance. We can also compare the fluency of  $\\xi$  against the corpus-extracted \"groundtruth\" text, and render more fine-grained natural language feedback indicating which base-constraints are met and which not (see Section A.2)."
+        ],
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+    {
+        "type": "text",
+        "text": "4 COLLIE-V1 DATASET",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We construct COLLIE-v1 using constraints structures from Table [1], which contains 2,080 constraint instances from 13 constraint types, with 1,435 unique constraint prompts. The broader NLP community can contribute to future dataset releases by adding additional constraints, metrics, data sources. The curated constraint set can co-evolve with models to become more challenging and comprehensive as model capabilities improve.",
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+    {
+        "type": "text",
+        "text": "4.1 CONSTRAINT SPECIFICATION AND EXTRACTION",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Constraint specification. We begin by defining 13 constraint structures. We chose these 13 structures to span various generation levels (word, sentence, paragraph and passage generation) and challenges (counting, position). In total, we have 3 word-level, 4 sentence-level, 5 paragraph-level, and 1 passage-level constraint structures. Of these 13 constraint structures, 5 are single-level and the remaining 8 are multi-level constraints. See Table  $\\boxed{1}$  for the exact constraint structures we use.",
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+    {
+        "type": "text",
+        "text": "Constraint extraction. While constructing constraint structures is straightforward using our grammar, choosing constraint targets is challenging for two reasons: (1) Not all targets will admit a conforming natural language string. For instance, the constraint, \"Generate a two word sentence beginning with the word The.\" has no grammatically acceptable answer. (2) Even if a constraint admits a possible answer, it may not admit a plausible answer. For instance, \"Generate a sentence with 1928 words\" is possible, but any such sentence is very unlikely to appear in regular discourse.",
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+    {
+        "type": "text",
+        "text": "To address both challenges, we sample constraint target values from natural language corpora, which we denote as the data source. Given a constraint structure  $\\mathcal{C}$  and documents  $\\bar{\\mathcal{D}} = \\{d_1,\\dots,d_n\\}$ , we chunk each document into a series of strings  $d_{i} = \\{s_{1},\\ldots ,s_{m}\\}$ , where each  $s_i$  can be a sentence, paragraph, or passage as required by  $\\mathcal{C}$ . Each string  $s_i$  undergoes source-specific automated filtering and post-processing to remove artifacts, which we detail in Section B.4. Given  $\\mathcal{C}$  and  $s_i$ , we extract target values such that  $\\mathcal{C}$  is satisfied. In most cases, the satisfying target values can be directly extracted using our provided utilities. For example, for constraints with structure \"sentence with  $x$  words\", we can directly apply word tokenization and counting to the example string  $s_i$ . In cases in which direct extraction is not possible, (e.g. \"do not include word  $w$ \", we specify a range of possible targets (e.g.  $\\{\\text{the, and, of}\\}$ ) to sweep over. All in all, our approach ensures that (1) there exists a natural language string that can satisfy each constraint and target pair, and (2) the targets follow a",
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+        "type": "header",
+        "text": "Published as a conference paper at ICLR 2024",
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+        "text": "5",
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+        "img_path": "images/01ce8992ba7b73db65efdf9993dc1d61d35679af620de85fa810c35b9457cd50.jpg",
+        "image_caption": [
+            "Figure 3: Data statistics. (a) Number of constraints from each constraint structure. (b) Fraction of strings removed by automated filtering. (c) Length statistics for different levels for each data source."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "plausible distribution induced by natural language corpora. Our extraction system is extensible, and can operate on new constraints and data sources with minimal modifications.",
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+        "text": "Extensibility Adding additional data sources to the extraction pipeline is similarly easy, requiring a text delimiter, and optional string filtering and post-processing functions. As a case-study on the extensibility of COLLIE, we demonstrate how to extend constraints to include POS-tags such as \"Generate a sentence with verbs\". Details are in section B.5",
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+    {
+        "type": "text",
+        "text": "4.2 DATA SOURCES",
+        "text_level": 1,
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+        "type": "text",
+        "text": "To adequately cover diverse styles and content, we extract constraint targets from three distinct data sources: Wikipedia (Wiki) (Foundation 2022), Common Crawl News (CC-News) (Hamborg et al., 2017), and the Project Gutenberg Corpus (Guten) (Brooke et al., 2015). We provide an overview of these data sources below and leave source-specific filtering and post-processing details to Section B.4.",
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+        "type": "text",
+        "text": "Wiki. Wikipedia (Wiki) (Foundation, 2022) consists of over 6 million English Wikipedia articles. We included this data source for the diverse subject matter present in the corpus.",
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+        "text": "CC-News. The Common Crawl News corpus (CC-News) (Hamborg et al., 2017) consists of 708,241 English language news articles published between Jan 2017 and December 2019. We include CC-News to include interview dialogues, as well as popular culture and current events.",
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+        "text": "Gutenberg. The Project Gutenberg corpus (Gutenberg) (Brooke et al., 2015) consists of over 50,000 documents that include fiction, histories, biographies, and other works that are in the public domain in the United States. We include this corpus for its variety in genres (e.g. non-fiction, fiction, plays, etc.) and style from different time periods.",
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+    {
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+        "text": "4.3 DATA VALIDATION AND STATISTICS",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We extract constraints from 300 randomly sampled documents from each source. After extracting the target values, we sample up to 100 targets for each constraint structure on each data source. We remove any string targets by that begins or ends with any character that is not a letter or number. We randomly sample 5 out of these 100 targets and their supporting examples to qualitatively verify their validity. Since the extraction process is relatively fast, we modify filters and post-processors if there are systemic issues and re-run the extraction phase. We provide statistics of the final number of constraints from each constraint structure in Figure 3(a). Some constraints (e.g. number of sentences per paragraph) are tightly clustered around the mean, and thus do not induce many valid constraint targets. The fraction of strings filtered for each data source and level is presented in Figure 3(b). The automated filtering removes a large fraction of the strings in most cases, as high recall is important to ensure quality. The high fraction of omitted passages is due to the removal of passages  $< 2$  paragraphs in length. Mean lengths for each level and data source is presented in Figure 3(c).",
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+    {
+        "type": "header",
+        "text": "Published as a conference paper at ICLR 2024",
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+        "text": "6",
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+        "image_caption": [
+            "Figure 4: Model comparison. (a) Overall model performance summarized by weighted average across all constraint groups. (b) -(f) Constraint satisfaction rates of generated texts by GPT-4, GPT-3.5, PaLM, Vicuna-7B, and Alpaca-7B across various constraint groups. Error bars represent standard error. Constraint group names are in Table[1]. Sample sizes are reported in Figure[11]."
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+        "text": "5 RESULTS",
+        "text_level": 1,
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+        "text": "Our main experiments in this paper focus on a zero-shot prompting setup with the following language models (LMs): 1) larger and closed-source LMs such as OpenAI GPT (Brown et al., 2020; OpenAI, 2023b) (gpt-3.5-turbo, gpt-4) and Google PaLM-2 (Anil et al., 2023) (text-bison-001); 2) smaller and open-source LMs such as Alpaca-7B (Taori et al., 2023), Vicuna-7B (Chiang et al., 2023). We performed additional one-shot prompting and find GPT performances similar to zero-shot performance, see Section C.1 By default, we use a sampling temperature of 0.7, and sample multiple trials (20 for GPT/PaLM, 5 for Alpaca/Vicuna). All experiments were run in July, 2023.",
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+        "text": "Zero-shot performance comparison. As evidenced in Figures  $\\boxed{4}$  (a), GPT-4 consistently surpassed other models in zero-shot constrained text generation performances, achieving more than twice the constraint satisfaction rate than other non-GPT models. The overarching performance trend observed shows GPT-4 leading the pack, followed by GPT-3.5 and PaLM with a large gap, and then followed closely by the smaller models, Vicuna-7B and Alpaca-7B.",
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+        "type": "text",
+        "text": "Constraints all models can follow. Certain tasks, specifically word01 (generating a word with at least  $a$  letters), sent04 (generating a sentence containing words X, Y, Z), and para01 (generating a paragraph with each sentence starting with the word X), posed minimal challenge to the majority of contemporary language models. These tasks demonstrate the proficiency of current models at simple constraints ensuring existence, as depicted in Figure 9(f).",
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+        "type": "text",
+        "text": "Constraints partially solved by GPT-4 only. However, a notable distinction arose when tasks incorporated more counting/position constraints and requested longer generations. Tasks such as word03, para04, para05, and pass01 were only partially addressed by GPT-4, with constraint satisfaction rates ranging between  $40\\%$  and  $70\\%$ . Despite GPT-4's partial success in these tasks, other models failed to deliver any satisfactory performance.",
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+        "type": "text",
+        "text": "Constraints remaining very challenging. Furthermore, some tasks proved challenging across all models. Tasks word02, sent01, sent02, and para03 present challenges in terms of arbitrary position constraints and mixed counting levels (see Section 5.1 for detailed analysis), indicating areas that necessitate further advancements in language model technology. Moreover, the average pass@20 rate of GPT-4 was above  $63\\%$  across all constraints, significantly higher than the  $32\\%$  achieved by GPT-3.5, as depicted in Figure 5. Although GPT-4 demonstrated a significant performance advantage, its constraint satisfaction rate of  $63\\%$  is far from perfect. This suggests considerable scope for improvement in controllable text generation with language models. These findings underscore the opportunities and challenges in the continued evolution of language models.",
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+        "text": "Published as a conference paper at ICLR 2024",
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+        "image_caption": [
+            "Figure 5: Pass@k performance. We sample the model-generated text 20 times for all instruction prompts in the dataset. The curves represent the average pass rate across all instruction prompts up to  $k$  samples. The shaded areas indicate the standard errors."
+        ],
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+        "image_caption": [
+            "Figure 6: Position effect. Satisfaction rates of LMs on tasks involving pos( $\\xi$ , level, i). The tasks word02 and sent02 impose constraints on characters and words at arbitrary positions. The task para01 constrains the first word. The tasks word03, para05, and pass01 constrain the last characters, words, and sentences."
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+        "image_caption": [
+            "Figure 7: Counting level effect. Satisfaction rates for LMs on tasks involving count  $(\\xi, \\text{level}, \\varphi)$ . Task word01 sets a minimum word length of  $a$ . Task sent01 requires exactly  $a$  characters in a sentence. Task sent03 asks a sentence to contain at least  $b$  words, with each word no longer than  $a$  letters. Task para04 asks a paragraph to consist of at least  $b$  sentences, each containing a minimum of  $a$  words. Task para03 further imposes an upper limit on the number of words per sentence."
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+        "text": "5.1 ANALYSIS",
+        "text_level": 1,
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+        "text": "Performance consistency across data sources. We observe a high degree of consistency in the performance of models on a given constraint structure, regardless of the data source. This uniformity is evident across all models, as highlighted in Figure 9(g). This indicates that the ability of a language model to adhere to the logic of constraints takes precedence over the specific target values or the distribution of the data.",
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+        "type": "text",
+        "text": "Position effect. As depicted in Figure 6 the pos( $\\xi$ , level,  $i$ ) function, constraining the  $i$ -th sub-string (letter, word, or sentence), exhibits varying levels of difficulty depending on the value of  $i$ . Models generally perform well when the positional constraint is applied to the first sub-string ( $i = 1$ , task para01). However, only GPT-4 displays partial success with the last positional constraints ( $i = -1$ , tasks word03, para05, pass01). Notably, all models encounter difficulties when generating text that satisfies positional constraints at arbitrary positions  $i$ . Additionally, we find that the position effect exhibits a lower sensitivity to constraint levels.",
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+        "type": "text",
+        "text": "Counting level effect. Counting characters within a word is easier than within a sentence for models, as illustrated in Figure 7. Furthermore, tasks demanding exact equality (task sent01) prove more",
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+        "text": "Published as a conference paper at ICLR 2024",
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+            "(a) Constraint satisfaction rate -GPT-4 (4th round)"
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+        "image_caption": [
+            "Figure 8: GPT-4 interactive generation performance. (a) Constraint satisfaction rate of GPT-4 generated texts in the 4th round across various constraint groups. (b) GPT-4 overall performance in different feedback rounds. The 1st round is zero-shot, and the 2nd - 4th rounds are with feedback."
+        ],
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+    {
+        "type": "text",
+        "text": "challenging than those requiring a range (task para03), and are considerably more difficult than tasks specifying just an upper or lower bound (tasks word01, sent03, para04).",
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+        "type": "text",
+        "text": "Increased difficulty with logical composition. The incorporation of logical compositions into constraints considerably increases their difficulty. Task sent03 serves as an example of this, adding an extra constraint at the sentence level compared to task word01. Despite the assumption that the added constraint should be manageable for all models, performance on task sent03 uniformly trails behind that on task word01, as shown in Figure 7. This highlights the intricacy and challenge introduced by logical compositions within constraints.",
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+        "text": "Performance enhancement through feedback and interaction. We utilize COLLIE to generate automated natural language feedback (e.g., \"Your task is to generate a word with exactly 2 character 'v' and exactly 3 character 'i'. However, you generate a word with 3 character 'v' and 4 character 'i') and engage LLMs in a generation-feedback dialogue. In Figure 8 we observe a significant  $20\\%$  improvement in GPT-4 performance after the second round of feedback. However, the model's performance plateaus at  $66\\%$  even after three additional rounds of feedback, comparable to pass@5 using i.i.d. sampling. The extent of performance improvement varies across tasks, with word03's constraint satisfaction rate increasing from  $62.1\\%$  to  $10\\%$ . Conversely, word02, sent01, and sent02 tasks remain challenging for the model. These findings suggest that there is still room for improvement, highlighting the difficulty of our dataset, and emphasizing the need for further research on better ways to incorporate natural language feedback.",
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+        "type": "text",
+        "text": "6 CONCLUSION",
+        "text_level": 1,
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+        "type": "text",
+        "text": "In this work, we present COLLIE, a grammar-based framework for specifying textual constraints. COLLIE simplifies the process of creating constrained-generation datasets by enabling researchers to focus on specifying high level constraint structures, while COLLIE automatically extracts constraint values, renders natural language instructions, and assesses model performance. To demonstrate the utility of the COLLIE framework, we construct COLLIE-v1 with 1,132 constraints from 13 different types, extracted from 3 different data sources. We evaluate five state-of-the-art LLMs of various sizes on COLLIE-v1, and find that it provides fine-grained insights into model capabilities and shortcomings. We hope that model developers can use COLLIE-v1 to develop more capable models, while future releases of COLLIE can continue to adapt to the capabilities and needs of future models and users.",
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+    {
+        "type": "text",
+        "text": "LIMITATIONS AND SOCIETAL IMPACTS",
+        "text_level": 1,
+        "bbox": [
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+        "type": "text",
+        "text": "Although care was taken to design the filtering and processing functions, such automated approaches are never perfect and remaining artifacts in corpora might lead to unnatural reference texts or constraints. Further filtering (e.g., by grammar checkers, parsers, or humans) could improve the dataset quality. Our representative constraint structures were selected to encompass diverse constrained generation challenges, but as with all generation benchmarks, they cannot capture all dimensions",
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+    {
+        "type": "header",
+        "text": "Published as a conference paper at ICLR 2024",
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+    },
+    {
+        "type": "page_number",
+        "text": "9",
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+    {
+        "type": "text",
+        "text": "and nuances of model capabilities. Benchmarks are highly influential in shaping model development, the capabilities and limitations of which may disproportionately impact different communities. Our benchmark is no exception. However, by providing an extensible, easy-to-use framework for constraint development, we hope COLLIE will enable diverse stakeholders to engage with dataset building, helping ensure that future model capabilities serve diverse interests and needs.",
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+    {
+        "type": "text",
+        "text": "ACKNOWLEDGEMENTS",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "We thank Xiao Liu for Vicuna/Alpaca APIs that supported our preliminary experiments, and Princeton NLP Group for helpful discussion and feedback in general. We acknowledge support from a Princeton SEAS Innovation grant and the National Science Foundation under Grant No. 2239363. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "REFERENCES",
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2024/COLLIE_ Systematic Construction of Constrained Text Generation Tasks/a385f7c5-58d0-4428-b174-3123a2838efe_model.json

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+    [
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+            "angle": 0,
+            "content": "Published as a conference paper at ICLR 2024"
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "content": "COLLIE: SYSTEMATIC CONSTRUCTION OF CONSTRAINED TEXT GENERATION TASKS"
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+            "content": "Shunyu Yao* Howard Chen* Austin W. Hanjie* Runzhe Yang* Karthik Narasimhan"
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+            "content": "Department of Computer Science, Princeton University"
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+            "content": "{shunyuy, hc22, hjwang, runzhey, karthikn}@princeton.edu"
+        },
+        {
+            "type": "title",
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+            "content": "ABSTRACT"
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+            "bbox": [
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+            "content": "With the rapid improvement of large language models capabilities, there has been increasing interest in challenging constrained text generation problems. However, existing benchmarks for constrained generation usually focus on fixed constraint types (e.g. generate a sentence containing certain words) that have proved to be easy for state-of-the-art models like GPT-4. We present COLLIE, a grammar-based framework that allows the specification of rich, compositional constraints with diverse generation levels (word, sentence, paragraph, passage) and modeling challenges (e.g. language understanding, logical reasoning, counting, semantic planning). We also develop tools for automatic extraction of task instances given a constraint structure and a raw text corpus. Using COLLIE, we compile the COLLIEv1 dataset with 2,080 instances comprising 13 constraint structures. We perform systematic experiments across five state-of-the-art instruction-tuned language models and analyze their performances to reveal shortcomings. COLLIE is designed to be extensible and lightweight, and we hope the community finds it useful to develop more complex constraints and evaluations in the future."
+        },
+        {
+            "type": "title",
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+            "content": "1 INTRODUCTION"
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+            "content": "Large language models (LLMs) are increasingly capable of generating coherent and fluent text when provided with high-level prompts (OpenAI 2023a). Such capabilities have raised the bar for automated text generation, allowing us to explore more nuanced ways of utilizing LMs. One such line of inquiry is constrained text generation, whereby the LM is asked to adhere to a particular topic (Keskar et al., 2019; Dathathri et al., 2020), or avoid using certain words (Lu et al., 2021; 2022). However, these works scratch the surface of a broader phenomenon — LMs do not just generate text, as evidenced by their use in more structured tasks like problem solving (Yao et al., 2022), code generation (Chen et al., 2022b) and even tool use through API calls (Schick et al., 2023)."
+        },
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+            "content": "This raises a natural question — 'what is the next iteration of text generation benchmarks that can evaluate these advanced capabilities in LLMs'? We posit that one direction is incorporating logical and compositional challenges via constrained text generation. Existing benchmarks for constrained generation, however, focus only on particular constraint types, require tailored pipelines to collect data and annotations, and/or can only evaluate a specific aspect of LM strengths (Lin et al., 2020; Chen et al., 2022a). They also suffer from challenges in scalable dataset construction."
+        },
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+            "content": "In this paper, we propose COLLIE, a grammar-based framework that enables systematic construction of compositional constraints over diverse generation levels (e.g., words, sentences, paragraphs) and semantic requirements (e.g., language understanding, logical reasoning, counting). Operationally, COLLIE allows researchers to 1) easily specify constraint templates, and then automatically 2) extract constraint values from language corpora, 3) render them into natural language instructions, and 4) evaluate model generations against the constraint instructions."
+        },
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+            "content": "Existing benchmarks for constrained generation focus only on particular constraint types and formats (e.g., \"generate a sentence with words...\"). These limitations mean that benchmarks become quickly obsolete as LLMs progress. In contrast, the modular and extensible design of COLLIE allows the"
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+            "content": "*Equal contribution. Project site with code and data: https://collie-benchmark.github.io/Collie is a herding dog that can help guide domesticated animals like llamas and alpacas."
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+            "angle": 0,
+            "content": "Published as a conference paper at ICLR 2024"
+        },
+        {
+            "type": "image",
+            "bbox": [
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+        },
+        {
+            "type": "image_caption",
+            "bbox": [
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+            "angle": 0,
+            "content": "Figure 1: Our COLLIE framework for constraint structure specification, ground truth extraction, instruction rendering, and evaluation. First, the user specifies the constraint structure without a specific target value (expressed in \\(*\\)). Second, the constraint structure is used to extract ground truth examples from text corpora that contain the target values. Third, the constraint structure and target values are rendered into a natural language instruction. Finally, the model's generation is evaluated against the constraint and the ground truth. The model (gpt-3.5-turbo) violates the constraints by exceeding word limits and leaving the word 'mankind' at the end instead of the specified position."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "broader NLP community to contribute additional constraints that can co-evolve with LLM capabilities over time, while also providing a convenient endpoint for users that only want to evaluate their model without developing their own constraints. The flexibility of such a grammar-based framework may not only be useful for evaluation, but also in practice (e.g. word constraints, words blacklist, etc.)."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "content": "We construct the dataset COLLIE-v1 with 2,080 constraint instances across 13 different types, using three different corpora: Wikipedia (Foundation 2022), CC-News (Hamborg et al., 2017), and Project Gutenberg (Brooke et al., 2015). We perform zero-shot evaluations of five state-of-the-art LLMs of varying sizes including GPT-4 (OpenAI 2023a) and PaLM (Anil et al., 2023). While GPT-4 comparatively performs the best, it still achieves an average constraint satisfaction rate of only \\(50.9\\%\\). We find that challenges correlate with position – for instance, instructing models to begin a sentence with a specific word leads to a \\(100\\%\\) success rate for GPT-4, while asking models to end a sentence with a particular word results in a success rate of \\(40\\% -60\\%\\). These insights can help us diagnose LLMs, which in turn can improve LLM capabilities, and further advance the benchmark itself."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "content": "To summarize, we make the following contributions: (1) We introduce COLLIE, a framework for systematic generation of compositional constraints, that is flexible and extensible. (2) We use COLLIE to curate a new dataset COLLIE-v1 comprising of 13 constraint structures. (3) We perform a comprehensive evaluation of five state-of-the-art LLMs of varying sizes and provide useful insights for both model and benchmark development in the future."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "2 RELATED WORK"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "content": "Constrained text generation (CTG). Early work in controllable text generation used control codes to steer the generation towards desired topics or to reduce undesirable content, by controlling for broad attributes such as sentiment or toxicity (Hu et al., 2017; Keskar et al., 2019; Dathathri et al., 2020; Krause et al., 2021). Other work on constrained decoding provides to the language model a collection of lexical items as constraints to be included or excluded in the final generated text (Hokamp and Liu, 2017; Hasler et al., 2018; Dinu et al., 2019; Hu et al., 2019; Lin et al., 2020; Lu et al., 2021; Li et al., 2022b). Recent advances in instruction tuning LLMs (Ouyang et al., 2022) have brought major improvements to controllability. These advancements have made it challenging to use existing controllable generation datasets to fully assess the capabilities of modern LLMs. InstructCTG (Zhou et al., 2023) is a concurrent work that also constructed a dataset with text constraints. However, it mainly focuses on synthesizing 5 types of simple CTG instructions for tuning small language models such as T5-11B (Raffel et al., 2020), whereas COLLIE serves to construct much more challenging and open-ended CTG tasks to evaluate and diagnose start-of-the-art LLMs like GPT-4 (OpenAI, 2023b). Lastly, there is a line of work that sets up CTG in more practical downstream applications, such as controllable summarization (Zhang et al., 2023). The flexibility of COLLIE allows these \"functional constraints\" to be incorporated for more usefulness, which we leave for future work."
+        },
+        {
+            "type": "page_number",
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+            "content": "2"
+        }
+    ],
+    [
+        {
+            "type": "header",
+            "bbox": [
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+            "angle": 0,
+            "content": "Published as a conference paper at ICLR 2024"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.17,
+                0.104,
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+            ],
+            "angle": 0,
+            "content": "Grammar-based compositional tests. Building benchmarks with data synthesized from grammars has been explored previously in the context of question answering (Weston et al., 2015), instruction following (Chevalier-Boisvert et al., 2019; Ruis et al., 2020)) and visual reasoning (Johnson et al., 2017). These benchmarks showcased the utility of grammars to systematically generate a comprehensive set of test cases or to specify some fixed constraints. In contrast, COLLIE aims to enable flexible, and dynamic constraint construction that can co-evolve with models. Furthermore, previous datasets were synthetic with limited linguistic diversity and practical applicability to real-world scenarios. In contrast, since our COLLIE framework extracts values and examples from natural language corpora to construct the constraints, it represents a more realistic challenge for modern LLMs."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.171,
+                0.236,
+                0.828,
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+            ],
+            "angle": 0,
+            "content": "Systematic and scalable language benchmarks. The emergence of increasingly powerful general-purpose language models has created a need for scalable benchmarks that can systematically and comprehensively evaluate them. A few recent examples include HELM (Liang et al., 2022), BIG-Bench (Srivastava et al., 2022), MMLU (Hendrycks et al., 2020), TaskBench500 (Li et al., 2022a), and Natural Instructions (Wang et al., 2022). However, building such benchmarks require considerable human effort, and may become obsolete when stronger models enter the arena. We provide a new perspective in this race between model capabilities and challenging benchmarks: leverage compositionality to construct automatic and scalable benchmarks with minimal human effort that can co-evolve with model capabilities to remain challenging and relevant."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "3 COLLIE FRAMEWORK TO CONSTRUCT CONSTRAINED TEXT GENERATION"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "COLLIE allows researchers to easily 1) specify textual constraint structures via a grammar, then automatically 2) extract constraint values from text corpora, 3) render constraints into natural language instructions, and 4) evaluate generations with respect to constraints."
+        },
+        {
+            "type": "text",
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+            "content": "Grammar. Two observations about text constraints motivate a grammar characterization: 1) they involve different levels of text, e.g. character, word, sentence, or paragraph; and 2) many of them specify either the count or position at a certain text level (existence is equivalent to count \\(>0\\))."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "content": "Let capitalized letters \\((S,M,C,T)\\) denote non-terminal variables, and other symbols \\((\\ell ,\\circ ,\\oplus ,v)\\) denote terminals. A full constraint specification within our grammar \\(S\\) (Eq. 1) consists of two parts: a generation level \\((\\mathrm{level}(\\xi) = \\ell)\\) specifying whether the generated text \\(\\xi\\) should be a word, a sentence, a paragraph, or a document, and a multi-constraint \\(M\\) (Eq. 2), which is a logical composition of one or more base-constraints \\(C\\). A text \\(T\\) (Eq. 4) within these constraints can either be the full generated text \\(\\xi\\), or a part of it when qualified with a pos(\\(\\cdot\\)). For example, pos(pos(\\(\\xi\\), paragraph, 3), sentence, -1) means \"the last sentence of the 3rd paragraph of the generated text\". For terminal variables, we define a level \\(\\ell\\) of a text (Eq. 5), a string or number relation \\(\\circ\\) or \\(\\oplus\\) (Eq. 6), and a string or number value \\(v_{\\mathrm{str}}\\) or \\(v_{\\mathrm{num}}\\) (Eq. 7). \\(\\wedge\\) represents the logical 'and' operator, and \\(\\vee\\) represents the logical 'or'. With these definitions, we construct the following grammar:"
+        },
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+            "content": "\\[\nS \\rightarrow (\\text {l e v e l} (\\xi) = \\ell) \\wedge M \\quad (\\text {c o n s t r a i n t s p e c i f i c a t i o n}) \\tag {1}\n\\]"
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+        {
+            "type": "equation",
+            "bbox": [
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+            "content": "\\[\nM \\rightarrow C \\mid C \\wedge M \\mid C \\vee M \\quad (\\text {m u l t i - c o n s t r a i n t}) \\tag {2}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
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+            "angle": 0,
+            "content": "\\[\nC \\rightarrow \\operatorname {c o u n t} (T, \\ell , v _ {\\mathrm {s t r}} \\mid \\ell^ {\\prime}) \\oplus v _ {\\mathrm {n u m}} \\mid \\operatorname {p o s} (T, \\ell , v _ {\\mathrm {n u m}}) \\circ v _ {\\mathrm {s t r}} \\quad (\\text {b a s e - c o n s t r a i n t}) \\tag {3}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
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+            "angle": 0,
+            "content": "\\[\nT \\rightarrow \\xi \\mid \\operatorname {p o s} (T, \\ell , v _ {\\text {n u m}}) \\tag {4}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
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+                0.826,
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+            "angle": 0,
+            "content": "\\[\n\\ell \\rightarrow \\text {c h a r} | \\text {w o r d} | \\text {s e n t e n c e} | \\text {p a r a g r a p h} | \\text {p a s s a g e} \\tag {5}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
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+            "angle": 0,
+            "content": "\\[\n\\circ \\rightarrow = | \\neq \\quad \\oplus \\rightarrow = | \\neq | > | <   | \\leq | \\geq \\tag {6}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
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+            "angle": 0,
+            "content": "\\[\nv _ {\\mathrm {s t r}} \\in \\Sigma^ {*} \\quad v _ {\\mathrm {n u m}} \\in \\mathbb {Z} \\tag {7}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "At the core of our grammar, we consider two (symmetrical) types of base-constraints \\(C\\) (Eq. 3):"
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+            "content": "1. Count constraints. count \\((T,\\ell ,v_{\\mathrm{str}})\\oplus v_{\\mathrm{num}}\\) constrains the occurrences of a particular level- \\(\\ell\\) string \\(v_{\\mathrm{str}}\\). For example, count \\((T,\\) word, happy') \\(\\leq 3\\) means \"T should contain the word happy' no more than 3 times\". In contrast, count \\((T,\\ell ,\\ell^{\\prime})\\oplus v_{\\mathrm{num}}\\) constrains the occurrences of level- \\(\\ell\\) strings in each level- \\(\\ell^{\\prime}\\) unit of text T. For example, count \\((T,\\) char, sentence) \\(= 50\\) means \"each sentence of text T should have exactly 50 characters\"."
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+            "content": "2. Position constraints. \\( \\text{pos}(T, \\ell, v_{\\text{num}}) \\circ v_{\\text{str}} \\) specifies that a particular part of the text \\( T \\) should equal (or not equal) the given string \\( v_{\\text{str}} \\). For example, \\( \\text{pos}(T, \\text{word}, 3) = \\text{'happy'} \\) means \"the 3rd word should be 'happy' in text \\( T \\)\". We also allow negative indices for reverse counting, e.g. \\( \\text{pos}(T, \\text{char}, -1) \\neq x \\) means \"the last letter should not be 'x' in text \\( T \\)\"."
+        },
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+            "angle": 0,
+            "content": "3"
+        }
+    ],
+    [
+        {
+            "type": "header",
+            "bbox": [
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+                0.033,
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+                0.049
+            ],
+            "angle": 0,
+            "content": "Published as a conference paper at ICLR 2024"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.171,
+                0.104,
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+            "angle": 0,
+            "content": "Note that the grammar above can easily be extended to accommodate more types of base-constraints (e.g. part of speech, sentiment) by implementing the corresponding semantic checks — we leave this to future work. Also for convenience, we use constraint structure to refer to a family of constraint specifications that only differ in their values (e.g. generate a sentence with exactly \\( x \\) words, \\( x \\in \\mathbb{N} \\)), and constraint to refer to a particular constraint specification with concrete values (e.g. generate a sentence with exactly 5 words)."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "content": "Examples and conceptual challenges. Our grammar can express a wide range of constraints through logical compositions of base-constraints across different text levels. Table II illustrates some structures across generation levels, identified by names such as para01 for paragraph generation, etc."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "In addition to the generation levels, count and pos across different levels introduce a variety of challenges. For example, word01 and sent01 challenge token-based language models to count characters; pass01 requires high-level semantic planning for models to generate a coherent passage under constraints; sent04 and para02 challenge models to generate text with presence or absence of particular words; sent03, para03, and para04 require counting at multiple levels; and word02, word03, sent02, para05, and pass01 combine counting and positional challenges at different levels, which can be considered most demanding conceptually. We empirically assess the difficulty of constraint structures in Section 5. Example COLLIE usage is presented in Figure 2"
+        },
+        {
+            "type": "code",
+            "bbox": [
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+                0.255,
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+            "angle": 0,
+            "content": "from collieconstraints import ( Constraint, TargetLevel, Count, Relation   \n）   \nc \\(=\\) Constraint( target_level \\(\\equiv\\) TargetLevel('word'), transformation \\(\\equiv\\) Count(), relation \\(\\equiv\\) Relation('==')，   \n）   \ntext \\(=\\) 'This is a good sentence.'   \nprint(c.check(text,5)) # True"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
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+            "angle": 0,
+            "content": "Figure 2: Example COLLIE code for a simple number of words constraint."
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
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+            "angle": 0,
+            "content": "Table 1: List of all constraint structures used in COLLIE-v1, with (simplified) example values."
+        },
+        {
+            "type": "table",
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+            "content": "<table><tr><td>ID</td><td>Example instruction</td><td>Multi-constraint M</td></tr><tr><td>word01</td><td>Generate a word with at least 15 letters.</td><td>count(ξ, char, word) ≥ 15</td></tr><tr><td>word02</td><td>Generate a word with 10 letters, where letter 1 is &#x27;s&#x27;, letter 3 is &#x27;r&#x27;, letter 9 is &#x27;e&#x27;.</td><td>count(ξ, char, word) = 10 ∧ pos(ξ, char, 1) = &#x27;s&#x27; ∧ pos(ξ, char, 3) = &#x27;r&#x27; ∧ pos(ξ, char, 9) = &#x27;e&#x27;</td></tr><tr><td>word03</td><td>Generate a word with at most 10 letters and ends with &quot;r&quot;.</td><td>count(ξ, char, word) ≤ 10 ∧ pos(ξ, char, -1) = &#x27;r&#x27;</td></tr><tr><td>sent01</td><td>Please generate a sentence with exactly 82 characters. Include whitespace into your character count.</td><td>count(ξ, char, sentence) = 82</td></tr><tr><td>sent02</td><td>Generate a sentence with 10 words, where word 3 is &quot;soft&quot; and word 7 is &quot;beach&quot; and word 10 is &quot;math&quot;.</td><td>count(ξ, word, sentence) = 10 ∧ pos(ξ, word, 3) = &quot;soft&quot; ∧ pos(ξ, word, 7) = &quot;beach&quot; ∧ pos(ξ, word, 10) = &quot;math&quot;</td></tr><tr><td>sent03</td><td>Generate a sentence with at least 20 words, and each word less than six characters.</td><td>count(ξ, word, sentence) ≥ 20 ∧ count(ξ, char, word) ≤ 6</td></tr><tr><td>sent04</td><td>Generate a sentence but be sure to include the words &quot;soft&quot;, &quot;beach&quot; and &quot;math&quot;.</td><td>count(ξ, word, &#x27;soft&#x27;) &gt; 0 ∧ count(ξ, word, &#x27;beach&#x27;) &gt; 0 ∧ count(ξ, word, &#x27;math&#x27;) &gt; 0</td></tr><tr><td>para01</td><td>Generate a paragraph where each sentence begins with the word &quot;soft&quot;.</td><td>pos(pos(ξ, sentence, 1), word, 1) = &#x27;soft&#x27; ∧ pos(pos(ξ, sentence, 2), word, 1) = &#x27;soft&#x27; ∧ ...</td></tr><tr><td>para02</td><td>Generate a paragraph with at least 4 sentences, but do not use the words &quot;the&quot;, &quot;and&quot; or &quot;of&quot;.</td><td>count(ξ, sentence, paragraph) ≥ 4 ∧ count(ξ, word, &#x27;the&#x27;) = 0 ∧ count(ξ, word, &#x27;and&#x27;) = 0 ∧ count(ξ, word, &#x27;of&#x27;) = 0</td></tr><tr><td>para03</td><td>Generate a paragraph with exactly 4 sentences, each with between 10 and 15 words.</td><td>count(ξ, sentence, paragraph) = 4 ∧ count(ξ, word, sentence) ≥ 10 ∧ count(ξ, word, sentence) ≤ 15</td></tr><tr><td>para04</td><td>Generate a paragraph with at least 3 sentences, each with at least 15 words.</td><td>count(ξ, sentence, paragraph) ≥ 3 ∧ count(ξ, word, sentence) ≥ 15</td></tr><tr><td>para05</td><td>Generate a paragraph with 2 sentences that end in &quot;math&quot; and &quot;rock&quot; respectively.</td><td>count(ξ, sentence, paragraph) = 2 ∧ pos(pos(ξ, sentence, 1), word, -1) = &quot;math&quot; ∧ pos(pos(ξ, sentence, 2), word, -1) = &quot;rock&quot;</td></tr><tr><td>pass01</td><td>Generate a passage with 2 paragraphs, each ending in &quot;I sit.&quot; and &quot;I cry.&quot; respectively.</td><td>count(ξ, paragraph, passage) = 2 ∧ pos(pos(ξ, paragraph, 1), sentence, -1) = &quot;I sit.&quot; ∧ pos(pos(ξ, paragraph, 2), sentence, -1) = &quot;I cry.&quot;</td></tr></table>"
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+            "content": "4"
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+    ],
+    [
+        {
+            "type": "header",
+            "bbox": [
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+            "angle": 0,
+            "content": "Published as a conference paper at ICLR 2024"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "In conjunction with the grammar, we develop a set of compiling tools to help construct datasets with minimal human efforts. Concretely, the pipeline of dataset construction involves 4 stages (Figure 1):"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "1. Specify constraint structures. Researchers can specify constraint structures (e.g. Table [1]), and optionally with a value range (e.g. \"generate a sentence with \\( x \\) words\", and \\( 5 \\leq x \\leq 10 \\)). This is the only stage that involves manual effort."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "2. Extract constraint values from corpora. We design an automatic extraction algorithm that runs through a given text corpus to find strings that fit a constraint structure with some value ranges. For example, given the constraint structure count(\\(\\xi\\), word, \\(\\emptyset\\)) = \\(x\\) with value range \\(5 \\leq x \\leq 10\\), the extraction algorithm returns sentences in the corpus that have 5-10 words, with associated word counts. This ensures each constraint has at least one natural solution. More details are in Section 4.1."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "3. Render natural language instructions. Each constraint can be rendered into a natural language instruction (Table I) via ruled-based translation, thanks to the compositionality grammar of COLLIE. For example, a constraint count \\((\\xi ,\\mathrm{char},\\mathrm{'v'}) = 2\\land \\mathrm{count}(\\xi ,\\mathrm{char},\\mathrm{'i'}) = 3\\) can be synthetically rendered into the instruction \"Please generate a word with exactly 2 character 'v' and exactly 3 character 'i'\". It is also possible to improve the instruction fluency or naturalness by adding additional rules to the synthetic translation, or use LLMs to polish instructions. More details are in Section A.1"
+        },
+        {
+            "type": "text",
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+            ],
+            "angle": 0,
+            "content": "4. Evaluate generations. Given text \\(\\xi\\) generated by a model, we use a parser to evaluate it against a constraint specification \\(S\\) and derive a True/False value, indicating if \\(\\xi\\) satisfies \\(S\\). We use an average success rate as the main metric to evaluate constraint conformance. We can also compare the fluency of \\(\\xi\\) against the corpus-extracted \"groundtruth\" text, and render more fine-grained natural language feedback indicating which base-constraints are met and which not (see Section A.2)."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.171,
+                0.14,
+                0.827,
+                0.428
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.172,
+                0.451,
+                0.383,
+                0.467
+            ],
+            "angle": 0,
+            "content": "4 COLLIE-V1 DATASET"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.171,
+                0.485,
+                0.827,
+                0.556
+            ],
+            "angle": 0,
+            "content": "We construct COLLIE-v1 using constraints structures from Table [1], which contains 2,080 constraint instances from 13 constraint types, with 1,435 unique constraint prompts. The broader NLP community can contribute to future dataset releases by adding additional constraints, metrics, data sources. The curated constraint set can co-evolve with models to become more challenging and comprehensive as model capabilities improve."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+                0.547,
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+            ],
+            "angle": 0,
+            "content": "4.1 CONSTRAINT SPECIFICATION AND EXTRACTION"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.171,
+                0.604,
+                0.825,
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+            "angle": 0,
+            "content": "Constraint specification. We begin by defining 13 constraint structures. We chose these 13 structures to span various generation levels (word, sentence, paragraph and passage generation) and challenges (counting, position). In total, we have 3 word-level, 4 sentence-level, 5 paragraph-level, and 1 passage-level constraint structures. Of these 13 constraint structures, 5 are single-level and the remaining 8 are multi-level constraints. See Table \\(\\boxed{1}\\) for the exact constraint structures we use."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "Constraint extraction. While constructing constraint structures is straightforward using our grammar, choosing constraint targets is challenging for two reasons: (1) Not all targets will admit a conforming natural language string. For instance, the constraint, \"Generate a two word sentence beginning with the word The.\" has no grammatically acceptable answer. (2) Even if a constraint admits a possible answer, it may not admit a plausible answer. For instance, \"Generate a sentence with 1928 words\" is possible, but any such sentence is very unlikely to appear in regular discourse."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "To address both challenges, we sample constraint target values from natural language corpora, which we denote as the data source. Given a constraint structure \\(\\mathcal{C}\\) and documents \\(\\bar{\\mathcal{D}} = \\{d_1,\\dots,d_n\\}\\), we chunk each document into a series of strings \\(d_{i} = \\{s_{1},\\ldots ,s_{m}\\}\\), where each \\(s_i\\) can be a sentence, paragraph, or passage as required by \\(\\mathcal{C}\\). Each string \\(s_i\\) undergoes source-specific automated filtering and post-processing to remove artifacts, which we detail in Section B.4. Given \\(\\mathcal{C}\\) and \\(s_i\\), we extract target values such that \\(\\mathcal{C}\\) is satisfied. In most cases, the satisfying target values can be directly extracted using our provided utilities. For example, for constraints with structure \"sentence with \\(x\\) words\", we can directly apply word tokenization and counting to the example string \\(s_i\\). In cases in which direct extraction is not possible, (e.g. \"do not include word \\(w\\)\", we specify a range of possible targets (e.g. \\(\\{\\text{the, and, of}\\}\\)) to sweep over. All in all, our approach ensures that (1) there exists a natural language string that can satisfy each constraint and target pair, and (2) the targets follow a"
+        },
+        {
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+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "5"
+        }
+    ],
+    [
+        {
+            "type": "header",
+            "bbox": [
+                0.173,
+                0.033,
+                0.48,
+                0.049
+            ],
+            "angle": 0,
+            "content": "Published as a conference paper at ICLR 2024"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.178,
+                0.101,
+                0.825,
+                0.245
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.171,
+                0.256,
+                0.828,
+                0.286
+            ],
+            "angle": 0,
+            "content": "Figure 3: Data statistics. (a) Number of constraints from each constraint structure. (b) Fraction of strings removed by automated filtering. (c) Length statistics for different levels for each data source."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.171,
+                0.323,
+                0.825,
+                0.352
+            ],
+            "angle": 0,
+            "content": "plausible distribution induced by natural language corpora. Our extraction system is extensible, and can operate on new constraints and data sources with minimal modifications."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.17,
+                0.378,
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+            ],
+            "angle": 0,
+            "content": "Extensibility Adding additional data sources to the extraction pipeline is similarly easy, requiring a text delimiter, and optional string filtering and post-processing functions. As a case-study on the extensibility of COLLIE, we demonstrate how to extend constraints to include POS-tags such as \"Generate a sentence with verbs\". Details are in section B.5"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.172,
+                0.464,
+                0.324,
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+            ],
+            "angle": 0,
+            "content": "4.2 DATA SOURCES"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.17,
+                0.495,
+                0.827,
+                0.553
+            ],
+            "angle": 0,
+            "content": "To adequately cover diverse styles and content, we extract constraint targets from three distinct data sources: Wikipedia (Wiki) (Foundation 2022), Common Crawl News (CC-News) (Hamborg et al., 2017), and the Project Gutenberg Corpus (Guten) (Brooke et al., 2015). We provide an overview of these data sources below and leave source-specific filtering and post-processing details to Section B.4."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.171,
+                0.557,
+                0.827,
+                0.587
+            ],
+            "angle": 0,
+            "content": "Wiki. Wikipedia (Wiki) (Foundation, 2022) consists of over 6 million English Wikipedia articles. We included this data source for the diverse subject matter present in the corpus."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.171,
+                0.592,
+                0.825,
+                0.636
+            ],
+            "angle": 0,
+            "content": "CC-News. The Common Crawl News corpus (CC-News) (Hamborg et al., 2017) consists of 708,241 English language news articles published between Jan 2017 and December 2019. We include CC-News to include interview dialogues, as well as popular culture and current events."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.171,
+                0.641,
+                0.827,
+                0.699
+            ],
+            "angle": 0,
+            "content": "Gutenberg. The Project Gutenberg corpus (Gutenberg) (Brooke et al., 2015) consists of over 50,000 documents that include fiction, histories, biographies, and other works that are in the public domain in the United States. We include this corpus for its variety in genres (e.g. non-fiction, fiction, plays, etc.) and style from different time periods."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.172,
+                0.727,
+                0.461,
+                0.74
+            ],
+            "angle": 0,
+            "content": "4.3 DATA VALIDATION AND STATISTICS"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.17,
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+            "angle": 0,
+            "content": "We extract constraints from 300 randomly sampled documents from each source. After extracting the target values, we sample up to 100 targets for each constraint structure on each data source. We remove any string targets by that begins or ends with any character that is not a letter or number. We randomly sample 5 out of these 100 targets and their supporting examples to qualitatively verify their validity. Since the extraction process is relatively fast, we modify filters and post-processors if there are systemic issues and re-run the extraction phase. We provide statistics of the final number of constraints from each constraint structure in Figure 3(a). Some constraints (e.g. number of sentences per paragraph) are tightly clustered around the mean, and thus do not induce many valid constraint targets. The fraction of strings filtered for each data source and level is presented in Figure 3(b). The automated filtering removes a large fraction of the strings in most cases, as high recall is important to ensure quality. The high fraction of omitted passages is due to the removal of passages \\(< 2\\) paragraphs in length. Mean lengths for each level and data source is presented in Figure 3(c)."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+                0.96
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+            "angle": 0,
+            "content": "6"
+        }
+    ],
+    [
+        {
+            "type": "header",
+            "bbox": [
+                0.174,
+                0.033,
+                0.48,
+                0.049
+            ],
+            "angle": 0,
+            "content": "Published as a conference paper at ICLR 2024"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.177,
+                0.103,
+                0.353,
+                0.201
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
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+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
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+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.378,
+                0.208,
+                0.6,
+                0.31
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.601,
+                0.208,
+                0.822,
+                0.311
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
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+                0.323,
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+            ],
+            "angle": 0,
+            "content": "Figure 4: Model comparison. (a) Overall model performance summarized by weighted average across all constraint groups. (b) -(f) Constraint satisfaction rates of generated texts by GPT-4, GPT-3.5, PaLM, Vicuna-7B, and Alpaca-7B across various constraint groups. Error bars represent standard error. Constraint group names are in Table[1]. Sample sizes are reported in Figure[11]."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.173,
+                0.422,
+                0.283,
+                0.436
+            ],
+            "angle": 0,
+            "content": "5 RESULTS"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.17,
+                0.465,
+                0.828,
+                0.563
+            ],
+            "angle": 0,
+            "content": "Our main experiments in this paper focus on a zero-shot prompting setup with the following language models (LMs): 1) larger and closed-source LMs such as OpenAI GPT (Brown et al., 2020; OpenAI, 2023b) (gpt-3.5-turbo, gpt-4) and Google PaLM-2 (Anil et al., 2023) (text-bison-001); 2) smaller and open-source LMs such as Alpaca-7B (Taori et al., 2023), Vicuna-7B (Chiang et al., 2023). We performed additional one-shot prompting and find GPT performances similar to zero-shot performance, see Section C.1 By default, we use a sampling temperature of 0.7, and sample multiple trials (20 for GPT/PaLM, 5 for Alpaca/Vicuna). All experiments were run in July, 2023."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.171,
+                0.569,
+                0.825,
+                0.64
+            ],
+            "angle": 0,
+            "content": "Zero-shot performance comparison. As evidenced in Figures \\(\\boxed{4}\\) (a), GPT-4 consistently surpassed other models in zero-shot constrained text generation performances, achieving more than twice the constraint satisfaction rate than other non-GPT models. The overarching performance trend observed shows GPT-4 leading the pack, followed by GPT-3.5 and PaLM with a large gap, and then followed closely by the smaller models, Vicuna-7B and Alpaca-7B."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.171,
+                0.646,
+                0.826,
+                0.717
+            ],
+            "angle": 0,
+            "content": "Constraints all models can follow. Certain tasks, specifically word01 (generating a word with at least \\(a\\) letters), sent04 (generating a sentence containing words X, Y, Z), and para01 (generating a paragraph with each sentence starting with the word X), posed minimal challenge to the majority of contemporary language models. These tasks demonstrate the proficiency of current models at simple constraints ensuring existence, as depicted in Figure 9(f)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.171,
+                0.722,
+                0.825,
+                0.793
+            ],
+            "angle": 0,
+            "content": "Constraints partially solved by GPT-4 only. However, a notable distinction arose when tasks incorporated more counting/position constraints and requested longer generations. Tasks such as word03, para04, para05, and pass01 were only partially addressed by GPT-4, with constraint satisfaction rates ranging between \\(40\\%\\) and \\(70\\%\\). Despite GPT-4's partial success in these tasks, other models failed to deliver any satisfactory performance."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.171,
+                0.799,
+                0.827,
+                0.926
+            ],
+            "angle": 0,
+            "content": "Constraints remaining very challenging. Furthermore, some tasks proved challenging across all models. Tasks word02, sent01, sent02, and para03 present challenges in terms of arbitrary position constraints and mixed counting levels (see Section 5.1 for detailed analysis), indicating areas that necessitate further advancements in language model technology. Moreover, the average pass@20 rate of GPT-4 was above \\(63\\%\\) across all constraints, significantly higher than the \\(32\\%\\) achieved by GPT-3.5, as depicted in Figure 5. Although GPT-4 demonstrated a significant performance advantage, its constraint satisfaction rate of \\(63\\%\\) is far from perfect. This suggests considerable scope for improvement in controllable text generation with language models. These findings underscore the opportunities and challenges in the continued evolution of language models."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+                0.949,
+                0.504,
+                0.96
+            ],
+            "angle": 0,
+            "content": "7"
+        }
+    ],
+    [
+        {
+            "type": "header",
+            "bbox": [
+                0.174,
+                0.033,
+                0.48,
+                0.049
+            ],
+            "angle": 0,
+            "content": "Published as a conference paper at ICLR 2024"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.177,
+                0.109,
+                0.465,
+                0.271
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.483,
+                0.104,
+                0.837,
+                0.271
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.171,
+                0.284,
+                0.47,
+                0.368
+            ],
+            "angle": 0,
+            "content": "Figure 5: Pass@k performance. We sample the model-generated text 20 times for all instruction prompts in the dataset. The curves represent the average pass rate across all instruction prompts up to \\( k \\) samples. The shaded areas indicate the standard errors."
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.479,
+                0.284,
+                0.842,
+                0.368
+            ],
+            "angle": 0,
+            "content": "Figure 6: Position effect. Satisfaction rates of LMs on tasks involving pos(\\(\\xi\\), level, i). The tasks word02 and sent02 impose constraints on characters and words at arbitrary positions. The task para01 constrains the first word. The tasks word03, para05, and pass01 constrain the last characters, words, and sentences."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.177,
+                0.39,
+                0.825,
+                0.573
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.17,
+                0.585,
+                0.828,
+                0.657
+            ],
+            "angle": 0,
+            "content": "Figure 7: Counting level effect. Satisfaction rates for LMs on tasks involving count \\((\\xi, \\text{level}, \\varphi)\\). Task word01 sets a minimum word length of \\(a\\). Task sent01 requires exactly \\(a\\) characters in a sentence. Task sent03 asks a sentence to contain at least \\(b\\) words, with each word no longer than \\(a\\) letters. Task para04 asks a paragraph to consist of at least \\(b\\) sentences, each containing a minimum of \\(a\\) words. Task para03 further imposes an upper limit on the number of words per sentence."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.172,
+                0.687,
+                0.289,
+                0.7
+            ],
+            "angle": 0,
+            "content": "5.1 ANALYSIS"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.171,
+                0.714,
+                0.825,
+                0.785
+            ],
+            "angle": 0,
+            "content": "Performance consistency across data sources. We observe a high degree of consistency in the performance of models on a given constraint structure, regardless of the data source. This uniformity is evident across all models, as highlighted in Figure 9(g). This indicates that the ability of a language model to adhere to the logic of constraints takes precedence over the specific target values or the distribution of the data."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.171,
+                0.791,
+                0.827,
+                0.889
+            ],
+            "angle": 0,
+            "content": "Position effect. As depicted in Figure 6 the pos(\\(\\xi\\), level, \\(i\\)) function, constraining the \\(i\\)-th sub-string (letter, word, or sentence), exhibits varying levels of difficulty depending on the value of \\(i\\). Models generally perform well when the positional constraint is applied to the first sub-string (\\(i = 1\\), task para01). However, only GPT-4 displays partial success with the last positional constraints (\\(i = -1\\), tasks word03, para05, pass01). Notably, all models encounter difficulties when generating text that satisfies positional constraints at arbitrary positions \\(i\\). Additionally, we find that the position effect exhibits a lower sensitivity to constraint levels."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.171,
+                0.896,
+                0.827,
+                0.926
+            ],
+            "angle": 0,
+            "content": "Counting level effect. Counting characters within a word is easier than within a sentence for models, as illustrated in Figure 7. Furthermore, tasks demanding exact equality (task sent01) prove more"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.494,
+                0.949,
+                0.504,
+                0.96
+            ],
+            "angle": 0,
+            "content": "8"
+        }
+    ],
+    [
+        {
+            "type": "header",
+            "bbox": [
+                0.173,
+                0.033,
+                0.48,
+                0.049
+            ],
+            "angle": 0,
+            "content": "Published as a conference paper at ICLR 2024"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.182,
+                0.107,
+                0.466,
+                0.134
+            ],
+            "angle": 0,
+            "content": "(a) Constraint satisfaction rate -GPT-4 (4th round)"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.19,
+                0.139,
+                0.49,
+                0.274
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.51,
+                0.106,
+                0.822,
+                0.278
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.171,
+                0.289,
+                0.825,
+                0.332
+            ],
+            "angle": 0,
+            "content": "Figure 8: GPT-4 interactive generation performance. (a) Constraint satisfaction rate of GPT-4 generated texts in the 4th round across various constraint groups. (b) GPT-4 overall performance in different feedback rounds. The 1st round is zero-shot, and the 2nd - 4th rounds are with feedback."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.171,
+                0.358,
+                0.825,
+                0.387
+            ],
+            "angle": 0,
+            "content": "challenging than those requiring a range (task para03), and are considerably more difficult than tasks specifying just an upper or lower bound (tasks word01, sent03, para04)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.171,
+                0.393,
+                0.825,
+                0.477
+            ],
+            "angle": 0,
+            "content": "Increased difficulty with logical composition. The incorporation of logical compositions into constraints considerably increases their difficulty. Task sent03 serves as an example of this, adding an extra constraint at the sentence level compared to task word01. Despite the assumption that the added constraint should be manageable for all models, performance on task sent03 uniformly trails behind that on task word01, as shown in Figure 7. This highlights the intricacy and challenge introduced by logical compositions within constraints."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.171,
+                0.483,
+                0.827,
+                0.637
+            ],
+            "angle": 0,
+            "content": "Performance enhancement through feedback and interaction. We utilize COLLIE to generate automated natural language feedback (e.g., \"Your task is to generate a word with exactly 2 character 'v' and exactly 3 character 'i'. However, you generate a word with 3 character 'v' and 4 character 'i') and engage LLMs in a generation-feedback dialogue. In Figure 8 we observe a significant \\(20\\%\\) improvement in GPT-4 performance after the second round of feedback. However, the model's performance plateaus at \\(66\\%\\) even after three additional rounds of feedback, comparable to pass@5 using i.i.d. sampling. The extent of performance improvement varies across tasks, with word03's constraint satisfaction rate increasing from \\(62.1\\%\\) to \\(10\\%\\). Conversely, word02, sent01, and sent02 tasks remain challenging for the model. These findings suggest that there is still room for improvement, highlighting the difficulty of our dataset, and emphasizing the need for further research on better ways to incorporate natural language feedback."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.172,
+                0.657,
+                0.321,
+                0.672
+            ],
+            "angle": 0,
+            "content": "6 CONCLUSION"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.171,
+                0.678,
+                0.827,
+                0.803
+            ],
+            "angle": 0,
+            "content": "In this work, we present COLLIE, a grammar-based framework for specifying textual constraints. COLLIE simplifies the process of creating constrained-generation datasets by enabling researchers to focus on specifying high level constraint structures, while COLLIE automatically extracts constraint values, renders natural language instructions, and assesses model performance. To demonstrate the utility of the COLLIE framework, we construct COLLIE-v1 with 1,132 constraints from 13 different types, extracted from 3 different data sources. We evaluate five state-of-the-art LLMs of various sizes on COLLIE-v1, and find that it provides fine-grained insights into model capabilities and shortcomings. We hope that model developers can use COLLIE-v1 to develop more capable models, while future releases of COLLIE can continue to adapt to the capabilities and needs of future models and users."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+                0.496,
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+            "angle": 0,
+            "content": "LIMITATIONS AND SOCIETAL IMPACTS"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.171,
+                0.855,
+                0.827,
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+            "angle": 0,
+            "content": "Although care was taken to design the filtering and processing functions, such automated approaches are never perfect and remaining artifacts in corpora might lead to unnatural reference texts or constraints. Further filtering (e.g., by grammar checkers, parsers, or humans) could improve the dataset quality. Our representative constraint structures were selected to encompass diverse constrained generation challenges, but as with all generation benchmarks, they cannot capture all dimensions"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+                0.949,
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+            ],
+            "angle": 0,
+            "content": "9"
+        }
+    ],
+    [
+        {
+            "type": "header",
+            "bbox": [
+                0.173,
+                0.033,
+                0.48,
+                0.049
+            ],
+            "angle": 0,
+            "content": "Published as a conference paper at ICLR 2024"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.171,
+                0.104,
+                0.828,
+                0.175
+            ],
+            "angle": 0,
+            "content": "and nuances of model capabilities. Benchmarks are highly influential in shaping model development, the capabilities and limitations of which may disproportionately impact different communities. Our benchmark is no exception. However, by providing an extensible, easy-to-use framework for constraint development, we hope COLLIE will enable diverse stakeholders to engage with dataset building, helping ensure that future model capabilities serve diverse interests and needs."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.173,
+                0.196,
+                0.369,
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+            ],
+            "angle": 0,
+            "content": "ACKNOWLEDGEMENTS"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.171,
+                0.226,
+                0.828,
+                0.298
+            ],
+            "angle": 0,
+            "content": "We thank Xiao Liu for Vicuna/Alpaca APIs that supported our preliminary experiments, and Princeton NLP Group for helpful discussion and feedback in general. We acknowledge support from a Princeton SEAS Innovation grant and the National Science Foundation under Grant No. 2239363. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation."
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+            "content": "S. Yao, J. Zhao, D. Yu, N. Du, I. Shafran, K. Narasimhan, and Y. Cao. React: Synergizing reasoning and acting in language models. In International Conference on Learning Representations (ICLR), 2022. URL https://arxiv.org/abs/2210.03629"
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2024/COLLIE_ Systematic Construction of Constrained Text Generation Tasks/a385f7c5-58d0-4428-b174-3123a2838efe_origin.pdf

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2024/COLLIE_ Systematic Construction of Constrained Text Generation Tasks/full.md

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+# COLLIE: SYSTEMATIC CONSTRUCTION OF CONSTRAINED TEXT GENERATION TASKS
+
+Shunyu Yao* Howard Chen* Austin W. Hanjie* Runzhe Yang* Karthik Narasimhan
+
+Department of Computer Science, Princeton University
+
+{shunyuy, hc22, hjwang, runzhey, karthikn}@princeton.edu
+
+# ABSTRACT
+
+With the rapid improvement of large language models capabilities, there has been increasing interest in challenging constrained text generation problems. However, existing benchmarks for constrained generation usually focus on fixed constraint types (e.g. generate a sentence containing certain words) that have proved to be easy for state-of-the-art models like GPT-4. We present COLLIE, a grammar-based framework that allows the specification of rich, compositional constraints with diverse generation levels (word, sentence, paragraph, passage) and modeling challenges (e.g. language understanding, logical reasoning, counting, semantic planning). We also develop tools for automatic extraction of task instances given a constraint structure and a raw text corpus. Using COLLIE, we compile the COLLIEv1 dataset with 2,080 instances comprising 13 constraint structures. We perform systematic experiments across five state-of-the-art instruction-tuned language models and analyze their performances to reveal shortcomings. COLLIE is designed to be extensible and lightweight, and we hope the community finds it useful to develop more complex constraints and evaluations in the future.
+
+# 1 INTRODUCTION
+
+Large language models (LLMs) are increasingly capable of generating coherent and fluent text when provided with high-level prompts (OpenAI 2023a). Such capabilities have raised the bar for automated text generation, allowing us to explore more nuanced ways of utilizing LMs. One such line of inquiry is constrained text generation, whereby the LM is asked to adhere to a particular topic (Keskar et al., 2019; Dathathri et al., 2020), or avoid using certain words (Lu et al., 2021; 2022). However, these works scratch the surface of a broader phenomenon — LMs do not just generate text, as evidenced by their use in more structured tasks like problem solving (Yao et al., 2022), code generation (Chen et al., 2022b) and even tool use through API calls (Schick et al., 2023).
+
+This raises a natural question — 'what is the next iteration of text generation benchmarks that can evaluate these advanced capabilities in LLMs'? We posit that one direction is incorporating logical and compositional challenges via constrained text generation. Existing benchmarks for constrained generation, however, focus only on particular constraint types, require tailored pipelines to collect data and annotations, and/or can only evaluate a specific aspect of LM strengths (Lin et al., 2020; Chen et al., 2022a). They also suffer from challenges in scalable dataset construction.
+
+In this paper, we propose COLLIE, a grammar-based framework that enables systematic construction of compositional constraints over diverse generation levels (e.g., words, sentences, paragraphs) and semantic requirements (e.g., language understanding, logical reasoning, counting). Operationally, COLLIE allows researchers to 1) easily specify constraint templates, and then automatically 2) extract constraint values from language corpora, 3) render them into natural language instructions, and 4) evaluate model generations against the constraint instructions.
+
+Existing benchmarks for constrained generation focus only on particular constraint types and formats (e.g., "generate a sentence with words..."). These limitations mean that benchmarks become quickly obsolete as LLMs progress. In contrast, the modular and extensible design of COLLIE allows the
+
+![](images/ba2dd8c8fe7730e2a5c11bddb24304f879a9eb8165b6082d9cbac8f8b2496501.jpg)  
+Figure 1: Our COLLIE framework for constraint structure specification, ground truth extraction, instruction rendering, and evaluation. First, the user specifies the constraint structure without a specific target value (expressed in  $*$ ). Second, the constraint structure is used to extract ground truth examples from text corpora that contain the target values. Third, the constraint structure and target values are rendered into a natural language instruction. Finally, the model's generation is evaluated against the constraint and the ground truth. The model (gpt-3.5-turbo) violates the constraints by exceeding word limits and leaving the word 'mankind' at the end instead of the specified position.
+
+broader NLP community to contribute additional constraints that can co-evolve with LLM capabilities over time, while also providing a convenient endpoint for users that only want to evaluate their model without developing their own constraints. The flexibility of such a grammar-based framework may not only be useful for evaluation, but also in practice (e.g. word constraints, words blacklist, etc.).
+
+We construct the dataset COLLIE-v1 with 2,080 constraint instances across 13 different types, using three different corpora: Wikipedia (Foundation 2022), CC-News (Hamborg et al., 2017), and Project Gutenberg (Brooke et al., 2015). We perform zero-shot evaluations of five state-of-the-art LLMs of varying sizes including GPT-4 (OpenAI 2023a) and PaLM (Anil et al., 2023). While GPT-4 comparatively performs the best, it still achieves an average constraint satisfaction rate of only  $50.9\%$ . We find that challenges correlate with position – for instance, instructing models to begin a sentence with a specific word leads to a  $100\%$  success rate for GPT-4, while asking models to end a sentence with a particular word results in a success rate of  $40\% -60\%$ . These insights can help us diagnose LLMs, which in turn can improve LLM capabilities, and further advance the benchmark itself.
+
+To summarize, we make the following contributions: (1) We introduce COLLIE, a framework for systematic generation of compositional constraints, that is flexible and extensible. (2) We use COLLIE to curate a new dataset COLLIE-v1 comprising of 13 constraint structures. (3) We perform a comprehensive evaluation of five state-of-the-art LLMs of varying sizes and provide useful insights for both model and benchmark development in the future.
+
+# 2 RELATED WORK
+
+Constrained text generation (CTG). Early work in controllable text generation used control codes to steer the generation towards desired topics or to reduce undesirable content, by controlling for broad attributes such as sentiment or toxicity (Hu et al., 2017; Keskar et al., 2019; Dathathri et al., 2020; Krause et al., 2021). Other work on constrained decoding provides to the language model a collection of lexical items as constraints to be included or excluded in the final generated text (Hokamp and Liu, 2017; Hasler et al., 2018; Dinu et al., 2019; Hu et al., 2019; Lin et al., 2020; Lu et al., 2021; Li et al., 2022b). Recent advances in instruction tuning LLMs (Ouyang et al., 2022) have brought major improvements to controllability. These advancements have made it challenging to use existing controllable generation datasets to fully assess the capabilities of modern LLMs. InstructCTG (Zhou et al., 2023) is a concurrent work that also constructed a dataset with text constraints. However, it mainly focuses on synthesizing 5 types of simple CTG instructions for tuning small language models such as T5-11B (Raffel et al., 2020), whereas COLLIE serves to construct much more challenging and open-ended CTG tasks to evaluate and diagnose start-of-the-art LLMs like GPT-4 (OpenAI, 2023b). Lastly, there is a line of work that sets up CTG in more practical downstream applications, such as controllable summarization (Zhang et al., 2023). The flexibility of COLLIE allows these "functional constraints" to be incorporated for more usefulness, which we leave for future work.
+
+Grammar-based compositional tests. Building benchmarks with data synthesized from grammars has been explored previously in the context of question answering (Weston et al., 2015), instruction following (Chevalier-Boisvert et al., 2019; Ruis et al., 2020)) and visual reasoning (Johnson et al., 2017). These benchmarks showcased the utility of grammars to systematically generate a comprehensive set of test cases or to specify some fixed constraints. In contrast, COLLIE aims to enable flexible, and dynamic constraint construction that can co-evolve with models. Furthermore, previous datasets were synthetic with limited linguistic diversity and practical applicability to real-world scenarios. In contrast, since our COLLIE framework extracts values and examples from natural language corpora to construct the constraints, it represents a more realistic challenge for modern LLMs.
+
+Systematic and scalable language benchmarks. The emergence of increasingly powerful general-purpose language models has created a need for scalable benchmarks that can systematically and comprehensively evaluate them. A few recent examples include HELM (Liang et al., 2022), BIG-Bench (Srivastava et al., 2022), MMLU (Hendrycks et al., 2020), TaskBench500 (Li et al., 2022a), and Natural Instructions (Wang et al., 2022). However, building such benchmarks require considerable human effort, and may become obsolete when stronger models enter the arena. We provide a new perspective in this race between model capabilities and challenging benchmarks: leverage compositionality to construct automatic and scalable benchmarks with minimal human effort that can co-evolve with model capabilities to remain challenging and relevant.
+
+# 3 COLLIE FRAMEWORK TO CONSTRUCT CONSTRAINED TEXT GENERATION
+
+COLLIE allows researchers to easily 1) specify textual constraint structures via a grammar, then automatically 2) extract constraint values from text corpora, 3) render constraints into natural language instructions, and 4) evaluate generations with respect to constraints.
+
+Grammar. Two observations about text constraints motivate a grammar characterization: 1) they involve different levels of text, e.g. character, word, sentence, or paragraph; and 2) many of them specify either the count or position at a certain text level (existence is equivalent to count  $>0$ ).
+
+Let capitalized letters  $(S,M,C,T)$  denote non-terminal variables, and other symbols  $(\ell ,\circ ,\oplus ,v)$  denote terminals. A full constraint specification within our grammar  $S$  (Eq. 1) consists of two parts: a generation level  $(\mathrm{level}(\xi) = \ell)$  specifying whether the generated text  $\xi$  should be a word, a sentence, a paragraph, or a document, and a multi-constraint  $M$  (Eq. 2), which is a logical composition of one or more base-constraints  $C$ . A text  $T$  (Eq. 4) within these constraints can either be the full generated text  $\xi$ , or a part of it when qualified with a pos( $\cdot$ ). For example, pos(pos( $\xi$ , paragraph, 3), sentence, -1) means "the last sentence of the 3rd paragraph of the generated text". For terminal variables, we define a level  $\ell$  of a text (Eq. 5), a string or number relation  $\circ$  or  $\oplus$  (Eq. 6), and a string or number value  $v_{\mathrm{str}}$  or  $v_{\mathrm{num}}$  (Eq. 7).  $\wedge$  represents the logical 'and' operator, and  $\vee$  represents the logical 'or'. With these definitions, we construct the following grammar:
+
+$$
+S \rightarrow (\text {l e v e l} (\xi) = \ell) \wedge M \quad (\text {c o n s t r a i n t s p e c i f i c a t i o n}) \tag {1}
+$$
+
+$$
+M \rightarrow C \mid C \wedge M \mid C \vee M \quad (\text {m u l t i - c o n s t r a i n t}) \tag {2}
+$$
+
+$$
+C \rightarrow \operatorname {c o u n t} (T, \ell , v _ {\mathrm {s t r}} \mid \ell^ {\prime}) \oplus v _ {\mathrm {n u m}} \mid \operatorname {p o s} (T, \ell , v _ {\mathrm {n u m}}) \circ v _ {\mathrm {s t r}} \quad (\text {b a s e - c o n s t r a i n t}) \tag {3}
+$$
+
+$$
+T \rightarrow \xi \mid \operatorname {p o s} (T, \ell , v _ {\text {n u m}}) \tag {4}
+$$
+
+$$
+\ell \rightarrow \text {c h a r} | \text {w o r d} | \text {s e n t e n c e} | \text {p a r a g r a p h} | \text {p a s s a g e} \tag {5}
+$$
+
+$$
+\circ \rightarrow = | \neq \quad \oplus \rightarrow = | \neq | > | <   | \leq | \geq \tag {6}
+$$
+
+$$
+v _ {\mathrm {s t r}} \in \Sigma^ {*} \quad v _ {\mathrm {n u m}} \in \mathbb {Z} \tag {7}
+$$
+
+At the core of our grammar, we consider two (symmetrical) types of base-constraints  $C$  (Eq. 3):
+
+1. Count constraints. count  $(T,\ell ,v_{\mathrm{str}})\oplus v_{\mathrm{num}}$  constrains the occurrences of a particular level-  $\ell$  string  $v_{\mathrm{str}}$ . For example, count  $(T,$  word, happy')  $\leq 3$  means "T should contain the word happy' no more than 3 times". In contrast, count  $(T,\ell ,\ell^{\prime})\oplus v_{\mathrm{num}}$  constrains the occurrences of level-  $\ell$  strings in each level-  $\ell^{\prime}$  unit of text T. For example, count  $(T,$  char, sentence)  $= 50$  means "each sentence of text T should have exactly 50 characters".  
+2. Position constraints.  $\text{pos}(T, \ell, v_{\text{num}}) \circ v_{\text{str}}$  specifies that a particular part of the text  $T$  should equal (or not equal) the given string  $v_{\text{str}}$ . For example,  $\text{pos}(T, \text{word}, 3) = \text{'happy'}$  means "the 3rd word should be 'happy' in text  $T$ ". We also allow negative indices for reverse counting, e.g.  $\text{pos}(T, \text{char}, -1) \neq x$  means "the last letter should not be 'x' in text  $T$ ".
+
+Note that the grammar above can easily be extended to accommodate more types of base-constraints (e.g. part of speech, sentiment) by implementing the corresponding semantic checks — we leave this to future work. Also for convenience, we use constraint structure to refer to a family of constraint specifications that only differ in their values (e.g. generate a sentence with exactly  $x$  words,  $x \in \mathbb{N}$ ), and constraint to refer to a particular constraint specification with concrete values (e.g. generate a sentence with exactly 5 words).
+
+Examples and conceptual challenges. Our grammar can express a wide range of constraints through logical compositions of base-constraints across different text levels. Table II illustrates some structures across generation levels, identified by names such as para01 for paragraph generation, etc.
+
+In addition to the generation levels, count and pos across different levels introduce a variety of challenges. For example, word01 and sent01 challenge token-based language models to count characters; pass01 requires high-level semantic planning for models to generate a coherent passage under constraints; sent04 and para02 challenge models to generate text with presence or absence of particular words; sent03, para03, and para04 require counting at multiple levels; and word02, word03, sent02, para05, and pass01 combine counting and positional challenges at different levels, which can be considered most demanding conceptually. We empirically assess the difficulty of constraint structures in Section 5. Example COLLIE usage is presented in Figure 2
+
+```python
+from collieconstraints import ( Constraint, TargetLevel, Count, Relation   
+）   
+c  $=$  Constraint( target_level  $\equiv$  TargetLevel('word'), transformation  $\equiv$  Count(), relation  $\equiv$  Relation('==')，   
+）   
+text  $=$  'This is a good sentence.'   
+print(c.check(text,5)) # True
+```
+
+Figure 2: Example COLLIE code for a simple number of words constraint.
+
+Table 1: List of all constraint structures used in COLLIE-v1, with (simplified) example values.  
+
+<table><tr><td>ID</td><td>Example instruction</td><td>Multi-constraint M</td></tr><tr><td>word01</td><td>Generate a word with at least 15 letters.</td><td>count(ξ, char, word) ≥ 15</td></tr><tr><td>word02</td><td>Generate a word with 10 letters, where letter 1 is &#x27;s&#x27;, letter 3 is &#x27;r&#x27;, letter 9 is &#x27;e&#x27;.</td><td>count(ξ, char, word) = 10 ∧ pos(ξ, char, 1) = &#x27;s&#x27; ∧ pos(ξ, char, 3) = &#x27;r&#x27; ∧ pos(ξ, char, 9) = &#x27;e&#x27;</td></tr><tr><td>word03</td><td>Generate a word with at most 10 letters and ends with &quot;r&quot;.</td><td>count(ξ, char, word) ≤ 10 ∧ pos(ξ, char, -1) = &#x27;r&#x27;</td></tr><tr><td>sent01</td><td>Please generate a sentence with exactly 82 characters. Include whitespace into your character count.</td><td>count(ξ, char, sentence) = 82</td></tr><tr><td>sent02</td><td>Generate a sentence with 10 words, where word 3 is &quot;soft&quot; and word 7 is &quot;beach&quot; and word 10 is &quot;math&quot;.</td><td>count(ξ, word, sentence) = 10 ∧ pos(ξ, word, 3) = &quot;soft&quot; ∧ pos(ξ, word, 7) = &quot;beach&quot; ∧ pos(ξ, word, 10) = &quot;math&quot;</td></tr><tr><td>sent03</td><td>Generate a sentence with at least 20 words, and each word less than six characters.</td><td>count(ξ, word, sentence) ≥ 20 ∧ count(ξ, char, word) ≤ 6</td></tr><tr><td>sent04</td><td>Generate a sentence but be sure to include the words &quot;soft&quot;, &quot;beach&quot; and &quot;math&quot;.</td><td>count(ξ, word, &#x27;soft&#x27;) &gt; 0 ∧ count(ξ, word, &#x27;beach&#x27;) &gt; 0 ∧ count(ξ, word, &#x27;math&#x27;) &gt; 0</td></tr><tr><td>para01</td><td>Generate a paragraph where each sentence begins with the word &quot;soft&quot;.</td><td>pos(pos(ξ, sentence, 1), word, 1) = &#x27;soft&#x27; ∧ pos(pos(ξ, sentence, 2), word, 1) = &#x27;soft&#x27; ∧ ...</td></tr><tr><td>para02</td><td>Generate a paragraph with at least 4 sentences, but do not use the words &quot;the&quot;, &quot;and&quot; or &quot;of&quot;.</td><td>count(ξ, sentence, paragraph) ≥ 4 ∧ count(ξ, word, &#x27;the&#x27;) = 0 ∧ count(ξ, word, &#x27;and&#x27;) = 0 ∧ count(ξ, word, &#x27;of&#x27;) = 0</td></tr><tr><td>para03</td><td>Generate a paragraph with exactly 4 sentences, each with between 10 and 15 words.</td><td>count(ξ, sentence, paragraph) = 4 ∧ count(ξ, word, sentence) ≥ 10 ∧ count(ξ, word, sentence) ≤ 15</td></tr><tr><td>para04</td><td>Generate a paragraph with at least 3 sentences, each with at least 15 words.</td><td>count(ξ, sentence, paragraph) ≥ 3 ∧ count(ξ, word, sentence) ≥ 15</td></tr><tr><td>para05</td><td>Generate a paragraph with 2 sentences that end in &quot;math&quot; and &quot;rock&quot; respectively.</td><td>count(ξ, sentence, paragraph) = 2 ∧ pos(pos(ξ, sentence, 1), word, -1) = &quot;math&quot; ∧ pos(pos(ξ, sentence, 2), word, -1) = &quot;rock&quot;</td></tr><tr><td>pass01</td><td>Generate a passage with 2 paragraphs, each ending in &quot;I sit.&quot; and &quot;I cry.&quot; respectively.</td><td>count(ξ, paragraph, passage) = 2 ∧ pos(pos(ξ, paragraph, 1), sentence, -1) = &quot;I sit.&quot; ∧ pos(pos(ξ, paragraph, 2), sentence, -1) = &quot;I cry.&quot;</td></tr></table>
+
+In conjunction with the grammar, we develop a set of compiling tools to help construct datasets with minimal human efforts. Concretely, the pipeline of dataset construction involves 4 stages (Figure 1):
+
+1. Specify constraint structures. Researchers can specify constraint structures (e.g. Table [1]), and optionally with a value range (e.g. "generate a sentence with  $x$  words", and  $5 \leq x \leq 10$ ). This is the only stage that involves manual effort.  
+2. Extract constraint values from corpora. We design an automatic extraction algorithm that runs through a given text corpus to find strings that fit a constraint structure with some value ranges. For example, given the constraint structure count( $\xi$ , word,  $\emptyset$ ) =  $x$  with value range  $5 \leq x \leq 10$ , the extraction algorithm returns sentences in the corpus that have 5-10 words, with associated word counts. This ensures each constraint has at least one natural solution. More details are in Section 4.1.  
+3. Render natural language instructions. Each constraint can be rendered into a natural language instruction (Table I) via ruled-based translation, thanks to the compositionality grammar of COLLIE. For example, a constraint count  $(\xi ,\mathrm{char},\mathrm{'v'}) = 2\land \mathrm{count}(\xi ,\mathrm{char},\mathrm{'i'}) = 3$  can be synthetically rendered into the instruction "Please generate a word with exactly 2 character 'v' and exactly 3 character 'i'". It is also possible to improve the instruction fluency or naturalness by adding additional rules to the synthetic translation, or use LLMs to polish instructions. More details are in Section A.1  
+4. Evaluate generations. Given text  $\xi$  generated by a model, we use a parser to evaluate it against a constraint specification  $S$  and derive a True/False value, indicating if  $\xi$  satisfies  $S$ . We use an average success rate as the main metric to evaluate constraint conformance. We can also compare the fluency of  $\xi$  against the corpus-extracted "groundtruth" text, and render more fine-grained natural language feedback indicating which base-constraints are met and which not (see Section A.2).
+
+# 4 COLLIE-V1 DATASET
+
+We construct COLLIE-v1 using constraints structures from Table [1], which contains 2,080 constraint instances from 13 constraint types, with 1,435 unique constraint prompts. The broader NLP community can contribute to future dataset releases by adding additional constraints, metrics, data sources. The curated constraint set can co-evolve with models to become more challenging and comprehensive as model capabilities improve.
+
+# 4.1 CONSTRAINT SPECIFICATION AND EXTRACTION
+
+Constraint specification. We begin by defining 13 constraint structures. We chose these 13 structures to span various generation levels (word, sentence, paragraph and passage generation) and challenges (counting, position). In total, we have 3 word-level, 4 sentence-level, 5 paragraph-level, and 1 passage-level constraint structures. Of these 13 constraint structures, 5 are single-level and the remaining 8 are multi-level constraints. See Table  $\boxed{1}$  for the exact constraint structures we use.
+
+Constraint extraction. While constructing constraint structures is straightforward using our grammar, choosing constraint targets is challenging for two reasons: (1) Not all targets will admit a conforming natural language string. For instance, the constraint, "Generate a two word sentence beginning with the word The." has no grammatically acceptable answer. (2) Even if a constraint admits a possible answer, it may not admit a plausible answer. For instance, "Generate a sentence with 1928 words" is possible, but any such sentence is very unlikely to appear in regular discourse.
+
+To address both challenges, we sample constraint target values from natural language corpora, which we denote as the data source. Given a constraint structure  $\mathcal{C}$  and documents  $\bar{\mathcal{D}} = \{d_1,\dots,d_n\}$ , we chunk each document into a series of strings  $d_{i} = \{s_{1},\ldots ,s_{m}\}$ , where each  $s_i$  can be a sentence, paragraph, or passage as required by  $\mathcal{C}$ . Each string  $s_i$  undergoes source-specific automated filtering and post-processing to remove artifacts, which we detail in Section B.4. Given  $\mathcal{C}$  and  $s_i$ , we extract target values such that  $\mathcal{C}$  is satisfied. In most cases, the satisfying target values can be directly extracted using our provided utilities. For example, for constraints with structure "sentence with  $x$  words", we can directly apply word tokenization and counting to the example string  $s_i$ . In cases in which direct extraction is not possible, (e.g. "do not include word  $w$ ", we specify a range of possible targets (e.g.  $\{\text{the, and, of}\}$ ) to sweep over. All in all, our approach ensures that (1) there exists a natural language string that can satisfy each constraint and target pair, and (2) the targets follow a
+
+![](images/01ce8992ba7b73db65efdf9993dc1d61d35679af620de85fa810c35b9457cd50.jpg)  
+Figure 3: Data statistics. (a) Number of constraints from each constraint structure. (b) Fraction of strings removed by automated filtering. (c) Length statistics for different levels for each data source.
+
+plausible distribution induced by natural language corpora. Our extraction system is extensible, and can operate on new constraints and data sources with minimal modifications.
+
+Extensibility Adding additional data sources to the extraction pipeline is similarly easy, requiring a text delimiter, and optional string filtering and post-processing functions. As a case-study on the extensibility of COLLIE, we demonstrate how to extend constraints to include POS-tags such as "Generate a sentence with verbs". Details are in section B.5
+
+# 4.2 DATA SOURCES
+
+To adequately cover diverse styles and content, we extract constraint targets from three distinct data sources: Wikipedia (Wiki) (Foundation 2022), Common Crawl News (CC-News) (Hamborg et al., 2017), and the Project Gutenberg Corpus (Guten) (Brooke et al., 2015). We provide an overview of these data sources below and leave source-specific filtering and post-processing details to Section B.4.
+
+Wiki. Wikipedia (Wiki) (Foundation, 2022) consists of over 6 million English Wikipedia articles. We included this data source for the diverse subject matter present in the corpus.
+
+CC-News. The Common Crawl News corpus (CC-News) (Hamborg et al., 2017) consists of 708,241 English language news articles published between Jan 2017 and December 2019. We include CC-News to include interview dialogues, as well as popular culture and current events.
+
+Gutenberg. The Project Gutenberg corpus (Gutenberg) (Brooke et al., 2015) consists of over 50,000 documents that include fiction, histories, biographies, and other works that are in the public domain in the United States. We include this corpus for its variety in genres (e.g. non-fiction, fiction, plays, etc.) and style from different time periods.
+
+# 4.3 DATA VALIDATION AND STATISTICS
+
+We extract constraints from 300 randomly sampled documents from each source. After extracting the target values, we sample up to 100 targets for each constraint structure on each data source. We remove any string targets by that begins or ends with any character that is not a letter or number. We randomly sample 5 out of these 100 targets and their supporting examples to qualitatively verify their validity. Since the extraction process is relatively fast, we modify filters and post-processors if there are systemic issues and re-run the extraction phase. We provide statistics of the final number of constraints from each constraint structure in Figure 3(a). Some constraints (e.g. number of sentences per paragraph) are tightly clustered around the mean, and thus do not induce many valid constraint targets. The fraction of strings filtered for each data source and level is presented in Figure 3(b). The automated filtering removes a large fraction of the strings in most cases, as high recall is important to ensure quality. The high fraction of omitted passages is due to the removal of passages  $< 2$  paragraphs in length. Mean lengths for each level and data source is presented in Figure 3(c).
+
+![](images/6b6eab43112355755f7b14a01044efd6d5914b3325db40ab1afacdd8e70213c5.jpg)
+
+![](images/1825101045b3b15ff858efe1e838cecfd41095f5a2dce0272f5af54be9b90efb.jpg)
+
+![](images/3a32528f3008e967250353b651fbbcd29d6aa9f41102f6cd2a007bed377f8659.jpg)
+
+![](images/7746b3793a446682089bca37b96b155db9322db1b0f84229443c62c0b84f390a.jpg)  
+Figure 4: Model comparison. (a) Overall model performance summarized by weighted average across all constraint groups. (b) -(f) Constraint satisfaction rates of generated texts by GPT-4, GPT-3.5, PaLM, Vicuna-7B, and Alpaca-7B across various constraint groups. Error bars represent standard error. Constraint group names are in Table[1]. Sample sizes are reported in Figure[11].
+
+![](images/faea035ee0248327fc781704a1967adccd662af44781b93a8dfa9e6528aa8759.jpg)
+
+![](images/3990fa850e201da5848b8ef95819c04532ce077cb1efe581fe659fd3ac0bf35d.jpg)
+
+# 5 RESULTS
+
+Our main experiments in this paper focus on a zero-shot prompting setup with the following language models (LMs): 1) larger and closed-source LMs such as OpenAI GPT (Brown et al., 2020; OpenAI, 2023b) (gpt-3.5-turbo, gpt-4) and Google PaLM-2 (Anil et al., 2023) (text-bison-001); 2) smaller and open-source LMs such as Alpaca-7B (Taori et al., 2023), Vicuna-7B (Chiang et al., 2023). We performed additional one-shot prompting and find GPT performances similar to zero-shot performance, see Section C.1 By default, we use a sampling temperature of 0.7, and sample multiple trials (20 for GPT/PaLM, 5 for Alpaca/Vicuna). All experiments were run in July, 2023.
+
+Zero-shot performance comparison. As evidenced in Figures  $\boxed{4}$  (a), GPT-4 consistently surpassed other models in zero-shot constrained text generation performances, achieving more than twice the constraint satisfaction rate than other non-GPT models. The overarching performance trend observed shows GPT-4 leading the pack, followed by GPT-3.5 and PaLM with a large gap, and then followed closely by the smaller models, Vicuna-7B and Alpaca-7B.
+
+Constraints all models can follow. Certain tasks, specifically word01 (generating a word with at least  $a$  letters), sent04 (generating a sentence containing words X, Y, Z), and para01 (generating a paragraph with each sentence starting with the word X), posed minimal challenge to the majority of contemporary language models. These tasks demonstrate the proficiency of current models at simple constraints ensuring existence, as depicted in Figure 9(f).
+
+Constraints partially solved by GPT-4 only. However, a notable distinction arose when tasks incorporated more counting/position constraints and requested longer generations. Tasks such as word03, para04, para05, and pass01 were only partially addressed by GPT-4, with constraint satisfaction rates ranging between  $40\%$  and  $70\%$ . Despite GPT-4's partial success in these tasks, other models failed to deliver any satisfactory performance.
+
+Constraints remaining very challenging. Furthermore, some tasks proved challenging across all models. Tasks word02, sent01, sent02, and para03 present challenges in terms of arbitrary position constraints and mixed counting levels (see Section 5.1 for detailed analysis), indicating areas that necessitate further advancements in language model technology. Moreover, the average pass@20 rate of GPT-4 was above  $63\%$  across all constraints, significantly higher than the  $32\%$  achieved by GPT-3.5, as depicted in Figure 5. Although GPT-4 demonstrated a significant performance advantage, its constraint satisfaction rate of  $63\%$  is far from perfect. This suggests considerable scope for improvement in controllable text generation with language models. These findings underscore the opportunities and challenges in the continued evolution of language models.
+
+![](images/6f67cbdcb1076513d92bcedd29649678189a4abc57e724a9560c725e7a2a21f9.jpg)  
+Figure 5: Pass@k performance. We sample the model-generated text 20 times for all instruction prompts in the dataset. The curves represent the average pass rate across all instruction prompts up to  $k$  samples. The shaded areas indicate the standard errors.
+
+![](images/8956c2d695e53a39a8e708e0b11f41011a926dbd79ecccb2984d0cf4cf340927.jpg)  
+Figure 6: Position effect. Satisfaction rates of LMs on tasks involving pos( $\xi$ , level, i). The tasks word02 and sent02 impose constraints on characters and words at arbitrary positions. The task para01 constrains the first word. The tasks word03, para05, and pass01 constrain the last characters, words, and sentences.
+
+![](images/fcfac2bc7b35d16406eeabc7718fc32ba808e0bc8940f349d3736a77429f107c.jpg)  
+Figure 7: Counting level effect. Satisfaction rates for LMs on tasks involving count  $(\xi, \text{level}, \varphi)$ . Task word01 sets a minimum word length of  $a$ . Task sent01 requires exactly  $a$  characters in a sentence. Task sent03 asks a sentence to contain at least  $b$  words, with each word no longer than  $a$  letters. Task para04 asks a paragraph to consist of at least  $b$  sentences, each containing a minimum of  $a$  words. Task para03 further imposes an upper limit on the number of words per sentence.
+
+# 5.1 ANALYSIS
+
+Performance consistency across data sources. We observe a high degree of consistency in the performance of models on a given constraint structure, regardless of the data source. This uniformity is evident across all models, as highlighted in Figure 9(g). This indicates that the ability of a language model to adhere to the logic of constraints takes precedence over the specific target values or the distribution of the data.
+
+Position effect. As depicted in Figure 6 the pos( $\xi$ , level,  $i$ ) function, constraining the  $i$ -th sub-string (letter, word, or sentence), exhibits varying levels of difficulty depending on the value of  $i$ . Models generally perform well when the positional constraint is applied to the first sub-string ( $i = 1$ , task para01). However, only GPT-4 displays partial success with the last positional constraints ( $i = -1$ , tasks word03, para05, pass01). Notably, all models encounter difficulties when generating text that satisfies positional constraints at arbitrary positions  $i$ . Additionally, we find that the position effect exhibits a lower sensitivity to constraint levels.
+
+Counting level effect. Counting characters within a word is easier than within a sentence for models, as illustrated in Figure 7. Furthermore, tasks demanding exact equality (task sent01) prove more
+
+![](images/471269170ae74081720e4f808fc6a4a9801d20359d50c5746ef9e75f651cea1f.jpg)  
+(a) Constraint satisfaction rate -GPT-4 (4th round)
+
+![](images/82f1151ff67057b168d70e00c3bdb0bdd39065ae2de3a056d0899d07bf93d226.jpg)  
+Figure 8: GPT-4 interactive generation performance. (a) Constraint satisfaction rate of GPT-4 generated texts in the 4th round across various constraint groups. (b) GPT-4 overall performance in different feedback rounds. The 1st round is zero-shot, and the 2nd - 4th rounds are with feedback.
+
+challenging than those requiring a range (task para03), and are considerably more difficult than tasks specifying just an upper or lower bound (tasks word01, sent03, para04).
+
+Increased difficulty with logical composition. The incorporation of logical compositions into constraints considerably increases their difficulty. Task sent03 serves as an example of this, adding an extra constraint at the sentence level compared to task word01. Despite the assumption that the added constraint should be manageable for all models, performance on task sent03 uniformly trails behind that on task word01, as shown in Figure 7. This highlights the intricacy and challenge introduced by logical compositions within constraints.
+
+Performance enhancement through feedback and interaction. We utilize COLLIE to generate automated natural language feedback (e.g., "Your task is to generate a word with exactly 2 character 'v' and exactly 3 character 'i'. However, you generate a word with 3 character 'v' and 4 character 'i') and engage LLMs in a generation-feedback dialogue. In Figure 8 we observe a significant  $20\%$  improvement in GPT-4 performance after the second round of feedback. However, the model's performance plateaus at  $66\%$  even after three additional rounds of feedback, comparable to pass@5 using i.i.d. sampling. The extent of performance improvement varies across tasks, with word03's constraint satisfaction rate increasing from  $62.1\%$  to  $10\%$ . Conversely, word02, sent01, and sent02 tasks remain challenging for the model. These findings suggest that there is still room for improvement, highlighting the difficulty of our dataset, and emphasizing the need for further research on better ways to incorporate natural language feedback.
+
+# 6 CONCLUSION
+
+In this work, we present COLLIE, a grammar-based framework for specifying textual constraints. COLLIE simplifies the process of creating constrained-generation datasets by enabling researchers to focus on specifying high level constraint structures, while COLLIE automatically extracts constraint values, renders natural language instructions, and assesses model performance. To demonstrate the utility of the COLLIE framework, we construct COLLIE-v1 with 1,132 constraints from 13 different types, extracted from 3 different data sources. We evaluate five state-of-the-art LLMs of various sizes on COLLIE-v1, and find that it provides fine-grained insights into model capabilities and shortcomings. We hope that model developers can use COLLIE-v1 to develop more capable models, while future releases of COLLIE can continue to adapt to the capabilities and needs of future models and users.
+
+# LIMITATIONS AND SOCIETAL IMPACTS
+
+Although care was taken to design the filtering and processing functions, such automated approaches are never perfect and remaining artifacts in corpora might lead to unnatural reference texts or constraints. Further filtering (e.g., by grammar checkers, parsers, or humans) could improve the dataset quality. Our representative constraint structures were selected to encompass diverse constrained generation challenges, but as with all generation benchmarks, they cannot capture all dimensions
+
+and nuances of model capabilities. Benchmarks are highly influential in shaping model development, the capabilities and limitations of which may disproportionately impact different communities. Our benchmark is no exception. However, by providing an extensible, easy-to-use framework for constraint development, we hope COLLIE will enable diverse stakeholders to engage with dataset building, helping ensure that future model capabilities serve diverse interests and needs.
+
+# ACKNOWLEDGEMENTS
+
+We thank Xiao Liu for Vicuna/Alpaca APIs that supported our preliminary experiments, and Princeton NLP Group for helpful discussion and feedback in general. We acknowledge support from a Princeton SEAS Innovation grant and the National Science Foundation under Grant No. 2239363. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
+
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+# COPLANNER: PLAN TO ROLL OUT CONSERVATIVELY BUT TO EXPLORE OPTIMISTICALLY FOR MODEL-BASED RL
+
+Xiyao Wang $^{1}$  Ruijie Zheng $^{1}$  Yanchao Sun $^{2}$   
+Ruonan Jia $^{3}$  Wichayaporn Wongkamjan $^{1}$  Huazhe Xu $^{3,4}$  Furong Huang $^{1}$ $^{1}$ University of Maryland, College Park  $^{2}$ JPMorgan AI Research  
+ $^{3}$ Tsinghua University  $^{4}$ Shanghai Qi Zhi Institute  
+{xywang, rzheng12, wwongkam, furongh}@umd.edu  
+yanchao.sun@jpmchase.com jiaruanan97@gmail.com  
+huazhe_xu@mail.tsinghua.edu.cn
+
+# ABSTRACT
+
+Dyna-style model-based reinforcement learning contains two phases: model rollouts to generate sample for policy learning and real environment exploration using current policy for dynamics model learning. However, due to the complex real-world environment, it is inevitable to learn an imperfect dynamics model with model prediction error, which can further mislead policy learning and result in sub-optimal solutions. In this paper, we propose COPlanner, a planning-driven framework for model-based methods to address the inaccurately learned dynamics model problem with conservative model rollouts and optimistic environment exploration. COPlanner leverages an uncertainty-aware policy-guided model predictive control (UP-MPC) component to plan for multi-step uncertainty estimation. This estimated uncertainty then serves as a penalty during model rollouts and as a bonus during real environment exploration respectively, to choose actions. Consequently, COPlanner can avoid model uncertain regions through conservative model rollouts, thereby alleviating the influence of model error. Simultaneously, it explores high-reward model uncertain regions to reduce model error actively through optimistic real environment exploration. COPlanner is a plug-and-play framework that can be applied to any dyna-style model-based methods. Experimental results on a series of proprioceptive and visual continuous control tasks demonstrate that both sample efficiency and asymptotic performance of strong model-based methods are significantly improved combined with COPlanner. Our code is available at https://github.com/umd-huang-lab/COPlanner.
+
+# 1 INTRODUCTION
+
+Model-Based Reinforcement Learning (MBRL) has emerged as a promising approach to improve the sample efficiency of model-free RL methods. Most MBRL methods contain two phases that are alternated during training: 1) the first phase where the agent interacts with the real environment using a policy to obtain samples for dynamics model learning; 2) the second phase where the learned dynamics model rolls out to generate massive samples for updating the policy. Consequently, learning an accurate dynamics model is critical as the model-generated samples with high bias can mislead the policy learning (Deisenroth and Rasmussen, 2011; Wu et al., 2022).
+
+![](images/043872ffbd2d77995abdf89d726290702748b13e4b41cb1cff58f0b39a6a120e.jpg)  
+Figure 1: Mean performance of COplanner compared with baselines across 3 diverse benchmarks.
+
+However, dynamics model errors are inevitable due to the complex real-world environment. Existing methods try to avoid model errors in two main ways. 1) Design different mechanisms such as filtering out error-prone samples to mitigate the influence of model errors after model rollouts (Buckman et al., 2018; Yu et al., 2020; Pan et al., 2020; Yao et al., 2021). 2) Actively reduce model errors during
+
+![](images/26cc1baa5992537cb20c541df90b6f5dceea2a31c202bbeb493a498c5f643889.jpg)  
+Figure 2: COPlanner Framework. The most essential part of COplanner is the Uncertainty-aware Policy-Guided MPC (UP-MPC) phase in which we plan trajectories of length  $H$ , according to the learned dynamics model and learned policy network  $\pi$ , to select the action with highest trajectory reward. This UP-MPC phase is implemented differently for the two different purposes: environment exploration v.s. dynamics model rollouts. In environment exploration, trajectory reward has an uncertainty bonus term to encourage exploring uncertain regions in the environment. In dynamics model rollouts, trajectory reward, on the contrary, has an uncertainty penalty term to encourage policy learning on confident regions of the learned dynamics model.
+
+real environment interaction through uncertainty-guided exploration (Shyam et al., 2019; Ratzlaff et al., 2020; Sekar et al., 2020; Mendonca et al., 2021). While both categories of methods have achieved advancements, each comes with its own set of limitations. For the first category, although these approaches are shown to be empirically effective, they primarily concentrate on estimating uncertainty at the current step, often neglecting the long-term implications that present samples might have on model rollouts. Moreover, post-processing samples after model rollouts can compromise rollout efficiency as many model-generated samples are discarded or down-weighted. As for the second category, it is intrinsically challenging to achieve low model error and high long-term reward without sacrificing the sample efficiency by learning exploration policies.
+
+To tackle the aforementioned limitations, we introduce a novel framework, COPlanner, which mitigates the model errors from two aspects: 1) avoid being misled by the existing model errors via conservative model rollouts, and 2) keep reducing the model error via optimistic environment exploration. The two aspects are achieved simultaneously by a novel uncertainty-aware multi-step planning method, which requires no extra exploration policy training nor additional samples, resulting in stable policy updates and high sample efficiency. COPlanner is structured around three core components: the Planner, conservative model rollouts, and optimistic environment exploration. In the Planner, we employ an Uncertainty-aware Policy-guided Model Predictive Control (UP-MPC) to forecast future trajectories in terms of selecting actions and to estimate the long-term uncertainty associated with each action. As shown in Figure 2, this long-term uncertainty serves as dual roles. In the model rollouts phase, the uncertainty acts as a penalty on the total planning trajectory, guiding the selection of conservative actions. Conversely, during the model learning phase, it serves as a bonus on the total planning trajectory, steering towards optimistic actions for environment exploration.
+
+Compared to previous methods, COPlanner has the following advantages: (a) COPlanner has higher exploration efficiency, as it focuses on investigating high-reward uncertain regions to broaden the dynamics model, thereby preventing unnecessary excessive exploration of areas with low rewards. (b) COPlanner has higher model-generated sample utilization rate. Through planning for multi-step model uncertainty estimation, COPlanner can prevent model rolled out trajectories from falling into uncertain areas, thereby avoiding model errors before model rollouts and improving the utility of model generated samples. (c) COPlanner enjoys an unified policy framework. Unlike previous methods (Sekar et al., 2020; Mendonca et al., 2021) that require training two separate policies for different usage, COPlanner only requires training a single policy and we only change the way model-based planning is utilized, thus improving training efficiency and resolving potential policy distribution mismatches. (d) COPlanner ensures undistracted policy optimization. Notably, COPlanner diverges from existing approaches by not using long-term uncertainty as an intrinsic reward. Instead, the policy's objective remains focused on maximizing environmental rewards, thereby avoiding the introduction of spurious behaviors due to model uncertainty.
+
+Summary of Contributions: (1) We introduce COPlanner framework which can mitigate the influence of model errors during model rollouts and explore the environment to actively reduce model errors simultaneously by leveraging our proposed uncertainty-aware policy-guided MPC. (2)
+
+COPlanner is a plug-and-play framework that can be applicable to any dyna-style MBRL method. (3) After being integrated with other MBRL baseline methods, COPlanner improves the sample efficiency of these baselines by nearly double. (4) Besides, COPlanner also significantly improves the performance on a suite of proprioceptive and visual control tasks compared with other MBRL baseline methods (16.9% on proprioceptive DMC, 32.8% on GYM, and 9.6% on visual DMC).
+
+# 2 PRELIMINARIES
+
+Model-based reinforcement learning. We consider a Markov Decision Process (MDP) defined by the tuple  $(S, A, T, \rho_0, r, \gamma)$ , where  $S$  and  $A$  are the state space and action space respectively,  $T(s'|s, a)$  is the transition dynamics,  $\rho_0$  is the initial state distribution,  $r(s, a)$  is the reward function and  $\gamma$  is the discount factor. In model-based RL, the transition dynamics  $T$  in the real world is unknown, and we aim to construct a model  $\hat{T}(s'|s, a)$  of transition dynamics and use it to find an optimal policy  $\pi$  which can maximize the expected sum of discounted rewards,
+
+$$
+\pi = \underset {\pi} {\operatorname {a r g m a x}} \mathbb {E} _ {s _ {t} \sim \hat {T} (\cdot | s _ {t - 1}, a _ {t - 1})} \left[ \sum_ {t = 0} ^ {\infty} \gamma^ {t} r (s _ {t}, a _ {t}) \right]. \tag {1}
+$$
+
+Model predictive control. Model predictive control (MPC) has a long history in robotics and control systems (Garcia et al., 1989; Qin and Badgwell, 2003). MPC find the optimal action through trajectory optimization. Specifically, given the transition dynamics  $T$  in the real world, the agent obtains a local solution at each step  $t$  by estimating optimal actions over a finite horizon  $H$  (i.e., from  $t$  to  $t + H$ ) and executing the first action  $a_{t}$  from the computed optimal sequence at time step  $t$ :
+
+$$
+a _ {t} = \underset {a _ {t: t + H}} {\operatorname {a r g m a x}} \mathbb {E} \left[ \sum_ {i = t} ^ {H} \gamma^ {i} r \left(s _ {i}, a _ {i}\right) \right], s _ {i} \sim T (\cdot | s _ {i - 1}, a _ {i - 1}), \tag {2}
+$$
+
+where  $\gamma$  is typically set to 1. In model-based control methods, the transition dynamics  $T$  is simulated by the learned dynamics model  $\hat{T}$  (Chua et al., 2018; Wang and Ba, 2019; Hansen et al., 2022).
+
+# 3 THE COPLANNER FRAMEWORK
+
+In this section, we will introduce COPlanner framework. COPlanner consists of three components: the Planner, conservative model rollouts, and optimistic environment exploration. Within the Planner, we propose using an Uncertainty-aware Policy-guided MPC to predict potential future trajectories when selecting different actions under the current state and estimate the long-term uncertainty associated with each action, which will be introduced in Sec 3.1. Depending on the phase, this long-term uncertainty is used to further guide the selection of conservative actions for policy learning or optimistic actions for environment exploration which will be introduced in Sec 3.2 and Sec 3.3.
+
+# 3.1 "THE PLANNER": UNCERTAINTY-AWARE POLICY-GUIDED MPC
+
+In this section, we present the core part of our proposed framework which is called Uncertainty-aware Policy-guided MPC (UP-MPC). Inspired by MPC, we apply the random shooting method (Rao, 2009) to introduce a long-term vision. Specifically, given the current state  $s_t$ , before each interaction with the
+
+![](images/3d0b57e7c183e2f6d863a9faded684c141634cc888d13c553c19ebfe8ca099c2.jpg)  
+Figure 3: The Planner.
+
+model or real environment, we first generate an action candidate set containing  $K$  actions using the policy:  $\pmb{a}_{t} = \{a_{t}^{(1)}, a_{t}^{(2)}, \dots, a_{t}^{(k)}\}$ . Then, for each action candidate, we perform  $H_{p}$ -step planning and calculate the reward  $r$ , and model uncertainty  $u$  for each step. Finally, we select the action according to accumulated reward and model uncertainty, (to interact with the learned dynamics for the model rollouts or to interact with the environment for the model learning), as will be discussed in details in Sec 3.2 and Sec 3.3.
+
+Incorporating model uncertainty is crucial for action selection to compensate for model error. As illustrated in Algorithm 1, we calculate the model uncertainty  $u$  through the model disagreement
+
+(Pathak et al., 2019) method. Model disagreement is closely related to model learning and is currently the most common way to estimate model uncertainty in MBRL (Yu et al., 2020; Kidambi et al., 2020; Pan et al., 2020; Sekar et al., 2020; Yao et al., 2021; Mendonca et al., 2021). We train a dynamics model ensemble  $\hat{T}_{\theta} = \{\hat{T}_{\theta}^{(1)}, \hat{T}_{\theta}^{(2)}, \dots, \hat{T}_{\theta}^{(n)}\}$  to predict the next state given the current state-action pair  $(s_t, a_t)$  as input. Utilizing the ensemble, we approximate the model uncertainty by calculating the variance over predicted states of the different ensemble members. This estimation closely represents the expected information gain (Pathak et al., 2019):
+
+$$
+u \left(s _ {t}, a _ {t}\right) = \frac {1}{N - 1} \sum_ {n} \left(\hat {T} _ {\theta} ^ {(n)} \left(s _ {t}, a _ {t}\right) - \mu^ {\prime}\right) ^ {2}, \quad \mu^ {\prime} = \frac {1}{N} \sum_ {n} \hat {T} _ {\theta} ^ {(n)} \left(s _ {t}, a _ {t}\right). \tag {3}
+$$
+
+See Figure 3 for the illustration of the process. The pseudocode for the Planner, i.e., the UP-MPC process, is summarized in Algorithm 1.
+
+Algorithm 1 The Planner: UP-MPC  $(\pi_{\phi}, s, \hat{T}_{\theta}, K, H, \alpha)$
+
+Require: Policy  $\pi_{\phi}$ , State  $s$ , learned dynamics model  $\hat{T}_{\theta}$ , number of candidates actions  $K$ , planning horizon  $H_{p}$ , optimistic/conservative parameter  $\alpha$
+
+1: Initialize  $R^{(k)} = 0$  for  $k = 1, \dots, K$ ,  $s_0^{(k)} = s$  for  $k = 1, \dots, K$  
+2: for  $k = 1$  to  $K$  do  
+3: for  $t = 0$  to  $H_{p} - 1$  do  
+4: Sample  $a_{t}^{(k)}\sim \pi_{\phi}(\cdot |s_{t}^{(k)})$  
+5: Rollout dynamics model  $r_t^{(k)} = \hat{R}(\cdot | s_t^{(k)}, a_t^{(k)})$ ,  $s_{t+1}^{(k)} \sim \hat{T}_{\theta}(\cdot | s_t^{(k)}, a_t^{(k)})$  
+6: Compute model uncertainty  $u_{t}^{(k)}$  according to Eq. 3  
+7:  $R^{(k)} = R^{(k)} + r_t^{(k)} + \alpha u_t^{(k)}$  
+8: Select  $k^* = \arg \max_{k=1,\dots,K} R^{(k)}$  
+9: return  $a_0^{(k^*)}$
+
+Although in Algorithm 1 model uncertainty  $u$  is implemented through model disagreement, our proposed UP-MPC is a generic framework, any method for calculating intrinsic rewards to encourage exploration can be embedded into our framework for computing  $u$ . In Appendix D.5 we provide an ablation study of uncertainty estimation methods to further illustrate this point.
+
+# 3.2 CONSERVATIVE MODEL ROLLOUTS
+
+In model-based RL, due to the limited samples available for model learning, model prediction errors are inevitable. If a policy is trained using model-generated samples with a large error, these samples will not provide correct gradient and may mislead the policy update. Previous methods estimate the model uncertainty of each sample after generation and re-weight or discarded samples with high uncertainty. However, re-weighting samples based on uncertainty still leads to samples with high uncertainty participating in the policy learning process, while filtering requires manually setting an uncertainty threshold, and determining the optimal threshold is difficult. Discarding too many samples can result in inefficient rollouts.
+
+We apply our Planner to plan for maximizing the future reward while minimizing the model uncertainty during model rollouts before executing the action. After calculating the reward and model uncertainty for the  $H_{p}$ -step trajectories of  $K$  action candidates (line 5 and 6 in Algorithm 1), we replace  $\alpha = -\alpha_{c}$ , for a positive  $\alpha_{c} > 0$  at line 7 in Algorithm 1. Mathematically, we select the action according to Eq. 4 to interact with the model for model rollouts:
+
+$$
+a = \operatorname {a r g m a x} _ {a _ {t} \in \boldsymbol {a} _ {t}} \left[ r \left(s _ {t}, a _ {t}\right) + \sum_ {i = 1} ^ {H _ {p}} r \left(\hat {s} _ {t + i}, \pi \left(\hat {s} _ {t + i}\right)\right) - \alpha_ {c} \sum_ {i = 1} ^ {H _ {p}} u \left(\hat {s} _ {t + i}, \pi \left(\hat {s} _ {t + i}\right)\right) \right], \hat {s} _ {t + i} \sim \hat {T} (\cdot | \hat {s} _ {t + i - 1}, a _ {t + i - 1}). \tag {4}
+$$
+
+The negative  $-\alpha_{c}$  is a coefficient that adds the model uncertainty as a penalty term to the trajectory total reward. By employing this approach, we can prevent model rollout trajectories from falling into model-uncertain regions while obtaining samples with higher rewards.
+
+# 3.3 OPTIMISTIC ENVIRONMENT EXPLORATION
+
+In addition to model rollouts, another crucial part of MBRL is interacting with the real environment to obtain samples to improve the dynamics model. Since the main purpose of MBRL is to improve
+
+sample efficiency, we should acquire more meaningful samples for improving the dynamics model within a limited number of interactions. Therefore, unlike previous methods that merely aimed to thoroughly explore the environment to obtain a comprehensive model (Shyam et al., 2019; Ratzlaff et al., 2020; Sekar et al., 2020), we do not expect the dynamics model to learn all samples in the state space. This is because many low-reward samples do not contribute to policy improvement. Instead, we hope to obtain samples with both high rewards and high model uncertainty to sufficiently expand the model and reduce model uncertainty.
+
+Similar to model rollouts, we also employ our Planner in the process of selecting actions when interacting with the environment. However, the difference lies in that we replace  $\alpha = \alpha_{o}$ , for a positive  $\alpha_{o} > 0$  at line 7 in Algorithm 1. Mathematically, we choose the action with both high cumulative rewards and model uncertainty according to Eq. 5, which is a symmetric form of Eq. 4.  $\alpha_{o}$  is a hyperparameter to balance the reward and exploration. Such an action can guide the trajectory towards regions with high rewards and model uncertainty in the real environment, thereby effectively expanding the learned dynamics model.
+
+$$
+a = \operatorname {a r g m a x} _ {a _ {t} \in \boldsymbol {a} _ {t}} \left[ r \left(s _ {t}, a _ {t}\right) + \sum_ {i = 1} ^ {H _ {p}} r \left(\hat {s} _ {t + i}, \pi \left(\hat {s} _ {t + i}\right)\right) + \alpha_ {o} \sum_ {i = 1} ^ {H _ {p}} u \left(\hat {s} _ {t + i}, \pi \left(\hat {s} _ {t + i}\right)\right) \right], \hat {s} _ {t + i} \sim \hat {T} (\cdot | \hat {s} _ {t + i - 1}, a _ {t + i - 1}) \tag {5}
+$$
+
+In summary, by simultaneously using conservative model rollouts and optimistic environment exploration, COPlanner effectively alleviates the model error problem in MBRL. As we will show in Section 5, this is of great help in improving the sample efficiency and performance. The pseudocode of COPlanner is shown in Algorithm 2, and a more detailed figure is shown in Appendix A. Very importantly, COPlanner achieves both conservative model rollouts and optimistic environment exploration using a single policy. Different from prior exploration methods, the policy that COPlanner learns does not have to be an "exploration" policy which is inevitably suboptimal.
+
+Algorithm 2 Main Algorithm: COPlanner  
+Require: Interaction epochs  $I$ , rollout horizon  $H_{r}$ , planning horizon  $H_{p}$ , number of candidates actions  $K$ , conservative rate  $\alpha_{c}$ , optimistic rate  $\alpha_{o}$   
+1: Initialize policy  $\pi_{\phi}$ , dynamics model  $\hat{T}$ , real sample buffer  $\mathcal{D}_e$ , model sample buffer  $\mathcal{D}_m$   
+2: for  $I$  epochs do  
+3: while not Done do  
+4: Select action  $a_{t} = \mathbf{UP - MPC}(\pi_{\phi}, s_{t}, \hat{T}_{\theta}, K, H_{p}, \alpha_{o})$   
+5: Execute in real environment, add  $(s_{t}, a_{t}, r_{t}, s_{t + 1})$  to  $\mathcal{D}_e$   
+6: Train dynamics model  $\hat{T}_{\theta}$  with  $\mathcal{D}_e$   
+7: for  $M$  model rollouts do  
+8: Sample initial states from real sample buffer  $\mathcal{D}_e$   
+9: for  $h = 0$  to  $H_{r}$  do  
+10: Select action  $\hat{a}_{t + h} = \mathbf{UP - MPC}(\pi_{\phi}, \hat{s}_{h}, \hat{T}_{\theta}, K, H_{p}, -\alpha_{c})$   
+11: Rollout learned dynamics model and add to  $\mathcal{D}_m$   
+12: Update current policy  $\pi_{\phi}$  with  $\mathcal{D}_m$
+
+# 4 RELATED WORK
+
+Mitigating model error by improving rollout strategies. Prior methods primarily focus on using dynamics model ensembles (Kurutach et al.; Chua et al., 2018) to assess model uncertainty of samples after they were generated by the model, and then apply weighting techniques (Buckman et al., 2018; Yao et al., 2021), penalties (Kidambi et al., 2020; Yu et al., 2020) or filtering (Pan et al., 2020; Wang et al., 2022) to those high uncertainty samples to mitigate the influence of model error. These methods only quantify uncertainty after generating the samples and since their uncertainty metrics are based on the current step and are myopic, these metrics can not evaluate the potential influence of the current sample on future trajectories. Therefore, they fail to prevent the trajectories, which is generated through model rollout on the current policy, from entering high uncertainty regions, eventually leading to a failed policy update. Wu et al. (Wu et al., 2022) proposed Plan to Predict (P2P), which reverses the roles of the model and policy during model learning to learn an uncertainty-foreseeing model, aiming to avoid model uncertain regions during model rollouts. Combined with MPC, their method achieved promising results. However, their approach lacks effective exploration of the environment. Branched rollout (Janner et al., 2019) and bidirectional rollout (Lai et al., 2020) take advantage of
+
+small model errors in the early stages of rollouts and uses shorter rollout horizons to avoid model errors, but these approaches limit the planning capabilities of the learned dynamics model. Besides, different model learning objectives (Shen et al., 2020; Eysenbach et al., 2022; Wang et al., 2023; Zheng et al., 2023b) are designed to solve objective mismatch (Lambert et al., 2020) in model-based RL and further mitigate model error during model rollouts.
+
+Reducing model error by improving environment exploration. Another approach to mitigate model error is to expand the dynamics model by obtaining more diverse samples through exploration during interactions with the environment. However, previous methods mostly focused on pure exploration, i.e., how to make the dynamics model learn more comprehensively (Lowrey et al., 2018; Shyam et al., 2019; Ratzlaff et al., 2020; Sekar et al., 2020; Seyde et al., 2020; Ball et al., 2020; Mendonca et al., 2021; Hu et al., 2023). In complex environments, thoroughly exploring the entire environment is very sample-inefficient and not practical in real-world applications. Moreover, using pure exploration to expand the model may lead to the discovery of many low-reward samples, which are not very useful for policy learning. Mendonca et al. (Mendonca et al., 2021) proposed Latent Explorer Achiever (LEXA) which involves a explorer for exploring the environment and one achiever for solving diverse tasks based on collected samples, but the explorer and achiever may experience policy distribution shift under specific single-task settings, causing the achiever to potentially not converge to the optimal solution.
+
+Mitigating model error from both sides. One most relevant work is Model-Ensemble Exploration and Exploitation (MEEE) (Yao et al., 2021) which simultaneously expands the dynamics model and reduces the impact of model error during model rollouts. During the rollout process, it uses uncertainty to weight the loss calculated for each sample to update the policy and the critic. Before interacting with the environment, they first generate  $k$  action candidates and then select the action with the highest sum of Q-value and one-step model uncertainty to execute. However, as we mentioned earlier, weighting samples cannot fundamentally prevent the impact of model errors on policy learning, and it may still mislead policy updates. Moreover, since the one-step prediction error of dynamics models is often small (Pan et al., 2020), relying only on the sum of Q-values and one-step model uncertainty may not effectively differentiate action candidates. As a result, samples collected during interactions with the environment might not efficiently expand the model.
+
+# 5 EXPERIMENT
+
+In this section, we conduct experiments to investigate following questions: (a) Can COplanner be applied to both proprioceptive control MBRL and visual control MBRL methods, to improve their sample efficiency and asymptotic performance? (b) How does each component of COplanner impact the performance? (c) How does COplanner influence model learning and model rollouts?
+
+# 5.1 EXPERIMENT ON PROPRIOCEPTIVE CONTROL TASKS
+
+Baselines: In this section, we conduct experiments to demonstrate the effectiveness of COPlanner on proprioceptive control MBRL methods. We combine COPlanner with MBPO (Janner et al., 2019), the most classic method in proprioceptive control dyna-style MBRL, and we name the combined method as COPlanner-MBPO. The implementation details can be found in Appendix B. Consequently, MBPO naturally becomes one of our baselines. The other three baselines are P2P-MPC (Wu et al., 2022), MEEE (Yao et al., 2021), and M2AC (Pan et al., 2020). These three methods also aim to mitigate the impact of model errors in model-based RL. We choose one of the most popular model-free RLatheod D4PG (Barth-Maron et al., 2018) as another baseline. More details of P2P-MPC, MEEE, and M2AC can be found in Section 4. We also provide comparison with more proprioceptive control MBRL methods in Appendix D.1.
+
+Environment and hyperparameter settings: We conduct experiments on 8 proprioceptive continuous control tasks of DeepMind Control (DMC) and 4 proprioceptive control tasks of MuJoCo-GYM (GYM). MBPO trains an ensemble of 7 networks as the dynamics model while using the Soft Actor-Critic (SAC) as the policy network. In COPlanner-MBPO, we adopt the setting of MBPO and directly use the dynamics model ensemble to calculate model uncertainty for action selection in Policy-Guided MPC. For hyperparameter setting, we set optimistic rate  $\alpha_{o}$  to be 1, conservative rate  $\alpha_{c}$  to be 2 in all tasks, and set action candidate number  $K$ , planning horizon  $H_{p}$  equal to 5 in all tasks. The specific setting are shown in the Appendix C.1.
+
+![](images/5ef5d05215a99bf6cdadcaa9cd58343f349c9b1c2028b98cf1d9961115f24e07.jpg)
+
+![](images/4f4d2c211a4c3d0c91e5f7dc540f3207519d291192ada8cf75bba2f0026b4143.jpg)
+
+![](images/5515cd5bbdb336172b7b5d5b68de3b9195710ad2be6b9333c69685c1a1b87c2f.jpg)
+
+![](images/513ea153d7ec185f529a834b8a8e5111020dfb7d9ae30e25bbc54b7fedd440c1.jpg)
+
+![](images/1cfdf983a1fce1aa778a90bd8471b4b0cdcf5053b96fa8857729d663a4a8cf65.jpg)
+
+![](images/47c35323ad5972784860e5b5526515aff56c566419072a6cd538bb7f1113ce43.jpg)
+
+![](images/ad978f52282844835865419980be2fafc7790abefd685cb508c730fc7c88d19e.jpg)
+
+![](images/95176d0ddede74bdc7aad454b6d11627fe010575e9e1705168c5a9d9a5fadd5d.jpg)
+
+![](images/1bf968076e08bd3c8b81da0446b4063b0a43fc0f80dcd48ad639359802b037b0.jpg)  
+Figure 4: Experiment results of COPlanner-MBPO and other five baselines on proprioceptive control environments. The curves in the first eight figures originate from DM Control tasks, while those in the last four are from GYM tasks. The results are averaged over 8 random seeds, and shaded regions correspond to the  $95\%$  confidence interval among seeds. During evaluation, for each seed of each method, we test for up to 1000 steps in the test environment and perform 10 evaluations to obtain an average value. The evaluation interval is every 1000 environment steps.
+
+![](images/4a0dc7f06af44ce961445f3d4e78024d167135f09b39e6a496e712903bb93ffa.jpg)
+
+![](images/2e862d411e47621e00482a9ade9ed19141daf4b0835223c19731b1a4f102daf0.jpg)
+
+![](images/108c7a95db204f3d3c47b124f06a5a619a9c5dc2db84e367307389da64578c9c.jpg)
+
+COPlanner significantly improves the sample efficiency and performance of MBPO: Through the results in Figure 4 we can find that both sample efficiency and performance of MBPO have a significant improvement after combining COplanner. (a) Sample efficiency: In proprioceptive control DMC, the sample efficiency is improved by  $40\%$  on average compared to MBPO. For example, in the Walker-walk task, MBPO requires 100k steps for the performance to reach 700, while COplanner-MBPO only needs approximately 60k steps. In more complex GYM tasks, the improvement brought by COplanner is even more significant. Compared to MBPO, the sample efficiency of COplanner-MBPO has almost doubled. (b) Performance: From the performance perspective, as shown in Figure 1, the performance of MBPO has improved by  $16.9\%$  after combining COplanner. Moreover, it is worth noting that our method successfully solves the Walker-run task, which MBPO fails to address, further demonstrating the effectiveness of our proposed framework. In GYM tasks, the average performance at convergence has increased by  $32.8\%$ . Besides, COplanner-MBPO also outperforms other baselines.
+
+# 5.2 EXPERIMENT ON VISUAL CONTROL TASKS
+
+Baselines: We conduct experiments to demonstrate the effectiveness of our proposed framework on visual control environments. We integrate our algorithm with DreamerV3 (Hafner et al., 2023), the state-of-the-art Dyna-style model-based RL approach recently introduced for visual control. The implementation details can be found in Appendix B. We choose LEXA (Mendonca et al., 2021) as our another baseline. LEXA uses Plan2Explore (Sekar et al., 2020) as intrinsic reward to explore the environment and learn a world model, then using this model to train a policy to solve diverse tasks such as goal achieving. Since pure exploration base on Plan2Explore is sample inefficient for model learning when solving specific tasks, we use the real reward provided by environment as extrinsic reward and add it to intrinsic reward provided by Plan2Explore to train the explorer. We adopt this method on DreamerV3 and call it LEXA-reward-DreamerV3. Besides, we compare our method with the SOTA model-free visual RL method DrQV2 (Yarats et al., 2021). We also provide comparison with more visual control MFRL and MBRL methods in Appendix D.2.
+
+Environment and hyperparameter settings: We use 8 visual control tasks of DMC as our environment. In COPlanner-DreamerV3, we learn a latent one-step prediction dynamics model as Plan2Explore (Sekar et al., 2020), the ensemble size is 8. We set action candidate number  $K$  and planning horizon  $H_{p}$  equal to 4 in all tasks. For optimistic rate  $\alpha_{o}$  and conservative rate  $\alpha_{c}$ , we set them to be 1 and 0.5, respectively. Other hyperparameters remain consistent with DreamerV3 paper.
+
+COPlanner significantly improves the sample efficiency and performance of DreamerV3: From the experiment results in Figure 5, we observe that COPlanner-DreamerV3 improves the
+
+![](images/0645fc82d4f7c4dd41abbec1adb5136fe46a619b1860f6fb899278dd03c8f14a.jpg)
+
+![](images/a3ddf6f995104aaf8597cd2a338ba43cf3b93ce07ed36c743951c5cb752778e0.jpg)
+
+![](images/094cad4cbcea6918becb652030f344e204307adf60aa1fed86088fb2991a13d8.jpg)
+
+![](images/4e3b47efbb406f29132efb6bd6021fac79e80bb89feb9820abbbfb3206a06c81.jpg)
+
+![](images/38c8e7d3ecc5301c9349fd524286f80166fa62f698c5741a91f2569c1bb63652.jpg)  
+Figure 5: Experiment results of COPlanner-Dreamerv3 and other three baselines on pixel-input DMC. The results are averaged over 8 random seeds, and shaded regions correspond to the  $95\%$  confidence interval among seeds. During evaluation, for each seed of each method, we test for up to 1000 steps in the test environment and perform 10 evaluations to obtain an average value. The evaluation interval is every 1000 environment steps.
+
+![](images/5c5ab64d4310953a87e6b30711ff0a80eea3a1d7cbc5f2019ed31101551e2ae2.jpg)
+
+![](images/91f58ef78ed2a33657e0abbe64be8f63e281584db2d484790f1e93bcb46954bc.jpg)
+
+![](images/3a8e2381c428c3187fb87940efe6b76f9fb20fdf1d5ddc93ed7d1318f7142033.jpg)
+
+sample efficiency and performance significantly over DreamerV3, and it demonstrated a significant advantage over DrQv2. The sample efficiency of COPlanner-DreamerV3 is more than twice that of DreamerV3, and the performance is improved by  $9.6\%$ . After adding real reward as extrinsic reward for explorer learning, LEXA-reward-DreamerV3 delivers performance comparable to DreamerV3 in most environments. It outperforms DreamerV3 in Cartpole-swingup-sparse and Hopper-stand. However, its performance and sample efficiency are still worse than COPlanner-DreamerV3, further indicates the effectiveness of COPlanner.
+
+# 5.3 ABLATION STUDY
+
+In this section, we aim to investigate the impact of different components within COPlanner on the sample efficiency and performance. We conduct experiments on two proprioceptive control DMC tasks (Walker-stand and Walker-run) using MBPO as baseline and two visual control DMC tasks (Hopper-hop and Cartpole-swingup-sparse) with DreamerV3 as baseline. The results are demonstrated in Figure 6. Due to page limitations, we provide the ablation study on various hyperparameters of COPlanner in Appendix D.4 and the ablation study of uncertainty estimation methods in Appendix D.5.
+
+From this ablation study, we can see that effectively combining optimistic exploration and conservative rollouts is necessary to achieve the best results. We find that when only using optimistic exploration (COPlanner w. Explore only), the sample efficiency and performance in all tasks are significantly improved, which highlights the importance of expanding the model. When only using conservative rollouts (COPlanner w. Rollout only), there is some improvement in sample efficiency and performance but to a lesser extent. In more complex visual control tasks, only using conservative rollouts may lead to over-conservatism, resulting in an inability to learn an effective policy in sparse reward environments (as observed with a broken seed in Cartpole-swingup-sparse) or a decrease in sample efficiency during the early stages of learning (Hopper-hop). This is reasonable because conservative rollouts may avoid high uncertainty and high reward areas to ensure the stability of policy updates. Moreover, without efficiently expanding the model, it is challenging to find better solutions using only conservative rollouts in complex visual control tasks. Experimental results show that both optimistic exploration and conservative rollouts are crucial, and using either one individually can lead to an improvement in performance. When combining the two (as in COPlanner), we can achieve the best results, further demonstrating the effectiveness of our method.
+
+# 5.4 MODEL ERROR AND ROLLOUT UNCERTAINTY ANALYSIS
+
+In this section, we will investigate the impact of COPlanner on model learning and model rollouts. We provide the curves of how model prediction error and rollout uncertainty change as the environment step increases in Figure 7. We conduct experiments on two proprioceptive control DMC tasks (Cheetah-run and Walker-run) and two visual control DMC tasks (Hopper-hop and Cartpole-swingup-sparse).
+
+![](images/703e16586b0bc4e1ea2368c62a880e879444097ed8086c1d7983142d0b4a51e6.jpg)  
+Figure 6: Ablation studies of optimistic exploration and conservative rollouts on different tasks using different mbrl baselines. In the first two proprioceptive control tasks we use MBPO as baseline. For the last two visual control tasks we employ DreamerV3. The results are averaged over 8 random seeds. We can observe that the best results are achieved when combining optimistic exploration and conservative rollouts. The benefit is more pronounced in more-challenging visual tasks.
+
+![](images/48ac0dd5f176ac2a8d7e812f37da66d9adcb7ff244b9e252b5d231ed2b3a55e7.jpg)
+
+![](images/0d3ae2b04ad33d7c1ef4b0f36f280502bbbfbca11b99030ab826602bcb45d8b6.jpg)
+
+![](images/7ec280d3a56ad95bea52cb3059f11aef05738ed42b1220d0ff9c268555168468.jpg)
+
+![](images/0c41139b5e336b190a54872138dbe550ef37999aa357cf5520f9a4308ec45adb.jpg)  
+Figure 7: Model learning loss and rollout uncertainty curves for COplanner and two other model-based RL baselines. The left four are proprioceptive control DMC tasks, and the right four are visual control DMC tasks.
+
+![](images/3d65d4ba26d28d4c757141746996b01f2405bc2e7d0114ae56a28e7c81249ad8.jpg)
+
+![](images/c4ec617a499598ea4049a695d3adbe08edf073918f7b933dbe0d9e3c536779cc.jpg)
+
+![](images/8e5b6504b47416faf444908bdae8f45931b4ec36cbc405e1fedb7b5dd1ced454.jpg)
+
+(1) In proprioceptive control DMC, we use the MSE loss between model prediction and ground truth next state to evaluate model prediction error during training, while in visual control DMC, we use the KL divergence between the latent dynamics prediction and the next stochastic representation to compute latent model prediction error. We observe that after integrating COplanner in proprioceptive control tasks, the model prediction error is significantly reduced. In more complex visual control tasks, due to obtaining more diverse samples through exploration in the early stages of training, the model prediction error of COplanner is higher than the baseline (DreamerV3). However, as training progresses, the model prediction error rapidly decreases, becoming significantly lower than the model prediction error of DreamerV3. This allows the model to fully learn from the diverse samples, leading to an improvement in policy performance. (2) For the evaluation of rollouts uncertainty, we calculate the model disagreement for each sample in the model-generated replay buffer used for policy training using dynamics model ensemble. We find that COplanner significantly reduces rollout uncertainty due to conservative rollouts, suggesting that the impact of model errors on policy learning is minimized. This experiment further demonstrates that the success of COplanner is attributed to both optimistic exploration and conservative rollouts.
+
+# 6 CONCLUSION AND DISCUSSION
+
+We investigate how to effectively address the inaccurate learned dynamics model problem in MBRL. We propose COPlanner, a general framework that can be applied to any dyna-style MBRL method. COPlanner utilizes Uncertainty-aware Policy-Guided MPC phase to predict the cumulative uncertainty of future steps and symmetrically uses this uncertainty as a penalty or bonus to select actions for conservative model rollouts or optimistic environment exploration. In this way, COPlanner can avoid model uncertain areas before model rollouts to minimize the impact of model error, while also exploring high-reward model-uncertain areas in the environment to expand the model and reduce model error. Experiments on a range of continuous control tasks demonstrate the effectiveness of our method. One drawback of COPlanner is that MPC can lead to additional computational time and we provide a detailed computational time consumption in Appendix D.6. We can improve computational efficiency by parallelizing planning, which we leave for future work.
+
+# ACKNOWLEDGEMENT
+
+Wang, Zheng, and Huang are supported by National Science Foundation NSF-IIS-2147276 FAI, DOD-ONR-Office of Naval Research under award number N00014-22-1-2335, DOD-AFOSR-Air Force Office of Scientific Research under award number FA9550-23-1-0048, DOD-DARPA-Defense Advanced Research Projects Agency Guaranteeing AI Robustness against Deception (GARD) HR00112020007, Adobe, Capital One and JP Morgan faculty fellowships.
+
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+
+# Appendix
+
+# A DETAILED FIGURE OF COPLANNER
+
+We present a more detailed figure to illustrate our COPlanner framework. During environment exploration, we first choose an action using UP-MPC with multi-step uncertainty bonus, then interact with the real environment to obtain real samples for dynamics model learning. In dynamics model rollouts, at each rollout step, we select the actions using UP-MPC with multi-step uncertainty penalty to avoid model uncertain regions and interact with the learned dynamics model to get model-generated samples to update the policy.
+
+![](images/61a916b67d20eac8e7854fda188977aa3850d2e11a33ab76e9cec339ac0be853.jpg)  
+Figure 8: Figure illustration of COPlanner framework with more details.
+
+# B IMPLEMENTATION
+
+COPlanner framework is versatile and applicable to any dyna-style MBRL algorithm. In this section, we are going to introduce the implementation of two algorithms we used for experiment in Section 5: COPlanner-MBPO for proprioceptive control and COPlanner-DreamerV3 for visual control.
+
+# B.1 COPLANNER-MBPO
+
+MBPO (Janner et al., 2019) trains an ensemble of probabilistic neural networks (Chua et al., 2018) as dynamics model. It utilises negative log-likelihood loss to update each network in the ensemble:
+
+$$
+\mathcal {L} (\theta) = \sum_ {n = 1} ^ {N} \left[ \mu_ {\theta} ^ {b} \left(s _ {n}, a _ {n}\right) - s _ {n + 1} \right] ^ {\top} \Sigma_ {\theta} ^ {b - 1} \left(s _ {n}, a _ {n}\right) \left[ \mu_ {\theta} ^ {b} \left(s _ {n}, a _ {n}\right) - s _ {n + 1} \right] + \log \det  \Sigma_ {\theta} ^ {b} \left(s _ {n}, a _ {n}\right) \tag {6}
+$$
+
+For the policy component, MBPO adopts soft actor-critic (Haarnoja et al., 2018). We combine COplanner with MBPO, the pseudocode is shown in Algorithm 3.
+
+# B.2 COPLANNER-DREAMERV3
+
+DreamerV3 (Hafner et al., 2023) is a dyna-style MBRL method that solves long-horizon tasks from visual inputs purely by latent imagination. Its world model consists of an image encoder, a Recurrent
+
+Algorithm 3 COPlanner-MBPO  
+Require: interaction epochs  $I$  , rollout horizon  $H_{r}$  , planning horizon  $H_{p}$  , number of candidates actions  $K$  , conservative rate  $\alpha_{c}$  , optimistic rate  $\alpha_{o}$    
+1: Initialize policy  $\pi_{\phi}$  dynamics model ensemble  $\hat{T}_{\theta} = \{\hat{T}_{\theta}^{1},\dots,\hat{T}_{\theta}^{i}\}$  , real sample buffer  $\mathcal{D}_e$  , model sample buffer  $\mathcal{D}_m$    
+2: for I epochs do   
+3: for t = 1 to T do   
+4: // Optimistic environment exploration   
+5: Select action with optimistic rate  $a_{t} = \mathbf{UP - MPC}\bigl (\pi_{\phi},s_{t},\hat{T}_{\theta},K,H_{p},\alpha_{o}\bigr)$    
+6: Interact with the real environment with  $a_{t}$  , add real sample  $(s_t,a_t,r_t,s_{t + 1})$  to real sample buffer  $\mathcal{D}_e$    
+7: Train dynamics model  $\hat{T}_{\theta}$  via Equation 6   
+8: for M model rollouts do   
+9: Sample initial rollout states from real sample buffer  $\mathcal{D}_e$    
+10: for h = 0 to  $H_{r} - 1$  do   
+11: // Conservative model rollouts   
+12:  $\hat{a}_h = \mathbf{UP - MPC}\bigl (\pi_\phi ,\hat{s}_h,\hat{T}_\theta ,K,H_p, - \alpha_c\bigr)$  (Select action with conservative rate), rollout learned dynamics model and add to model sample buffer  $\mathcal{D}_m$    
+13: for  $G$  gradient updates do   
+14: Update current policy  $\pi_{\phi}$  using model-generated samples from model sample buffer  $\mathcal{D}_m$
+
+State-Space Model (RSSM) (Hafner et al., 2019b) to learn the dynamics, and predictors for the image, reward, and discount factor. The world model components are:
+
+Recurrent model:  $h_t = f_\phi(h_{t-1}, z_{t-1}, a_{t-1})$
+
+Representation model:  $z_{t} \sim q_{\phi}(z_{t}|h_{t},x_{t})$
+
+Transition predictor:  $\hat{z}_t\sim p_\phi (\hat{z}_t|h_t)$
+
+Image predictor:  $\hat{x}_t\sim p_\phi (\hat{x}_t|h_t,z_t)$
+
+Reward predictor:  $\hat{r}_t\sim p_\phi (\hat{r}_t|h_t,z_t)$
+
+Discount predictor:  $\hat{\gamma}_t\sim p_\phi (\hat{\gamma}_t|h_t,z_t)$
+
+where the recurrent model, the representation model, and the transition predictor are components of RSSM. The loss function for the world model learning is:
+
+$$
+\begin{array}{l} \mathcal {L} (\phi) = \mathbb {E} _ {q _ {\phi} (z _ {1: T} | a _ {1: T}, x _ {1: T})} [ \sum_ {t = 1} ^ {T} (- \ln p _ {\phi} (x _ {t} | h _ {t}, z _ {t}) - \ln p _ {\phi} (r _ {t} | h _ {t}, z _ {t}) - \ln p _ {\phi} (\gamma_ {t} | h _ {t}, z _ {t}) \tag {7} \\ + \beta_ {1} \max  (1, \mathrm {K L} [ s g (q _ {\phi} (z _ {t} | h _ {t}, x _ {t})) | | p _ {\phi} (z _ {t} | h _ {t}) ]) \\ + \beta_ {2} \max  (1, \mathrm {K L} [ q _ {\phi} (z _ {t} | h _ {t}, x _ {t}) | | s g (p _ {\phi} (z _ {t} | h _ {t}))) ]), \\ \end{array}
+$$
+
+where sg means stop gradient. Besides, DreamerV3 also use actor-critic framework as their policy. In particular, they leverage a stochastic actor that chooses actions and a deterministic critic. The actor and critic are trained cooperatively. The actor goal is to output actions leading to states that maximize the critic output, while the critic aims to accurately estimate the sum of future rewards that the actor can achieve from each imagined state (or model rollout state). For more training details about DreamerV3, please refer to their original paper (Hafner et al., 2023).
+
+To estimate model uncertainty in COPlanner-DreamerV3, we train an ensemble of one-step predictive models  $\hat{T}_{\theta} = \{\hat{T}_{\theta}^{1},\dots,\hat{T}_{\theta}^{i}\}$ , each of these models takes a latent stochastic state  $z_{t}$  and action  $a_{t}$  as input and predicts the next latent deterministic recurrent states  $h_t$ . The ensemble is trained using MSE loss. During model rollouts, we use the world model to generate trajectories, and the one-step model ensemble to evaluate the uncertainty of sample at each rollout step. Here we provide the pseudocode of COPlanner-DreamerV3 in Algorithm 4.
+
+Algorithm 4 COPlanner-DreamerV3  
+Require: Rollout horizon  $H_{r}$  , planning horizon  $H_{p}$  , number of candidates actions  $K$  , conservative rate  $\alpha_{c}$  , optimistic rate  $\alpha_{o}$    
+1: Initialize real sample buffer  $\mathcal{D}_e$  with S random seed episodes.   
+2: Initialize policy  $\pi_{\psi}$  , critic  $v_{\xi}$  , one-step model ensemble  $\hat{T}_{\theta} = \{\hat{T}_{\theta}^{1},\dots,\hat{T}_{\theta}^{i}\}$  , world model parameter  $\phi$    
+3: while not converged do   
+4: for update step  $c = 1..C$  do   
+5: Draw  $\mathcal{B}$  data sequences  $\{(a_t,x_t,r_t)\}_{t = k}^{k + L}\sim \mathcal{D}_e$    
+6: Compute a latent stochastic states  $z_{t}\sim q_{\phi}(z_{t}|h_{t},x_{t})$    
+7: Update world model parameter  $\phi$  via Equation 7   
+8: // Conservative model rollouts   
+9: Imagine trajectories  $\{(z_{\tau},a_{\tau})\}_{\tau = t}^{t + H_r}$  from each  $z_{t}$  with  $a_{\tau}$  = UP-MPC  $(\pi_{\psi},z_{\tau},\hat{T}_{\theta},K,H_{p}, - \alpha_{c})$    
+10: Update  $v_{\xi}$  and  $\pi_{\psi}$  using imagined trajectories.   
+11: for time step  $t = 1..T$  do   
+12: Compute  $z_{t}\sim q_{\phi}(z_{t}|h_{t},x_{t})$    
+13: // Optimistic environment exploration   
+14: Select action  $a_{t} = \mathrm{UP - MPC}(\pi_{\psi},z_{t},\hat{T}_{\theta},K,H_{p},\alpha_{o})$    
+15: Interact with the real environment and obatin  $(x_{t},a_{t},r_{t},x_{t} + 1)$    
+16: Add experience to  $\mathcal{D}_e\gets \mathcal{D}_e\cup \{(x_t,a_t,r_t,x_t + 1)\}_{t = 1}^T$
+
+# C HYPERPARAMETERS
+
+In this section, we provide the specific parameters used in each task in our experiments.
+
+Table 1: Hyperparameters of COPlanner-MBPO on proprioceptive control DMC.  
+
+<table><tr><td>Parameter</td><td>Value</td></tr><tr><td>Conservative rate αc</td><td>2</td></tr><tr><td>Optimistic rate αo</td><td>1</td></tr><tr><td>Action candidate number K</td><td>5</td></tr><tr><td>Planning horizon Hp</td><td>5</td></tr><tr><td rowspan="3">Real ratio</td><td>0.5 Reacher-xx</td></tr><tr><td>0.8 Finger-spin</td></tr><tr><td>0 Others</td></tr><tr><td rowspan="2">Rollout horizon Hr</td><td>[20, 150, 1, 1] Finger-spin</td></tr><tr><td>[20, 150, 1, 4] Others</td></tr></table>
+
+# C.1 PROPRIOCEPTIVE CONTROL DMC AND MUJOCO
+
+We use COPlanner-MBPO in all proprioceptive control tasks. For the dynamics model ensemble, we adopted the same setup as MBPO (Janner et al., 2019) original paper, with an ensemble size of 7 and an elite number of 5, which means each time we select the best five out of seven neural networks for model rollouts. Each network in the ensemble is MLP with 4 hidden layers of size 200, using ReLU as the activation function. We train the dynamics model every 250 interaction steps with the environment. The actor and critic structures are both MLP with 4 hidden layers. In proprioceptive control DMC, the hidden layer size of actor and critic is 512, and updated 10 times each environment step, while in MuJoCo the hidden layer size is 256, and they are updated 20 times each environment step. The batch size for model training and policy training is both 256. The learning rate for model training is 1e-3, while the learning rate for policy training is 3e-4.
+
+In MBPO, the authors use samples from both the real sample buffer and the model sample buffer to train the policy, and the ratio of the two is referred to as the real ratio. In addition, MBPO has a unique
+
+mechanism for the rollout horizon  $H_{r}$ , which linearly increases with the increase of environment epochs, with each environment epoch including 1000 environment steps.  $[a,b,x,y]$  denotes a thresholded linear function, i.e. at epoch  $e$ , rollout horizon is  $h = \min(\max(x + \frac{e - a}{b - a}(y - x), x), y)$ . The settings for conservative rate  $\alpha_{c}$ , optimistic rate  $\alpha_{o}$ , action candidate number  $K$ , planning horizon  $H_{p}$  and the above two parameters in different environments are provided in Table 1 and 2.
+
+Table 2: Hyperparameters of COPlanner-MBPO on MuJoCo.  
+
+<table><tr><td>Parameter</td><td>Value</td></tr><tr><td>Conservative rate αc</td><td>2</td></tr><tr><td>Optimistic rate αo</td><td>1</td></tr><tr><td>Action candidate number K</td><td>5</td></tr><tr><td>Planning horizon Hp</td><td>5</td></tr><tr><td>Real ratio</td><td>0.05</td></tr><tr><td rowspan="4">Rollout horizon Hr</td><td>[20, 100, 1, 4] Hopper</td></tr><tr><td>1 Walker</td></tr><tr><td>[20, 150, 1, 15] Ant</td></tr><tr><td>[20, 300, 1, 15] Humanoid</td></tr></table>
+
+# C.2 VISUAL CONTROL DMC
+
+In Visual control DMC, we use the COPlanner-DreamerV3 method. We keep all parameters consistent with the DreamerV3 original paper (Hafner et al., 2023), except for our newly introduced conservative rate  $\alpha_{c}$ , optimistic rate  $\alpha_{o}$ , action candidate number  $K$ , and planning horizon  $H_{p}$ . In Table 3, we provide the specific settings of conservative rate  $\alpha_{c}$ , optimistic rate  $\alpha_{o}$ , action candidate number  $K$ , and planning horizon  $H_{p}$  for each task. It's worth noting that, although using a conservative rate of 0.5 can perform well, we find that for the two tasks in Quadruped, using a conservative rate of 2 yields the best sample efficiency and performance. For other parameters, please refer to the original DreamerV3 paper. For the one-step predictive model ensemble, we use a model ensemble with ensemble size of 8. Each network in the ensemble is MLP with 5 hidden layers of size 1024.
+
+Table 3: Hyperparameters of COPlanner-DreamerV3 on visual control DMC. We keep all other hyperparameters consistent with the DreamerV3 original paper.  
+
+<table><tr><td>Parameter</td><td>Value</td></tr><tr><td>Conservative rate αc</td><td>0.5</td></tr><tr><td>Optimistic rate αo</td><td>1</td></tr><tr><td>Action candidate number K</td><td>4</td></tr><tr><td>Planning horizon Hp</td><td>4</td></tr></table>
+
+# D MORE EXPERIMENTS
+
+# D.1 COMPARISON WITH MORE PROPRIICE CONTROL MBRL METHODS
+
+In this section, we compared our approach with more proprioceptive control MBRL methods on MuJoCo tasks. In addition to the three baseline methods from Section 5.1, MBPO (Janner et al., 2019), P2P-MPC (Wu et al., 2022), and MEEE (Yao et al., 2021), we introduced two more baselines: PDML (Wang et al., 2023), a method that dynamically adjusts the weights of each sample in the real sample buffer to enhance the prediction accuracy of the learned dynamics model for the current policy, thereby significantly improving the performance of MBPO. And MoPAC (Morgan et al., 2021), a method that also uses policy-guided MPC to reduce model bias. Unlike our approach, MoPAC's policy-guided MPC is solely used for multi-step prediction during rollout based on total reward to
+
+select actions. It does not incorporate a measure of model uncertainty, and therefore, cannot achieve the optimistic exploration and conservative rollouts of COPlanner. The experiment results are shown in Table 4.
+
+As can be seen from Table 4, our method still holds a significant advantage, achieving the best performance in three tasks (Hopper, Walker2d, and Ant). In Humanoid task, it is only surpassed by PDML but is substantially better than the other methods. It's worth mentioning that our approach is orthogonal to PDML, and they can be combined. We believe that by integrating COPlanner with PDML, the performance can be further enhanced.
+
+Table 4: Comparison of different MBRL methods on proprioceptive control MuJoCo tasks. Performance is averaged over 8 random seeds.  
+
+<table><tr><td></td><td>Hopper (70k)</td><td>Walker2d (150k)</td><td>Ant (150k)</td><td>Humanoid (150k)</td></tr><tr><td>Ours</td><td>3360.3 ± 165.0</td><td>4595.3 ± 350.2</td><td>5268.3 ± 291.4</td><td>4833.7 ± 320.1</td></tr><tr><td>PDML</td><td>3274.2 ± 224.1</td><td>4378.5 ± 248.9</td><td>4992.5 ± 365.1</td><td>5396.7 ± 391.3</td></tr><tr><td>MBPO</td><td>2844.6 ± 158.0</td><td>4221.1 ± 281.1</td><td>2311.1 ± 252.5</td><td>1706.0 ± 976.3</td></tr><tr><td>P2P-MPC</td><td>2316.8 ± 459.9</td><td>4151.7 ± 516.9</td><td>4681.7 ± 591.6</td><td>3706.1 ± 1360.4</td></tr><tr><td>MEEE</td><td>3076.4 ± 165.3</td><td>3873.8 ± 549.6</td><td>3932.8 ± 352.7</td><td>654.2 ± 94.7</td></tr><tr><td>MoPAC</td><td>3174.2 ± 233.8</td><td>2893.6 ± 472.6</td><td>4382.5 ± 301.7</td><td>1084.6 ± 573.2</td></tr></table>
+
+Besides, we also conduct comparisons with DreamerV3 and D4PG on six medium-difficulty proprioceptive control DMC tasks, with the experimental results shown in the Figure 9. We find that after integrating with COPlanner, both sample efficiency and performance of DreamerV3 are improved significantly.
+
+![](images/1f65ed4a2c5cff37c3417a15bb258251e91225807b52acbc4bf82e5051bb225a.jpg)  
+Figure 9: Experiment results of COPlanner-DreamerV3 on 6 medium-difficulty proprioceptive control DMC tasks. The results are averaged over 8 random seeds, and shaded regions correspond to the  $95\%$  confidence interval among seeds.
+
+# D.2 COMPARISON WITH MORE VISUAL CONTROL METHODS
+
+In this section, we conducted comparisons with more MFRL and MBRL methods for visual control on 8 tasks from visual DMC. In addition to DreamerV3 (Hafner et al., 2023) and LEXA-reward-DreamerV3 (LEXA-RW), we introduced five more baselines. The first is TDMPC (Hansen et al., 2022). TDMPC learns a task-oriented latent dynamics model and uses this model for planning. During the planning process, TDMPC also learns a policy to sample a small number of actions, thereby accelerating MPC. The second is PlaNet (Hafner et al., 2019b). PlaNet uses the RSSM latent model, which is the same as the Dreamer series (Hafner et al., 2019a; 2020; 2023), and directly uses
+
+this model to perform MPC in the latent space to select actions. Additionally, we also include three more model-free visual RL baselines: TACO (Zheng et al., 2023a), DrM (Xu et al., 2024) and DrQ-v2 (Yarats et al., 2021). The experiment results are shown in Table 5. From the results, it is evident that our method has a significant advantage over all the baselines. In future work, as the representation in COPlanner is learned from scratch, we will also integrat pretrained visual representations such as Zheng et al. (2024); Majumdar et al. (2023); Nair et al. (2022) into the COPlanner algorithm framework to accelerate the learning process.
+
+Table 5: Performance comparison of different MBRL and MFRL methods on visual DMC tasks at 1 million environment steps.  
+
+<table><tr><td></td><td>Hopper-stand</td><td>Hopper-hop</td><td>Quadruped-walk</td><td>Quadruped-run</td></tr><tr><td>Ours</td><td>937.8 ± 9.7</td><td>444.2 ± 113.2</td><td>803.9 ± 59.3</td><td>787.9 ± 111.9</td></tr><tr><td>DreamerV3</td><td>888.5 ± 60.7</td><td>395.3 ± 50.1</td><td>749.2 ± 65.3</td><td>696.0 ± 132.2</td></tr><tr><td>LEXA-RW</td><td>905.7 ± 25.1</td><td>353.0 ± 33.8</td><td>591.0 ± 110.9</td><td>549.5 ± 186.2</td></tr><tr><td>TDMPC</td><td>821.6 ±70.8</td><td>189.2 ± 19.7</td><td>427.8 ± 50.2</td><td>393.8 ± 40.9</td></tr><tr><td>PlaNet (5m)</td><td>5.96</td><td>0.37</td><td>238.90</td><td>280.45</td></tr><tr><td>TACO</td><td>923 ± 22</td><td>261 ± 52</td><td>798 ± 15</td><td>531 ± 38</td></tr><tr><td>DrM</td><td>910 ± 15</td><td>162 ± 82</td><td>750 ± 29</td><td>452 ± 32</td></tr><tr><td>DrQ-v2</td><td>918 ± 12</td><td>192 ± 41</td><td>702 ± 42</td><td>407 ± 21</td></tr><tr><td></td><td>Acrobot-swingup</td><td>Cartpole-swingup-sparse</td><td>Finger-turn-easy</td><td>Finger-turn-hard</td></tr><tr><td>Ours</td><td>434.4 ± 31.0</td><td>787.5 ± 37.5</td><td>889.8 ± 28.3</td><td>867.1 ± 50.6</td></tr><tr><td>DreamerV3</td><td>354.9 ± 37.9</td><td>814.7 ± 22.3</td><td>853.9 ± 37.5</td><td>751.3 ± 93.1</td></tr><tr><td>LEXA-RW</td><td>337.7 ± 24.9</td><td>683.5 ± 145.6</td><td>825.5 ± 55.9</td><td>740.7 ± 162.0</td></tr><tr><td>TDMPC</td><td>227.5 ± 16.9</td><td>668.3 ± 49.1</td><td>703.8 ± 65.2</td><td>402.7 ± 112.6</td></tr><tr><td>PlaNet (5m)</td><td>3.21</td><td>0.64</td><td>451.22</td><td>312.55</td></tr><tr><td>TACO</td><td>241 ± 21</td><td>802 ± 21</td><td>752 ± 45</td><td>618 ± 17</td></tr><tr><td>DrM</td><td>228 ± 15</td><td>799 ± 7</td><td>692 ± 39</td><td>459 ± 36</td></tr><tr><td>DrQ-v2</td><td>210 ± 12</td><td>794 ± 14</td><td>576 ± 42</td><td>248 ± 52</td></tr></table>
+
+# D.3 EXPERIMENTS COMBINED WITH DREAMERV2
+
+We also combine COplanner with DreamerV2 (Hafner et al., 2020) for experimentation, with the results shown in Figure 10. After integrating with DreamerV2, our method also achieves a significant improvement in both sample efficiency and performance.
+
+![](images/46474934379a14288687b90cb1d98cce206cb9e7639eaf1f0daca78643cd6a8b.jpg)
+
+![](images/e0cd957db8bb4b1845466f64f18fe1d6500e75aef868f45958ca1b214cd7f1d7.jpg)
+
+![](images/4d88d0c08a112f9970a51298ef126e5382cc815ddbdc0d67e566a1229086e1be.jpg)
+
+![](images/0e722ef29407e726b3efe57e2c3558eecc7508cad26af76b502c79cbbe9e5562.jpg)
+
+![](images/c7451c55ad1304e3a78ab2ef1d7f2dcbe5a13d589264b087ce61fb2eb85ede63.jpg)  
+Figure 10: Experiment results of COPlanner-DreamerV2 on 7 visual control DMC tasks. The results are averaged over 4 random seeds, and shaded regions correspond to the  $95\%$  confidence interval among seeds. During evaluation, for each seed of each method, we test for up to 1000 steps in the test environment and perform 10 evaluations to obtain an average value. The evaluation interval is every 1000 environment steps.
+
+![](images/b563224bd2688cc9b54d4fa4b4f54a8b6b786ba480fb01a6e94fe146f42282d9.jpg)
+
+![](images/76642771d05cbc1e8fcbd8e913e8ea45fb62173f4397929644b406f3fbc7c038.jpg)
+
+![](images/29ca254b76a01857231cfc99870091b1ad0bbaa3599234d821ec060c000034d6.jpg)
+
+# D.4 HYPERPARAMETER STUDY
+
+![](images/12ddb6f2ddb0c08f94d85a5d86eedcee3b41c818f87c634ba70d1e33dc9b2859.jpg)  
+(a) COPlanner-MBPO on proprioceptive Walker-run
+
+![](images/5b10c50c57a9a26980e196854f5aa9ae2b3fbaae3037d1fa5576f5e662f7a1ee.jpg)
+
+![](images/2e9a0e47a7801a0a148d84ef94d323e6d7ec7841b25f38de79ac6591292a9580.jpg)
+
+![](images/b1ae9655caa5106a4fd276062998d4d3480474254baf914be7b85413b27e701b.jpg)
+
+![](images/9b54e48ebcf20c9f9084f8cd2f4258dfd36bb1c0de7c1ec5e09d9a851afe8962.jpg)  
+(b) COPlanner-MBPO on proprioceptive Cheetah-run
+
+![](images/ffec9d2a1d32c6a5516bf5f92261c1c23b8f4606adc7aefba2850d8e846b08bb.jpg)
+
+![](images/a47a403910eedcbf2936b15133a202ed00d7ad00bb5e8d50ca312acc625d818e.jpg)
+
+![](images/828e6240cf6cda5da34d782201713192d87687ce3bd82a6b5faabcec016e5c18.jpg)
+
+![](images/011eb7b7f53b948f4bdf94b617947ef6062b80b37694e9ddb89b47e37b958334.jpg)  
+(c) COPlanner-DreamerV3 on proprioceptive Hopper-hop
+
+![](images/8033b5aed5de068288619c1c3f39e56a74a16cdbfc2f0b1417b621c9da454608.jpg)  
+Figure 11: Ablation studies of COPlanner's different hyperparameters. Experiments are conducted using COPlanner-MBPO on proprioceptive Walker-run and proprioceptive Cheetah-run, and using COPlanner-DreamerV3 on proprioceptive Hopper-hop. The results are averaged over 4 random seeds. From left to right, the results are for different parameters of optimistic rate  $\alpha_{o}$ , conservative rate  $\alpha_{c}$ , action candidate number  $K$ , and planning horizon  $H_{p}$ .
+
+![](images/6f3b13f2c33ad23b51f687dc074d0ace77d796f809be9b1f0baf87abbb442d7a.jpg)
+
+![](images/120c0ca4e76dbb20c532b02a0c5723702a09d85a6b5fee0095651e75219ddb7f.jpg)
+
+In this section, we conduct hyperparameter studies to investigate the impact of different hyperparameters on COPlanner. We perform experiments on the Walker-run and Cheetah-run task of proprioceptive control DMC using COPlanner-MBPO, and on the Hopper-hop using COPlanner-DreamerV3. The original hyperparameter settings are: optimistic rate  $\alpha_{o}$  is 1, conservative rate  $\alpha_{c}$  is 2, action candidate number  $K$  is 5, and planning horizon  $H_{p}$  is 5. When conducting ablation experiments for each hyperparameter, other parameters remain unchanged. The results are shown together in Figure 11.
+
+Optimistic rate  $\alpha_{o}$ : we observe that the best  $\alpha_{o}$  lies between 0.5 to 1. When the  $\alpha_{o}$  is too large, COPplanner tends to excessively explore high uncertainty areas while neglecting rewards, leading to a decrease in sample efficiency and performance. On the other hand, when the  $\alpha_{o}$  is too small, COPplanner fails to achieve the desired exploration effect.
+
+Conservative rate  $\alpha_{c}$ : the optimal range for the  $\alpha_{c}$  is between 1 and 2. A too large  $\alpha_{c}$  may lead to overly conservative selection of low-reward actions, while a too small  $\alpha_{c}$  would be unable to make model rollouts avoid model uncertain areas.
+
+Action candidate number  $K$ : we find that  $K$  has a significant impact on sample efficiency and performance. When  $K$  is set to 2, the improvement of COPlanner over MBPO in terms of performance and sample efficiency is relatively limited. This is reasonable because if there are only a few action candidates, our selection space is very limited, and even with the use of uncertainty bonus and penalty to select actions, there may not be much difference. When  $K$  increases to more than 5, the effect of COPlanner becomes very stable, and more candidates do not bring noticeable improvements in performance and sample efficiency.
+
+Planning horizon  $H_{p}$ : when  $H_{p}$  is 1, we find that COPlanner's improvement on performance and sample efficiency is relatively limited. This also confirms what we mentioned in Section 1: only considering the current step while ignoring the long-term uncertainty impact cannot completely avoid model errors, as samples with low current model uncertainty might still lead to future rollout trajectories falling into model uncertain regions. As the planning horizon gradually increases, performance and sample efficiency also rise. When the planning horizon is too long ( $H_{p}$  equals to 7 or 9), it is possible that due to the bottleneck of the model planning capability, most action candidates' corresponding trajectories fall into model uncertain areas, leading to a slight decline in performance and sample efficiency.
+
+# D.5 ABLATION STUDY OF MODEL UNCERTAINTY ESTIMATION METHODS
+
+We conduct an ablation study on the Hopper-hop task in visual control DMC to evaluate different uncertainty estimation methods. We adopt two methods, RE3 (Seo et al., 2021) and MADE (Zhang et al., 2021), which are used to estimate intrinsic rewards in pixel input, to replace the disagreement in calculating  $u(s,a)$  in Equation 4 and 5. The results are shown in Figure 12. We find that the performance achieved using these two methods is similar to that of disagreement. This demonstrates that using disagreement to calculate uncertainty is not the primary reason for the observed performance improvement.
+
+![](images/d75d6c08fc563726f51a89562dc6d8c3e28b4fb908b5407ec10c304008370827.jpg)  
+Figure 12: Ablation study of different uncertainty estimation methods.
+
+# D.6 COMPUTATIONAL TIME CONSUMPTION OF COPLANNER
+
+We provide a comparison of the computational time consumption between the baseline methods and COplanner across different domains in Table 6. All timings are reported using a single NVIDIA 2080ti GPU.
+
+Table 6: Average time consumption (h).  
+
+<table><tr><td></td><td>MuJoCo</td><td>Proprioceptive DMC</td><td>Visual DMC</td></tr><tr><td>COPlanner-MBPO</td><td>41.2</td><td>11.3</td><td>N/A</td></tr><tr><td>MBPO</td><td>33.78</td><td>10.6</td><td>N/A</td></tr><tr><td>COPlanner-DreamerV3</td><td>N/A</td><td>N/A</td><td>17.9</td></tr><tr><td>DreamerV3</td><td>N/A</td><td>N/A</td><td>13.1</td></tr></table>
+
+# D.7 DIVERSITY EVALUATION OF REAL SAMPLE BUFFER
+
+In this section, to further demonstrate that our method achieves better exploration of the environment, we evaluate the average state entropy of the real sample buffer obtained using our method and DreamerV3 at 1 million environment steps. A higher average state entropy implies that the real sample buffer covers more states in the real environment, indicating that the samples in the real sample buffer are more diverse and thus suggesting more thorough exploration of the environment (Seo et al., 2021). We conduct evaluations on four visual DMC tasks include Hopper-hop, Quadruped-walk, Acrobot-swingup, and Finger-turn-hard. Following the work of RE3 (Seo et al., 2021), in order to estimate state entropy in environments with high-dimensional observations, we utilize a k-nearest neighbor entropy estimator in the low-dimensional representation space of a randomly initialized encoder. Our encoder consists of three convolutional layers with  $3 \times 3$  kernels, a stride of 2, and padding of 1, followed by a flattening layer. The activation function between each layer is ReLU. After passing through the encoder, each image from the replay buffer is compressed into a 512-dimensional latent state, and the k-nearest neighbor state entropy is estimated as follows:
+
+$$
+e \left(s _ {i}\right) = \log \left(\left\| y _ {i} - y _ {i} ^ {k - N N} \right\| _ {2} + 1\right), \tag {8}
+$$
+
+where where  $y_{i} = f_{\theta}(s_{i})$  is a fixed representation from a random encoder and  $y_{i}^{k - NN}$  is the k-nearest neighbor of  $y_{i}$  within a set of  $N$  representations  $\{y_1,y_2,\dots ,y_n\}$ . We set  $N = 1024$ . Then we average the k-nearest neighbor state entropy of each sample in real sample buffer. The final results are shown in Figure 13.
+
+![](images/3dcd3a2637f2af9d32c533af6f8f4246a8160131a891e977e358407ab76a84a4.jpg)  
+Figure 13: K-nearest neighbor state entropy estimation on different visual DMC tasks compared with DreamerV3.
+
+The figure clearly shows that the state entropy of the real sample buffer significantly increases after integrating our method. This indicates that the real samples obtained by our method are more diverse, achieving better exploration of the environment.
+
+# D.8 VISUALIZATION OF EXPERIMENT RESULTS
+
+![](images/b1de769544568208c66f9220329b28e1ef728554dca4f3bedadd1ae65a584a8c.jpg)  
+Figure 14: Visualization of policy learned by DreamerV3 on Hopper-hop.
+
+![](images/b766321298ed8fe2d80d5da772846b762fce4e332b488371a2c82d5593b737db.jpg)  
+Figure 15: Visualization of policy learned by COPlanner-DreamerV3 on Hopper-hop.
+
+![](images/8ca90cd114294903b0223ec7ac6c0fafaa8859a69a251f898c643570eab8c608.jpg)  
+Figure 16: Visualization of policy learned by DreamerV3 on Quadruped-walk.
+
+![](images/2af683b529dd8f3e1772ab652f88648b82f0c583dcb038c194927ba00e73c1c3.jpg)  
+Figure 17: Visualization of policy learned by COPlanner-DreamerV3 on Quadruped-walk.
+
+In this section, to better demonstrate the improvements brought by our method, we visualize the trajectories obtained from evaluations in the real environment after convergence using DreamerV3 and our method (COPlanner-DreamerV3). We visualize trajectories in Hopper-hop and Quadruped-walk tasks, as shown in Figure 14, 15, 16, and 17.
+
+From the comparison between Figure 14 and Figure 15, we can observe that in the Hopper hop task, DreamerV3 is only able to learn to jump using the knee, whereas our method can learn to jump using the feet and perform somersaults during the jump. Through the comparison of Figure 16 and Figure 17, we can see that in the Quadruped-walk task, our method is able to learn a more stable behavior of walking using all four legs, as opposed to DreamerV3, which learns to walk using only three legs.

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2024/CORN_ Contact-based Object Representation for Nonprehensile Manipulation of General Unseen Objects/1d7a7b6b-a145-4b8c-b679-d80f7046b674_content_list.json

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+[
+    {
+        "type": "text",
+        "text": "CORN: CONTACT-BASED OBJECT REPRESENTATION FOR NONPREHENSILE MANIPULATION OF GENERAL UNSEEN OBJECTS",
+        "text_level": 1,
+        "bbox": [
+            171,
+            98,
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+    {
+        "type": "text",
+        "text": "Yoonyoung Cho\\*, Junhyek Han\\*, Yoontae Cho, Beomjoon Kim",
+        "bbox": [
+            179,
+            194,
+            620,
+            210
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Korea Advanced Institute of Science and Technology",
+        "bbox": [
+            179,
+            210,
+            532,
+            223
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "{yoonyoung.cho, junhyek.han, yoontae.cho, beomjoon.kim}@kaist.ac.kr",
+        "bbox": [
+            179,
+            223,
+            836,
+            238
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT",
+        "text_level": 1,
+        "bbox": [
+            450,
+            273,
+            545,
+            289
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Nonprehensile manipulation is essential for manipulating objects that are too thin, large, or otherwise ungraspable in the wild. To sidestep the difficulty of contact modeling in conventional modeling-based approaches, reinforcement learning (RL) has recently emerged as a promising alternative. However, previous RL approaches either lack the ability to generalize over diverse object shapes, or use simple action primitives that limit the diversity of robot motions. Furthermore, using RL over diverse object geometry is challenging due to the high cost of training a policy that takes in high-dimensional sensory inputs. We propose a novel contact-based object representation and pretraining pipeline to tackle this. To enable massively parallel training, we leverage a lightweight patch-based transformer architecture for our encoder that processes point clouds, thus scaling our training across thousands of environments. Compared to learning from scratch, or other shape representation baselines, our representation facilitates both time- and data-efficient learning. We validate the efficacy of our overall system by zero-shot transferring the trained policy to novel real-world objects. Code and videos are available at https://sites.google.com/view/contact-non-prehensile.",
+        "bbox": [
+            228,
+            308,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION",
+        "text_level": 1,
+        "bbox": [
+            171,
+            561,
+            336,
+            577
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Robot manipulators can transform our day-to-day lives by alleviating humans from taxing physical labor. Despite this potential, they have remained largely confined to picking and placing objects in limited settings such as manufacturing or logistics facilities. One key reason for such confined usage is their limited action repertoire: while prehensile manipulation has made great improvements (Mahler et al., 2017; Wan et al., 2023), there are several situations in the wild where pick-and-place is not an option. For instance, consider the scenarios in Figure 1, where the robot is tasked to manipulate diverse household objects to a target pose. While the effective strategy differs for each object, the predominant approach of grasping and placing objects is not viable. To manipulate such objects in the wild, the robot must perform nonprehensile actions such as pushing, dragging, and toppling by reasoning about the object geometry (Kao et al., 2016).",
+        "bbox": [
+            169,
+            595,
+            826,
+            736
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Traditionally, this problem has been tackled using planning algorithms that model the dynamics of the system and compute motions using optimization (Posa et al., 2014) or tree search (Cheng et al., 2022). However, this necessitates full system information about object geometry and inertial parameters, which are generally unavailable from sensory observations, especially for novel objects. Even when such models are available, the complex search space renders planning algorithms impractically slow. Recently, deep reinforcement learning (RL) has surfaced as a promising alternative, where a nonprehensile policy is trained in a simulator (Kim et al., 2023; Zhou et al., 2023), then zero-shot transferred to the real world. However, no algorithm offers the level of generality over object shapes and diversity in motions necessary for our problem: they either generalize over objects but are confined to rudimentary motions such as poking (Zhou et al., 2023) or affords rich motions but uses a rudimentary object representation that precludes generalization over shapes (Kim et al., 2023).",
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+        "text": "Published as a conference paper at ICLR 2024",
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+        "type": "page_footnote",
+        "text": "*equal contribution",
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+            "Figure 1: Snapshot of our robot performing diverse real-world object manipulation tasks. The first column shows the initial and goal object pose (transparent) of the task, and the green region marks the robot's workspace. Row 1: Raising a cup bottom-side up. The cup's grasp and placement poses are occluded by the collision with the table; since the cup is dynamically unstable, the robot must also support the object to avoid toppling the object out of the workspace during manipulation. Row 2: Flipping the wipe dispenser upside down, which is too wide to grasp. Since it may roll erratically, frequent re-contacts and dense closed-loop motions are required to stabilize the object during manipulation. Row 3: Moving a book that is too thin to be grasped; to drag the book, the robot must finely adjust the pressure to allow for both reorientation and translation. Row 4: Flipping a toy crab. Given its concave geometry, the robot must utilize the interior contacts to pivot the crab.",
+            "(a) Case where the robot tries to topple the cup.",
+            "Figure 2: Even among similar-looking states, the interaction outcome varies drastically depending on the presence of contact. (a-left) the gripper passes near the cup, yet not quite in contact. As the robot narrowly misses the object, the object remains still. (a-right) the gripper engages with the cup, leading to a successful topple. (b-left) The robot relocates to the left of the block to push it to the goal(dark). By avoiding unintended collision, it is well-positioned to push the object. (b-right) due to spurious contact, the gripper accidentally topples the block, making the goal farther to reach."
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+            "(b) Case where the robot tries to push the block."
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+    {
+        "type": "text",
+        "text": "We propose a novel object representation learning algorithm for nonprehensile manipulation that can be jointly used with the action-space from Kim et al. (2023) to achieve both generality over shapes and diversity in motions. The key challenge is defining the pretraining task. Given that our objective is to generalize across shapes, one naive approach is to employ self-supervised shape-learning, where the geometric representation is trained on contrastive or shape-reconstruction objectives (Pang et al., 2022; Yu et al., 2022; Xie et al., 2020; Zeid et al., 2023). However, reconstructing the full shape representation is needlessly complex: the full shape includes many intricate features, such as internal geometry, concavities, or surface details, which may not directly influence the performance of the manipulation policy. Even for a complex object, only a subset of its surface interacts with the gripper. Thus, while the contactable parts of an object must be represented at high fidelity, the remainder can be omitted without influencing the performance of the downstream policy.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Our key insight is that recognizing the presence and location of contacts between the object and the robot's hand is crucial for nonprehensile manipulation. For RL, a good representation must necessarily distinguish between states with high and low values, and in contact-rich manipulation, this is primarily determined by what forces and torques can be applied to the object in the given state.",
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+    {
+        "type": "header",
+        "text": "Published as a conference paper at ICLR 2024",
+        "bbox": [
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+        "text": "2",
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+    {
+        "type": "text",
+        "text": "This, in turn, depends on the presence and position of the contact between the object and the robot's hand. This intuition is demonstrated in Figure 2. Based on this insight, we propose a pretraining task where the point cloud encoder is trained to predict what part of the object is in collision with the robot's end-effector.",
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+    {
+        "type": "text",
+        "text": "Our other contribution is the design of an efficient architecture that can process high-dimensional point clouds, in a way that can scale to massively parallel GPU-backed simulations. Existing well-known point-cloud processing architectures such as PointNet (Qi et al., 2016; 2017) inherently incur substantial inference time and memory usage while processing individual points. Inspired by the recent success of patch-based vision architectures (Dosovitskiy et al., 2020; Yu et al., 2022; Pang et al., 2022; Zhang et al., 2022; Zeid et al., 2023), we leverage a patch-based transformer to efficiently encode the point cloud. Since a single point in a point cloud does not carry significant information, grouping local points into a single unit(patch) (Yu et al., 2022) can effectively reduce the computational burden of launching thousands of point-wise operations as in PointNets (Qi et al., 2016) or Point-based Transformers (Zhao et al., 2021), resulting in significant computational gains.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We call our framework Contact-based Object Representation for Nonprehensile manipulation (CORN). We show that by leveraging CORN, we can efficiently train a nonprehensile manipulation policy that can execute dexterous closed-loop joint-space maneuvers without being restricted to predefined motion primitives. Further, by employing an efficient patch-based point-cloud processing backbone, we can achieve highly time-efficient training by allowing the policy to scale to massively parallel environments. By adopting our full system, we demonstrate state-of-the-art performance in nonprehensile manipulation of general objects in simulated environments and zero-shot transfer to unseen real-world objects.",
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+    {
+        "type": "text",
+        "text": "2 RELATED WORK",
+        "text_level": 1,
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+        "text": "Planning algorithms In planning-based approaches, a nonprehensile manipulation problem is often tackled using gradient-based optimization or graph search. In optimization, the primary challenge arises from optimizing the system of discontinuous dynamics, stemming from contact mode transitions. To combat this, prior works resort to softening contact mode decision variables (Mordatch et al., 2012) or introducing complementarity constraints (Posa et al., 2014; Moura et al., 2022). However, due to the imprecision from the smooth approximation of contact mode transitions, inexact contact dynamics models, and difficulty in precisely satisfying contact constraints, the resulting motions are difficult to realize in the real world. On the other hand, graph-search approaches handle discontinuous system dynamics by formulating the problem as a search over a graph on nodes encoding states such as the robot's configuration and the object's contact mode, and the edges encoding transition feasibility and relative motion between the nodes (Maeda & Arai, 2005; Maeda et al., 2001; Miyazawa et al., 2005). As a result of handling discrete dynamics transitions without approximation, these methods can output more physically realistic motions that can be deployed in the real world (Cheng et al., 2022; Liang et al., 2022). However, to make the search tractable, they resort to strong simplifications such as quasi-static assumption on the space of motions (Cheng et al., 2022; Hou & Mason, 2019), or restricting the edges to predefined primitives or contact modes (Zito et al., 2012). As a result, these works have been limited to tasks that only require simple motions and sparse contact-mode transitions.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Moreover, because both of these approaches must compute a plan in a large hybrid search space with discontinuous dynamics, they are too slow to use in practice. Further, they also require the physical parameters of objects, such as mass and friction coefficients, to be known a priori, which undermines the practicality of these methods. Since the objects may vary significantly in the wild (Figure 5), acquiring ground-truth geometric and physical attributes of target objects is intractable.",
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+    {
+        "type": "text",
+        "text": "Reinforcement learning algorithms Recently, several works have proposed to leverage learning to directly map sensory inputs to actions in nonprehensile manipulation tasks, circumventing the computational cost of planning, inaccuracy of hybrid dynamics models, and difficulty in system identification from high dimensional sensory inputs (Yuan et al., 2018; 2019; Lowrey et al., 2018; Peng et al., 2018; Ferrandis et al., 2023; Kim et al., 2023; Zhou & Held, 2023; Zhou et al., 2023). In Kim et al. (2023), they propose an approach that outputs diverse motions and effectively performs time-varying hybrid force and position control (Bogdanovic et al., 2020), by using the end-effector target pose and controller gains as action space. However, since they represent object geometry via",
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+    {
+        "type": "header",
+        "text": "Published as a conference paper at ICLR 2024",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "page_number",
+        "text": "3",
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+    {
+        "type": "text",
+        "text": "its bounding box, their approach has a limited generalization capability across shapes. Similarly, other approaches only handle simple shapes such as cuboids (Yuan et al., 2018; 2019; Ferrandis et al., 2023; Zhou & Held, 2023), pucks (Peng et al., 2018), or cylinders (Lowrey et al., 2018).",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In HACMan (Zhou et al., 2023), they propose an approach that generalizes to diverse object shapes using end-to-end training. However, they are limited to 3D push primitives defined as fixed-direction poking motions applied on a point on the point cloud. Due to this, they must retract the arm after each execution to observe the next potential contact locations. Further, as end-to-end training with point clouds requires a significant memory footprint, it is difficult to use with massively parallel GPU-based simulations (Makoviychuk et al., 2021): the large resource consumption significantly limits the number of environments that can be simulated in parallel, undermining the parallelism and damaging the training time. Moreover, end-to-end RL on high-dimensional inputs is prone to instability (Eysenbach et al., 2022) and sample-inefficiency: noisy gradients from RL serve as poor training signals for the representation model (Banino et al., 2022), and distributional shift that occurs whenever the encoder gets updated (Shah & Kumar, 2021) slows down policy training. We believe for these reasons, they had to resort to simple primitives that make exploration easier. We use pretraining and efficient architecture to get around these problems.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Along with HACMan, other methods use simple primitives (Yuan et al., 2019; Zhou et al., 2023). But for problems we are contemplating, use of such open-loop primitives precludes dense feedback motions. This is problematic for highly unstable (e.g. rolling or pivoting) objects that move erratically, which require the robot to continuously adjust the contact. For instance, in Figure 1 (row 1, column 3), the robot must adjust the contact to prevent spurious pivoting of the ceramic cup while rolling the handle to the other side; in Figure 1 (row 2, column 6), the robot must align the contact with the rotational axis while lifting the wipe dispenser to prevent accidentally toppling the dispenser to either side. In our work, we adopt a controller with end-effector subgoals with variable gains (Bogdanovic et al., 2020; Kim et al., 2023) as our action space, which allows us to perform dense, closed-loop control of the object.",
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+    {
+        "type": "text",
+        "text": "Representation learning on point clouds Diverse pretraining tasks have been proposed for learning a representation for point cloud inputs, such as PointContrast (Xie et al., 2020), which uses a contrastive loss on point correspondences, or OcCo (Wang et al., 2021), which reconstructs occluded points from partial views. More recently, inspired by advances from NLP (Devlin et al., 2018) and 2D vision (He et al., 2022; Baevski et al., 2022), self-supervised representation learning methods on masked transformers have gained attention (Yu et al., 2022; Zhang et al., 2022; Pang et al., 2022; Zeid et al., 2023). While Point-BERT (Yu et al., 2022), PointM2AE (Zhang et al., 2022) and PointMAE (Pang et al., 2022) reconstruct the masked points from the remaining points, Point2Vec (Zeid et al., 2023) follows Data2Vec (Baevski et al., 2022) and instead estimate the latent patch embeddings, outperforming above baselines in shape classification and segmentation.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "As a result, these methods learn highly performant shape representations, demonstrating state-of-the-art performance across tasks such as shape classification or segmentation (Zeid et al., 2023). However, the same impressive performance is often inaccessible with smaller models (Fang et al., 2021; Shi et al., 2022) due to the difficulty of the pretraining task (Fang et al., 2021) or model collapse (Shi et al., 2022). While this necessitates large models, adopting a large encoder for policy training in GPU-based simulators is undesirable, as it can dominate the compute-cost and memory footprint during policy rollout, limiting the parallelism in massively-parallel RL setups.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In robotics, several alternative representation learning approaches have been proposed. Huang et al. (2021) pretrains their point cloud encoder by predicting object class and relative offset from the goal orientation. Similarly, Chen et al. (2022) pretrains a sparse 3D CNN on object class, relative orientation from the goal, and the joint positions of the robot hand. While these methods have been proven effective on in-hand re-orientation tasks for inferring the object's pose from point cloud observations, the benefits are smaller for nonprehensile manipulation tasks which are more sensitive to the specific presence and location of contacts (see Figure 2). In comparison, we directly represent an object with an embedding that is used to predict such information.",
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+    {
+        "type": "header",
+        "text": "Published as a conference paper at ICLR 2024",
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+    },
+    {
+        "type": "page_footnote",
+        "text": "<sup>1</sup>While (Chen et al., 2022) demonstrated that in-hand reorientation task can be solved solely from pose-based observations without observing the underlying object geometry, the same success cannot be achieved in our domain (Figure 6)",
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+    {
+        "type": "page_number",
+        "text": "4",
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+    {
+        "type": "image",
+        "img_path": "images/e23f572a0d39e5762930c8d1f77ea48437cd4f37a75789cf562a96100b4bd0e5.jpg",
+        "image_caption": [
+            "(a) Real-world setup."
+        ],
+        "image_footnote": [],
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+        "page_idx": 4
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+    {
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+        "img_path": "images/50438aac09b23ff369a79ea24112fb8406a0b5b9356bc6fa74c78d2836f288b1.jpg",
+        "image_caption": [
+            "(b) Simulation setup.",
+            "Figure 3: Our real-world (left) and simulated (right) domains."
+        ],
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+        "type": "text",
+        "text": "3 CONTACT-BASED OBJECT REPRESENTATION FOR NON-PREHENSILE MANIPULATION",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We tackle the problem of rearranging an object of arbitrary geometry on a tabletop to a specified 6D relative pose from the initial pose using nonprehensile manipulation, such as pushing, toppling, and pivoting. Our setup includes a manipulator with a simple gripper, equipped with a proprioceptive sensor and table-mounted depth cameras. We assume that a rigid-body target object is well-singulated on the table, and both the initial and goal poses are stable at rest. Figure 3 illustrates our environment setup.",
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+    {
+        "type": "text",
+        "text": "3.1 OVERVIEW",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Our framework goes through three stages of training before being deployed in the real world: (1) pretraining, (2) teacher policy training with privileged information, and (3) student policy training with partial information only available in the real world. These three stages happen entirely in simulation based on Isaac Gym (Makoviychuk et al., 2021). Our overall system is shown in Figure 4.",
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+    {
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+        "img_path": "images/f412dae92e60c860afcfcc8b9808a7ee9df9b26c5332e2e2584adcb369be4c6b.jpg",
+        "image_caption": [
+            "Figure 4: Our system and model architecture. The contact network consists of a point cloud encoder (red) and contact-prediction decoder (green), passing the point cloud embeddings to the teacher policy module (blue). Student module (orange, omitted) is detailed in Section A.1."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "In the pretraining phase, we train our encoder module (Figure 4, red), which takes in point-cloud observations  $\\in \\mathbb{R}^{512\\times 3}$  and the hand state  $\\in \\mathbb{R}^9$  (position and 6D orientation (Zhou et al., 2019)), and outputs a patch-wise embedding of the object cloud. To train the network, we pass the embeddings through a contact prediction header (Figure 4, green) that classifies whether each patch intersects with the gripper. During this phase, the point-cloud encoder and collision decoder are trained jointly.",
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+    {
+        "type": "text",
+        "text": "During policy training, we discard the collision decoder and freeze the encoder, so that only the weights of the policy module are learned. The policy consumes the object point cloud embedding from the encoder, and other task-relevant inputs comprising robot's joint position and velocity, the",
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+        "page_idx": 4
+    },
+    {
+        "type": "header",
+        "text": "Published as a conference paper at ICLR 2024",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "5",
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+    },
+    {
+        "type": "text",
+        "text": "previous action (end-effector subgoal and controller gains), the object's pose relative to the goal, and its physical properties (mass, friction, and restitution). These inputs are tokenized via an MLP layer to produce query tokens for the cross-attention layer against the point cloud embeddings to extract task-relevant features. These features are concatenated again with the task-relevant inputs and processed by a shared MLP before being split into actor and critic networks. We train the policy module via PPO (Schulman et al., 2017). Since full-cloud observations and physics parameters of objects are not available in the real world, we distill the teacher policy into a student policy. We use DAgger (Ross et al., 2011) to imitate the teacher's actions solely based on information available in the real world: the partial point cloud of the object, robot's joint states, the previous action, and the relative object pose from the goal. We utilize ndiffrast (Laine et al., 2020) to efficiently render the partial point cloud of the scene on the GPU during training.",
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+    {
+        "type": "text",
+        "text": "3.2 LEARNING CORN",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Algorithm 1 outlines the data generation procedure for our network, inspired by (Son & Kim, 2023). We first sample the SE(3) transforms within the workspace for the gripper and object (L1-2). We then compute the nearest displacement between the surface points of the object and the gripper (L3) and move the gripper in that direction plus a small Gaussian noise (L4-6) to approach a configuration near or in a collision. To compute the labels, we sample points from the object's surface (L7), then label each point according to whether they intersect with the gripper (L8-10). This process generates about half of the gripper poses in collision with the object, and the other half in a near-collision pose with the object. To disambiguate these cases, the model must precisely reason about the object's geometry.",
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+    {
+        "type": "text",
+        "text": "Algorithm 1 Dataset generation for CORN.",
+        "text_level": 1,
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Require: object shape  $\\mathcal{O}$ , gripper shape  $\\mathcal{G}$ , workspace  $\\mathcal{W}$ , noise level  $\\sigma$",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Ensure: gripper pose  $T_{G}$ , object cloud  $X$ , contact label  $L$",
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+        "sub_type": "text",
+        "list_items": [
+            "1:  $T_O, T_G \\gets \\text{SamplePoses}(\\mathcal{W})$",
+            "2:  $\\mathcal{O}'\\gets T_O\\cdot \\mathcal{O};\\mathcal{G}'\\gets T_G\\cdot \\mathcal{G}$",
+            "3:  $\\vec{\\delta} \\gets \\text{Nearest Displacement}(\\mathcal{O}', \\mathcal{G}')$",
+            "4:  $s\\sim \\mathcal{N}(1,\\sigma /\\lvert\\lvert\\vec{\\delta}\\rvert\\rvert)$",
+            "5:  $T_{d}\\gets \\left[ \\begin{array}{cc}I_{3\\times 3} & -s\\cdot \\bar{\\delta}\\\\ 0 & 1 \\end{array} \\right]$",
+            "6:  $\\mathcal{G}''\\gets \\bar{T}_d\\cdot \\mathcal{G}'$",
+            "7:  $X \\sim \\text{SampleSurfacePoints}(\\mathcal{O}')$",
+            "8: for  $x_{i}\\in X$  do",
+            "9:  $L_{i}\\gets \\text{PointInMesh}(x_{i},\\mathcal{G}^{\\prime \\prime})$",
+            "0: end for"
+        ],
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Afterward, the model is trained by classifying",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "whether each patch of the object intersects with the gripper at the given pose. A patch is labeled as positive if any point within it intersects with the gripper. We use binary cross-entropy between the patchwise decoder logits and the collision labels to train the model(Figure 4, green block)",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "3.3 PATCH-BASED ARCHITECTURE FOR CORN",
+        "text_level": 1,
+        "bbox": [
+            171,
+            656,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "To efficiently train a policy by simultaneously simulating thousands of environments using GPUs, we leverage a patch-based transformer to encode the object point cloud shown in Figure 4 (red), which pass the patch embeddings to the policy module (blue).",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Patch Tokenization. In line with previous work (Pang et al., 2022), we divide the point cloud into a set of patches (Figure 4, red block, top left). To define each patch, we identify  $N$  representative points using farthest-point sampling (FPS). The k-nearest neighbor (kNN) points from these representatives constitute a patch, which is normalized by subtracting its center from its constituent points (Pang et al., 2022; Zeid et al., 2023; Yu et al., 2022) to embed the local shape. These patches are then tokenized via a Multi-Layer Perceptron (MLP) as input tokens to a transformer.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Unlike past methods that use a small PointNet for tokenizing the patches (Pang et al., 2022; Zeid et al., 2023), we tokenize the patches with a lightweight MLP. Using an MLP is sufficient since the patch size is constant, fully determined by the size of  $k$  during kNN lookup. By sorting the points within each patch by their distance from the patch center, we can ensure that points within a patch always follow a consistent order. Thus, we can avoid using a costly permutation-invariant PointNet tokenizer. After computing the local patch embeddings, we add learnable positional embeddings of the patch centers to restore the global position information (Pang et al., 2022).",
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+        "page_idx": 5
+    },
+    {
+        "type": "header",
+        "text": "Published as a conference paper at ICLR 2024",
+        "bbox": [
+            171,
+            32,
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+            47
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "6",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Additional Encoder Inputs. By leveraging a transformer backbone, our architecture can easily mix heterogeneous task-related inputs as extra tokens, such as hand state, together with raw point-cloud observations as shown in Figure 4. Unlike PointNet-derived models that can only concatenate such inputs after the point-processing layers, this has an advantage in that the network can pay attention to parts of the point cloud in accordance with the hand state, such as the ones near the robot's hand that would interact with the gripper.",
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4 EXPERIMENTS",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.1 EXPERIMENTAL SETUP",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/5b295f7e9248bf1b8db643666959517157ffc5ae540de34cc9a6cb74acb08ec7.jpg",
+        "image_caption": [
+            "Figure 5: Set of 16 real-world objects that we test in the real world."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Training setup For each scene, we randomly draw an object from a subset of 323 geometrically diverse objects from DexGraspNet dataset (Wang et al., 2023), detailed in Section A.6.2. For each episode, we first place the object in a random stable pose on the table. Then, we reset the robot arm at a joint configuration uniformly sampled within predefined joint bounds slightly above the workspace. By doing so, we can avoid initializing the robot in spurious collision with the table or the object. Afterward, we sample a 6D stable goal pose randomly on the table, spaced at least  $0.1\\mathrm{m}$  away from the initial pose to prevent immediately achieving success at initialization. To sample valid initial and goal poses for each object, we pre-compute a set of stable poses for each object. This procedure is elaborated in Section A.6.1.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Action, Rewards, and Success Criteria Following Kim et al. (2023), the action space of the robot comprises the subgoal residual of the hand, and the joint-space gains of a variable impedance controller (Details in Section A.2). We also follow the same curriculum learning scheme on the subgoal residual from Kim et al. (2023) to facilitate transferring our policy to the real world. The reward in our domain is defined as  $r = r_{suc} + r_{reach} + r_{contact} - c_{energy}$ , comprising the task success reward  $r_{suc}$ , goal-reaching reward  $r_{reach}$ , contact-inducing reward  $r_{contact}$ , and energy penalty  $c_{energy}$ . The task success reward  $r_{suc} = \\mathbb{1}_{suc}$  is given when the pose of the object is within 0.05m and 0.1 radians of the target pose. We add dense rewards  $r_{reach}$  and  $r_{contact}$  to facilitate learning, based on a potential function (Ng et al., 1999) and has the form  $r = \\gamma \\phi(s') - \\phi(s)$  where  $\\gamma \\in [0,1)$  is the discount factor. For  $r_{reach}$ , we have  $\\phi_{reach}(s) = k_g \\gamma^{k_d \\cdot d_{o,g}(s)}$  and for  $r_{contact}$ , we have  $\\phi_{contact}(s) = k_r \\gamma^{k_d \\cdot d_{h,o}(s)}$  where  $k_g, k_d, k_r \\in \\mathbb{R}$  are scaling coefficients;  $d_{o,g}(s)$  is the distance from the current object pose to the goal pose, measured using the bounding-box based distance measure from Allshire et al. (2022);  $d_{h,o}(s)$  is the hand-object distance between the object's center of mass and the tip of the gripper. Energy penalty term is defined as  $c_{energy} = k_e \\cdot \\sum_{i=1}^{7} \\tau_i \\cdot \\dot{q}_i$ , where  $k_e \\in \\mathbb{R}$  is a scaling coefficient,  $\\tau_i$  and  $\\dot{q}_i$  are joint torque and velocity of the  $i^{th}$  joint. The scaling coefficients for the rewards are included in Table A.1.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Domain Randomization. During training, we randomize the mass, scale of the object, and friction and restitution of the object, table, and the robot gripper. We set the scale of the object by setting the largest diameter of the object within a predefined range. To facilitate real-world transfer, we also add a small noise to the torque command, object point cloud, and the goal pose when training the student. Detailed parameters for domain randomization are described in Table A.4.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Real-World Setup. Our real-world setup is shown in Figure 3a. We use three RealSense D435 cameras to extract the point clouds, and use Iterative Closest Point (ICP) To estimate the error between the object's current and target poses. We further use April tags (Wang & Olson, 2016) to track symmetric objects that cannot be readily tracked via ICP. We also wrap the gripper of the",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "header",
+        "text": "Published as a conference paper at ICLR 2024",
+        "bbox": [
+            171,
+            32,
+            478,
+            47
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "7",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "robot with a high-friction glove to match the simulation. We emphasize that all training is done in simulation, and the policy is zero-shot transferred to the real world.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.2 RESULTS",
+        "text_level": 1,
+        "bbox": [
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+            150,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We'd like to evaluate the following claims: (1) Pretraining CORN enables training a nonprehensile manipulation policy in a time- and data-efficient manner. (2) Patch-based transformer architecture enables efficiently scaling to thousands of point-cloud based RL agents in parallel. (3) Our system can generalize to domain shifts such as unseen objects in the real world. To support claims 1 and 2, we compare our pretraining task and architecture (OURS) against the baseline encoders in Figure 6.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Compared to ours, P2V uses a pretrained Point2Vec (Zeid et al., 2023) encoder, using the author's weights; P2V-LITE is pretrained as in P2V, but uses the same architecture as Ours; ROT also shares the architecture with Ours, but is pretrained with relative rotation estimation as in (Huang et al., 2021; Chen et al., 2022); E2E also shares the architecture, but is trained in an end-to-end manner without pretraining; PN uses a three-layer PointNet encoder, pretrained on point-wise collision prediction, analogous to CORN; and STATE trains a geometry-unaware policy that only receives object bounding box inputs as the object representation, rather than point clouds. Note that P2V, P2V-LITE, ROT, E2E have the same downstream policy architectures as ours. For PN and STATE, they also have the same policy architecture except that they do not use cross-attention.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/c864e9a28d337b61201ea5ff7133a7cdd112426d2314d3c7a46ef06f41f1fcb7.jpg",
+        "image_caption": [
+            "Figure 6: Training progression and baselines. Plots show the mean (solid) and standard deviations (transparent) for each baseline. (Left) Success rate vs. number of interaction steps. Interaction steps are reported as the total number of steps aggregated across 4096 parallel environments. (Middle) Success rate vs. number of hours. All baselines are allowed to interact at most  $2e9$  time steps. (Right) Comparison of baselines. PT: Patch Transformer."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Figure 6 shows the progression of success rates across different baselines in simulation. To support claim 1, we consider the performance of the policy after 2 billion interactions (in steps) and 24 hours (in time), respectively. First, E2E takes significantly longer compared to Ours, in terms of both steps and time: by pretraining CORN, Ours achieves  $88.0\\%$  suc RATE (steps) and  $88.5\\%$  (time), while E2E only reaches  $31.4\\%$  (in time) and  $54.4\\%$  (in steps), respectively. This is due to the overhead of jointly training the encoder and policy networks in E2E. Among pretrained representations, we first compare with P2V. While P2V is similar to Ours in steps  $(85.6\\%)$ , it is significantly slower in time  $(3.55\\%)$ , due to the inference overhead of the large representation model. To isolate the effect of the pretraining task, we also compare with P2V-LITE: pretrained as in P2V, yet with same architecture as Ours. While the resulting policy is reasonably time-efficient due to faster rollouts  $(73.4\\%)$  in time), it is less data-efficient  $(68.8\\%)$  in steps) due to the reduced performance of the smaller model (Shi et al., 2022; Fang et al., 2021). Another baseline, ROT from in-hand reorientation literature (Huang et al., 2021; Chen et al., 2022) performs slightly worse in both measures  $(64.2\\%$  (steps);  $67.0\\%$  (time)): we believe this is due to the increased demand for the awareness of object geometry in our task. To see this, we note that the pose-only policy STATE), unaware of object geometry, cannot learn at all in our domain, in contrast to the positive result from Chen et al. (2022). This highlights the fact that our task requires greater awareness of the object's geometric features: just knowing the object's pose is insufficient, and a deeper understanding of its geometry is necessary.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "To see CORN learns a suitable representation for manipulation, we inspect the attention scores of the policy amid different motions in Figure 7. For pushing and toppling motions (row 1,3), our policy primarily attends to the current or future contact between the hand and the object, which is consistent",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "header",
+        "text": "Published as a conference paper at ICLR 2024",
+        "bbox": [
+            171,
+            32,
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+            47
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "8",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/b85ac9607befaec86eaad4b635f0b246b8dd4c48d43241389d53a05b1a44a414.jpg",
+        "image_caption": [
+            "Figure 7: Visualization of the scores from the cross-attention layers of the policy, summed over all heads. We colorize the attention for each patch normalized to range  $(0,1)$ , then project the patchwise colors on the surface of the object for visualization with VIRIDIS colormap."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            287,
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+            297
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "with the premise of our representation-learning scheme. While pivoting or rolling motions (row 2,4) share the same trend, our policy also attends to the pivot points of the object against the table.",
+        "bbox": [
+            169,
+            378,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "To support claim 2, we show that our patch-transformer architecture is more performant in both compute- and memory-cost compared to PointNet (Qi et al., 2016). In particular, we evaluate PN, where the primary difference is the use of PointNet in place of the patch transformer. While the performance degradation from the architecture change is only modest in steps (88.3% v. 70.2%), the large computational overhead of PointNet renders it slowest in time(0.223%) among all baselines. To support claim 3, we evaluate our policy in the real-world setting as described in Section 4.1. Figure 5 shows the objects that we evaluate in our real-world experiments, exhibiting wide diversity in terms of shape, mass, and materials; Figure 1 shows four representative real-world episodes.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "table",
+        "img_path": "images/68ffa8fe55e2f1dce8e86f8160395293e5d9d4705d4415a55e9cf18f0dc4cf62.jpg",
+        "table_caption": [
+            "Table 1: Real world run results. All of the objects in the real-world setup are unseen except for 3D-printed objects marked with  $\\dagger$ ."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Object name</td><td>Success/Trial</td><td>Object name</td><td>Success/Trial</td><td>Object name</td><td>Success/Trial</td><td>Object name</td><td>Success/Trial</td></tr><tr><td>Red Card</td><td>4/5</td><td>Cube Block</td><td>4/5</td><td>Ceramic Cup</td><td>4/5</td><td>Red Dripper</td><td>3/5</td></tr><tr><td>Toy Puppy†</td><td>4/5</td><td>Iced Tea Box</td><td>3/5</td><td>Nutella Bottle</td><td>3/5</td><td>Coaster Holder</td><td>3/5</td></tr><tr><td>Toy Bulldozer</td><td>4/5</td><td>Wipe Dispenser</td><td>5/5</td><td>Coffee Jar</td><td>2/5</td><td>Thick Book</td><td>4/5</td></tr><tr><td>Blue Holder</td><td>5/5</td><td>Toy Table†</td><td>3/5</td><td>Lemona Box</td><td>3/5</td><td>Candy Box</td><td>3/5</td></tr><tr><td>Success rate</td><td></td><td></td><td></td><td></td><td></td><td></td><td>57/80 (71.3%)</td></tr></table>",
+        "bbox": [
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+            578,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "The results from our policy execution in the real-world are organized in Table 1. Overall, our policy demonstrates  $71.3\\%$  success rate in the real world. These results indicate that, with distillation, our system can zero-shot transfer to the real world despite only training in a simulation.",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Limitations. We find that our policy struggles more with concave objects (coaster-holder, red dripper;  $60\\%$ ) or unstable objects (iced tea box, coffee jar, red dripper;  $53\\%$ ). Concave objects cause perception challenge in the real world due to severe ambiguity when occluded by the robot, leading to timeouts as the agent oscillates between actions or stops amid a maneuver. Unstable objects tend to abruptly spin out of the workspace after minor collisions, and the dexterity of our robot platform and speed of our real-world perception pipeline cannot catch up with such rapid motions.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "5 CONCLUSION",
+        "text_level": 1,
+        "bbox": [
+            171,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "In this work, we present a system for effectively training a non-prehensile object manipulation policy that can generalize over diverse object shapes. We show that by pretraining a contact-informed representation of the object, coupled with an efficient patch-based transformer architecture, we can train the policy in a data- and time-efficient manner. With student-teacher distillation, we find that our policy can zero-shot transfer to the real world, achieving success rates of  $71.3\\%$  in the real world across both seen and unseen objects despite only training in a simulation.",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "header",
+        "text": "Published as a conference paper at ICLR 2024",
+        "bbox": [
+            173,
+            32,
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+            47
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "page_number",
+        "text": "9",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "ACKNOWLEDGEMENT",
+        "text_level": 1,
+        "bbox": [
+            171,
+            103,
+            359,
+            118
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "This work was supported by Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government(MSIT) (No.2019-0-00075, Artificial Intelligence Graduate School Program(KAIST)), (No.2022-0-00311, Development of Goal-Oriented Reinforcement Learning Techniques for Contact-Rich Robotic Manipulation of Everyday Objects), (No. 2022-0-00612, Geometric and Physical Commonsense Reasoning based Behavior Intelligence for Embodied AI).",
+        "bbox": [
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "REPRODUCIBILITY STATEMENT",
+        "text_level": 1,
+        "bbox": [
+            171,
+            238,
+            439,
+            253
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "We describe our real-world system and perception pipeline in detail in Section A.4. The procedure for data generation and pretraining for our model and other baselines is detailed in Section 3.2 and Section A.3, respectively. We include the set of 323 training objects from DexGraspNet (Wang et al., 2023) that we used for policy training as supplementary materials. We include the student-model architecture and distillation pipeline for real-world transfer in Section A.1. We describe the simulation setup regarding data preprocessing(Section A.6), and describe the hyperparameters associated with our network architecture(Table A.2), domain-randomization(Table A.4), and policy training(Section A.3). We also release our code at https://github.com/contact-non-prehensile/corn.",
+        "bbox": [
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "REFERENCES",
+        "text_level": 1,
+        "bbox": [
+            171,
+            415,
+            287,
+            430
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
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+        ],
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+    {
+        "type": "text",
+        "text": "A APPENDIX",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "A.1 STUDENT MODEL",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/aef91ba63a2083e115447ce59a1063bfab7a3570d93ca8d7841a641b20f69421.jpg",
+        "image_caption": [
+            "Figure A.1: Student Model Architecture in DAgger."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The student policy shares a similar architecture with the teacher policy, with two distinctions. Unlike teacher policy, which employs joint state, previous action, and goal inputs for generating query tokens for cross-attention, we incorporate these tokens into the input of the patch transformer within the encoder to facilitate extracting task-relevant features from partial point clouds. Given that these inputs are already incorporated in the input of the encoder, we use learned query tokens for cross-attention.",
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+    {
+        "type": "text",
+        "text": "Since the student policy can only perceive limited shape information of objects at any given moment due to occlusion, we incorporate a two-layer Gated Recurrent Unit (GRU) (Cho et al., 2014) on top of the student point cloud encoder. This enables the student model to aggregate partial observations of object geometry based on historical observations.",
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+    {
+        "type": "text",
+        "text": "We train the student with DAgger with truncated backpropagation through time (BPTT). In particular, we run the student for 8 time-steps and update its parameters to minimize KL-divergence between the action distribution of the teacher policy and the student policy.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "A.2 DETAILS ON POLICY ACTION SPACE",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The action space of our policy consists of the subgoal residual of the end-effector  $\\Delta T_{ee}$  and joint-space gains. The subgoal residual is parameterized by the translational offset  $\\Delta t\\in \\mathbb{R}^3$  and axis-angle representation of the residual rotation in the world frame  $\\Delta r\\in \\mathbb{R}^3$ . The joint-space gains are parameterized by proportional terms  $(k_{p}\\in \\mathbb{R}^{7})$  and damping factors  $(\\rho \\in \\mathbb{R}^7)$  of a variable impedance controller. Based on this, we compute the joint position target by solving inverse kinematics with damped least squares method (Buss, 2004) as  $q_{target} = q_t + IK(\\Delta T_{ee})$ . The torque command for each joint is computed based on the joint position error and the predicted joint-space gains and damping factors as  $\\tau = k_p(q_{target} - q_t) - k_d\\dot{q}_t$ ,  $k_{d} = \\rho \\cdot \\sqrt{k_{p}}$ .",
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+    {
+        "type": "text",
+        "text": "A.3 DATA GENERATION AND PRETRAINING PIPELINES",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "P2V-LITE. For pretraining P2V-LITE, we follow the same procedure as Zeid et al. (2023), except we use the same architecture as OURs. Due to the use of a significantly lighter model, we apply two modifications to the original training setup, as follows: first, since we only use a two-layer transformer, instead of averaging over the last 6 layers of the teacher, we take the result after layer-normalization of the final layer, which keeps the ratio consistent (50% of layers). Second, we replace DropPath layers with dropout since the model is shallow. Otherwise, we follow the original hyper",
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+        "page_idx": 13
+    },
+    {
+        "type": "header",
+        "text": "Published as a conference paper at ICLR 2024",
+        "bbox": [
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+        "page_idx": 13
+    },
+    {
+        "type": "page_number",
+        "text": "14",
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+    },
+    {
+        "type": "text",
+        "text": "parameters from the paper and the author's code(https://github.com/kabouzeid/point2vec).",
+        "bbox": [
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+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "ROT. For pretraining ROT, we follow the procedure described in Chen et al. (2022). Since the authors report that adding the classification objective does not influence the encoder quality, we omit the classification terms. For the training data, we use ShapeNet Chang et al. (2015) dataset. We apply two different SO(3) transformations to the same point cloud, and pass it through the encoder to obtain the patchwise embeddings. We concatenate the patchwise embeddings from both streams, then pass it through a 3-layer MLP (512, 64, 6). We train the encoder on the regression task, where the task for the decoder is to regress the parameters for a 6D rotation Zhou et al. (2019) as recommended from Chen et al. (2022).",
+        "bbox": [
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+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "OURS-PN. For pretraining PN, we use the same dataset from OURs. Since PointNet does not produce patchwise embeddings, we instead adopt a U-Net architecture based on PyG Fey & Lenssen (2019). To inform the model about the end-effector, we concatenate the hand pose (position and orientation Zhou et al. (2019)) to each point in the channel dimension.",
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+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "A.4 REAL WORLD SYSTEM AND PERCEPTION PIPELINE",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Point Cloud Segmentation. In the point cloud segmentation phase, we integrate three RealSense D435 cameras. Points outside the predefined 3D bounding-box workspace above table are first removed, and those within a distance less than the threshold  $\\epsilon = 1\\mathrm{cm}$  from the table surface are removed next. These parameters were determined empirically to handle outliers without removing too much of the object. For thin objects such as cards, we alternatively employ color-based segmentation to remove the table from the point cloud, avoiding the risk of inadvertently removing object points.",
+        "bbox": [
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+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "After removing the table, only the object and the robot remains. To remove the robot, we compute the transform of all robot links based on the robot kinematics, then query the points as to whether it is contained within each link mesh. For efficiency, we first apply convex decomposition on the robot geometry, and employ point-convex intersection to check whether the point belongs to the robot. We initially tried using robot-points removal based on raycasting the point-to-robot mesh distances, but we found it was much slower than the convex-hull based method.",
+        "bbox": [
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+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "To reduce noise in the point cloud, we employ a radius outlier removal logic with  $r = 2$  cm and  $n_{\\mathrm{min}} = 96$  points, which is the minimum number of points that the inlier should contain within the neighborhood. Finally, to identify the object point cluster, we used DBSCAN clustering algorithm. Clusters were computed with  $\\epsilon = 1$  cm and the number of neighbors as 4 to form the core-set.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "To enhance processing speed, we optimized the entire segmentation pipeline to utilize tensor operations executed on the GPU. The output object point cloud of this segmentation process serves as input for both our policy and object pose tracking pipeline.",
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+    },
+    {
+        "type": "text",
+        "text": "Object Pose Tracking. To trade-off tracking speed and performance, we first subsample the object point clouds randomly to  $n_{\\mathrm{track}} = 2048$  points. Empirically, we found that this avoids compromising the quality of the ICP(Iterative Closest Point) algorithm, while remaining reasonably fast.",
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+    {
+        "type": "text",
+        "text": "We employ ICP for tracking. Given the object point cloud  $C_t$  at current time step  $t$ , we conduct point-to-plane ICP registrations with point cloud of previous timestep  $C_{t-1}$ , resulting in a transformation  $P_{t,t-1} = \\mathrm{ICP}(C_t, C_{t-1})$ . The current object pose  $T_{O_t}$  is obtained by recursively applying pairwise transformations:  $T_{O_t} = P_{t,t-1} \\cdot T_{O_{t-1}}$ . In the case that the transform drifts over time, we also perform an additional ICP match with the initial object point cloud  $P_{t,0} = \\mathrm{ICP}(C_t, C_0)$  to correct the error. If the fitness score  $Fitness_{t,0}$  exceeds 60%, current object pose is calculated as  $T_{O_t} = P_{t,0} \\cdot T_{O_0}$ .",
+        "bbox": [
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+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "For thin objects, we utilize point-to-point ICP matching since their point cloud nearly forms a single plane. While the ICP tracker performs well for large and non-symmetrical objects, it struggles with highly symmetrical objects, or objects with point-matching ambiguity under occlusion (e.g. when cup handles are occluded by the robot).",
+        "bbox": [
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+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "To address this challenge, we tried color-based ICP to resolve the ambiguity based on surface texture. However, we found that it did not improve tracking performance and, in some cases, even",
+        "bbox": [
+            169,
+            895,
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+            926
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "header",
+        "text": "Published as a conference paper at ICLR 2024",
+        "bbox": [
+            171,
+            32,
+            478,
+            47
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "page_number",
+        "text": "15",
+        "bbox": [
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+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "worsened it. As such, we used april-tag tracker to maintain object pose tracking accuracy for highly symmetrical objects.",
+        "bbox": [
+            169,
+            103,
+            823,
+            133
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "A.5 EXAMPLE TRAJECTORIES",
+        "text_level": 1,
+        "bbox": [
+            171,
+            148,
+            397,
+            162
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "Example trajectories can be observed from the video in the supplementary material, or from http://sites.google.com/view/contact-non-prehensile.",
+        "bbox": [
+            169,
+            174,
+            823,
+            204
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "A.6 SIMULATION SETUP",
+        "text_level": 1,
+        "bbox": [
+            171,
+            219,
+            359,
+            233
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "A.6.1 STABLE POSES GENERATION",
+        "text_level": 1,
+        "bbox": [
+            171,
+            244,
+            433,
+            258
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "To sample stable poses for training, we drop the objects in a simulation and extract the poses after stabilization. In  $80\\%$  of the trials, we drop the object  $0.2\\mathrm{m}$  above the table in a uniformly random orientation. In the remaining  $20\\%$ , we drop the objects from their canonical orientations, to increase the chance of landing in standing poses, as they are less likely to occur naturally. If the object remains stationary for 10 consecutive timesteps, and its center of mass projects within the support polygon of the object, then we consider the pose to be stable. We repeat this process to collect at least 128 initial candidates for each object, then keep the unique orientations by pruning equivalent orientations that only differ by a planar rotation about the z-axis.",
+        "bbox": [
+            169,
+            268,
+            826,
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+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "A.6.2 OBJECTS FOR TRAINING",
+        "text_level": 1,
+        "bbox": [
+            171,
+            395,
+            405,
+            409
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "We sample 323 objects from the DexGraspNet dataset (Wang et al., 2023), shown in Figure A.2. To increase the simulation speed and stability, we apply convex decomposition on every mesh using CoACD (Wei et al., 2022), after generating the watertight mesh with simplification using Manifold (Huang et al., 2018).",
+        "bbox": [
+            169,
+            419,
+            823,
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+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "image",
+        "img_path": "images/d9742d011dc7627afa77e2c3b49c1ea2ab65d9103965732f717e2790b115fe42.jpg",
+        "image_caption": [
+            "Figure A.2: 323 object meshes that were used for training."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            238,
+            488,
+            759,
+            888
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "header",
+        "text": "Published as a conference paper at ICLR 2024",
+        "bbox": [
+            171,
+            32,
+            478,
+            47
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "page_number",
+        "text": "16",
+        "bbox": [
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+            946,
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+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "A.7 HYPERPARAMETERS",
+        "text_level": 1,
+        "bbox": [
+            171,
+            103,
+            362,
+            118
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "table",
+        "img_path": "images/60e53b21568c98c9b3722ae776390e9a7282b597fac2915ec84e98955286d9bd.jpg",
+        "table_caption": [
+            "Table A.1: Hyperparameters for reward computation."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Parameter</td><td>Value</td><td>Description</td></tr><tr><td>kg</td><td>0.302</td><td>Goal-reaching reward coefficient</td></tr><tr><td>kr</td><td>0.0604</td><td>Hand-reaching reward coefficient</td></tr><tr><td>ke</td><td>0.0001</td><td>Energy penalty coefficient</td></tr><tr><td>kd</td><td>243.12</td><td>Decay factor for potential-based reward</td></tr></table>",
+        "bbox": [
+            334,
+            159,
+            663,
+            227
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "table",
+        "img_path": "images/bb89ec5449f11ec0bf0b4f1a4877216e3d88e4d29310a7ec0aaeccc29648eb1d.jpg",
+        "table_caption": [
+            "Table A.2: Hyperparameters for Encoder and Policy."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Hyperparameter</td><td>Value</td><td>Hyperparameter</td><td>Value</td><td>Hyperparameter</td><td>Value</td></tr><tr><td>Num. points</td><td>512</td><td>Hidden dim.</td><td>128</td><td>Shared MLP</td><td>MLP (512, 256, 128)</td></tr><tr><td>Num. patches</td><td>16</td><td>Num. layer</td><td>2</td><td>Actor</td><td>MLP (64, 1)</td></tr><tr><td>Patch size</td><td>32</td><td>Num. attention head in self-attention</td><td>4</td><td>Critic</td><td>MLP(64, 20)</td></tr><tr><td>Concatenate context input</td><td>True</td><td>Num. attention head in cross-attention (teacher/student)</td><td>16/4</td><td></td><td></td></tr></table>",
+        "bbox": [
+            173,
+            273,
+            823,
+            407
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "table",
+        "img_path": "images/442b05afd9be72cdaafde706ae8b816e4b82b46ee4fe7bf1e24eeddc716aa5e9.jpg",
+        "table_caption": [
+            "Table A.3: Hyperparameters for PPO."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Hyperparameter</td><td>Value</td><td>Hyperparameter</td><td>Value</td><td>Hyperparameter</td><td>Value</td><td>Hyperparameter</td><td>Value</td></tr><tr><td>Max Num. epoch</td><td>8</td><td>Base learning rate</td><td>0.0003</td><td>GAE parameter</td><td>0.95</td><td>Num. environment</td><td>4096</td></tr><tr><td>Early-stopping KL target</td><td>0.024</td><td>Adaptive-LR KL target</td><td>0.016</td><td>Discount factor</td><td>0.99</td><td>Episode length</td><td>300</td></tr><tr><td>Entropy regularization</td><td>0</td><td>Learning rate schedule</td><td>adaptive</td><td>PPO clip range</td><td>0.3</td><td>Update frequency</td><td>8</td></tr><tr><td>Policy loss coeff.</td><td>2</td><td>Value loss coeff.</td><td>0.5</td><td>Bound loss coeff.</td><td>0.02</td><td></td><td></td></tr></table>",
+        "bbox": [
+            173,
+            452,
+            823,
+            508
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "table",
+        "img_path": "images/092601fc5fb90413559aa90478c705112dd60b06647b3d37fa217bc77891ed8e.jpg",
+        "table_caption": [
+            "Table A.4: Range for domain randomization.  $\\mathcal{U}[min, max]$  denotes uniform distribution, and  $\\mathcal{N}[\\mu, \\sigma]$  denotes Normal distribution. Point cloud noise and Goal pose noise are added to the normalized input."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Parameter</td><td>Range</td></tr><tr><td>Object mass (kg)</td><td>U[0.1, 0.5]</td></tr><tr><td>Object scale (m)</td><td>U[0.1, 0.3]</td></tr><tr><td>Object friction</td><td>U[0.7, 1.0]</td></tr><tr><td>Table friction</td><td>U[0.3, 0.8]</td></tr><tr><td>Gripper friction</td><td>U[1.0, 1.5]</td></tr><tr><td>Torque noise</td><td>N[0.0, 0.03]</td></tr><tr><td>Point cloud noise</td><td>N[0.0, 0.005]</td></tr><tr><td>Goal pose noise</td><td>N[0.0, 0.005]</td></tr></table>",
+        "bbox": [
+            383,
+            583,
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+            726
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "header",
+        "text": "Published as a conference paper at ICLR 2024",
+        "bbox": [
+            171,
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+        "page_idx": 16
+    },
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2024/CORN_ Contact-based Object Representation for Nonprehensile Manipulation of General Unseen Objects/1d7a7b6b-a145-4b8c-b679-d80f7046b674_origin.pdf

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2024/CORN_ Contact-based Object Representation for Nonprehensile Manipulation of General Unseen Objects/full.md

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+# CORN: CONTACT-BASED OBJECT REPRESENTATION FOR NONPREHENSILE MANIPULATION OF GENERAL UNSEEN OBJECTS
+
+Yoonyoung Cho\*, Junhyek Han\*, Yoontae Cho, Beomjoon Kim
+
+Korea Advanced Institute of Science and Technology
+
+{yoonyoung.cho, junhyek.han, yoontae.cho, beomjoon.kim}@kaist.ac.kr
+
+# ABSTRACT
+
+Nonprehensile manipulation is essential for manipulating objects that are too thin, large, or otherwise ungraspable in the wild. To sidestep the difficulty of contact modeling in conventional modeling-based approaches, reinforcement learning (RL) has recently emerged as a promising alternative. However, previous RL approaches either lack the ability to generalize over diverse object shapes, or use simple action primitives that limit the diversity of robot motions. Furthermore, using RL over diverse object geometry is challenging due to the high cost of training a policy that takes in high-dimensional sensory inputs. We propose a novel contact-based object representation and pretraining pipeline to tackle this. To enable massively parallel training, we leverage a lightweight patch-based transformer architecture for our encoder that processes point clouds, thus scaling our training across thousands of environments. Compared to learning from scratch, or other shape representation baselines, our representation facilitates both time- and data-efficient learning. We validate the efficacy of our overall system by zero-shot transferring the trained policy to novel real-world objects. Code and videos are available at https://sites.google.com/view/contact-non-prehensile.
+
+# 1 INTRODUCTION
+
+Robot manipulators can transform our day-to-day lives by alleviating humans from taxing physical labor. Despite this potential, they have remained largely confined to picking and placing objects in limited settings such as manufacturing or logistics facilities. One key reason for such confined usage is their limited action repertoire: while prehensile manipulation has made great improvements (Mahler et al., 2017; Wan et al., 2023), there are several situations in the wild where pick-and-place is not an option. For instance, consider the scenarios in Figure 1, where the robot is tasked to manipulate diverse household objects to a target pose. While the effective strategy differs for each object, the predominant approach of grasping and placing objects is not viable. To manipulate such objects in the wild, the robot must perform nonprehensile actions such as pushing, dragging, and toppling by reasoning about the object geometry (Kao et al., 2016).
+
+Traditionally, this problem has been tackled using planning algorithms that model the dynamics of the system and compute motions using optimization (Posa et al., 2014) or tree search (Cheng et al., 2022). However, this necessitates full system information about object geometry and inertial parameters, which are generally unavailable from sensory observations, especially for novel objects. Even when such models are available, the complex search space renders planning algorithms impractically slow. Recently, deep reinforcement learning (RL) has surfaced as a promising alternative, where a nonprehensile policy is trained in a simulator (Kim et al., 2023; Zhou et al., 2023), then zero-shot transferred to the real world. However, no algorithm offers the level of generality over object shapes and diversity in motions necessary for our problem: they either generalize over objects but are confined to rudimentary motions such as poking (Zhou et al., 2023) or affords rich motions but uses a rudimentary object representation that precludes generalization over shapes (Kim et al., 2023).
+
+![](images/6f1553cb60226231e7753f5f8cffa793434e9f02552066a5d8263401823dad8e.jpg)
+
+![](images/f42266ddf457cb2b1aaa1a6b553b60f096688d7ee2ef8ba9993d585a06ba17c4.jpg)  
+Figure 1: Snapshot of our robot performing diverse real-world object manipulation tasks. The first column shows the initial and goal object pose (transparent) of the task, and the green region marks the robot's workspace. Row 1: Raising a cup bottom-side up. The cup's grasp and placement poses are occluded by the collision with the table; since the cup is dynamically unstable, the robot must also support the object to avoid toppling the object out of the workspace during manipulation. Row 2: Flipping the wipe dispenser upside down, which is too wide to grasp. Since it may roll erratically, frequent re-contacts and dense closed-loop motions are required to stabilize the object during manipulation. Row 3: Moving a book that is too thin to be grasped; to drag the book, the robot must finely adjust the pressure to allow for both reorientation and translation. Row 4: Flipping a toy crab. Given its concave geometry, the robot must utilize the interior contacts to pivot the crab.  
+(a) Case where the robot tries to topple the cup.  
+Figure 2: Even among similar-looking states, the interaction outcome varies drastically depending on the presence of contact. (a-left) the gripper passes near the cup, yet not quite in contact. As the robot narrowly misses the object, the object remains still. (a-right) the gripper engages with the cup, leading to a successful topple. (b-left) The robot relocates to the left of the block to push it to the goal(dark). By avoiding unintended collision, it is well-positioned to push the object. (b-right) due to spurious contact, the gripper accidentally topples the block, making the goal farther to reach.
+
+![](images/0f4b1e95f427c05d37def0b4735931d2614f4b4b7f091c25793da21d8a228437.jpg)  
+(b) Case where the robot tries to push the block.
+
+We propose a novel object representation learning algorithm for nonprehensile manipulation that can be jointly used with the action-space from Kim et al. (2023) to achieve both generality over shapes and diversity in motions. The key challenge is defining the pretraining task. Given that our objective is to generalize across shapes, one naive approach is to employ self-supervised shape-learning, where the geometric representation is trained on contrastive or shape-reconstruction objectives (Pang et al., 2022; Yu et al., 2022; Xie et al., 2020; Zeid et al., 2023). However, reconstructing the full shape representation is needlessly complex: the full shape includes many intricate features, such as internal geometry, concavities, or surface details, which may not directly influence the performance of the manipulation policy. Even for a complex object, only a subset of its surface interacts with the gripper. Thus, while the contactable parts of an object must be represented at high fidelity, the remainder can be omitted without influencing the performance of the downstream policy.
+
+Our key insight is that recognizing the presence and location of contacts between the object and the robot's hand is crucial for nonprehensile manipulation. For RL, a good representation must necessarily distinguish between states with high and low values, and in contact-rich manipulation, this is primarily determined by what forces and torques can be applied to the object in the given state.
+
+This, in turn, depends on the presence and position of the contact between the object and the robot's hand. This intuition is demonstrated in Figure 2. Based on this insight, we propose a pretraining task where the point cloud encoder is trained to predict what part of the object is in collision with the robot's end-effector.
+
+Our other contribution is the design of an efficient architecture that can process high-dimensional point clouds, in a way that can scale to massively parallel GPU-backed simulations. Existing well-known point-cloud processing architectures such as PointNet (Qi et al., 2016; 2017) inherently incur substantial inference time and memory usage while processing individual points. Inspired by the recent success of patch-based vision architectures (Dosovitskiy et al., 2020; Yu et al., 2022; Pang et al., 2022; Zhang et al., 2022; Zeid et al., 2023), we leverage a patch-based transformer to efficiently encode the point cloud. Since a single point in a point cloud does not carry significant information, grouping local points into a single unit(patch) (Yu et al., 2022) can effectively reduce the computational burden of launching thousands of point-wise operations as in PointNets (Qi et al., 2016) or Point-based Transformers (Zhao et al., 2021), resulting in significant computational gains.
+
+We call our framework Contact-based Object Representation for Nonprehensile manipulation (CORN). We show that by leveraging CORN, we can efficiently train a nonprehensile manipulation policy that can execute dexterous closed-loop joint-space maneuvers without being restricted to predefined motion primitives. Further, by employing an efficient patch-based point-cloud processing backbone, we can achieve highly time-efficient training by allowing the policy to scale to massively parallel environments. By adopting our full system, we demonstrate state-of-the-art performance in nonprehensile manipulation of general objects in simulated environments and zero-shot transfer to unseen real-world objects.
+
+# 2 RELATED WORK
+
+Planning algorithms In planning-based approaches, a nonprehensile manipulation problem is often tackled using gradient-based optimization or graph search. In optimization, the primary challenge arises from optimizing the system of discontinuous dynamics, stemming from contact mode transitions. To combat this, prior works resort to softening contact mode decision variables (Mordatch et al., 2012) or introducing complementarity constraints (Posa et al., 2014; Moura et al., 2022). However, due to the imprecision from the smooth approximation of contact mode transitions, inexact contact dynamics models, and difficulty in precisely satisfying contact constraints, the resulting motions are difficult to realize in the real world. On the other hand, graph-search approaches handle discontinuous system dynamics by formulating the problem as a search over a graph on nodes encoding states such as the robot's configuration and the object's contact mode, and the edges encoding transition feasibility and relative motion between the nodes (Maeda & Arai, 2005; Maeda et al., 2001; Miyazawa et al., 2005). As a result of handling discrete dynamics transitions without approximation, these methods can output more physically realistic motions that can be deployed in the real world (Cheng et al., 2022; Liang et al., 2022). However, to make the search tractable, they resort to strong simplifications such as quasi-static assumption on the space of motions (Cheng et al., 2022; Hou & Mason, 2019), or restricting the edges to predefined primitives or contact modes (Zito et al., 2012). As a result, these works have been limited to tasks that only require simple motions and sparse contact-mode transitions.
+
+Moreover, because both of these approaches must compute a plan in a large hybrid search space with discontinuous dynamics, they are too slow to use in practice. Further, they also require the physical parameters of objects, such as mass and friction coefficients, to be known a priori, which undermines the practicality of these methods. Since the objects may vary significantly in the wild (Figure 5), acquiring ground-truth geometric and physical attributes of target objects is intractable.
+
+Reinforcement learning algorithms Recently, several works have proposed to leverage learning to directly map sensory inputs to actions in nonprehensile manipulation tasks, circumventing the computational cost of planning, inaccuracy of hybrid dynamics models, and difficulty in system identification from high dimensional sensory inputs (Yuan et al., 2018; 2019; Lowrey et al., 2018; Peng et al., 2018; Ferrandis et al., 2023; Kim et al., 2023; Zhou & Held, 2023; Zhou et al., 2023). In Kim et al. (2023), they propose an approach that outputs diverse motions and effectively performs time-varying hybrid force and position control (Bogdanovic et al., 2020), by using the end-effector target pose and controller gains as action space. However, since they represent object geometry via
+
+its bounding box, their approach has a limited generalization capability across shapes. Similarly, other approaches only handle simple shapes such as cuboids (Yuan et al., 2018; 2019; Ferrandis et al., 2023; Zhou & Held, 2023), pucks (Peng et al., 2018), or cylinders (Lowrey et al., 2018).
+
+In HACMan (Zhou et al., 2023), they propose an approach that generalizes to diverse object shapes using end-to-end training. However, they are limited to 3D push primitives defined as fixed-direction poking motions applied on a point on the point cloud. Due to this, they must retract the arm after each execution to observe the next potential contact locations. Further, as end-to-end training with point clouds requires a significant memory footprint, it is difficult to use with massively parallel GPU-based simulations (Makoviychuk et al., 2021): the large resource consumption significantly limits the number of environments that can be simulated in parallel, undermining the parallelism and damaging the training time. Moreover, end-to-end RL on high-dimensional inputs is prone to instability (Eysenbach et al., 2022) and sample-inefficiency: noisy gradients from RL serve as poor training signals for the representation model (Banino et al., 2022), and distributional shift that occurs whenever the encoder gets updated (Shah & Kumar, 2021) slows down policy training. We believe for these reasons, they had to resort to simple primitives that make exploration easier. We use pretraining and efficient architecture to get around these problems.
+
+Along with HACMan, other methods use simple primitives (Yuan et al., 2019; Zhou et al., 2023). But for problems we are contemplating, use of such open-loop primitives precludes dense feedback motions. This is problematic for highly unstable (e.g. rolling or pivoting) objects that move erratically, which require the robot to continuously adjust the contact. For instance, in Figure 1 (row 1, column 3), the robot must adjust the contact to prevent spurious pivoting of the ceramic cup while rolling the handle to the other side; in Figure 1 (row 2, column 6), the robot must align the contact with the rotational axis while lifting the wipe dispenser to prevent accidentally toppling the dispenser to either side. In our work, we adopt a controller with end-effector subgoals with variable gains (Bogdanovic et al., 2020; Kim et al., 2023) as our action space, which allows us to perform dense, closed-loop control of the object.
+
+Representation learning on point clouds Diverse pretraining tasks have been proposed for learning a representation for point cloud inputs, such as PointContrast (Xie et al., 2020), which uses a contrastive loss on point correspondences, or OcCo (Wang et al., 2021), which reconstructs occluded points from partial views. More recently, inspired by advances from NLP (Devlin et al., 2018) and 2D vision (He et al., 2022; Baevski et al., 2022), self-supervised representation learning methods on masked transformers have gained attention (Yu et al., 2022; Zhang et al., 2022; Pang et al., 2022; Zeid et al., 2023). While Point-BERT (Yu et al., 2022), PointM2AE (Zhang et al., 2022) and PointMAE (Pang et al., 2022) reconstruct the masked points from the remaining points, Point2Vec (Zeid et al., 2023) follows Data2Vec (Baevski et al., 2022) and instead estimate the latent patch embeddings, outperforming above baselines in shape classification and segmentation.
+
+As a result, these methods learn highly performant shape representations, demonstrating state-of-the-art performance across tasks such as shape classification or segmentation (Zeid et al., 2023). However, the same impressive performance is often inaccessible with smaller models (Fang et al., 2021; Shi et al., 2022) due to the difficulty of the pretraining task (Fang et al., 2021) or model collapse (Shi et al., 2022). While this necessitates large models, adopting a large encoder for policy training in GPU-based simulators is undesirable, as it can dominate the compute-cost and memory footprint during policy rollout, limiting the parallelism in massively-parallel RL setups.
+
+In robotics, several alternative representation learning approaches have been proposed. Huang et al. (2021) pretrains their point cloud encoder by predicting object class and relative offset from the goal orientation. Similarly, Chen et al. (2022) pretrains a sparse 3D CNN on object class, relative orientation from the goal, and the joint positions of the robot hand. While these methods have been proven effective on in-hand re-orientation tasks for inferring the object's pose from point cloud observations, the benefits are smaller for nonprehensile manipulation tasks which are more sensitive to the specific presence and location of contacts (see Figure 2). In comparison, we directly represent an object with an embedding that is used to predict such information.
+
+![](images/e23f572a0d39e5762930c8d1f77ea48437cd4f37a75789cf562a96100b4bd0e5.jpg)  
+(a) Real-world setup.
+
+![](images/50438aac09b23ff369a79ea24112fb8406a0b5b9356bc6fa74c78d2836f288b1.jpg)  
+(b) Simulation setup.  
+Figure 3: Our real-world (left) and simulated (right) domains.
+
+# 3 CONTACT-BASED OBJECT REPRESENTATION FOR NON-PREHENSILE MANIPULATION
+
+We tackle the problem of rearranging an object of arbitrary geometry on a tabletop to a specified 6D relative pose from the initial pose using nonprehensile manipulation, such as pushing, toppling, and pivoting. Our setup includes a manipulator with a simple gripper, equipped with a proprioceptive sensor and table-mounted depth cameras. We assume that a rigid-body target object is well-singulated on the table, and both the initial and goal poses are stable at rest. Figure 3 illustrates our environment setup.
+
+# 3.1 OVERVIEW
+
+Our framework goes through three stages of training before being deployed in the real world: (1) pretraining, (2) teacher policy training with privileged information, and (3) student policy training with partial information only available in the real world. These three stages happen entirely in simulation based on Isaac Gym (Makoviychuk et al., 2021). Our overall system is shown in Figure 4.
+
+![](images/f412dae92e60c860afcfcc8b9808a7ee9df9b26c5332e2e2584adcb369be4c6b.jpg)  
+Figure 4: Our system and model architecture. The contact network consists of a point cloud encoder (red) and contact-prediction decoder (green), passing the point cloud embeddings to the teacher policy module (blue). Student module (orange, omitted) is detailed in Section A.1.
+
+In the pretraining phase, we train our encoder module (Figure 4, red), which takes in point-cloud observations  $\in \mathbb{R}^{512\times 3}$  and the hand state  $\in \mathbb{R}^9$  (position and 6D orientation (Zhou et al., 2019)), and outputs a patch-wise embedding of the object cloud. To train the network, we pass the embeddings through a contact prediction header (Figure 4, green) that classifies whether each patch intersects with the gripper. During this phase, the point-cloud encoder and collision decoder are trained jointly.
+
+During policy training, we discard the collision decoder and freeze the encoder, so that only the weights of the policy module are learned. The policy consumes the object point cloud embedding from the encoder, and other task-relevant inputs comprising robot's joint position and velocity, the
+
+previous action (end-effector subgoal and controller gains), the object's pose relative to the goal, and its physical properties (mass, friction, and restitution). These inputs are tokenized via an MLP layer to produce query tokens for the cross-attention layer against the point cloud embeddings to extract task-relevant features. These features are concatenated again with the task-relevant inputs and processed by a shared MLP before being split into actor and critic networks. We train the policy module via PPO (Schulman et al., 2017). Since full-cloud observations and physics parameters of objects are not available in the real world, we distill the teacher policy into a student policy. We use DAgger (Ross et al., 2011) to imitate the teacher's actions solely based on information available in the real world: the partial point cloud of the object, robot's joint states, the previous action, and the relative object pose from the goal. We utilize ndiffrast (Laine et al., 2020) to efficiently render the partial point cloud of the scene on the GPU during training.
+
+# 3.2 LEARNING CORN
+
+Algorithm 1 outlines the data generation procedure for our network, inspired by (Son & Kim, 2023). We first sample the SE(3) transforms within the workspace for the gripper and object (L1-2). We then compute the nearest displacement between the surface points of the object and the gripper (L3) and move the gripper in that direction plus a small Gaussian noise (L4-6) to approach a configuration near or in a collision. To compute the labels, we sample points from the object's surface (L7), then label each point according to whether they intersect with the gripper (L8-10). This process generates about half of the gripper poses in collision with the object, and the other half in a near-collision pose with the object. To disambiguate these cases, the model must precisely reason about the object's geometry.
+
+# Algorithm 1 Dataset generation for CORN.
+
+Require: object shape  $\mathcal{O}$ , gripper shape  $\mathcal{G}$ , workspace  $\mathcal{W}$ , noise level  $\sigma$
+
+Ensure: gripper pose  $T_{G}$ , object cloud  $X$ , contact label  $L$
+
+1:  $T_O, T_G \gets \text{SamplePoses}(\mathcal{W})$  
+2:  $\mathcal{O}'\gets T_O\cdot \mathcal{O};\mathcal{G}'\gets T_G\cdot \mathcal{G}$  
+3:  $\vec{\delta} \gets \text{Nearest Displacement}(\mathcal{O}', \mathcal{G}')$  
+4:  $s\sim \mathcal{N}(1,\sigma /\lvert\lvert\vec{\delta}\rvert\rvert)$  
+5:  $T_{d}\gets \left[ \begin{array}{cc}I_{3\times 3} & -s\cdot \bar{\delta}\\ 0 & 1 \end{array} \right]$  
+6:  $\mathcal{G}''\gets \bar{T}_d\cdot \mathcal{G}'$  
+7:  $X \sim \text{SampleSurfacePoints}(\mathcal{O}')$  
+8: for  $x_{i}\in X$  do  
+9:  $L_{i}\gets \text{PointInMesh}(x_{i},\mathcal{G}^{\prime \prime})$  
+0: end for
+
+Afterward, the model is trained by classifying
+
+whether each patch of the object intersects with the gripper at the given pose. A patch is labeled as positive if any point within it intersects with the gripper. We use binary cross-entropy between the patchwise decoder logits and the collision labels to train the model(Figure 4, green block)
+
+# 3.3 PATCH-BASED ARCHITECTURE FOR CORN
+
+To efficiently train a policy by simultaneously simulating thousands of environments using GPUs, we leverage a patch-based transformer to encode the object point cloud shown in Figure 4 (red), which pass the patch embeddings to the policy module (blue).
+
+Patch Tokenization. In line with previous work (Pang et al., 2022), we divide the point cloud into a set of patches (Figure 4, red block, top left). To define each patch, we identify  $N$  representative points using farthest-point sampling (FPS). The k-nearest neighbor (kNN) points from these representatives constitute a patch, which is normalized by subtracting its center from its constituent points (Pang et al., 2022; Zeid et al., 2023; Yu et al., 2022) to embed the local shape. These patches are then tokenized via a Multi-Layer Perceptron (MLP) as input tokens to a transformer.
+
+Unlike past methods that use a small PointNet for tokenizing the patches (Pang et al., 2022; Zeid et al., 2023), we tokenize the patches with a lightweight MLP. Using an MLP is sufficient since the patch size is constant, fully determined by the size of  $k$  during kNN lookup. By sorting the points within each patch by their distance from the patch center, we can ensure that points within a patch always follow a consistent order. Thus, we can avoid using a costly permutation-invariant PointNet tokenizer. After computing the local patch embeddings, we add learnable positional embeddings of the patch centers to restore the global position information (Pang et al., 2022).
+
+Additional Encoder Inputs. By leveraging a transformer backbone, our architecture can easily mix heterogeneous task-related inputs as extra tokens, such as hand state, together with raw point-cloud observations as shown in Figure 4. Unlike PointNet-derived models that can only concatenate such inputs after the point-processing layers, this has an advantage in that the network can pay attention to parts of the point cloud in accordance with the hand state, such as the ones near the robot's hand that would interact with the gripper.
+
+# 4 EXPERIMENTS
+
+# 4.1 EXPERIMENTAL SETUP
+
+![](images/5b295f7e9248bf1b8db643666959517157ffc5ae540de34cc9a6cb74acb08ec7.jpg)  
+Figure 5: Set of 16 real-world objects that we test in the real world.
+
+Training setup For each scene, we randomly draw an object from a subset of 323 geometrically diverse objects from DexGraspNet dataset (Wang et al., 2023), detailed in Section A.6.2. For each episode, we first place the object in a random stable pose on the table. Then, we reset the robot arm at a joint configuration uniformly sampled within predefined joint bounds slightly above the workspace. By doing so, we can avoid initializing the robot in spurious collision with the table or the object. Afterward, we sample a 6D stable goal pose randomly on the table, spaced at least  $0.1\mathrm{m}$  away from the initial pose to prevent immediately achieving success at initialization. To sample valid initial and goal poses for each object, we pre-compute a set of stable poses for each object. This procedure is elaborated in Section A.6.1.
+
+Action, Rewards, and Success Criteria Following Kim et al. (2023), the action space of the robot comprises the subgoal residual of the hand, and the joint-space gains of a variable impedance controller (Details in Section A.2). We also follow the same curriculum learning scheme on the subgoal residual from Kim et al. (2023) to facilitate transferring our policy to the real world. The reward in our domain is defined as  $r = r_{suc} + r_{reach} + r_{contact} - c_{energy}$ , comprising the task success reward  $r_{suc}$ , goal-reaching reward  $r_{reach}$ , contact-inducing reward  $r_{contact}$ , and energy penalty  $c_{energy}$ . The task success reward  $r_{suc} = \mathbb{1}_{suc}$  is given when the pose of the object is within 0.05m and 0.1 radians of the target pose. We add dense rewards  $r_{reach}$  and  $r_{contact}$  to facilitate learning, based on a potential function (Ng et al., 1999) and has the form  $r = \gamma \phi(s') - \phi(s)$  where  $\gamma \in [0,1)$  is the discount factor. For  $r_{reach}$ , we have  $\phi_{reach}(s) = k_g \gamma^{k_d \cdot d_{o,g}(s)}$  and for  $r_{contact}$ , we have  $\phi_{contact}(s) = k_r \gamma^{k_d \cdot d_{h,o}(s)}$  where  $k_g, k_d, k_r \in \mathbb{R}$  are scaling coefficients;  $d_{o,g}(s)$  is the distance from the current object pose to the goal pose, measured using the bounding-box based distance measure from Allshire et al. (2022);  $d_{h,o}(s)$  is the hand-object distance between the object's center of mass and the tip of the gripper. Energy penalty term is defined as  $c_{energy} = k_e \cdot \sum_{i=1}^{7} \tau_i \cdot \dot{q}_i$ , where  $k_e \in \mathbb{R}$  is a scaling coefficient,  $\tau_i$  and  $\dot{q}_i$  are joint torque and velocity of the  $i^{th}$  joint. The scaling coefficients for the rewards are included in Table A.1.
+
+Domain Randomization. During training, we randomize the mass, scale of the object, and friction and restitution of the object, table, and the robot gripper. We set the scale of the object by setting the largest diameter of the object within a predefined range. To facilitate real-world transfer, we also add a small noise to the torque command, object point cloud, and the goal pose when training the student. Detailed parameters for domain randomization are described in Table A.4.
+
+Real-World Setup. Our real-world setup is shown in Figure 3a. We use three RealSense D435 cameras to extract the point clouds, and use Iterative Closest Point (ICP) To estimate the error between the object's current and target poses. We further use April tags (Wang & Olson, 2016) to track symmetric objects that cannot be readily tracked via ICP. We also wrap the gripper of the
+
+robot with a high-friction glove to match the simulation. We emphasize that all training is done in simulation, and the policy is zero-shot transferred to the real world.
+
+# 4.2 RESULTS
+
+We'd like to evaluate the following claims: (1) Pretraining CORN enables training a nonprehensile manipulation policy in a time- and data-efficient manner. (2) Patch-based transformer architecture enables efficiently scaling to thousands of point-cloud based RL agents in parallel. (3) Our system can generalize to domain shifts such as unseen objects in the real world. To support claims 1 and 2, we compare our pretraining task and architecture (OURS) against the baseline encoders in Figure 6.
+
+Compared to ours, P2V uses a pretrained Point2Vec (Zeid et al., 2023) encoder, using the author's weights; P2V-LITE is pretrained as in P2V, but uses the same architecture as Ours; ROT also shares the architecture with Ours, but is pretrained with relative rotation estimation as in (Huang et al., 2021; Chen et al., 2022); E2E also shares the architecture, but is trained in an end-to-end manner without pretraining; PN uses a three-layer PointNet encoder, pretrained on point-wise collision prediction, analogous to CORN; and STATE trains a geometry-unaware policy that only receives object bounding box inputs as the object representation, rather than point clouds. Note that P2V, P2V-LITE, ROT, E2E have the same downstream policy architectures as ours. For PN and STATE, they also have the same policy architecture except that they do not use cross-attention.
+
+![](images/c864e9a28d337b61201ea5ff7133a7cdd112426d2314d3c7a46ef06f41f1fcb7.jpg)  
+Figure 6: Training progression and baselines. Plots show the mean (solid) and standard deviations (transparent) for each baseline. (Left) Success rate vs. number of interaction steps. Interaction steps are reported as the total number of steps aggregated across 4096 parallel environments. (Middle) Success rate vs. number of hours. All baselines are allowed to interact at most  $2e9$  time steps. (Right) Comparison of baselines. PT: Patch Transformer.
+
+Figure 6 shows the progression of success rates across different baselines in simulation. To support claim 1, we consider the performance of the policy after 2 billion interactions (in steps) and 24 hours (in time), respectively. First, E2E takes significantly longer compared to Ours, in terms of both steps and time: by pretraining CORN, Ours achieves  $88.0\%$  suc RATE (steps) and  $88.5\%$  (time), while E2E only reaches  $31.4\%$  (in time) and  $54.4\%$  (in steps), respectively. This is due to the overhead of jointly training the encoder and policy networks in E2E. Among pretrained representations, we first compare with P2V. While P2V is similar to Ours in steps  $(85.6\%)$ , it is significantly slower in time  $(3.55\%)$ , due to the inference overhead of the large representation model. To isolate the effect of the pretraining task, we also compare with P2V-LITE: pretrained as in P2V, yet with same architecture as Ours. While the resulting policy is reasonably time-efficient due to faster rollouts  $(73.4\%)$  in time), it is less data-efficient  $(68.8\%)$  in steps) due to the reduced performance of the smaller model (Shi et al., 2022; Fang et al., 2021). Another baseline, ROT from in-hand reorientation literature (Huang et al., 2021; Chen et al., 2022) performs slightly worse in both measures  $(64.2\%$  (steps);  $67.0\%$  (time)): we believe this is due to the increased demand for the awareness of object geometry in our task. To see this, we note that the pose-only policy STATE), unaware of object geometry, cannot learn at all in our domain, in contrast to the positive result from Chen et al. (2022). This highlights the fact that our task requires greater awareness of the object's geometric features: just knowing the object's pose is insufficient, and a deeper understanding of its geometry is necessary.
+
+To see CORN learns a suitable representation for manipulation, we inspect the attention scores of the policy amid different motions in Figure 7. For pushing and toppling motions (row 1,3), our policy primarily attends to the current or future contact between the hand and the object, which is consistent
+
+![](images/b85ac9607befaec86eaad4b635f0b246b8dd4c48d43241389d53a05b1a44a414.jpg)  
+Figure 7: Visualization of the scores from the cross-attention layers of the policy, summed over all heads. We colorize the attention for each patch normalized to range  $(0,1)$ , then project the patchwise colors on the surface of the object for visualization with VIRIDIS colormap.
+
+with the premise of our representation-learning scheme. While pivoting or rolling motions (row 2,4) share the same trend, our policy also attends to the pivot points of the object against the table.
+
+To support claim 2, we show that our patch-transformer architecture is more performant in both compute- and memory-cost compared to PointNet (Qi et al., 2016). In particular, we evaluate PN, where the primary difference is the use of PointNet in place of the patch transformer. While the performance degradation from the architecture change is only modest in steps (88.3% v. 70.2%), the large computational overhead of PointNet renders it slowest in time(0.223%) among all baselines. To support claim 3, we evaluate our policy in the real-world setting as described in Section 4.1. Figure 5 shows the objects that we evaluate in our real-world experiments, exhibiting wide diversity in terms of shape, mass, and materials; Figure 1 shows four representative real-world episodes.
+
+Table 1: Real world run results. All of the objects in the real-world setup are unseen except for 3D-printed objects marked with  $\dagger$ .  
+
+<table><tr><td>Object name</td><td>Success/Trial</td><td>Object name</td><td>Success/Trial</td><td>Object name</td><td>Success/Trial</td><td>Object name</td><td>Success/Trial</td></tr><tr><td>Red Card</td><td>4/5</td><td>Cube Block</td><td>4/5</td><td>Ceramic Cup</td><td>4/5</td><td>Red Dripper</td><td>3/5</td></tr><tr><td>Toy Puppy†</td><td>4/5</td><td>Iced Tea Box</td><td>3/5</td><td>Nutella Bottle</td><td>3/5</td><td>Coaster Holder</td><td>3/5</td></tr><tr><td>Toy Bulldozer</td><td>4/5</td><td>Wipe Dispenser</td><td>5/5</td><td>Coffee Jar</td><td>2/5</td><td>Thick Book</td><td>4/5</td></tr><tr><td>Blue Holder</td><td>5/5</td><td>Toy Table†</td><td>3/5</td><td>Lemona Box</td><td>3/5</td><td>Candy Box</td><td>3/5</td></tr><tr><td>Success rate</td><td></td><td></td><td></td><td></td><td></td><td></td><td>57/80 (71.3%)</td></tr></table>
+
+The results from our policy execution in the real-world are organized in Table 1. Overall, our policy demonstrates  $71.3\%$  success rate in the real world. These results indicate that, with distillation, our system can zero-shot transfer to the real world despite only training in a simulation.
+
+Limitations. We find that our policy struggles more with concave objects (coaster-holder, red dripper;  $60\%$ ) or unstable objects (iced tea box, coffee jar, red dripper;  $53\%$ ). Concave objects cause perception challenge in the real world due to severe ambiguity when occluded by the robot, leading to timeouts as the agent oscillates between actions or stops amid a maneuver. Unstable objects tend to abruptly spin out of the workspace after minor collisions, and the dexterity of our robot platform and speed of our real-world perception pipeline cannot catch up with such rapid motions.
+
+# 5 CONCLUSION
+
+In this work, we present a system for effectively training a non-prehensile object manipulation policy that can generalize over diverse object shapes. We show that by pretraining a contact-informed representation of the object, coupled with an efficient patch-based transformer architecture, we can train the policy in a data- and time-efficient manner. With student-teacher distillation, we find that our policy can zero-shot transfer to the real world, achieving success rates of  $71.3\%$  in the real world across both seen and unseen objects despite only training in a simulation.
+
+# ACKNOWLEDGEMENT
+
+This work was supported by Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government(MSIT) (No.2019-0-00075, Artificial Intelligence Graduate School Program(KAIST)), (No.2022-0-00311, Development of Goal-Oriented Reinforcement Learning Techniques for Contact-Rich Robotic Manipulation of Everyday Objects), (No. 2022-0-00612, Geometric and Physical Commonsense Reasoning based Behavior Intelligence for Embodied AI).
+
+# REPRODUCIBILITY STATEMENT
+
+We describe our real-world system and perception pipeline in detail in Section A.4. The procedure for data generation and pretraining for our model and other baselines is detailed in Section 3.2 and Section A.3, respectively. We include the set of 323 training objects from DexGraspNet (Wang et al., 2023) that we used for policy training as supplementary materials. We include the student-model architecture and distillation pipeline for real-world transfer in Section A.1. We describe the simulation setup regarding data preprocessing(Section A.6), and describe the hyperparameters associated with our network architecture(Table A.2), domain-randomization(Table A.4), and policy training(Section A.3). We also release our code at https://github.com/contact-non-prehensile/corn.
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+Haizhou Shi, Youcai Zhang, Siliang Tang, Wenjie Zhu, Yaqian Li, Yandong Guo, and Yueting Zhuang. On the efficacy of small self-supervised contrastive models without distillation signals. In Proceedings of the AAAI Conference on Artificial Intelligence, 2022.  
+Dongwon Son and Beomjoon Kim. Local object crop collision network for efficient simulation of non-convex objects in GPU-based simulators. In Proceedings of Robotics: Science and Systems, Daegu, Republic of Korea, July 2023. doi: 10.15607/RSS.2023.XIX.033.  
+Weikang Wan, Haoran Geng, Yun Liu, Zikang Shan, Yaodong Yang, Li Yi, and He Wang. Unidex-grasp++: Improving dexterous grasping policy learning via geometry-aware curriculum and iterative generalist-specialist learning. arXiv preprint arXiv:2304.00464, 2023.
+
+Hanchen Wang, Qi Liu, Xiangyu Yue, Joan Lasenby, and Matthew J. Kusner. Unsupervised point cloud pre-training via occlusion completion. In International Conference on Computer Vision, ICCV, 2021.  
+John Wang and Edwin Olson. AprilTag 2: Efficient and robust fiducial detection. In Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), October 2016.  
+Ruicheng Wang, Jialiang Zhang, Jiayi Chen, Yinzhen Xu, Puhao Li, Tengyu Liu, and He Wang. Drexgraspt: A large-scale robotic dexterous grasp dataset for general objects based on simulation. In 2023 IEEE International Conference on Robotics and Automation (ICRA), pp. 11359-11366. IEEE, 2023.  
+Xinyue Wei, Minghua Liu, Zhan Ling, and Hao Su. Approximate convex decomposition for 3d meshes with collision-aware concavity and tree search. ACM Transactions on Graphics (TOG), 41(4):1-18, 2022.  
+Saining Xie, Jiatao Gu, Demi Guo, Charles R Qi, Leonidas Guibas, and Or Litany. Pointcontrast: Unsupervised pre-training for 3d point cloud understanding. In Computer Vision-ECCV 2020: 16th European Conference, Glasgow, UK, August 23-28, 2020, Proceedings, Part III 16, pp. 574-591. Springer, 2020.  
+Xumin Yu, Lulu Tang, Yongming Rao, Tiejun Huang, Jie Zhou, and Jiwen Lu. Point-bert: Pretraining 3d point cloud transformers with masked point modeling. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2022.  
+Weihao Yuan, Johannes A Stork, Danica Kragic, Michael Y Wang, and Kaiyu Hang. Rearrange-ment with Nonprehensile Manipulation Using Deep Reinforcement Learning. In International Conference on Robotics and Automation, 2018.  
+Weihao Yuan, Kaiyu Hang, Danica Kragic, Michael Y Wang, and Johannes A Stork. End-to-End Nonprehensile Rearrangement with Deep Reinforcement Learning and Simulation-to-Reality Transfer. Robotics and Autonomous Systems, 2019.  
+Karim Abou Zeid, Jonas Schult, Alexander Hermans, and Bastian Leibe. Point2vec for self-supervised representation learning on point clouds. arXiv preprint arXiv:2303.16570, 2023.  
+Renrui Zhang, Ziyu Guo, Peng Gao, Rongyao Fang, Bin Zhao, Dong Wang, Yu Qiao, and Hongsheng Li. Point-m2ae: multi-scale masked autoencoders for hierarchical point cloud pre-training. Advances in neural information processing systems, 35:27061-27074, 2022.  
+Hengshuang Zhao, Li Jiang, Jiaya Jia, Philip HS Torr, and Vladlen Koltun. Point transformer. In Proceedings of the IEEE/CVF international conference on computer vision, pp. 16259-16268, 2021.  
+Wenxuan Zhou and David Held. Learning to grasp the ungraspable with emergent extrinsic dexterity. In Conference on Robot Learning, pp. 150-160. PMLR, 2023.  
+Wenxuan Zhou, Bowen Jiang, Fan Yang, Chris Paxton, and David Held. Hacman: Learning hybrid actor-critic maps for 6d non-prehensile manipulation. In Conference on Robot Learning. PMLR, 2023.  
+Yi Zhou, Connelly Barnes, Jingwan Lu, Jimei Yang, and Hao Li. On the continuity of rotation representations in neural networks. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 5745-5753, 2019.  
+Claudio Zito, Rustam Stolkin, Marek Kopicki, and Jeremy L Wyatt. Two-Level RRT Planning for Robotic Push Manipulation. In International Conference on Intelligent Robots and Systems, 2012.
+
+# A APPENDIX
+
+# A.1 STUDENT MODEL
+
+![](images/aef91ba63a2083e115447ce59a1063bfab7a3570d93ca8d7841a641b20f69421.jpg)  
+Figure A.1: Student Model Architecture in DAgger.
+
+The student policy shares a similar architecture with the teacher policy, with two distinctions. Unlike teacher policy, which employs joint state, previous action, and goal inputs for generating query tokens for cross-attention, we incorporate these tokens into the input of the patch transformer within the encoder to facilitate extracting task-relevant features from partial point clouds. Given that these inputs are already incorporated in the input of the encoder, we use learned query tokens for cross-attention.
+
+Since the student policy can only perceive limited shape information of objects at any given moment due to occlusion, we incorporate a two-layer Gated Recurrent Unit (GRU) (Cho et al., 2014) on top of the student point cloud encoder. This enables the student model to aggregate partial observations of object geometry based on historical observations.
+
+We train the student with DAgger with truncated backpropagation through time (BPTT). In particular, we run the student for 8 time-steps and update its parameters to minimize KL-divergence between the action distribution of the teacher policy and the student policy.
+
+# A.2 DETAILS ON POLICY ACTION SPACE
+
+The action space of our policy consists of the subgoal residual of the end-effector  $\Delta T_{ee}$  and joint-space gains. The subgoal residual is parameterized by the translational offset  $\Delta t\in \mathbb{R}^3$  and axis-angle representation of the residual rotation in the world frame  $\Delta r\in \mathbb{R}^3$ . The joint-space gains are parameterized by proportional terms  $(k_{p}\in \mathbb{R}^{7})$  and damping factors  $(\rho \in \mathbb{R}^7)$  of a variable impedance controller. Based on this, we compute the joint position target by solving inverse kinematics with damped least squares method (Buss, 2004) as  $q_{target} = q_t + IK(\Delta T_{ee})$ . The torque command for each joint is computed based on the joint position error and the predicted joint-space gains and damping factors as  $\tau = k_p(q_{target} - q_t) - k_d\dot{q}_t$ ,  $k_{d} = \rho \cdot \sqrt{k_{p}}$ .
+
+# A.3 DATA GENERATION AND PRETRAINING PIPELINES
+
+P2V-LITE. For pretraining P2V-LITE, we follow the same procedure as Zeid et al. (2023), except we use the same architecture as OURs. Due to the use of a significantly lighter model, we apply two modifications to the original training setup, as follows: first, since we only use a two-layer transformer, instead of averaging over the last 6 layers of the teacher, we take the result after layer-normalization of the final layer, which keeps the ratio consistent (50% of layers). Second, we replace DropPath layers with dropout since the model is shallow. Otherwise, we follow the original hyper
+
+parameters from the paper and the author's code(https://github.com/kabouzeid/point2vec).
+
+ROT. For pretraining ROT, we follow the procedure described in Chen et al. (2022). Since the authors report that adding the classification objective does not influence the encoder quality, we omit the classification terms. For the training data, we use ShapeNet Chang et al. (2015) dataset. We apply two different SO(3) transformations to the same point cloud, and pass it through the encoder to obtain the patchwise embeddings. We concatenate the patchwise embeddings from both streams, then pass it through a 3-layer MLP (512, 64, 6). We train the encoder on the regression task, where the task for the decoder is to regress the parameters for a 6D rotation Zhou et al. (2019) as recommended from Chen et al. (2022).
+
+OURS-PN. For pretraining PN, we use the same dataset from OURs. Since PointNet does not produce patchwise embeddings, we instead adopt a U-Net architecture based on PyG Fey & Lenssen (2019). To inform the model about the end-effector, we concatenate the hand pose (position and orientation Zhou et al. (2019)) to each point in the channel dimension.
+
+# A.4 REAL WORLD SYSTEM AND PERCEPTION PIPELINE
+
+Point Cloud Segmentation. In the point cloud segmentation phase, we integrate three RealSense D435 cameras. Points outside the predefined 3D bounding-box workspace above table are first removed, and those within a distance less than the threshold  $\epsilon = 1\mathrm{cm}$  from the table surface are removed next. These parameters were determined empirically to handle outliers without removing too much of the object. For thin objects such as cards, we alternatively employ color-based segmentation to remove the table from the point cloud, avoiding the risk of inadvertently removing object points.
+
+After removing the table, only the object and the robot remains. To remove the robot, we compute the transform of all robot links based on the robot kinematics, then query the points as to whether it is contained within each link mesh. For efficiency, we first apply convex decomposition on the robot geometry, and employ point-convex intersection to check whether the point belongs to the robot. We initially tried using robot-points removal based on raycasting the point-to-robot mesh distances, but we found it was much slower than the convex-hull based method.
+
+To reduce noise in the point cloud, we employ a radius outlier removal logic with  $r = 2$  cm and  $n_{\mathrm{min}} = 96$  points, which is the minimum number of points that the inlier should contain within the neighborhood. Finally, to identify the object point cluster, we used DBSCAN clustering algorithm. Clusters were computed with  $\epsilon = 1$  cm and the number of neighbors as 4 to form the core-set.
+
+To enhance processing speed, we optimized the entire segmentation pipeline to utilize tensor operations executed on the GPU. The output object point cloud of this segmentation process serves as input for both our policy and object pose tracking pipeline.
+
+Object Pose Tracking. To trade-off tracking speed and performance, we first subsample the object point clouds randomly to  $n_{\mathrm{track}} = 2048$  points. Empirically, we found that this avoids compromising the quality of the ICP(Iterative Closest Point) algorithm, while remaining reasonably fast.
+
+We employ ICP for tracking. Given the object point cloud  $C_t$  at current time step  $t$ , we conduct point-to-plane ICP registrations with point cloud of previous timestep  $C_{t-1}$ , resulting in a transformation  $P_{t,t-1} = \mathrm{ICP}(C_t, C_{t-1})$ . The current object pose  $T_{O_t}$  is obtained by recursively applying pairwise transformations:  $T_{O_t} = P_{t,t-1} \cdot T_{O_{t-1}}$ . In the case that the transform drifts over time, we also perform an additional ICP match with the initial object point cloud  $P_{t,0} = \mathrm{ICP}(C_t, C_0)$  to correct the error. If the fitness score  $Fitness_{t,0}$  exceeds 60%, current object pose is calculated as  $T_{O_t} = P_{t,0} \cdot T_{O_0}$ .
+
+For thin objects, we utilize point-to-point ICP matching since their point cloud nearly forms a single plane. While the ICP tracker performs well for large and non-symmetrical objects, it struggles with highly symmetrical objects, or objects with point-matching ambiguity under occlusion (e.g. when cup handles are occluded by the robot).
+
+To address this challenge, we tried color-based ICP to resolve the ambiguity based on surface texture. However, we found that it did not improve tracking performance and, in some cases, even
+
+worsened it. As such, we used april-tag tracker to maintain object pose tracking accuracy for highly symmetrical objects.
+
+# A.5 EXAMPLE TRAJECTORIES
+
+Example trajectories can be observed from the video in the supplementary material, or from http://sites.google.com/view/contact-non-prehensile.
+
+# A.6 SIMULATION SETUP
+
+# A.6.1 STABLE POSES GENERATION
+
+To sample stable poses for training, we drop the objects in a simulation and extract the poses after stabilization. In  $80\%$  of the trials, we drop the object  $0.2\mathrm{m}$  above the table in a uniformly random orientation. In the remaining  $20\%$ , we drop the objects from their canonical orientations, to increase the chance of landing in standing poses, as they are less likely to occur naturally. If the object remains stationary for 10 consecutive timesteps, and its center of mass projects within the support polygon of the object, then we consider the pose to be stable. We repeat this process to collect at least 128 initial candidates for each object, then keep the unique orientations by pruning equivalent orientations that only differ by a planar rotation about the z-axis.
+
+# A.6.2 OBJECTS FOR TRAINING
+
+We sample 323 objects from the DexGraspNet dataset (Wang et al., 2023), shown in Figure A.2. To increase the simulation speed and stability, we apply convex decomposition on every mesh using CoACD (Wei et al., 2022), after generating the watertight mesh with simplification using Manifold (Huang et al., 2018).
+
+![](images/d9742d011dc7627afa77e2c3b49c1ea2ab65d9103965732f717e2790b115fe42.jpg)  
+Figure A.2: 323 object meshes that were used for training.
+
+# A.7 HYPERPARAMETERS
+
+Table A.1: Hyperparameters for reward computation.  
+
+<table><tr><td>Parameter</td><td>Value</td><td>Description</td></tr><tr><td>kg</td><td>0.302</td><td>Goal-reaching reward coefficient</td></tr><tr><td>kr</td><td>0.0604</td><td>Hand-reaching reward coefficient</td></tr><tr><td>ke</td><td>0.0001</td><td>Energy penalty coefficient</td></tr><tr><td>kd</td><td>243.12</td><td>Decay factor for potential-based reward</td></tr></table>
+
+Table A.2: Hyperparameters for Encoder and Policy.  
+
+<table><tr><td>Hyperparameter</td><td>Value</td><td>Hyperparameter</td><td>Value</td><td>Hyperparameter</td><td>Value</td></tr><tr><td>Num. points</td><td>512</td><td>Hidden dim.</td><td>128</td><td>Shared MLP</td><td>MLP (512, 256, 128)</td></tr><tr><td>Num. patches</td><td>16</td><td>Num. layer</td><td>2</td><td>Actor</td><td>MLP (64, 1)</td></tr><tr><td>Patch size</td><td>32</td><td>Num. attention head in self-attention</td><td>4</td><td>Critic</td><td>MLP(64, 20)</td></tr><tr><td>Concatenate context input</td><td>True</td><td>Num. attention head in cross-attention (teacher/student)</td><td>16/4</td><td></td><td></td></tr></table>
+
+Table A.3: Hyperparameters for PPO.  
+
+<table><tr><td>Hyperparameter</td><td>Value</td><td>Hyperparameter</td><td>Value</td><td>Hyperparameter</td><td>Value</td><td>Hyperparameter</td><td>Value</td></tr><tr><td>Max Num. epoch</td><td>8</td><td>Base learning rate</td><td>0.0003</td><td>GAE parameter</td><td>0.95</td><td>Num. environment</td><td>4096</td></tr><tr><td>Early-stopping KL target</td><td>0.024</td><td>Adaptive-LR KL target</td><td>0.016</td><td>Discount factor</td><td>0.99</td><td>Episode length</td><td>300</td></tr><tr><td>Entropy regularization</td><td>0</td><td>Learning rate schedule</td><td>adaptive</td><td>PPO clip range</td><td>0.3</td><td>Update frequency</td><td>8</td></tr><tr><td>Policy loss coeff.</td><td>2</td><td>Value loss coeff.</td><td>0.5</td><td>Bound loss coeff.</td><td>0.02</td><td></td><td></td></tr></table>
+
+Table A.4: Range for domain randomization.  $\mathcal{U}[min, max]$  denotes uniform distribution, and  $\mathcal{N}[\mu, \sigma]$  denotes Normal distribution. Point cloud noise and Goal pose noise are added to the normalized input.  
+
+<table><tr><td>Parameter</td><td>Range</td></tr><tr><td>Object mass (kg)</td><td>U[0.1, 0.5]</td></tr><tr><td>Object scale (m)</td><td>U[0.1, 0.3]</td></tr><tr><td>Object friction</td><td>U[0.7, 1.0]</td></tr><tr><td>Table friction</td><td>U[0.3, 0.8]</td></tr><tr><td>Gripper friction</td><td>U[1.0, 1.5]</td></tr><tr><td>Torque noise</td><td>N[0.0, 0.03]</td></tr><tr><td>Point cloud noise</td><td>N[0.0, 0.005]</td></tr><tr><td>Goal pose noise</td><td>N[0.0, 0.005]</td></tr></table>

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2024/COSA_ Concatenated Sample Pretrained Vision-Language Foundation Model/4c9218f4-c368-4834-86cf-99d68eedf0ed_origin.pdf

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+# COSA: CONCATENATED SAMPLE PRETRAINED VISION-LANGUAGE FOUNDATION MODEL
+
+Sihan Chen $^{12*}$  Xingjian He $^{2}$  Handong Li $^{12}$  Xiaojie Jin $^{3}$  Jiashi Feng $^{3}$  Jing Liu $^{12}$
+
+$^{1}$ School of Artificial Intelligence, University of Chinese Academy of Sciences  
+$^{2}$  Institute of Automation, Chinese Academy of Science  $^{3}$ Bytedance Inc.
+
+{sihan.chen, xingjian.he, jliu}@nlpr.ia.ac.cn
+
+lihandong2023@ia.ac.cn,{jinxiaojie,jshfeng}@bytedance.com
+
+# ABSTRACT
+
+Due to the limited scale and quality of video-text training corpus, most vision-language foundation models employ image-text datasets for pretraining and primarily focus on modeling visually semantic representations while disregarding temporal semantic representations and correlations. To address this issue, we propose COSA, a COncatenated SAmple pretrained vision-language foundation model. COSA can jointly model visual contents and event-level temporal cues using only image-text corpora. We achieve this by sequentially concatenating multiple image-text pairs as inputs for pretraining. This transformation effectively converts existing image-text corpora into a pseudo video-paragraph corpus, enabling richer scene transformations and explicit event-description correspondence. Extensive experiments demonstrate that COSA consistently improves performance across a broad range of semantic vision-language downstream tasks, including paragraph-to-video retrieval, text-to-video/image retrieval, video/image captioning and video QA. Notably, COSA achieves state-of-the-art results on various competitive benchmarks. Code and model are released at https://github.com/TXH-mercury/COSA.
+
+# 1 INTRODUCTION
+
+Image-text and video-text pretraining models have garnered increasing attention in recent years due to their strong capabilities in bridging the domains of vision and language. These models contribute significantly to various vision-language tasks such as cross-modality retrieval, vision captioning, and visual question answering (VQA). In the early stages, these models were independently trained using distinct cross-modality corpora, network architectures, and training objectives. However, considering that a video can be perceived as a sequence of multiple images (Lei et al., 2021), and an image can be seen as a frozen video (Bain et al., 2021), most researchers lean towards training unified foundation models using corpora from both domains, employing sparsely sampled frames as the video representation.
+
+Nevertheless, the majority of large-scale vision-language foundation models are usually trained solely on image-text corpora, disregarding the joint modeling of images and videos. This limitation stems from the restricted scale of video-text corpora, which is associated with the costly processes of video uploading, storage, and downloading: currently, open-sourced web-crawled video-text corpora, such as WebVid10M (Bain et al., 2021), are still two orders of magnitude smaller than its image-text counterpart (LAION-2B (Schuhmann et al., 2021)), which implies the dominance of image-text data in joint modeling. On the other hand, image-text pretraining can also bring benefits to video-related tasks. In fact, some large-scale image-text foundation models (Radford et al., 2021; Wang et al., 2022b) have achieved competitive or even superior performance on video tasks compared to dedicated video-language pretraining models.
+
+![](images/d77b37efba978140541afe7c156fbdfdfc296fe1f1a2885db54bb32a28169440.jpg)  
+Figure 1: Visualizations of the traditional image-text and video-text model pretraining pipeline and proposed unified foundation model COSA, which transforms the image-text corpus into a synthetic video-text corpus through online sample concatenation.
+
+Despite the fact that image-text foundation models have acquired a broad range of semantic correlations between visual concepts and language, they totally overlook temporal contexts within videos, which are crucial for video-language reasoning. This raises the question that whether we can utilize large-scale image-text corpora to train a unified foundation model capable of capturing both static and temporal information during the pretraining phase.
+
+Towards this goal, we propose a simple yet effective approach: training a foundation model with concatenated samples. As illustrated in Figure 1, instead of modeling independently modeling cross-modality samples via traditional single sample training (SST), COSA models the semantic and event-level temporal information among multiple samples by conducting online sample concatenation to transform image-text corpora into video-paragraph corpora, and thus further enhance the learning of both image-language and video-language representations. Specifically, at each training step, for every image-text training sample, we randomly select some other samples from current batch and concatenate them (both images and texts) together. Ablation studies have demonstrated that model trained with COSA can evidently outperform model trained with SST on 12 benchmarks including both video-text and image-text tasks. We attribute it to two main reasons: 1) Concatenated samples build connections between visual concepts and words within a sample group, which is more difficult than build them within single sample, due to that both negative unmatched visual concepts and textual words become more, and thus is helpful for learn more discriminative representations. 2) In comparison to current video-text corpora (Bain et al., 2021), the on-the-fly concatenated corpus offers richer scene transformations, reduced vision redundancy due to sampling randomness, and longer temporally fine-grained captions that describe every frame in sequential order, which encourages models to learn better event-level temporal understanding capabilities and thus further improve performance on video-text tasks.
+
+Enhanced by COSA, we deliver a unified vision-language foundation model. It possesses a simple architecture, takes concatenated samples as input during pretraining with training objectives modified to build connections among multiple cross-modality samples. Extensive experiments have shown that COSA model is capable of handling both discriminative and generative tasks such as cross-modality retrieval, captioning, question answering, and achieves new state-of-the-art results across a wide range of benchmarks under different model scale settings.
+
+# 2 RELATED WORK
+
+Temporal Learning in Video-Language Pretraining (VidLP). Temporal information is the essence that distinguishes videos from images. Early methods aimed to enhance temporal learning in VidLP by either employing models pretrained on action classification tasks as vision backbones (Bain et al., 2021; Li et al., 2022a; Fu et al., 2021; 2022) or designing specific training objectives such as frame order modeling (FOM) (Li et al., 2020; Zellers et al., 2021) or masked video modeling (MVM) (Fu et al., 2021; 2022). We divide temporal learning into two aspects, namely event-level and action-level temporal modeling, in which the former emphasize on the differences and relations across multiple events/scenes, while the latter concentrates the temporal relations of consecutive frames in single event/scene.
+
+![](images/9c1f37b665f3f87f429cbb54ee83b394c8fb03d62346fd0bd6d396616030a266.jpg)  
+Figure 2: Model architecture and training objectives of COSA. Circles and squares in the figure represent global and patch features, respectively.
+
+However, Singularity (Lei et al., 2022) reveals that temporal modeling in pretraining may not be necessary, as sampling a single frame can yield comparable performance to utilizing multiple frames. They attribute this to the static appearance bias in video-language downstream benchmarks. We hypothesize that another contributing factor lies in the limitation of current video-text corpus (WebVid-2.5M (Bain et al., 2021)) for both action-level and event-level temporal learning. In terms of action-level temporal learning, the corpus contains fewer annotated actions compared to recognition datasets like Kinetics-400 (Kay et al., 2017), and there is significant caption redundancy as actions are often associated with several predicates rather than the entire sentence. For event-level temporal learning, the corpus is typically constrained to a single scene and description, whereas rich scene transformations and event-sentence correspondence are crucial. To address these limitations, OmniVL (Wang et al., 2022d) extends the idea of UniCL (Lu et al., 2022) to the video domain and incorporates Kinetics-400 into the training corpus. HiTeA (Ye et al., 2022) tackles caption redundancy through specific fine-grained alignment designs. Compared to above two methods which target at enhancing action-level temporal learning, LF_VILA (Sun et al., 2022) constructs a long-form dataset from the large-scale HD_VILA_100M (Xue et al., 2022a) dataset to enhance event-level temporal learning. In contrast to the aforementioned methods, this work proposes concatenated sample learning to dynamically compose pseudo video-paragraph corpora from existing image-text or video-text corpus, and simultaneously enhance image-text and event-level temporal video-text learning.
+
+Unified Vision-Language Foundation Model. The Frozen model (Bain et al., 2021) was the first to leverage a mixture of image-text (CC3M (Sharma et al., 2018)) and video-text corpus (WebVid2.5M (Bain et al., 2021)) for training VidLP models by sparsely sampling the video corpus and treating the image corpus as frozen videos. Subsequent VidLP methods have followed this route to support both image-text and video-text tasks, with advanced vision backbones (Fu et al., 2021; 2022; Ye et al., 2022) or specially designed training objectives (Li et al., 2022a; Ye et al., 2022; Ge et al., 2022b).
+
+Regarding large-scale unified vision-language foundation models, they can be classified into two types: co-training methods and two-stage training methods. Co-training methods train on both image and video corpora simultaneously and a typical representative method is Flamingo (Alayrac et al., 2022). Two-stage training methods first train models on image-text corpora and then adapt them for video-text tasks. Image-text models can be trained via contrastive learning (Radford et al., 2021; Jia et al., 2021), generative learning (Wang et al., 2022b; Chen et al., 2022; Wang et al., 2021), or a combination of both them(Yu et al., 2022). Regarding adapting image-text models to video-text ones, CLIP-based models (Luo et al., 2022; Xue et al., 2022b) employ temporal fusion transformers and frame-word fine-grained alignment learning to enable text-to-video retrieval. GIT (Wang et al., 2022b) directly finetune models by concatenating multiple frame features as input to the text decoder and achieves state-of-the-art performance on most video captioning benchmarks. VideoCoCa (Yan et al., 2022) adapts the CoCa model (Yu et al., 2022) through continuous learning on video-language corpora. MaMMUT (Kuo et al., 2023) applies a similar temporal perceiving capability enhancement during finetuning as TubeViT (Piergiovanni et al., 2022). In comparison to the above methods, COSA simultaneously model image-text and video-text learning during the pretraining stage, with image-text corpora utilized only.
+
+# 3 METHOD
+
+# 3.1 SIMPLE MODEL ARCHITECTURE
+
+COSA adopts a simple architecture, consisting of a vision encoder (ViT (Dosovitskiy et al., 2020)) and a text encoder (BERT (Devlin et al., 2018)), which facilitates both single-modality encoding and cross-modality interaction. Specifically, we introduce additional cross-attention layers between the self-attention and feed-forward layers of BERT. These cross-attention layers are activated during the forward pass for cross-modality understanding or generation, while deactivated during the forward
+
+Table 1: Model configurations of COSA. CC14M is a combination of CC3M (Sharma et al., 2018), CC12M (Changpinyo et al., 2021), COCO (Lin et al., 2014), SBU (Ordonez et al., 2011), and VG (Krishna et al., 2017b) datasets. The largest 1.2B COSA model is trained with a data bootstrapping strategy inspired by BLIP (Li et al., 2022b), and captions in training corpora (marked with ‘*’) are generated by us through an additionally trained captioner, more details can be found in Appendix. The 400M image-text pairs used in CLIP and LAION-400M (Schuhmann et al., 2021) used in EVAClip are also included in the training examples statistics. LAION-102M is a randomly sampled subset from LAION-400M.
+
+<table><tr><td>Model</td><td>Vision Encoder</td><td>Param</td><td>Training corpora</td><td>Example</td><td>Step</td></tr><tr><td>COSA-B</td><td>Swin-B(Liu et al., 2021)</td><td>251M</td><td>CC3M+WebVid2.5M</td><td>5M</td><td>100K</td></tr><tr><td>COSA-B</td><td>Swin-B(Liu et al., 2021)</td><td>251M</td><td>CC14M+WebVid2.5M</td><td>17M</td><td>160K</td></tr><tr><td>COSA-L</td><td>CLIP/ViT-L/14(Radford et al., 2021)</td><td>468M</td><td>CC14M+WebVid2.5M</td><td>417M</td><td>160K</td></tr><tr><td>COSA</td><td>EVAClip/VIT-G/14(Sun et al., 2023)</td><td>1.2B</td><td>CC14M*+LAION-102M*</td><td>415M</td><td>150K</td></tr></table>
+
+pass for single-modality encoding. The text encoder can serve as a single-modality encoder, cross-modality encoder and decoder.
+
+# 3.2 CONCATENATED SAMPLE TRAINING
+
+Online Sample Concatenation. As illustrated in Figure 2, unlike traditional foundation models that take a single image-text pair or frames-text pair as input (SST, single sample training), COSA employs an online transformation to convert them into a pseudo video-paragraph corpus. To illustrate this process, let's consider the image-text corpus. Given a batch containing  $n_b$  image-text samples, for the  $i$ -th sample  $S_i$  with its image and text denoted as  $I_i$  and  $T_i$  respectively, we randomly select  $n_c$  ( $n_c = 3$  by default) other samples from the current batch and group them together. Consequently, the single sample ( $I_i, T_i$ ) is transformed into a grouped sample ( $I_{group} = [I_i, I_{j1}, \dots, I_{jn_c}]$ ,  $T_{group} = [T_i, T_{j1}, \dots, T_{jn_c}]$ ). Subsequently, we concatenate both the images and texts in the same order to establish their event-level temporal correspondence. Specifically, for the grouped images, we individually feed them into the vision encoder, incorporate learnable temporal embeddings into the output features, and concatenate them along the sequential dimension. Regarding the grouped texts, we directly concatenate them into a paragraph where the temporal relations can be encoded by BERT's vanilla position embedding layer. Through the process of in-order sample concatenation and the use of position embeddings, the model can learn explicit scene-level temporal alignment. This concatenation procedure is applied to all samples in the batch. COSA can also be applied on video-text corpus and in this scenario, we sample a single frame from each video and perform the same concatenation process.
+
+The concatenated images can be viewed as a series of snapshots from multiple clips within a pseudo video, where each clip captures a different scene accompanied by its corresponding descriptions. It is noted that these pseudo videos exhibit rapid scene changes with reduced visual redundancy but little semantic coherence due to the random sampling process. However, our experiments demonstrate that the cost of sacrificing clip coherence is negligible, and random sampling yields superior results compared to other settings where clip relevance is intentionally enforced.
+
+Training Objectives. We employ four training objectives, namely Image-Text Contrastive (ITC), Image-Text Matching (ITM), Masked Language Modeling (MLM), and Generative Modeling (GM), to enhance the model's cross-modality alignment, understanding, and generation capabilities. These objectives are modified to accommodate the use of concatenated samples as input, as opposed to single samples.
+
+Concatenated Image-Text Contrastive (CITC). The pseudo video frames are individually passed through the vision encoder, and the average pooling of the output [CLS] token features serves as the global representation of the pseudo videos. The [CLS] token feature from BERT is utilized as the paragraph representation. A bi-directional contrastive loss is employed to bring paired concatenated samples closer together while pushing away unpaired ones.
+
+Concatenated Image-Text Matching (CITM). This task requires the model to determine whether a pseudo video and a paragraph correspond to each other. Hard negative mining is used following the approach in (Li et al., 2021a). The [CLS] token feature from the multimodal encoder (text encoder) is used to compute a binary classification loss through a two-layer MLP.
+
+Table 2: Performance comparison on text-to-video retrieval benchmarks. For fair comparison, evaluation results before employing post-processing methods such as dual softmax (Cheng et al., 2021) are compared. Recall@1,5,10 are used as evaluation metrics.  
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">Example</td><td colspan="3">MSRVTT</td><td colspan="3">DiDeMo</td><td colspan="3">LSMDC</td><td colspan="3">ActivityNet</td></tr><tr><td>R@1</td><td>R@5</td><td>R@10</td><td>R@1</td><td>R@5</td><td>R@10</td><td>R@1</td><td>R@5</td><td>R@10</td><td>R@1</td><td>R@5</td><td>R@10</td></tr><tr><td>ClipBert(Lei et al., 2021)</td><td>5.4M</td><td>22.0</td><td>46.8</td><td>59.9</td><td>20.4</td><td>48.0</td><td>60.8</td><td>-</td><td>-</td><td>-</td><td>21.3</td><td>49.0</td><td>63.5</td></tr><tr><td>Frozen(Bain et al., 2021)</td><td>5M</td><td>31.0</td><td>59.5</td><td>70.5</td><td>34.6</td><td>65.0</td><td>74.7</td><td>15.0</td><td>30.8</td><td>39.8</td><td>-</td><td>-</td><td>-</td></tr><tr><td>BridgeFormer(Ge et al., 2022a)</td><td>5M</td><td>37.6</td><td>64.8</td><td>75.1</td><td>37.0</td><td>62.2</td><td>73.9</td><td>17.9</td><td>35.4</td><td>44.5</td><td>-</td><td>-</td><td>-</td></tr><tr><td>MILES(Ge et al., 2022b)</td><td>5M</td><td>37.7</td><td>63.6</td><td>73.8</td><td>36.6</td><td>63.9</td><td>74.0</td><td>17.8</td><td>35.6</td><td>44.1</td><td>-</td><td>-</td><td>-</td></tr><tr><td>OA-Trans(Wang et al., 2022c)</td><td>5M</td><td>35.8</td><td>63.4</td><td>76.5</td><td>34.8</td><td>64.4</td><td>75.1</td><td>18.2</td><td>34.3</td><td>43.7</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Clover(Huang et al., 2022)</td><td>5M</td><td>38.6</td><td>67.4</td><td>76.4</td><td>45.1</td><td>74.3</td><td>82.2</td><td>22.7</td><td>42.0</td><td>52.6</td><td>-</td><td>-</td><td>-</td></tr><tr><td>VIOLETv2(Fu et al., 2022)</td><td>5M</td><td>37.2</td><td>64.8</td><td>75.8</td><td>47.9</td><td>76.5</td><td>84.1</td><td>24.0</td><td>43.5</td><td>54.1</td><td>-</td><td>-</td><td>-</td></tr><tr><td>LF-VILA(Sun et al., 2022)</td><td>8.5M</td><td>-</td><td>-</td><td>-</td><td>35.0</td><td>64.5</td><td>75.8</td><td>-</td><td>-</td><td>-</td><td>35.3</td><td>65.4</td><td>-</td></tr><tr><td>COSA-B(Ours)</td><td>5M</td><td>42.2</td><td>69.0</td><td>79.0</td><td>57.8</td><td>80.6</td><td>87.9</td><td>27.3</td><td>46.7</td><td>55.2</td><td>55.6</td><td>80.7</td><td>89.1</td></tr><tr><td>OmniVL(Wang et al., 2022d)</td><td>17M</td><td>47.8</td><td>74.2</td><td>83.8</td><td>52.4</td><td>79.5</td><td>85.4</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>HiTeA(Ye et al., 2022)</td><td>17M</td><td>46.8</td><td>71.2</td><td>81.9</td><td>56.5</td><td>81.7</td><td>89.7</td><td>28.7</td><td>50.3</td><td>59.0</td><td>49.7</td><td>77.1</td><td>86.7</td></tr><tr><td>SINGULARITY(Lei et al., 2022)</td><td>17M</td><td>41.5</td><td>68.7</td><td>77.0</td><td>53.9</td><td>79.4</td><td>86.9</td><td>-</td><td>-</td><td>-</td><td>47.1</td><td>75.5</td><td>85.5</td></tr><tr><td>VINDLU-B(Cheng et al., 2022)</td><td>17M</td><td>45.3</td><td>69.9</td><td>79.6</td><td>59.2</td><td>84.1</td><td>89.5</td><td>-</td><td>-</td><td>-</td><td>54.4</td><td>80.7</td><td>89.0</td></tr><tr><td>LAVENDER(Li et al., 2022c)</td><td>30M</td><td>40.7</td><td>66.9</td><td>77.6</td><td>53.4</td><td>78.6</td><td>85.3</td><td>26.1</td><td>46.4</td><td>57.3</td><td>-</td><td>-</td><td>-</td></tr><tr><td>COSA-B(Ours)</td><td>17M</td><td>46.9</td><td>72.1</td><td>81.3</td><td>64.1</td><td>86.1</td><td>90.6</td><td>31.2</td><td>50.9</td><td>57.8</td><td>59.3</td><td>83.8</td><td>90.9</td></tr><tr><td>All-in-one(Wang et al., 2022a)</td><td>138M</td><td>37.9</td><td>68.1</td><td>77.1</td><td>32.7</td><td>61.4</td><td>73.5</td><td>22.4</td><td>53.7</td><td>67.7</td><td>-</td><td>-</td><td>-</td></tr><tr><td>CLIP4Clip(Luo et al., 2022)</td><td>400M</td><td>44.5</td><td>71.4</td><td>81.6</td><td>43.4</td><td>70.2</td><td>80.6</td><td>22.6</td><td>41.0</td><td>49.1</td><td>40.5</td><td>72.4</td><td>-</td></tr><tr><td>X-CLIP(Ma et al., 2022)</td><td>400M</td><td>49.3</td><td>75.8</td><td>84.8</td><td>47.8</td><td>79.3</td><td>-</td><td>26.1</td><td>48.4</td><td>46.7</td><td>46.2</td><td>75.5</td><td>-</td></tr><tr><td>mPLUG-2(Xu et al., 2023)</td><td>417M</td><td>53.1</td><td>77.6</td><td>84.7</td><td>56.4</td><td>79.1</td><td>85.2</td><td>34.4</td><td>55.2</td><td>65.1</td><td>-</td><td>-</td><td>-</td></tr><tr><td>UMT-L(Li et al., 2023b)</td><td>425M</td><td>58.8</td><td>81.0</td><td>87.1</td><td>70.4</td><td>90.1</td><td>93.5</td><td>43.0</td><td>65.5</td><td>73.0</td><td>66.8</td><td>89.1</td><td>94.9</td></tr><tr><td>VALOR-L(Chen et al., 2023)</td><td>433.5M</td><td>54.4</td><td>79.8</td><td>87.6</td><td>57.6</td><td>83.3</td><td>88.8</td><td>31.8</td><td>52.8</td><td>62.4</td><td>63.4</td><td>87.8</td><td>94.1</td></tr><tr><td>CLIP-VIP(Xue et al., 2022b)</td><td>500M</td><td>54.2</td><td>77.2</td><td>84.8</td><td>50.5</td><td>78.4</td><td>87.1</td><td>29.4</td><td>50.6</td><td>59.0</td><td>53.4</td><td>81.4</td><td>90.0</td></tr><tr><td>COSA-L(Ours)</td><td>417M</td><td>54.4</td><td>77.2</td><td>84.7</td><td>68.3</td><td>88.1</td><td>91.7</td><td>38.6</td><td>59.1</td><td>67.4</td><td>66.8</td><td>87.6</td><td>93.9</td></tr><tr><td>COSA(Ours)</td><td>415M</td><td>57.9</td><td>79.6</td><td>86.1</td><td>70.5</td><td>89.3</td><td>92.4</td><td>39.4</td><td>60.4</td><td>67.7</td><td>67.3</td><td>89.0</td><td>95.0</td></tr></table>
+
+Concatenated Masked Language Modeling (CMLM). We randomly mask  $15\%$  of the tokens in the paragraphs and employ BERT's vanilla prediction layer to reconstruct the masked tokens given the context of the pseudo videos.
+
+Concatenated Generation Modeling (CGM). We randomly mask  $60\%$  of the tokens in the paragraphs and utilize the same prediction layer as in CMLM to reconstruct the masked tokens in the context of the pseudo videos. CGM incorporates causal attention masks in the self-attention layers of BERT to prevent information leakage and enhance the model's capabilities for text generation.
+
+In addition to the four training objectives that utilize concatenated samples as input, we also include two vanilla objectives (ITC and ITM) that take raw single samples as input to enhance the model's ability to process single samples.
+
+# 4 EXPERIMENTS
+
+# 4.1 IMPLEMENTATION DETAILS
+
+We train COSA models using the PyTorch framework and 64 Tesla V100 cards. To ensure a fair comparison with state-of-the-art video-language pretraining models and vision-language foundation models, we train four model variants with different parameter and data sizes, as illustrated in Table 1. All models utilize BERT-Base as the text encoder. The initial learning rate is set to 1e-4, and a  $10\%$  warm-up strategy with a linear decay schedule is employed. The batch size is set to 2048. For ablation studies, we utilize the frozen CLIP/ViT-B/16 (Radford et al., 2021) as the vision encoder for efficiency purposes, and the models are trained on CC3M for 30K steps with a batch size of 1024, unless specified otherwise. Six training losses are equally weighted. For pretraining and video-text tasks finetuning, we use 224 image resolution, while for image-text tasks finetuning, we use higher resolution, which is presented together with Other details in Appendix.
+
+# 4.2 COMPARISON TO STATE-OF-THE-ART
+
+Text-to-Video Retrieval. We evaluate text-to-video retrieval on four benchmarks, including MSRVTT (Xu et al., 2016), DiDeMo (Anne Hendricks et al., 2017), LSMDC (Rohrbach et al., 2017), and ActivityNet (Krishna et al., 2017a). ITC and ITM are used as the training objectives. During testing, we rank all candidates using similarity scores computed by ITC and then rerank the top-50 candidates via ITM. As shown in Table 2, COSA-B (5M) outperforms previous models of similar scale by a significant margin on all four benchmarks, especially for the paragraph-to-video retrieval benchmarks (DiDeMo and ActivityNet). This demonstrates the effectiveness of concatenated sample training. It is noted that LF-VILA(Sun et al., 2022) is customized designed for paragraph-to-video retrieval with
+
+Table 3: Performance comparison on open-ended video QA benchmarks. Accuracy is used as the evaluation metric.  
+
+<table><tr><td>Method</td><td>Example</td><td>MSR</td><td>MSVD</td><td>TGIF</td><td>ANet</td></tr><tr><td>ClipBERT(Lei et al., 2021)</td><td>5.4M</td><td>37.4</td><td>-</td><td>60.3</td><td>-</td></tr><tr><td>ALPRO(Li et al., 2022a)</td><td>5M</td><td>42.1</td><td>45.9</td><td>-</td><td>-</td></tr><tr><td>VIOLETv2(Fu et al., 2022)</td><td>5M</td><td>44.5</td><td>54.7</td><td>72.8</td><td>-</td></tr><tr><td>Clover(Huang et al., 2022)</td><td>5M</td><td>43.9</td><td>51.9</td><td>71.4</td><td>-</td></tr><tr><td>COSA-B(Ours)</td><td>5M</td><td>46.2</td><td>54.3</td><td>73.4</td><td>46.5</td></tr><tr><td>OmniVL(Wang et al., 2022d)</td><td>17M</td><td>44.1</td><td>51.0</td><td></td><td></td></tr><tr><td>HiTeA(Ye et al., 2022)</td><td>17M</td><td>45.9</td><td>55.3</td><td>73.2</td><td>46.4</td></tr><tr><td>SINGULARITY(Lei et al., 2022)</td><td>17M</td><td>43.5</td><td>-</td><td>-</td><td>43.1</td></tr><tr><td>VINDLU-B(Cheng et al., 2022)</td><td>17M</td><td>43.8</td><td>-</td><td>-</td><td>44.6</td></tr><tr><td>LAVENDER(Li et al., 2022c)</td><td>30M</td><td>45.0</td><td>56.6</td><td>73.5</td><td>-</td></tr><tr><td>JustAsk(Yang et al., 2021)</td><td>69M</td><td>41.5</td><td>46.3</td><td>-</td><td>38.9</td></tr><tr><td>COSA-B(Ours)</td><td>17M</td><td>46.9</td><td>55.5</td><td>75.0</td><td>47.3</td></tr><tr><td>MERLOT(Zellers et al., 2021)</td><td>180M</td><td>43.1</td><td>-</td><td>69.5</td><td>41.4</td></tr><tr><td>All-in-one(Wang et al., 2022a)</td><td>228.5M</td><td>46.8</td><td>48.3</td><td>66.3</td><td>-</td></tr><tr><td>FrozenBiLM(Yang et al., 2022)</td><td>410M</td><td>47.0</td><td>54.8</td><td>68.6</td><td>43.2</td></tr><tr><td>mPLUG-2(Xu et al., 2023)</td><td>417M</td><td>48.0</td><td>58.1</td><td>75.4</td><td>-</td></tr><tr><td>UMT-L(Li et al., 2023b)</td><td>425M</td><td>47.1</td><td>55.2</td><td>-</td><td>47.9</td></tr><tr><td>VALOR-L(Chen et al., 2023)</td><td>433.5M</td><td>49.2</td><td>60.0</td><td>78.7</td><td>48.6</td></tr><tr><td>InternVideo(Wang et al., 2022g)</td><td>646M</td><td>47.1</td><td>55.5</td><td>72.2</td><td>-</td></tr><tr><td>GIT(Wang et al., 2022b)</td><td>1.7B</td><td>43.2</td><td>56.8</td><td>72.8</td><td>-</td></tr><tr><td>Flamingo(80B)(Alayrac et al., 2022)</td><td>2.3B</td><td>47.4</td><td>-</td><td>-</td><td>-</td></tr><tr><td>VideoCoCa (2.1B)(Yan et al., 2022)</td><td>4.8B</td><td>46.0</td><td>56.9</td><td>-</td><td>-</td></tr><tr><td>GIT2 (5.1B)(Wang et al., 2022b)</td><td>12.9B</td><td>45.6</td><td>58.2</td><td>74.9</td><td>-</td></tr><tr><td>COSA-L(Ours)</td><td>417M</td><td>48.8</td><td>58.6</td><td>77.6</td><td>49.2</td></tr><tr><td>COSA(Ours)(1.2B)</td><td>415M</td><td>49.2</td><td>60.0</td><td>79.5</td><td>49.9</td></tr></table>
+
+Table 4: Performance comparison on video captioning benchmarks. BLEU@4 (Papineni et al., 2002) (B@4) and CIDEr (Vedantam et al., 2015) (C) are used as metrics. Results of models utilizing additional modalities such as audio (Chen et al., 2023) and subtitle (Tang et al., 2021; Li et al., 2021b) are denoted by dashed color. Following (Tang et al., 2021; Chen et al., 2023; Wang et al., 2022b), we employ SCST finetuning (Rennie et al., 2017) on the VATEX benchmark, and the corresponding results are marked with  $*$ .  
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">Example</td><td colspan="2">MSRVTT</td><td colspan="2">MSVD</td><td colspan="2">VATEX</td><td colspan="2">YouCook2</td><td colspan="2">TVC</td></tr><tr><td>B@4</td><td>C</td><td>B@4</td><td>C</td><td>B@4</td><td>C</td><td>B@4</td><td>C</td><td>B@4</td><td>C</td></tr><tr><td>VIOLETv2(Fu et al., 2022)</td><td>5M</td><td>-</td><td>58.0</td><td>-</td><td>139.2</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>HiTeA(Ye et al., 2022)</td><td>5M</td><td>-</td><td>62.5</td><td>-</td><td>145.1</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>COSA-B(Ours)</td><td>5M</td><td>48.1</td><td>64.3</td><td>66.9</td><td>146.0</td><td>40.5</td><td>72.6</td><td>7.8</td><td>100.9</td><td>15.6</td><td>59.2</td></tr><tr><td>LAVENDER(Li et al., 2022c)</td><td>30M</td><td>-</td><td>60.1</td><td>-</td><td>150.7</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>COSA-B(Ours)</td><td>17M</td><td>48.5</td><td>64.7</td><td>68.7</td><td>150.9</td><td>41.4</td><td>74.4</td><td>8.6</td><td>106.2</td><td>16.2</td><td>61.0</td></tr><tr><td>VALUE(Li et al., 2021b)</td><td>136M</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>58.1</td><td>12.4</td><td>130.3</td><td>11.6</td><td>50.5</td></tr><tr><td>CLIP4Caption++(Tang et al., 2021)</td><td>400M</td><td>-</td><td>-</td><td>-</td><td>-</td><td>40.6*</td><td>85.7*</td><td>-</td><td>-</td><td>15.0</td><td>66.0</td></tr><tr><td>VALOR-L(Chen et al., 2023)</td><td>433.5M</td><td>54.4</td><td>74.0</td><td>80.7</td><td>178.5</td><td>45.6*</td><td>95.8*</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>GIT(Wang et al., 2022b)</td><td>1.7B</td><td>53.8</td><td>73.9</td><td>79.5</td><td>180.2</td><td>41.6*</td><td>91.5*</td><td>10.3</td><td>129.8</td><td>16.2</td><td>63.0</td></tr><tr><td>Flamingo(80B)(Alayrac et al., 2022)</td><td>2.3B</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>118.6</td><td>-</td><td>-</td></tr><tr><td>GIT2 (5.1B)(Wang et al., 2022b)</td><td>12.9B</td><td>54.8</td><td>75.9</td><td>82.2</td><td>185.4</td><td>42.7*</td><td>94.5*</td><td>9.4</td><td>131.2</td><td>16.9</td><td>66.1</td></tr><tr><td>COSA-L(Ours)</td><td>417M</td><td>53.2</td><td>72.1</td><td>74.0</td><td>169.1</td><td>45.4</td><td>84.4</td><td>10.2</td><td>125.8</td><td>17.7</td><td>67.5</td></tr><tr><td>COSA(Ours)(1.2B)</td><td>415M</td><td>53.7</td><td>74.7</td><td>76.5</td><td>178.5</td><td>43.7*</td><td>96.5*</td><td>10.1</td><td>131.3</td><td>18.8</td><td>70.7</td></tr></table>
+
+specialized framework and corpus, but fall behind COSA-B which takes a simple unified architecture as well as common corpora. In addition, COSA (17M) evidently surpasses VINDLU(Cheng et al., 2022) which have searched a best training recipe targeted at retrieval tasks. When compared to large-scale models, COSA achieves the best R@1 results on DiDeMo and ActivityNet datasets and comparable results on other benchmarks.
+
+Video QA. We evaluate video QA on four benchmarks, including MSRVTT-QA (Xu et al., 2017), MSVD-QA (Xu et al., 2017), TGIF-QA (Li et al., 2016), and ActivityNet-QA (Yu et al., 2019), and formulate it as an open-ended generative task to predict answers with questions as prefixes. As shown in Table 3, COSA-B (5M) and COSA-B (17M) outperform all models of similar scale by a significant margin. Under the large-scale pretraining scenario, COSA achieves state-of-the-art accuracy on 4 benchmarks, using only 415M training data and 1.2B parameters.
+
+Video Captioning. We evaluate video captioning on five benchmarks, including MSRVTT (Xu et al., 2016), MSVD (Chen & Dolan, 2011), VATEX (Wang et al., 2019), YouCook2 (Zhou et al., 2018), and TVC (Lei et al., 2020). The GM objective is used, and captions are autoregressively generated during inference. From the results in Table 4, we can see that COSA-B (5M) outperforms
+
+Table 5: Performance comparison on text-to-image retrieval, image captioning, and image QA benchmarks. 'ZS' stands for zero-shot evaluation. CIDEr (C) and SPICE (S) are reported for captioning. SCST finetuning is employed on COCO caption, and corresponding results are marked with '\*'.  
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">Example</td><td colspan="3">MSCOCO-Ret</td><td colspan="3">Flickr30K-Ret (ZS)</td><td colspan="2">MSCOCO-Cap</td><td colspan="2">VQAv2</td></tr><tr><td>R@1</td><td>R@5</td><td>R@10</td><td>R@1</td><td>R@5</td><td>R@10</td><td>C</td><td>S</td><td>dev</td><td>std</td></tr><tr><td>OFA(Wang et al., 2022e)</td><td>18M</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>154.9*</td><td>26.6*</td><td>82.0</td><td>82.0</td></tr><tr><td>BEiT-3(Wang et al., 2022f)</td><td>21M</td><td>67.2</td><td>87.7</td><td>92.8</td><td>81.5</td><td>95.6</td><td>97.8</td><td>147.6</td><td>25.4</td><td>84.19</td><td>84.03</td></tr><tr><td>BLIP(Li et al., 2022b)</td><td>129M</td><td>65.1</td><td>86.3</td><td>91.8</td><td>86.7</td><td>97.3</td><td>98.7</td><td>136.7</td><td>-</td><td>78.25</td><td>78.32</td></tr><tr><td>BLIP-2(Li et al., 2023a)</td><td>129M</td><td>68.3</td><td>87.7</td><td>92.6</td><td>89.7</td><td>98.1</td><td>98.9</td><td>145.8</td><td>-</td><td>82.19</td><td>82.30</td></tr><tr><td>mPLUG-2(Xu et al., 2023)</td><td>417M</td><td>65.7</td><td>87.1</td><td>92.6</td><td>-</td><td>-</td><td>-</td><td>137.7</td><td>23.7</td><td>81.11</td><td>81.13</td></tr><tr><td>VALOR(Chen et al., 2023)</td><td>433.5M</td><td>61.4</td><td>84.4</td><td>90.9</td><td>-</td><td>-</td><td>-</td><td>152.5*</td><td>25.7*</td><td>78.46</td><td>78.62</td></tr><tr><td>Florence(Yuan et al., 2021)</td><td>900M</td><td>63.2</td><td>85.7</td><td>-</td><td>76.7</td><td>93.6</td><td>-</td><td>-</td><td>-</td><td>80.16</td><td>80.36</td></tr><tr><td>GIT(Wang et al., 2022b)</td><td>1.7B</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>151.1*</td><td>26.3*</td><td>78.6</td><td>78.8</td></tr><tr><td>SimVLM(Wang et al., 2021)</td><td>1.8B</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>143.3</td><td>25.4</td><td>80.03</td><td>80.34</td></tr><tr><td>ALIGN(Jia et al., 2021)</td><td>1.8B</td><td>59.9</td><td>83.3</td><td>89.8</td><td>75.7</td><td>93.8</td><td>96.8</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Flamingo (80B))(Alayrac et al., 2022)</td><td>2.3B</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>138.1</td><td>-</td><td>82.0</td><td>82.1</td></tr><tr><td>CoCa(2.1B)(Yu et al., 2022)</td><td>4.8B</td><td>-</td><td>-</td><td>-</td><td>80.4</td><td>95.7</td><td>97.7</td><td>143.6</td><td>24.7</td><td>82.3</td><td>82.3</td></tr><tr><td>GIT2(5.1B)(Wang et al., 2022b)</td><td>12.9B</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>152.7*</td><td>26.4*</td><td>81.7</td><td>81.9</td></tr><tr><td>COSA(Ours)(1.2B)</td><td>415M</td><td>68.5</td><td>88.0</td><td>93.0</td><td>90.2</td><td>98.4</td><td>99.4</td><td>150.6*</td><td>27.0*</td><td>80.46</td><td>80.54</td></tr></table>
+
+Table 6: Experiment results of SST (baseline), COSA, and COSA variants on a broad range of video/image-language benchmarks. R@1, CIDEr, and Acc are reported for retrieval, captioning, and QA tasks, respectively.  
+
+<table><tr><td rowspan="2">Exp</td><td colspan="4">Video Ret</td><td colspan="3">Video Cap</td><td colspan="2">Video QA</td><td>Image Ret</td><td colspan="2">Image Cap</td></tr><tr><td>DiDeMo</td><td>ActivityNet</td><td>MSRVTT</td><td>VATEX</td><td>YouCook</td><td>VATEX</td><td>TVC</td><td>MSRVTT</td><td>TGIF-QA</td><td>MSCOCO</td><td>MSCOCO</td><td>VIST</td></tr><tr><td>SST</td><td>49.2</td><td>43.8</td><td>39.4</td><td>62.4</td><td>85.4</td><td>67.6</td><td>53.9</td><td>45.9</td><td>73.0</td><td>53.9</td><td>124.7</td><td>14.8</td></tr><tr><td>COSA</td><td>54.8</td><td>51.2</td><td>43.5</td><td>63.9</td><td>91.9</td><td>68.1</td><td>55.4</td><td>46.5</td><td>73.7</td><td>54.7</td><td>125.4</td><td>20.7</td></tr><tr><td>COSA-copy</td><td>43.5</td><td>39.3</td><td>42.3</td><td>60.8</td><td>84.6</td><td>65.8</td><td>52.0</td><td>45.4</td><td>72.2</td><td>51.6</td><td>122.7</td><td>11.9</td></tr><tr><td>COSA-shuffle</td><td>50.9</td><td>48.1</td><td>44.7</td><td>64.0</td><td>88.8</td><td>67.7</td><td>54.4</td><td>46.6</td><td>73.9</td><td>54.5</td><td>124.9</td><td>14.2</td></tr></table>
+
+VIOLETv2, and HiTeA which utilizes a more advanced vision backbone (MViTv2 (Fan et al., 2021)). COSA-B (17M) surpasses LAVENDER, which is trained on 30M vision-text pairs. When compared to large-scale foundation models, COSA achieves comparable performances on the MSRVTT and MSVD datasets. Additionally, COSA outperforms GIT2, which specializes in captioning tasks, and achieves new state-of-the-art performances on both open-domain benchmarks (Wang et al., 2019) and domain benchmarks (Zhou et al., 2018; Lei et al., 2020) (cooking and TV), using only  $24\%$  of its parameters and  $3.2\%$  of the training examples. It is worth noting that both GIT2 and COSA do not use any video-text corpus in the pretraining stage, but COSA can generate online pseudo video-paragraph pairs. Furthermore, utilizing the vision modality alone, COSA achieves higher CIDEr scores than VALOR and CLIP4Caption++, which additionally incorporate audio and subtitle modalities.
+
+Image-Text Benchmarks. We evaluate COSA on image-text benchmarks, including text-to-image retrieval on MSCOCO (Lin et al., 2014) and Flickr30K (Plummer et al., 2015) (zero-shot), captioning on MSCOCO, and image QA on VQAv2 (Goyal et al., 2017). As shown in Table 5, COSA surpasses BLIP-2 and BEiT-3, and achieves new state-of-the-art results on the MSCOCO and Flickr30K benchmarks. Additionally, COSA achieves the best SPICE score (27.0) on MSCOCO caption benchmark and comparable results on VQAv2 benchmark.
+
+# 4.3 ABLATION STUDY
+
+In this subsection, we conduct extensive ablation experiments to demonstrate the effectiveness of COSA when compared with SST and the method's robustness to different vision backbones and training corpora. We also explore the influence of training objectives, iterations, concatenation numbers, and sampling methods. Besides above mentioned benchmarks, we further evaluate the model on the Visual Storytelling Benchmark (VIST), which requires models to perceive the relationships among multiple images and describe them in sequential paragraphs, thus demanding strong narrative abilities.
+
+COSA vs SST. As presented in Table 6, COSA consistently improves performance on 12 benchmarks of video-text as well as image-text tasks, with significant margins compared to the SST baseline.
+
+Table 7: Experiment results of different training objectives for COSA. R, C, Q in the parentheses represent retrieval, captioning, and QA tasks, respectively.  
+
+<table><tr><td></td><td>ITC</td><td>ITM</td><td>MLM</td><td>GM</td><td>CITC</td><td>CITM</td><td>CMLM</td><td>CGM</td><td>DiD(R)</td><td>ANET(R)</td><td>MSR(R)</td><td>TVC(C)</td><td>TGIF(Q)</td></tr><tr><td>a</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td></td><td></td><td></td><td></td><td>49.2</td><td>43.8</td><td>39.4</td><td>53.9</td><td>73.0</td></tr><tr><td>b</td><td>✓</td><td>✓</td><td></td><td></td><td></td><td></td><td>✓</td><td>✓</td><td>53.0</td><td>50.6</td><td>42.8</td><td>55.7</td><td>73.7</td></tr><tr><td>c</td><td>✓</td><td>✓</td><td></td><td></td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>54.8</td><td>51.2</td><td>43.5</td><td>55.4</td><td>73.7</td></tr><tr><td>d</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>52.3</td><td>49.9</td><td>42.3</td><td>55.5</td><td>73.6</td></tr></table>
+
+Table 8: Experiment results of changing dataset and vision backbone (Enc).  
+
+<table><tr><td>Exp</td><td>Enc</td><td>Data</td><td>#Frame</td><td>DiD(R)</td><td>ANET(R)</td><td>MSR(R)</td><td>YOU(C)</td><td>VIST(C)</td><td>TVC(C)</td><td>MSR(Q)</td></tr><tr><td>SST</td><td>Swin-B</td><td>CC3M</td><td>-</td><td>35.3</td><td>30.4</td><td>34.7</td><td>91.2</td><td>14.3</td><td>51.6</td><td>44.6</td></tr><tr><td>COSA</td><td>Swin-B</td><td>CC3M</td><td>-</td><td>45.1</td><td>41.7</td><td>36.2</td><td>94.6</td><td>22.3</td><td>53.1</td><td>44.9</td></tr><tr><td>SST</td><td>CLIP-B</td><td>WebVid2.5M</td><td>1</td><td>43.6</td><td>40.2</td><td>40.7</td><td>89.3</td><td>12.2</td><td>53.5</td><td>46.0</td></tr><tr><td>SST</td><td>CLIP-B</td><td>WebVid2.5M</td><td>4</td><td>51.4</td><td>47.3</td><td>42.5</td><td>90.8</td><td>11.9</td><td>54.0</td><td>46.2</td></tr><tr><td>COSA</td><td>CLIP-B</td><td>WebVid2.5M</td><td>1</td><td>54.7</td><td>52.2</td><td>44.0</td><td>93.4</td><td>17.4</td><td>55.0</td><td>46.4</td></tr></table>
+
+We further investigate two COSA variants named COSA-copy and COSA-shuffle. COSA-copy simply duplicates a single sample (image and text) multiple times and concatenates them, instead of performing cross-sample concatenation as in COSA. On the other hand, COSA-shuffle concatenates cross-samples from a batch, but with the captions randomly shuffled before concatenation to disrupt event-level temporal correspondence. From the results we can find that 1) Both COSA and COSA-shuffle can outperform SST with huge margins on all benchmarks, demonstrating the effectiveness of modeling vision-language connections within sample group instead of single sample. 2) Due to maintaining the same concatenation order for image and text, model can learn better event-level temporal correspondence between visual scenes and descriptions, and thus improve the performance on most benchmarks especially on paragraph-to-video retrieval benchmarks such as ActivityNet, whose video and caption are relatively longer and contain more complicated scenes. 3) COSA-copy achieves lower performance than SST on most benchmarks, demonstrating that the improvement of COSA over SST comes from multiple samples concatenation, instead of longer visual and text sequences.
+
+Training Objectives. As depicted in Table 7, compared to the SST baseline, incorporating COSA while modifying the MLM and GM objectives to CMLM and CGM leads to evident improvements across all five benchmarks (b vs a). The default objectives (c) yield the best results for most benchmarks.
+
+Generality. We further explore the generality of COSA with respect to different vision encoders and training corpora. The previous experiments employed CLIP-B as the vision backbone and were conducted on the CC3M dataset. In this experiment, we replace them with Swin Transformer(Liu et al., 2021) and WebVid2.5M, respectively. From the results in Table 8, it is evident that COSA consistently outperforms SST under different backbone and corpus settings. Additionally, we observe that sampling multiple frames for SSL can improve downstream performance (except for VIST), but is still much less effective when compared with proposed COSA.
+
+Equal samples seen. In the previous experiments, models were trained for 30K steps for efficiency purposes. One might argue that the improvements of COSA could be attributed to faster convergence rather than cross-sample learning and introduced event-level temporal correspondence, as the model can see each sample multiple times per iteration. However, the results in Figure 4 demonstrate that as training iterations prolong, the performance gap between COSA and SST remains consistent, even when SST has already converged. Moreover, pretraining with COSA for 30K steps outperforms pretraining with SST for 120K steps on all benchmarks, which demonstrates COSA still outperforms SST with same samples seen and much less iterations.
+
+Concatenate Number. Figure 3 shows the performance of models trained with different concatenate numbers  $(n_c)$  ranging from 0 (SST) to 4. Based on the results, we choose  $n_c = 3$  as it consistently performs well across all benchmarks.
+
+Training Speed. We have made statistics that transferring from SST to COSA averagely cost  $0.9\mathrm{x}$  more training time when four samples are concatenated. We think this is unavoidable cause the frames become more and sentences become longer, but affordable because we only need to pretrain once, and the finetuning, testing, inference speed of COSA and SST are totally the same.
+
+Table 9: Experiment results of different sampling methods for online sample concatenation.  
+
+<table><tr><td>Sampling</td><td>DiD(R)</td><td>ANet(R)</td><td>MSR(R)</td><td>VAT(R)</td><td>TVC(C)</td><td>VIST(C)</td><td>MSR(Q)</td></tr><tr><td>random</td><td>54.8</td><td>51.2</td><td>43.5</td><td>63.9</td><td>55.4</td><td>20.7</td><td>46.5</td></tr><tr><td>vision similarity</td><td>53.7</td><td>50.9</td><td>43.0</td><td>63.6</td><td>55.1</td><td>20.4</td><td>46.4</td></tr><tr><td>text similarity</td><td>48.2</td><td>45.4</td><td>42.6</td><td>62.4</td><td>55.2</td><td>20.2</td><td>46.3</td></tr></table>
+
+![](images/4355e4b7b4ed69fa2b2620518df342da8931e64054f1c34376e42aff08144ca9.jpg)
+
+![](images/6d51d0b9176dae7150f51602dc1b7b368e1e2b56049c21a7b6906e01b829978e.jpg)
+
+![](images/b6a6c870d98f92dd1df3a105b357ac8b3b826493c93c49cd9883ae81d8aa888e.jpg)
+
+![](images/45a464e7bd115a6bc89fc8f9639a7dbc10ac5546ebe2317e3a30d8604b6aeee2.jpg)  
+Figure 3: Experiment results of different concatenation numbers used in COSA.
+
+![](images/22306f7c734b8cd24c9245c6f62750b7df17cb13d14701aea39883426d9836ad.jpg)
+
+![](images/03b6ccf083908d036a7675e6e63adfeeef5dce88252c6440970a561c33c252b7.jpg)
+
+Sampling Choice. By default, we randomly choose samples within a batch for grouping and concatenation. We also experimented with two alternative choices: selecting the top  $n_c$  most similar samples based on the similarity matrix computed by either the image or text encoder output features. The results in Table 9 demonstrate the importance of reducing semantic relevance among grouped samples through random sampling. More explanations and visualizations could be found in Appendix.
+
+![](images/e4fc6401f970a07ad8d583c0c82617066243583b2fd3b34d4ea3f25346071e03.jpg)
+
+![](images/9cceeb398f0158d994d016eb65fda7c2b2e013aaeec464c1c57f14df2f86767c.jpg)
+
+![](images/9a32715db84ec42a41fc10feef579e2048b94c86d1a1e90d624778d2cf05c320.jpg)
+
+![](images/2735886b6fb9ae1177204d6371d55133853b1efeebfeed72122903d595747edd.jpg)  
+Figure 4: Experiment results of SST and COSA when training for more iterations.
+
+![](images/e61b5759c167350cddc015319d8b6a41ddcdb937672c7c93fd208f6ccc7ed875.jpg)
+
+![](images/e34bc75231ec671a7bf51931f33e4b286048d250e4b4369fbbc0fd5d78d8d159.jpg)
+
+# 5 CONCLUSION
+
+This paper introduces COSA, a concatenated sample pretrained unified vision-language foundation model. COSA transforms image-text corpora into pseudo video-paragraph corpora, enabling explicit event-sentence correspondence and promoting event-level temporal learning in foundation models. Extensive ablation studies demonstrate the effectiveness of COSA in improving various downstream tasks, including video-language tasks and image-text tasks. COSA achieves state-of-the-art results on multiple benchmarks. However, it is important to note that the proposed COSA has only been proven effective in the vision-language pretraining field, and we hope that it can inspire further research on co-learning multiple samples in other AI communities.
+
+# ACKNOWLEDGMENTS
+
+This work was supported by the National Science and Technology Major Project (No.2022ZD0118801), National Natural Science Foundation of China (U21B2043, 62206279).
+
+# REFERENCES
+
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+Lisa Anne Hendricks, Oliver Wang, Eli Shechtman, Josef Sivic, Trevor Darrell, and Bryan Russell. Localizing moments in video with natural language. In Proceedings of the IEEE international conference on computer vision, pp. 5803-5812, 2017.  
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+
+# A APPENDIX
+
+# A.1 PRETRAINING SETTINGS
+
+Table 10: Pretraining Settings for COSA models. ’*’ means that captions in those corpora has been replaced by descriptions generated by a separately trained captioner.  
+
+<table><tr><td>Model</td><td>Vision Encoder</td><td>param</td><td>Sample</td><td>Training Corpus</td><td>Batch Size</td><td>Steps</td><td>Epoch</td></tr><tr><td rowspan="2">COSA-B</td><td rowspan="2">Swin-B</td><td rowspan="2">251M</td><td rowspan="2">5M</td><td>CC3M</td><td>2048</td><td>50000</td><td>35</td></tr><tr><td>WebVid2.5M</td><td>2048</td><td>50000</td><td>41</td></tr><tr><td rowspan="3">COSA-B</td><td rowspan="3">Swin-B</td><td rowspan="3">251M</td><td rowspan="3">17M</td><td>CC4M</td><td>2048</td><td>60000</td><td>25</td></tr><tr><td>CC12M</td><td>2048</td><td>60000</td><td>12</td></tr><tr><td>WebVid2.5M</td><td>2048</td><td>40000</td><td>33</td></tr><tr><td rowspan="3">COSA-L</td><td rowspan="3">CLIP-ViT-L</td><td rowspan="3">468M</td><td rowspan="3">(17+400)M</td><td>CC4M</td><td>2048</td><td>60000</td><td>25</td></tr><tr><td>CC12M</td><td>2048</td><td>60000</td><td>12</td></tr><tr><td>WebVid2.5M</td><td>2048</td><td>35000</td><td>29</td></tr><tr><td rowspan="3">COSA</td><td rowspan="3">EVAClip-ViT-G</td><td rowspan="3">1.2B</td><td rowspan="3">(15+400)M</td><td>CC4M</td><td>2048</td><td>50000</td><td>20</td></tr><tr><td>CC12M*</td><td>2048</td><td>50000</td><td>10</td></tr><tr><td>LAION-102M*</td><td>2048</td><td>50000</td><td>1</td></tr></table>
+
+The specific pretraining settings of all scales of COSA models are presented in Table 10. It is noted that the training corpus of the largest one (COSA) has been clean by a separately trained captioner. Specifically, the captioner takes the same model architecture of COSA and is pretrained with generative modeling loss (GM) only on the same corpus with original captions (CC4M, CC12M and LAION-102M) without concatenated samples applied. After pretraining, the captioner is finetuned with GM loss on a mixture of downstream of datasets including MSRVTT, VATEX, MSVD and MSCOCO. At last we use trained captioner to generate high-quality captions for CC12M and LAION-102M with top-10 sampling method.
+
+# A.2 DOWNSSTREAM DATASET DESCRIPTIONS
+
+COSA is evaluated on a series of downstream datasets including MSRVTT, MSVD, LSMDC, DiDeMo, VATEX, YouCook2, ActivityNet Caption, TGIF, TVC, MSCOCO, Flickr30K and VQAv2. Train/val/test splits of different benchmarks of those datasets are presented in Table 11.
+
+Specifically, MSRVTT (Xu et al., 2016) dataset consists of 10K video clips and 20K captions. Our evaluation encompasses text-to-video retrieval, video captioning, and video QA tasks on this dataset. For retrieval, we adopt the '1K-A split' and for captioning and QA, we adhere to the standard split. MSVD(Chen & Dolan, 2011) dataset comprises 1,970 videos, each accompanied by approximately 40 captions. Our evaluation involves video captioning using the official split and video QA using the split proposed by Xu et al.(Xu et al., 2017). LSMDC (Rohrbach et al., 2017) dataset consists of 118,000 clips from 202 movies, with each clip paired with a single caption. We evaluate text-to-video retrieval on this dataset using the official split. DiDeMo (Anne Hendricks et al., 2017) dataset includes 10K long-form videos sourced from Flickr. For each video, four short sentences are annotated in temporal order. We concatenate these short sentences and evaluate 'paragraph-to-video' retrieval and the official split is employed. VATEX(Wang et al., 2019) dataset contains 41,250 video clips sourced from the Kinetics-600 dataset(Kay et al., 2017), accompanied by 825,000 sentence-level descriptions. Our evaluation focuses on text-to-video retrieval and video captioning tasks. Regarding captioning, we employ the official split, while for retrieval, we follow the HGR (Chen et al., 2020) split protocol. YouCook2 (Zhou et al., 2018) dataset comprises 14K video clips extracted from 2K instructional cooking videos on YouTube. Each video showcases multiple actions performed by a chef, along with corresponding textual descriptions and temporal annotations. We assess video captioning on this dataset using the official splits. ActivityNet Caption(Krishna et al., 2017a) dataset encompasses 20K long-form videos sourced from YouTube whose average length are 180 seconds. We evaluate text-to-video retrieval and video QA on this dataset. For retrieval, we use the official split, while for video QA, we adopt the split proposed by Yu et al.(Yu et al., 2019). TGIF (Jang et al., 2017) dataset features three video QA benchmarks, including TGIF-Action, TGIF-Transition, and TGIF-Frame, with the first two being multiple-choice QA and the last one being open-ended
+
+Table 11: Downstream datasets splits.  
+
+<table><tr><td rowspan="2">Task</td><td rowspan="2">Benchmark</td><td colspan="3">#Videos/#Images</td><td colspan="3">#captions/#QA-pairs</td></tr><tr><td>Train</td><td>Val</td><td>Test</td><td>Train</td><td>Val</td><td>Test</td></tr><tr><td rowspan="4">Text-to-Video Retrieval</td><td>MSRVTT</td><td>9000</td><td>-</td><td>1000</td><td>180000</td><td>-</td><td>1000</td></tr><tr><td>DiDeMo</td><td>8394</td><td>1065</td><td>1003</td><td>8394</td><td>1065</td><td>1003</td></tr><tr><td>ANET</td><td>10009</td><td>-</td><td>4917</td><td>10009</td><td>-</td><td>4917</td></tr><tr><td>LSMDC</td><td>101046</td><td>7408</td><td>1000</td><td>101046</td><td>7408</td><td>1000</td></tr><tr><td rowspan="5">Video Captioning</td><td>MSRVTT</td><td>6513</td><td>497</td><td>2990</td><td>130260</td><td>9940</td><td>59800</td></tr><tr><td>YouCook2</td><td>10337</td><td>3492</td><td>-</td><td>10337</td><td>3492</td><td>-</td></tr><tr><td>MSVD</td><td>1200</td><td>100</td><td>670</td><td>48774</td><td>4290</td><td>27763</td></tr><tr><td>VATEX</td><td>25991</td><td>3000</td><td>6000</td><td>259910</td><td>30000</td><td>60000</td></tr><tr><td>TVC</td><td>86603</td><td>10841</td><td>-</td><td>174350</td><td>43580</td><td>-</td></tr><tr><td rowspan="4">Video QA</td><td>MSVD-QA</td><td>1200</td><td>250</td><td>520</td><td>30933</td><td>6,415</td><td>13157</td></tr><tr><td>TGIF-FrameQA</td><td>32345</td><td>-</td><td>7132</td><td>39389</td><td>-</td><td>13691</td></tr><tr><td>MSRVTT-QA</td><td>6513</td><td>497</td><td>2990</td><td>158581</td><td>12278</td><td>72821</td></tr><tr><td>ANET-QA</td><td>3200</td><td>1800</td><td>800</td><td>32000</td><td>18000</td><td>8000</td></tr><tr><td rowspan="2">Text-to-Image retrieval</td><td>MSCOCO</td><td>113287</td><td>5000</td><td>5000</td><td>566747</td><td>25010</td><td>25010</td></tr><tr><td>Flickr30K</td><td>29000</td><td>1014</td><td>1000</td><td>145000</td><td>5070</td><td>5000</td></tr><tr><td>Image Captioning</td><td>MSCOCO</td><td>113287</td><td>5000</td><td>5000</td><td>566747</td><td>25010</td><td>25010</td></tr><tr><td>Image QA</td><td>VQAv2</td><td>82783</td><td>40504</td><td>37K/81K</td><td>4437570</td><td>2143540</td><td>1.1M/4.5M</td></tr></table>
+
+QA. We evaluate VAST on the TGIF-Frame benchmark using the official split. TVC (Lei et al., 2020) dataset is a multi-channel video captioning dataset, comprising 108,000 video moments and 262,000 paired captions. Additional input in the form of video subtitles can be utilized. We evaluate video captioning on this benchmark using the official split with vision information utilized only. MSCOCO (Lin et al., 2014) dataset contains 123K images, each paired with five annotated captions. We evaluate text-to-image retrieval and image captioning tasks on this dataset using the Karpathy split (Karpathy & Fei-Fei, 2015). Flickr30K (Plummer et al., 2015) dataset consists of 31K images, with each image paired with five annotated captions. We assess text-to-image retrieval on this dataset using the Karpathy split (Karpathy & Fei-Fei, 2015). VQAv2 (Goyal et al., 2017) dataset comprises 1.1 million questions and 11.1 million answers related to MSCOCO images and we utilize train+val set for training and evaluate on the online test server.
+
+# A.3 VISUALIZATIONS OF DIFFERNET SAMPLING METHODS
+
+In our experiments, COSA trained with random sampling works better than the one trained with relevant sampling. As shown in figure 5, we observe a real video-language sample from ActivityNet caption dataset, which is shown in the top green part of figure, we can find that the 1) sampled vision frames are relevant and coherent, and 2) the corresponding texts are very informative and can strictly match to different frames in temporal order. Motivated by this, an ideal large-scale pretraining dataset for video-language tasks should also possess those two characteristics to help model learn the capabilities of perceiving evnets happed in videos and their relative order. In this work, we propose COSA to imitate those pretrain dataset from image-text data. And the examples of COSA with different sampling methods are shown in the bottom pink part of the figure, from which we can find that even though the random sampling example shows little relevance between four independent scenes, but it has the strength that each sentence can strictly correspond to one image, which satisfy the second charatersic. By contrast, even though relevant (vision/text similarity) sampling examples have shown vision relevance to some extent, they have strong semantic redundancy, and one sentence can correspond to many frames, which could confuse models' event-level temporal learning. And we think that's why it performs weaker than random sampling. In addition, considering that the scene changes are somewhat hard in random sampling, we think other soft sampling methods could be a future research direction.
+
+Real video-paragraph example from ActivityNet-caption dataset  
+![](images/ed168d5dfb2830a7f45b4399baad1109b31148d70d49e016b394751f165905e4.jpg)  
+A train goes by on a track, and several cars are seen driving on a wet road. A woman gets out, and crouches by a flat tire. She uses equipment to lift the car from the ground, then removes the tire. She replaces the bad tire with a spare. She then puts away her equipment and gives a thumbs up before driving safely away.
+
+random sampling
+
+Pesudo video-paragraph example from CC3M by COSA  
+![](images/b543b197962a14518d2bb9d25fc712f103f5f06e351d4044d7e06ef45b7dcac5.jpg)  
+a man has been fined £ 1,547 for drowning a squirrel who persistently ate from his bird feeder, and this is the table set for everyday use, full length portrait of elderly hikers walking towards the camera outdoors, tennis player competes against tennis player during day of the tournament
+
+vision-similarity sampling
+
+Figure 5: Visualization of different sampling methods of COSA. The top green part in the figure is the example from real video dataset (ActivityNet-captions), and bottom pink part in the figure are examples of COSA with different sampling methods.  
+![](images/1e39c2d65efc24b0ff6d8c27f4c7a0008addf833db71cd3f27e8a1ff5093e1a0.jpg)  
+actor and person attend the premiere, actor and person attend the premiere at amc empire theater, astronaut and person attend premiere at amc empire theater, pop artist and dramatist walk a red carpet during festival.
+
+text-similarity sampling
+
+![](images/7aa02bf8a568f47b51abf8bd5bac18f17c2287d70767cbeb043891603d68f851.jpg)  
+the old town of city, a square in the central part next, aerial view of the old town with castle, view of the old town hall and main street with a post box in the foreground.
+
+Table 12: Downstream task finetuning settings of COSA models. Lr, Bs, Epo, F_train, F_test and Res denote learning rate, batch size, epoch, training sampling frames, testing sampling frames and resolution, respectively.  
+
+<table><tr><td>Task</td><td>Benchmark</td><td>Lr</td><td>Bs</td><td>Epo</td><td>F_train</td><td>F_test</td><td>Res</td></tr><tr><td rowspan="5">Text-to-Video Retrieval</td><td>MSRVTT</td><td>2e-5</td><td>64</td><td>3.6</td><td>8</td><td>16</td><td>224</td></tr><tr><td>VATEX</td><td>2e-5</td><td>64</td><td>2.5</td><td>8</td><td>16</td><td>224</td></tr><tr><td>DiDeMo</td><td>2e-5</td><td>64</td><td>40</td><td>8</td><td>32</td><td>224</td></tr><tr><td>ANET</td><td>2e-5</td><td>64</td><td>20</td><td>8</td><td>32</td><td>224</td></tr><tr><td>LSMDC</td><td>2e-5</td><td>64</td><td>5</td><td>8</td><td>32</td><td>224</td></tr><tr><td rowspan="6">Video Captioning</td><td>MSRVTT</td><td>2e-5</td><td>128</td><td>10</td><td>8</td><td>8</td><td>224</td></tr><tr><td>YouCook2</td><td>3e-5</td><td>64</td><td>30</td><td>8</td><td>16</td><td>224</td></tr><tr><td>MSVD</td><td>1e-5</td><td>64</td><td>1.2</td><td>8</td><td>8</td><td>224</td></tr><tr><td>VATEX</td><td>2e-5</td><td>64</td><td>10</td><td>8</td><td>20</td><td>224</td></tr><tr><td>VATEX(SCST)</td><td>7e-6</td><td>64</td><td>5</td><td>8</td><td>20</td><td>224</td></tr><tr><td>TVC</td><td>3e-5</td><td>64</td><td>40</td><td>8</td><td>8</td><td>224</td></tr><tr><td rowspan="4">Video QA</td><td>MSVD-QA</td><td>1e-5</td><td>64</td><td>8</td><td>8</td><td>18</td><td>224</td></tr><tr><td>TGIF-FrameQA</td><td>2e-5</td><td>64</td><td>10</td><td>4</td><td>4</td><td>224</td></tr><tr><td>MSRVTT-QA</td><td>2e-5</td><td>64</td><td>4.5</td><td>8</td><td>8</td><td>224</td></tr><tr><td>ANET-QA</td><td>2e-5</td><td>64</td><td>10</td><td>8</td><td>16</td><td>224</td></tr><tr><td>Text-to-Image retrieval</td><td>MSCOCO</td><td>1e-5</td><td>256</td><td>5</td><td>-</td><td>-</td><td>384</td></tr><tr><td rowspan="2">Image Captioning</td><td>MSCOCO</td><td>1e-5</td><td>64</td><td>5</td><td>-</td><td>-</td><td>480</td></tr><tr><td>MSCOCO(SCST)</td><td>2.5e-6</td><td>64</td><td>2.5</td><td>-</td><td>-</td><td>480</td></tr><tr><td>Image QA</td><td>VQAv2</td><td>2e-5</td><td>128</td><td>20</td><td>-</td><td>-</td><td>384</td></tr></table>
+
+# A.4 FINETUNING SETTINGS
+
+Specific finetuning settings of COSA model such as learning rate, batch size, training epochs and sampled frames are presented in Table 12.
+
+# A.5 QUALITATIVE COMPARISON ON VIST BENCHMARK
+
+The qualitative comparisons between model trained with SST (Single Sample Training) and proposed COSA (Concatenated Sample Training) prediction on visual story telling benchmark (VIST) is shown in Figure 6, from which we can find that COSA can generate comprehensive captions (stories) for multiple frames under both zero-shot and finetuning settings, while SST can only generate one sentence describing limited contents under zero-shot setting, and is easy to generate duplicated captions under finetuning settings.
+
+![](images/9a023545fb3f0b11c378ae3af9f9641c13ec11911949a2df9c6d6697ccd2d930.jpg)  
+SST(ZS): english civil parish in the sunshine.
+
+![](images/6d6dca2156e7f366bcd6359ee4e47d16b38699e2d7f108eab1b66c42a1ec6a37.jpg)  
+SST(FT): this is where i grew up. this is where i grew up. this is where i grew up. this is where i grew up. this is where i grew up. this is where i am growing up.
+
+![](images/ec2ae0220021e63bb90be347d1130c9e2aca1a7d96c154e2c337df14fd7ed2ea.jpg)  
+COSA(ZS) : the front of the house. a view of the cathedral from outside the cathedral. a photo of a graduate and a student in a graduation ceremony. a city in the sunshine.
+
+![](images/fcab03ecb132b42fe90164d6e90c340724311cc7555b1aaa0323a500bee2dcdb.jpg)
+
+![](images/2738e33502177eadfb90d6c95a9d96a901fdc6c5b943c71b357dd75e4715703a.jpg)
+
+GroundTruth : this is where i go to school. i like the building a lot because it looks nice. at this angle it looks even better. a couple of my classmates are going to graduate. this is one beautiful building .
+
+![](images/2b1fb1b9f70032c667e166d6244a625f206772e6f6dfa422a5bd35a70b84987a.jpg)  
+SST(ZS): person, center, watches a game.
+
+![](images/abe91994aaa1a3b7f5e0e55b2e2edfefc4e30f2f5350c0962d872e492f62d48d.jpg)  
+COSA(FT): the lawn was very nice. the building was very nice. the architecture was very old. the students were very proud of themselves. the building was very beautiful.
+
+![](images/2fca6fcb3763552aa37fade368d03095018e021731064a04f27790af1c199a68.jpg)  
+SST(FT): we went to the baseball game. There were a lot of people there. Some of them were crazy. Some of the players didn't like it. the crowd was crazy.
+
+![](images/3234b9a9038045d5c23f06b6e35b82083cd487cff6d4aa3b9c56dd36bb2a486b.jpg)  
+COSA(ZS): baseball players warm up before a game. fans watch a baseball game. person, the mascot, is shown during a game against baseball team. a general view of the scoreboard.
+
+![](images/01a7929f57f74fb2b95368418750a214c42c0a7dae8f3ec55f43472786ac0520.jpg)
+
+Figure 6: Qualitative comparison between SST and COSA on the visual story telling (VIST) benchmark. ZS and FT denote zero-shot and finetuning, respectively.  
+![](images/7839222f3d944616c3cd33ea421305f90d0f936ab2b41551c5604d95ad44a307.jpg)  
+GroundTruth : we are going to watch a baseball game today. the players are doing a great job. we even got to interact with the crowd. the mascot was great , and very funny. final score is here , what a great day.
+
+![](images/3a7541926e280dfa142796ef7ab49fb9ed0894d130f4f0fc368da48ce883f59d.jpg)  
+SST(ZS): a graduate celebrates after receiving his diploma.
+
+![](images/328a58653e65d3270e667dc38c69820a7028dfacca409537c01df31a115d4620.jpg)  
+SST(ET): he was excited to finally graduate from college. the group of friends and family gathered in the pool for the graduation ceremony. the boy was very excited to finally graduate. the family was very proud of him.
+
+![](images/b4397983fc8d7cd571a8aeb12db4002e22ed238762ca664cb55b2c0def695966.jpg)  
+COSA(ZS) : person is all smiles after receiving his diploma during the graduation ceremony. person, waves to family and friends during the graduation ceremony. person, left, and person are all smiles after receiving his diploma at the school's commencement ceremony. the pool is full of people.
+
+![](images/46def5a05fdc717848e4f0f2dc82c7e3377b59f5f95d79ac82e4055eec386605.jpg)  
+COSA(FT): i went to the baseball game last weekend. there were a lot of people there. i took a lot of pictures. i got to meet some of the players. it was a great night.
+
+![](images/c8fc539490f001880e38fc84bc9b6be3d863f4d12c6f9fcda8378f56e1e5d63b.jpg)  
+COSA(ET): graduation day is finally here. all of the students line up to receive their diplomas. the students wave to the crowd. family and friends pose for a picture. after the ceremony, the family relaxes by the pool.  
+SST(ZS): a group of people pose for a photo.  
+SST(FT): there were a lot of people at the event today. the characters were very popular. the characters were very popular. the characters were very funny. the characters were very popular.  
+COSA(ZS): people walking in the street. person, left, and person, right, enjoy a day out. a bicycle with a basket attached to it. person with the girls at the party  
+COSA(FT): there were a lot of people at the festival today. there were a lot of funny characters. some of them were very cute. they rode their bikes around the city. it was a great time.  
+GroundTruth : the streets were filled during the festival. some came dressed in huge cartoon outfits. they were fun to dance and take pictures with. we got around using rent-able bikes. it was a memorable day.
+
+![](images/65fc9746bc4f50b76d45491087f7abe30ea68d0caefcec0a3d5b3fbff755ffac.jpg)  
+GroundTruth : graduation day has finally arrived. all the students started filing in. he was thrilled to finally be graduation. everyone posed for pictures outside the venue. and to cap off the day, we all hung out at the pool .
+
+![](images/bbb1c829fae79dfd256d14e50dd04d6b7b1cc439fc30fae264c937e053a03f84.jpg)
+
+![](images/fce7c26850013dac70ff4abd9625308ce2d0f70af4c76efd95cfc164ccfc62d6.jpg)
+
+![](images/b4f12fc5f1ed5e963d26e44c3cdcfb6d87085c3debad9e41349d80932ab915a2.jpg)

2024/COSA_ Concatenated Sample Pretrained Vision-Language Foundation Model/images.zip

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2024/CPPO_ Continual Learning for Reinforcement Learning with Human Feedback/0e602857-0d7f-4539-8ca2-d7b133d15df0_origin.pdf

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2024/CPPO_ Continual Learning for Reinforcement Learning with Human Feedback/full.md

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+# CPPO: CONTINUAL LEARNING FOR REINFORCEMENT LEARNING WITH HUMAN FEEDBACK
+
+Han Zhang $^{1,2}$ , Yu Lei $^{2*}$ , Lin Gui $^{3}$ , Min Yang $^{4}$ , Yulan He $^{4}$ , Hui Wang $^{2}$ , Ruifeng Xu $^{1,2,5*}$
+
+<sup>1</sup> Harbin Institute of Technology (Shenzhen)  
+2 Peng Cheng Laboratory  
+3 King's College London  
+4 Shenzhen Institutes of Advanced Technology  
+<sup>5</sup> Guangdong Provincial Key Laboratory of Novel Security Intelligence Technologies
+
+# ABSTRACT
+
+The approach of Reinforcement Learning from Human Feedback (RLHF) is widely used for enhancing pre-trained Language Models (LM), enabling them to better align with human preferences. Existing RLHF-based LMs however require complete retraining whenever new queries or feedback are introduced, as human preferences may differ across different domains or topics. LM retraining is often impracticable in most real-world scenarios, due to the substantial time and computational costs involved, as well as data privacy concerns. To address this limitation, we propose Continual Proximal Policy Optimization (CPPO), a novel method that is able to continually align LM with dynamic human preferences. Specifically, CPPO adopts a weighting strategy to decide which samples should be utilized for enhancing policy learning and which should be used for solidifying past experiences. This seeks a good trade-off between policy learning and knowledge retention. Our experimental results show that CPPO outperforms strong Continuous learning (CL) baselines when it comes to consistently aligning with human preferences. Furthermore, compared to PPO, CPPO offers more efficient and stable learning in non-continual scenarios.
+
+# 1 INTRODUCTION
+
+Recent studies (Stiennon et al., 2020; Bai et al., 2022a; Ouyang et al., 2022) have shown that Reinforcement Learning from Human Feedback (RLHF) can significantly enhance language models by aligning them with human intention. RLHF uses human preferences as a reward signal to fine-tune language models with the Proximal Policy Optimization (PPO) algorithm. The RLHF-based model can effectively generate answers preferred by humans for tasks that lack standardized solutions, such as summarization(Stiennon et al., 2020), translation(Kreutzer et al., 2018), and dialogue(Jaques et al., 2020), without over-optimizing metrics such as ROUGE(Lin, 2004) or BLEU(Papineni et al., 2002).
+
+In real-world applications, learning continuously changing human preferences is more practical than learning invariable human preferences. For example, the progression from the onset of the COVID-19 virus in human society to widespread infections and finally to achieving herd immunity has seen corresponding changes in government policies and human perspective. An AI agent that keeps pace with the times should exhibit behavior that aligns with current government policies and human understanding preferences at different stages, rather than remaining static.
+
+However, traditional alignment methods (Stiannon et al., 2020; Ouyang et al., 2022), lack flexibility for continual learning (CL) of human preferences. Recent approach (Bai et al., 2022a) tackles these problems by periodically retraining the Preference Model (PM) and policy based on both new and historical data, it might be inefficient and impractical due to the involved concerns of computational cost and data privacy.
+
+In this paper, we propose a more practical approach by enhancing RLHF with continual learning (CL), aiming to optimize two conflicting objectives: preserving old knowledge and acquiring new
+
+knowledge (Rolnick et al., 2019). This leads to a long-standing challenge known as the stability-plasticity $^{1}$  dilemma (Abraham & Robins, 2005). Moreover, due to the vast action space (vocabulary) of LMs, the RLHF algorithms (e.g., PPO) usually suffer from the issues of inefficiency and instability during training (Ramamurthy et al., 2022). To tackle these challenges, we attempt to seek a good tradeoff between policy learning and knowledge retention with stable learning by designing a sample-wise weighting strategy over the rollout $^{2}$  samples. Our weighting strategy is motivated by the fact that a desired policy should always generate high-reward results with high probabilities.
+
+Specifically, we first categorize the rollout samples into five types according to their rewards and generation probabilities, as shown in Figure 1. We then assign each rollout sample with a policy learning weight  $\alpha$  and a knowledge retention weight  $\beta$ , in the following way. 1) For a high-performance sample, we assign a high  $\alpha$  and a high  $\beta$ , in order to consolidate the knowledge of this sample. 2) For a high-variance or overfitting sample, we assign a high  $\alpha$  and a low  $\beta$ , so as to learn more knowledge of this sample and force the new policy to be different from the old one in generating such a sample. 3) For a noisy sample, we assign a low  $\alpha$  and a low  $\beta$  to decrease its impact on learning. 4) For a normal sample, we make no changes.
+
+Based on the above weighting strategy, we develop a novel PPO-based method, named continual proximal policy optimization (CPPO). CPPO implements the weighting strategy in two different ways: heuristic and learnable, resulting in two different CPPO methods (see Section 3.2 for details). The heuristic approach sets the weight with linear gain or decay according to strategy. The learnable approach converts the strategy into several inequality constraints and learns the best weight by optimizing the Lagrange function.
+
+Experimental results on real-world summarization datasets demonstrate that our proposed CPPO methods significantly outperform the PPO re-training methods and the strong CL baselines, in both CL and non-CL settings (detailed in Appendix F). Furthermore, additional experiments in both settings verify the superior training stability of CPPO compared to the original PPO algorithm.
+
+![](images/7d88f0ffb42b133bc66d2d1f2a9553e3cb67a6d66c909af9202eb9a015b6febb.jpg)  
+Figure 1: Five types of the rollout are utilized in our method.
+
+# 2 PRELIMINARY AND TASK FORMULATION
+
+PPO algorithm (Schulman et al., 2017) utilizes the clipped surrogate objective with a learned state-value function, and the entropy bonus (Mnih et al., 2016) is added to the original reward. The total objective is approximately maximized in each iteration step  $i = 1,2,\dots,I$  (in the NLP scene, step- $i$  denotes the generation of the  $i$ -th token):
+
+$$
+L _ {i} ^ {C L I P + V F} (\theta) = \mathbb {E} _ {i} \left[ L _ {i} ^ {C L I P} (\theta) - c \cdot L _ {i} ^ {V F} (\theta) \right] \tag {1}
+$$
+
+where  $c$  is the coefficient, and  $L_{i}^{VF}$  is a squared-error loss  $(V_{\theta}(s_i) - V_i^{targ})^2$ . The clipped policy learning objective is:  $L_{i}^{CLIP}(\theta) = \min (r_{i}(\theta)\cdot \mathbf{A}_{i},clip(r_{i}(\theta),1\pm \epsilon)\cdot \mathbf{A}_{i})$ , where  $r_i(\theta) = \frac{\pi_\theta(a_i|s_i)}{\pi_{\theta_{old}}(a_i|s_i)}$  is the probability ratio,  $\epsilon$  is the clip hyperparameter,  $s_i$  is the  $i$ -th state,  $\mathbf{A}_{\mathbf{i}}$  is the truncated version of generalized advantage estimation.
+
+Task Formulation: In this paper, we propose the task of continually learning human preferences under an offline continual learning setting(Biesialska et al., 2020). Formally, we consider a task sequence of  $\mathbb{T} = \{\mathcal{T}_1,\mathcal{T}_2,\ldots \}$  to continually learn a policy model on the corresponding human
+
+preference datasets  $\mathbb{H}\mathbb{F} = \{HF_1, HF_2, \ldots\}$  and prompt datasets  $\mathbb{S} = \{S_1, S_2, \ldots\}$ . For each task  $\mathcal{T}_t(t = 1, 2, \ldots)$ , the policy  $\pi_t$  is initialized by  $\pi_{t-1}$  and then is trained against the reward model  $r_t$  where the reward model  $r_t$  is learned on  $HF_t$ . The initial policy  $\pi_0$  is the SFT model, namely,  $\pi_0 = \pi_{SFT}$ . Let  $x = (s, a)$  denote the prompt  $s$  and answer  $a$  pair. The final objective is to learn a policy model  $\pi_\theta$  that maximizes the overall reward on all of the learned human preferences:
+
+$$
+\max  _ {\theta} \Sigma_ {t = 1} ^ {T} \mathbb {E} _ {s \sim S _ {t}, a \sim \pi_ {\theta} (\cdot | s)} [ r _ {t} (s, a) ] \tag {2}
+$$
+
+# 3 CONTINUAL PROXIMAL POLICY OPTIMIZATION
+
+# 3.1 MOTIVATION AND THEORETICAL ANALYSIS
+
+To optimize the objective 2 in the CL paradigm, the key is to balance the tradeoff between policy learning and knowledge retention, i.e., to learn a policy  $\pi_t$  that not only fits current task  $t$  but also retains the knowledge of previous tasks. This is typically accomplished by maximizing  $\pi_t$ 's average reward and meanwhile minimizing the difference between  $\pi_t$  and  $\pi_{t-1}$  by KL-based knowledge distillation (Kaplanis et al., 2019):
+
+$$
+\max  _ {\theta} \mathbb {E} _ {s \sim S _ {t}, a \sim \pi_ {\theta} (\cdot | s)} [ r _ {t} (s, a) ] - \mathbb {E} _ {s \in S _ {t - 1}} D _ {\mathrm {K L}} \left(P _ {\pi_ {\theta}} (a | s) \| P _ {\pi_ {t - 1}} (a | s)\right) \tag {3}
+$$
+
+where  $P_{\pi_\theta}(a|s)$  denotes the probability that policy  $\pi_\theta$  generates the answer  $a$  to the prompt  $s$ . However, in the RLHF setting, we argue that a more effective way to achieve policy learning is to maximize the rewards of the results that  $\pi_\theta$  has a high probability to generate. This is because LMs usually have a vast action space (vocabulary size) and adopt a sampling strategy such as beam search that favors high-probability generative results. For knowledge retention, on the other hand, it is more important to make  $\pi_\theta$  retain  $\pi_{t-1}$ 's certain knowledge that generates high-reward outputs rather than all.
+
+To accomplish the above ideas, we propose a theoretically desirable objective for continual RLHF at task  $\mathcal{T}_t$ :
+
+$$
+\max  _ {\theta} \mathbb {E} _ {(s, a) \in D _ {1}} r _ {t} (s, a) - \mathbb {E} _ {(s, a) \in D _ {2}} D _ {\mathrm {K L}} \left(P _ {\pi_ {\theta}} (a | s) \| P _ {\pi_ {t - 1}} (a | s)\right) \tag {4}
+$$
+
+where,  $D_{1} = \{(s,a)|s\sim S_{t},a\sim \pi_{\theta}(\cdot |s),P_{\pi_{\theta}}(a|s) > \mu_{a}[P_{\pi_{\theta}}(a|s)] + k\sigma_{a}[P_{\pi_{\theta}}(a|s)]\}$  and  $D_{2} = \{(s,a)|s\sim S_{t - 1},a\sim \pi_{t - 1}(\cdot |s),r_{t}(s,a) > \mu_{a}[r_{t}(s,a)] + k\sigma_{a}[r_{t}(s,a)]\}$  denote the sets of samples with high generation probability and high rewards, respectively.  $\mu$  and  $\sigma$  denote the mean and standard deviation respectively, and  $k$  is a hyperparameter. It is important to note that here we use  $r_t(s,a)$  instead of  $r_{t - 1}(s,a)$ . Since the reward model is continually learned, we assume  $r_{t - 1}(s,a)\approx r_t(s,a)$  when  $s\in S_{t - 1}$  and  $a\sim \pi_{\theta}(\cdot |s)$ . To simplify notation, the subsequent sections of the paper use  $x$  instead of  $(s,a)$ .
+
+The KL divergence term requires a significant amount of memory to store the probability distribution of each token across the vast vocabulary. To tackle this problem, we incorporate a low computational knowledge retention penalty term  $L_{i}^{KR}(\theta) = (\log P_{\pi_{\theta}}(x_{i}) - \log P_{\pi_{t-1}}(x_{i}))^{2}$ . We compute the L2 distance of the log generation probability of true tokens instead of the KL divergence of the entire vocabulary's probability distribution. We find the former is effective for knowledge retention and needs NOT to save the vocabulary's probability distribution in the memory<sup>3</sup>.
+
+We introduce  $I_{D_1}(x)$  and  $I_{D_2}(x)$  to denote the indicator functions of the sets of  $D_1$  and  $D_2$ , respectively. By introducing the actor-critic version, the clipped ratio, and the entropy bonus, we claim that Eq.(4) can be written to (the derivation is detailed in Appendix Section B):
+
+$$
+\begin{array}{l} \mathbf {J} ^ {\prime} (\theta) = L _ {i} ^ {I _ {D _ {1}} \cdot C L I P + I _ {D _ {2}} \cdot K R + V F} (\theta) \\ = \mathbb {E} _ {i} \left[ I _ {D _ {1}} (x) \cdot L _ {i} ^ {C L I P} (\theta) - I _ {D _ {2}} (x) \cdot L _ {i} ^ {K R} (\theta) - c \cdot L _ {i} ^ {V F} (\theta) \right] \tag {5} \\ \end{array}
+$$
+
+Compared with objective Eq. (1), Eq.(5) introduces the learning weights  $I_{D_1}(x)$ ,  $I_{D_2}(x)$ , and the  $L_i^{KR}$  loss. Unfortunately, it is still impractical to directly optimize the objective, since the training
+
+samples in  $D_{1}$  and  $D_{2}$  are seldom as indicated by the Cantelli Inequation<sup>4</sup>  $P(\mathbf{X} > \mu[\mathbf{X}] + k\sigma[\mathbf{X}]) < 1/(1 + k^{2})$ . To make Eq.(5) easy to optimize, we generalize the indicator functions  $I_{D_{1}}(x)$  and  $I_{D_{2}}(x)$  to positive real-valued functions  $\alpha(x)$  and  $\beta(x)$ , which gives each sample a non-zero learning weight.
+
+# 3.2 WEIGHTING STRATEGY
+
+Our method utilizes sample-wise balance weights  $\alpha(x)$  and  $\beta(x)$  to regulate the policy learning and knowledge retention processes, aiming to find a balance between knowledge retention and policy learning. The final objective is:
+
+$$
+\begin{array}{l} \mathbf {J} (\theta) = L _ {i} ^ {\alpha \cdot C L I P + \beta \cdot K R + V F} (\theta) \\ = \mathbb {E} _ {i} [ \alpha (x) L _ {i} ^ {C L I P} (\theta) - \beta (x) L _ {i} ^ {K R} (\theta) - c \cdot L _ {i} ^ {V F} (\theta) ] \tag {6} \\ \end{array}
+$$
+
+for task  $t = 1,2,\dots,T$ . Next, we propose a weighting strategy for balancing policy learning and knowledge retention.
+
+# 3.2.1 BALANCING POLICY LEARNING AND KNOWLEDGE RETENTION
+
+To simplify the expression, we define the operator  $F[\cdot ] = \mu [\cdot ] - k\sigma [\cdot ]$  and operator  $G[\cdot ] = \mu [\cdot ] + k\sigma [\cdot ]$ . As shown in Figure 1 and Table 1, we classify the rollout samples into 5 rollout types based on the joint distribution of  $(\mathbf{P}_{\pi_{\theta}}(x),\mathbf{R}(x))$ . If  $\mathbf{P}_{\pi_{\theta}}(x)$  or  $\mathbf{R}(x)$  is outside the discriminant interval  $(F[\cdot ],G[\cdot ])$ , it is considered as high or low. Now, we detail each rollout type and corresponding weight strategy.
+
+High-performance sample: If both  $\mathbf{P}_{\pi_{\theta}}(x)$  and  $\mathbf{R}(x)$  are high, it indicates that the old policy has high confidence to generate  $x$  which gets a high reward, implying that it is already performing well. In this case, we ask the new policy to enhance both policy learning and knowledge retention.
+
+Overfitting sample: A high  $\mathbf{P}_{\pi_{\theta}}(x)$  with a low  $\mathbf{R}(x)$  indicates that the old policy is likely overfitting (due to high
+
+Table 1: The determining condition of rollout type and corresponding weight strategy to balance policy learning and knowledge retention. We monitor the generating probability  $\mathbf{P}_{\pi_{\theta}}(x)$  and the corresponding reward score  $\mathbf{R}(x)$ . The rollout type of sample  $x$  depends on whether the  $\mathbf{P}_{\pi_{\theta}}(x)$  and  $\mathbf{R}(x)$  fall in or outside the discriminant interval  $(F[\cdot], G[\cdot])$ .
+
+<table><tr><td>ID</td><td>Rollout Type</td><td colspan="2">Determining Condition</td><td colspan="2">Weight Strategy</td></tr><tr><td>r1</td><td>High-performance</td><td>Pπθ(x) ≥ G[Pπθ]</td><td>R(x) ≥ G[R]</td><td>α(x) ↑</td><td>β(x) ↑</td></tr><tr><td>r2</td><td>Overfitting</td><td>Pπθ(x) ≥ G[Pπθ]</td><td>R(x) ≤ F[R]</td><td>α(x) ↑</td><td>β(x) ↓</td></tr><tr><td>r3</td><td>High-variance</td><td>Pπθ(x) ≤ F[Pπθ]</td><td>R(x) ≥ G[R]</td><td>α(x) ↑</td><td>β(x) ↓</td></tr><tr><td>r4</td><td>Noisy</td><td>Pπθ(x) ≤ F[Pπθ]</td><td>R(x) ≤ F[R]</td><td>α(x) ↓</td><td>β(x) ↓</td></tr><tr><td>r5</td><td>Normal</td><td colspan="2">Pπθ(x) or R(x) ∈ (F,G)</td><td>-</td><td>-</td></tr></table>
+
+probability) to the biased sample (due to low reward score). We aim to reduce the generation probability of the biased sample  $x$ , which can be achieved through policy learning. However, knowledge retention will maintain the high probability of the biased sample  $x$ . Therefore, we enhance policy learning and slow down knowledge retention.
+
+High-variance sample: If  $\mathbf{P}_{\pi_{\theta}}(x)$  is low while  $\mathbf{R}(x)$  is high, it suggests that sample  $x$  has high variance. Due to the low  $\mathbf{P}_{\pi_{\theta}}(x)$ , the likelihood of generating  $x$  next time is low. To achieve stable (low variance) performance, we aim to increase the generation probability of sample  $x$ , which can be accomplished through policy learning. However, knowledge retention will maintain a low generation probability. Therefore, we enhance policy learning and slow down knowledge retention.
+
+Noisy sample: If both  $\mathbf{P}_{\pi_{\theta}}(x)$  and  $\mathbf{R}(x)$  are low, sample  $x$  is considered noisy data which may lead to overoptimization against the PM (Gao et al., 2022). Therefore, we slow down both knowledge retention and policy learning.
+
+Normal sample: If at least one of  $\mathbf{P}_{\pi_{\theta}}(x)$  and  $\mathbf{R}(x)$  falls within the discriminant interval, we consider it a normal condition and do not alter the learning process.
+
+![](images/8b9d17ad2568a7642be04d661fc52cd3dda34abfc2a1075f267eaca3974dbb71.jpg)  
+(a) Surface of heuristic  $\alpha (x)$
+
+![](images/aeef1cbebed278cffd09fc8be826f1ff69006382d26092b0d672c8fc8b93bc14.jpg)  
+(b) Surface of heuristic  $\beta (x)$  
+Figure 2: The surfaces of heuristic weights. The weights are equal to 1 when rollout samples fall in the normal zone.
+
+# 3.2.2 HOW TO DETERMINE BALANCE WEIGHTS?
+
+The above weight strategies constitute several inequality constraints of  $\alpha(x)$  and  $\beta(x)$ , shown in Table 2. Determining balance weights requires finding a feasible solution that satisfies those constraints. We provide two methods to determine balance weights including the heuristic weight method and the learnable weight method.
+
+Table 2: The constraint of weights and heuristic weights.  
+
+<table><tr><td>ID</td><td>Constraint of α(x)</td><td>Constraint of β(x)</td><td>Heuristic α(x)</td><td>Heuristic β(x)</td></tr><tr><td>r1</td><td>α(xr5) - α(xr1) &lt; 0</td><td>β(xr5) - β(xr1) &lt; 0</td><td>min(ub, Pπθ(x) - μ[Pπθ]/kσ[πθ])</td><td>min(ub, R(x) - μ[R] / kσ[R])</td></tr><tr><td>r2</td><td>α(xr5) - α(xr2) &lt; 0</td><td>β(xr2) - β(xr5) &lt; 0</td><td>min(ub, Pπθ(x) - μ[Pπθ]/kσ[πθ])</td><td>max(lb, 2 + R(x) - μ[R] / kσ[R])</td></tr><tr><td>r3</td><td>α(xr5) - α(xr3) &lt; 0</td><td>β(xr3) - β(xr5) &lt; 0</td><td>min(ub, Pπθ(x) - μ[Pπθ]/kσ[πθ])</td><td>max(lb, 2 + R(x) - μ[R] / kσ[R])</td></tr><tr><td>r4</td><td>α(xr4) - α(xr5) &lt; 0</td><td>β(xr4) - β(xr5) &lt; 0</td><td>max(lb, 2 + Pπθ(x) - μ[Pπθ]/kσ[πθ])</td><td>max(lb, 2 + R(x) - μ[R] / kσ[R])</td></tr><tr><td>r5</td><td>-</td><td>-</td><td>1</td><td>1</td></tr><tr><td>All</td><td>E×~πt-1[α(x)] = 1</td><td>E×~πt-1[β(x)] = 1</td><td>-</td><td>-</td></tr></table>
+
+Heuristic  $\alpha(x)$  and  $\beta(x)$ : If  $\mathbf{P}_{\pi_{\theta}}(x)$  or  $\mathbf{R}(x)$  fall within the discriminant interval, the balance weights are set to 1. If they are further away from the discriminant interval, the weights will linearly increase or decrease (depending on the rollout type). We can plot the surfaces of  $\alpha(x)$  and  $\beta(x)$  in 3D coordinate systems, as shown in Figure 2. The heuristic weights  $\alpha(x)$  and  $\beta(x)$  for a given sample  $x$  can be calculated by the formula presented in Table 2.
+
+Learnable  $\alpha(x)$  and  $\beta(x)$ : Heuristic  $\alpha(x)$  and  $\beta(x)$  lack enough adaptation ability to the dynamic learning process. Hence, we propose the learnable balance weights to automatically balance policy learning and knowledge retention. We learn 2N parameters for each rollout batch in which the LM generates N responses, the 2N parameters can be discarded before the next rollout batch.
+
+Our goal is to find a set of weights that satisfy the constraints in Table 2. Unlike the typical optimization problem solved by the Lagrange Multiplier method, we do not need to minimize an additional objective function. It should be noted that the optimization objective of CPPO in Eq.6 is not directly optimized using the Lagrange Multiplier method.
+
+We employ a more straightforward strategy. We construct an unconstrained optimization objective by adding all the terms on the left side of the inequalities (in Table 2) together:
+
+$$
+\begin{array}{l} \mathbf {L} _ {\text {c o e f}} (\phi) = \mathbb {E} _ {x \sim \pi_ {t - 1}} [ (\alpha_ {\phi} (x) - 1) ^ {2} + (\beta_ {\phi} (x) - 1) ^ {2} ] + \tau (\alpha (x _ {r 5}) - \alpha (x _ {r 1}) + \beta (x _ {r 5}) - \beta (x _ {r 1}) \\ + \alpha \left(x _ {r _ {5}}\right) - \alpha \left(x _ {r _ {2}}\right) + \beta \left(x _ {r _ {2}}\right) - \beta \left(x _ {r _ {5}}\right) + \alpha \left(x _ {r _ {5}}\right) - \alpha \left(x _ {r _ {3}}\right) + \beta \left(x _ {r _ {3}}\right) - \beta \left(x _ {r _ {5}}\right) \tag {7} \\ + \alpha \left(x _ {r _ {4}}\right) - \alpha \left(x _ {r _ {5}}\right) + \beta \left(x _ {r _ {4}}\right) - \beta \left(x _ {r _ {5}}\right)) \\ \end{array}
+$$
+
+where,  $\alpha(x) = (ub - lb) \cdot sig(\phi_x^1) + lb$ ,  $\beta(x) = (ub - lb) \cdot sig(\phi_x^2) + lb$ , and  $sig$  is sigmoid function,  $lb$  and  $ub$  are lower and upper bound of  $\alpha(x)$  and  $\beta(x)$ . We directly optimize Eq. 7 using SGD to find
+
+a set of weights that satisfy the constraints. We set multiplier  $\tau$  as a hyperparameter, and  $\tau = 0.1$  is selected from  $\{0.01, 0.1, 0.5, 1.0\}$ . For more hyperparameter sensitivity analysis experiments, please refer to Appendix E.1. We found this simple idea is highly effective in our scenario. In Appendix E.2, we analyze the time and memory required for SGD to find feasible solutions and found that it does NOT significantly increase the overall training time and memory.
+
+# 4 EXPERIMENTS
+
+We assess the performance of CPPO and baseline methods in the domain incremental learning (DIL) summary task. We also evaluate CPPO on non-continual learning tasks (Appendix Section F).
+
+# 4.1 THE EXPERIMENTAL CONFIGURATION FOR CONTINUAL LEARNING FROM HUMAN PREFERENCES
+
+Dataset and split: In accordance with previous research (Stiannon et al., 2020), we evaluate our method using the Reddit TL;DR (Volske et al., 2017) dataset for summarization. We use the human preference data provided by CarperAI<sup>5</sup>. To the best of our knowledge, there are limited benchmark datasets proposed for evaluating continual RLHF methods. Consequently, we divide the Reddit TL;DR dataset based on domains into two parts, which are outlined in Table 3. Each part corresponds to a distinct alignment task.
+
+Experiment settings: We evaluate CPPO under the DIL setting with two tasks, and the historical data is assumed inaccessible. This scenario is typical in real-world applications, such as developers continually learning an open-Source
+
+Table 3: The dataset is utilized for continual learning. The human feedback data is used for training the reward model. The post (prompt) and summary (label) of Reddit TL;DR are used for SFT. The domain of "r/others" includes 28 categories, such as books, travel, and cooking. It's worth noting that the summary (label) data is not used in the reinforcement learning (RL) process.
+
+<table><tr><td>Task ID</td><td>Data</td><td>Data split</td><td>Train</td><td>Valid</td><td>Test</td><td>Domain</td></tr><tr><td rowspan="2">task-1</td><td>Human Feedback</td><td>part-1</td><td>52243</td><td>-</td><td>45148</td><td>r / relationships</td></tr><tr><td>Reddit TL;DR</td><td>part-1</td><td>63324</td><td>3462</td><td>3539</td><td>r / relationships</td></tr><tr><td rowspan="2">task-2</td><td>Human Feedback</td><td>part-2</td><td>40291</td><td>-</td><td>38481</td><td>r / others</td></tr><tr><td>Reddit TL;DR</td><td>part-2</td><td>53398</td><td>2985</td><td>3014</td><td>r / others</td></tr></table>
+
+RLHF model like vicuna(Chiang et al., 2023) in a special domain (e.g., game) without permission to access the pre-training corpus. For each task, we employ a 1.3B gpt2-xl (Radford et al., 2019) model with a value head as the reward model (RM). The RM is continually trained for 5 epochs on each task using the MAS(Aljundi et al., 2018) method. Since the policy is prone to over-optimize against the PM (Gao et al., 2022), we train a 6.7B gptj (Wang & Komatsuzaki, 2021) model as the reference PM (rPM) to measure the performance of alignment. The rPM is trained on entire human preferences data. We conduct experiments to evaluate the RM trained with and without MAS through accuracy and forgetting ratio (Chaudhry et al., 2018) (FR) of accuracy. The evaluation results of RM and rPM are shown in Table 4. The accuracy is computed by counting the percentage of the reward scores of human-preferred responses that are higher than the reward scores of human-NOT-preferred responses(Yuan et al., 2023). We initialize the SFT model from gpt2-s and train it on the Reddit TL;DR part-1 for 5 epochs. However, we do not perform the SFT process in task-2 as we observe no significant effects on performance.
+
+Metrics: We use the forgetting radio (Chaudhry et al., 2018) of the ROUGE and reference PM score to measure the extent to which the old policy is forgotten. Notably, we consider the alignment tax (Ouyang et al., 2022) as part of forgetting since it arises when the SFT model
+
+Table 4: The evaluation results of RMs and rPM.  
+
+<table><tr><td>Reward Model</td><td>Acc(HF1test)</td><td>Acc(HF2test)</td><td>FR</td></tr><tr><td>RM1</td><td>0.7441</td><td>-</td><td>-</td></tr><tr><td>RM2 w MAS</td><td>0.7203</td><td>0.7482</td><td>0.024</td></tr><tr><td>RM2 w/o MAS</td><td>0.6971</td><td>0.7496</td><td>0.047</td></tr><tr><td>rPM</td><td>0.7624</td><td>0.7592</td><td>-</td></tr></table>
+
+learns human preferences during the RL step. After learning all tasks, we evaluate the models on the entire test set using both reference PM score and ROUGE score. Table 5 presents the metrics used to
+
+evaluate each task, as well as the final evaluation metric. A well-performing model is expected to achieve high scores in both the reference PM and ROUGE metrics.
+
+Table 5: Metrics for our tasks.  $\mathbb{D}_i^{test}(i = 1,2)$  denote the test data of Reddit TL;DR data part-i, and  $rPM(M_i,\mathbb{D}_i^{test})(i = 1,2)$  denote the reference PM score of model  $M_{i}$  on dataset  $\mathbb{D}_i^{test}$ .  
+
+<table><tr><td></td><td>Metric</td><td>Definition</td></tr><tr><td>Task-1</td><td>reference PM Score on Task-1 (rPMS1, ↑)</td><td>rPM(M1, D1test)</td></tr><tr><td>Task-1</td><td>Alignment Tax (AT, ↓)</td><td>Rouge(MST, D1test) - Rouge(M1, D1test)</td></tr><tr><td>Task-2</td><td>reference PM Score on Task-2 (rPMS2, ↑)</td><td>rPM(M2, D2test)</td></tr><tr><td>Task-2</td><td>Score Forgetting Ratio (SFR, ↓)</td><td>rPM(M1, D1test) - rPM(M2, D1test)</td></tr><tr><td>Final eval</td><td>reference PM Score on entire test data (rPMS, ↑)</td><td>rPM(M2, D1test ∪ D2test)</td></tr></table>
+
+# 4.2 RESULTS OF CONTINUAL LEARNING FROM HUMAN PREFERENCES
+
+Table 6 shows the results of continual learning from human preferences on the summary task. We observe that CL methods, such as EWC (Kirkpatrick et al., 2017) regularization or policy consolidation (Kaplanis et al., 2019) can improve the training stability of the PPO method, thereby ensuring that the policy does not change too much with every policy gradient step. This leads to improved rPMS. Our method outperforms CL baselines by achieving the most significant enhancement in policy learning (rPMS) and possessing Backward Transfer (BWT) (Lopez-Paz & Ranzato, 2017) capability (negative SFR). This is because our learning strategy is sample-adaptive and balances policy learning and knowledge retention. Additionally, CPPO performs better than Iterated RLHF because PPO is not stable enough in the learning process. We observed that during PPO training, the KL divergence and value prediction errors tend to increase suddenly, as discussed in Section 4.4.
+
+Table 6: The main results of continual alignment on TL; DR dataset. For PPO (In order)*, we directly finetune the  $\mathrm{RM}_1$  on the novel data to obtain  $\mathrm{RM}_2$ , without using MAS regularization; and we directly train the policy model  $M_{\pi_1}$  against  $\mathrm{RM}_2$  to obtain  $M_{\pi_2}$ . For the Iterated RLHF†(PPO), we retrain the  $\mathrm{RM}_2$  and policy model  $M_{\pi_2}$  on the combination of the Task-1 and Task-2 corpus. Methods in italics are trained against the continually learned (by MAS) reward models. Details of the implementation can be found in Appendix G.  
+
+<table><tr><td>Method</td><td>rPMS1(↑)</td><td>Task-1 (Mπ1) rouge(↑)</td><td>AT (↓)</td><td>rPMS2(↑)</td><td>Task-2 (Mπ2) rouge(↑)</td><td>SFR (↓)</td><td colspan="2">Final eval (Mπ2) rouge(↑)</td></tr><tr><td>Human</td><td>2.958</td><td>-</td><td>-</td><td>2.805</td><td>-</td><td>-</td><td>2.903</td><td>-</td></tr><tr><td>ChatGPT</td><td>3.298</td><td>0.197</td><td>-</td><td>3.189</td><td>0.191</td><td>-</td><td>3.242</td><td>0.193</td></tr><tr><td>SFT (In order)</td><td>1.499 ±0.130</td><td>0.248 ±0.006</td><td>-</td><td>1.543 ±0.067</td><td>0.237 ±0.007</td><td>-</td><td>1.498 ±0.051</td><td>0.237 ±0.009</td></tr><tr><td>SFT (multi-tasks)</td><td>1.524 ±0.041</td><td>0.254 ±0.011</td><td>-</td><td>1.536 ±0.092</td><td>0.234 ±0.009</td><td>-</td><td>1.505 ±0.011</td><td>0.236 ±0.008</td></tr><tr><td>PPO (In order)*</td><td>2.629 ±0.183</td><td>0.196 ±0.050</td><td>0.052 ±0.044</td><td>2.546 ±0.201</td><td>0.151 ±0.022</td><td>0.144 ±0.024</td><td>2.502 ±0.242</td><td>0.186 ±0.016</td></tr><tr><td>Iterated RLHF†</td><td>2.629 ±0.183</td><td>0.196 ±0.050</td><td>0.052 ±0.044</td><td>2.732 ±0.163</td><td>0.211 ±0.011</td><td>0.061 ±0.018</td><td>2.666 ±0.124</td><td>0.200 ±0.010</td></tr><tr><td>PPO</td><td>2.629 ±0.183</td><td>0.196 ±0.050</td><td>0.052 ±0.044</td><td>2.687 ±0.126</td><td>0.184 ±0.017</td><td>0.080 ±0.017</td><td>2.612 ±0.191</td><td>0.188 ±0.013</td></tr><tr><td>PPO+OnlineL2 Reg</td><td>2.758 ±0.121</td><td>0.206 ±0.042</td><td>0.042 ±0.042</td><td>2.701 ±0.205</td><td>0.180 ±0.012</td><td>0.062 ±0.013</td><td>2.700 ±0.114</td><td>0.196 ±0.011</td></tr><tr><td>PPO+EWC (Kirkpatrick et al., 2017)</td><td>2.833 ±0.122</td><td>0.201 ±0.043</td><td>0.047 ±0.039</td><td>2.823 ±0.192</td><td>0.175 ±0.022</td><td>0.040 ±0.015</td><td>2.801 ±0.202</td><td>0.196 ±0.023</td></tr><tr><td>PPO+MAS (Aljundi et al., 2018)</td><td>2.712 ±0.132</td><td>0.211 ±0.051</td><td>0.034 ±0.037</td><td>2.726 ±0.189</td><td>0.157 ±0.021</td><td>0.039 ±0.020</td><td>2.714 ±0.167</td><td>0.179 ±0.011</td></tr><tr><td>PPO+LfW (Li &amp; Hoiem, 2018)</td><td>2.822 ±0.126</td><td>0.197 ±0.051</td><td>0.048 ±0.050</td><td>2.832 ±0.179</td><td>0.169 ±0.036</td><td>0.030 ±0.019</td><td>2.824 ±0.192</td><td>0.179 ±0.019</td></tr><tr><td>PPO+TFCL (Aljundi et al., 2019)</td><td>2.867 ±0.109</td><td>0.202 ±0.039</td><td>0.043 ±0.046</td><td>2.864 ±0.169</td><td>0.169 ±0.020</td><td>0.054 ±0.022</td><td>2.842 ±0.211</td><td>0.178 ±0.014</td></tr><tr><td>PC (Kaplanis et al., 2019)</td><td>2.692 ±0.117</td><td>0.209 ±0.048</td><td>0.036 ±0.055</td><td>2.723 ±0.195</td><td>0.165 ±0.019</td><td>0.047 ±0.017</td><td>2.703 ±0.191</td><td>0.187 ±0.016</td></tr><tr><td>HN-PPO (Schöpf et al., 2022)</td><td>2.859 ±0.105</td><td>0.212 ±0.034</td><td>0.036 ±0.042</td><td>2.868 ±0.132</td><td>0.171 ±0.017</td><td>0.028 ±0.029</td><td>2.846 ±0.177</td><td>0.201 ±0.011</td></tr><tr><td>NLPO (Ramamurthy et al., 2022)</td><td>2.784 ±0.102</td><td>0.185 ±0.041</td><td>0.060 ±0.050</td><td>2.796 ±0.116</td><td>0.172 ±0.021</td><td>0.012 ±0.012</td><td>2.799 ±0.146</td><td>0.181 ±0.022</td></tr><tr><td>CPPO (Heuristic)</td><td>3.020 ±0.137</td><td>0.213 ±0.024</td><td>0.035 ±0.023</td><td>2.978 ±0.113</td><td>0.174 ±0.019</td><td>-0.164 ±0.009</td><td>3.099 ±0.153</td><td>0.179 ±0.016</td></tr><tr><td>CPPO (Learn)</td><td>3.180 ±0.154</td><td>0.220 ±0.040</td><td>0.028 ±0.042</td><td>3.085 ±0.134</td><td>0.164 ±0.024</td><td>-0.161 ±0.008</td><td>3.207 ±0.113</td><td>0.179 ±0.008</td></tr></table>
+
+# 4.3 ABLATION STUDY
+
+We conduct an ablation study on our proposed CPPO method. To analyze the effect of the balance weights, we conduct experiments by setting either  $\alpha(x)$  or  $\beta(x)$  to 1. To analyze the effect of the knowledge retention penalty, we set  $\beta(x) \equiv 0$ . The training curves of different weights are shown in Figure 3, and the evaluation results are presented in Table 7. We observe that the training process becomes unstable when setting  $\beta(x)$  to 0. When setting  $\alpha(x)$  to 1 reduces the rPMS, the noisy samples are learned together with normal samples without distinction, hence the reward increase is slower than CPPO. When setting  $\beta(x)$  to 1 increases the SFR, the overfitting samples, high-variance samples, and noisy samples are consolidated the in the knowledge retention process, hence the final reward value is lower than CPPO. The above experiments indicate that the sample-wise balance weights are helpful for both policy learning and knowledge retention.
+
+Table 7: Ablation study. PPO is a special case of CPPO ( $*\alpha \equiv 1, \beta \equiv 0$ ).  
+
+<table><tr><td rowspan="2">Method</td><td colspan="3">Task-1</td><td colspan="3">Task-2</td></tr><tr><td>rPMS1(↑)</td><td>rouge (↑)</td><td>AT (↓)</td><td>rPMS2(↑)</td><td>rouge (↑)</td><td>SFR (↓)</td></tr><tr><td>CPPO / Heuristic</td><td>3.020 ±0.137</td><td>0.213 ±0.024</td><td>0.035 ±0.023</td><td>2.978 ±0.113</td><td>0.174 ±0.019</td><td>-0.164 ±0.009</td></tr><tr><td>CPPO / Learn</td><td>3.180 ±0.154</td><td>0.220 ±0.040</td><td>0.028 ±0.042</td><td>3.085 ±0.134</td><td>0.164 ±0.024</td><td>-0.161 ±0.008</td></tr><tr><td>PPO / α ≈ 1, β ≈ 0</td><td>2.629 ±0.183</td><td>0.196 ±0.050</td><td>0.052 ±0.044</td><td>2.687 ±0.126</td><td>0.184 ±0.017</td><td>0.080 ±0.017</td></tr><tr><td>CPPO / α ≈ 1</td><td>2.837 ±0.124</td><td>0.196 ±0.029</td><td>0.047 ±0.041</td><td>2.745 ±0.121</td><td>0.169 ±0.020</td><td>-0.031 ±0.010</td></tr><tr><td>CPPO / β ≈ 1</td><td>2.476 ±0.117</td><td>0.185 ±0.021</td><td>0.063 ±0.025</td><td>2.520 ±0.119</td><td>0.186 ±0.017</td><td>0.051 ±0.009</td></tr><tr><td>CPPO / β ≈ 0</td><td>2.012 ±0.186</td><td>0.209 ±0.022</td><td>0.038 ±0.045</td><td>2.436 ±0.141</td><td>0.174 ±0.021</td><td>0.142 ±0.015</td></tr></table>
+
+![](images/e67ffd6e5b0de348486204ad6081be5030c3eefea2fe20bfd9c3c4c277d3eb62.jpg)  
+(a) reward
+
+![](images/9a1b3e76c02919238bd82ab3a2df9b3e0c6c8f0d1ad724bc22a2381435d69cb2.jpg)  
+(b) approx_kl  
+Figure 3: The curves of different weights in task-1. The knowledge retention weights penalty can improve the training stability of the PPO algorithm. However, setting  $\beta(x) \equiv 1$  slows down the increase of the reward compared with CPPO. On the other hand, the policy learning weights  $\alpha(x)$  can boost the increase of the reward compared with  $\alpha(x) \equiv 1$ .
+
+![](images/fd589f0e7ba8548d1095dd4ce281a6b8e6b7396fcea9e87e3b9058490c723839.jpg)  
+(c) value errors
+
+# 4.4 STABILITY ANALYSIS
+
+In this section, we analyze the stability of the CPPO, PPO, and PPO with the knowledge retention penalty. Previous work (Bai et al., 2022a) argues that small models are more prone to be unstable in PPO training. However, we find that CPPO can learn stably without the need for invalid-action masking(Ramamurthy et al., 2022), even with small models. As shown in Figure 4, the vanilla PPO performers unstably on the new data distribution. PPO with a knowledge retention penalty is more stable than PPO, but policy learning is slow. CPPO gets fast convergence on reward score and shows stable performance on the KL divergence and value prediction. This is because the sample-wise learning strategy of CPPO restricts the learning of noisy samples.
+
+![](images/95412e8f367fd9167af5c8e311fb03f3f2d599aa8a5b4e34a983e30c3a22bfe0.jpg)  
+(a) reward  
+Figure 4: Training process of Task-2. The PPO algorithm is unstable at 7k steps and is unable to continuously increase the reward score.
+
+![](images/5c9d4f05ebab78b4a5a0c95e45713eb3c2ba37abb0031f4fb3ab7098fc4fbd3e.jpg)  
+(b) approx_kl
+
+![](images/4fa4811cef85a434a6da09a333c84cffdd4ecc4e50ace86cab400d029aa444dd.jpg)  
+(c) value errors
+
+# 4.5 HUMAN EVALUATION ON REDDIT TL;DR
+
+We train two gpt2-xl models using CPPO and PPO, respectively, and compare their summaries with those generated by humans and ChatGPT using a Likert scale(Likert, 1932). The results are shown in Table 8. During the human evaluation, we observe that ChatGPT tends to generate longer summaries than humans and our models, but its performance remains stable across the test samples.
+
+Although humans provide the best summaries, they still made mistakes, such as obfuscating important details. Our model achieves comparable performance with ChatGPT but still makes mistakes that the
+
+small model often makes, such as repeating words and sentences. Due to the training inefficiency and instability, the performance of gpt2-x1 trained by PPO is not satisfactory.
+
+# 5 RELATED WORK
+
+# 5.1 REINFORCEMENT LEARNING FROM HUMAN OR AI FEEDBACKS
+
+Learning from human preferences has been studied in the game field (Bradley Knox & Stone, 2008) and has recently been introduced into the NLP domain, such as dialogue systems (Li et al., 2023; Zhao et al., 2023; 2024). Previous work (Stiennon et al., 2020) utilizes the PPO algorithm to fine-tune a language model (LM) for summarization and demonstrates that RLHF can improve the LM's generalization ability, which serves as the technology prototype for InstructGPT (Ouyang
+
+Table 8: Human evaluation on 100 posts from the Reddit TL;DR.  
+
+<table><tr><td>Method</td><td>Likert score</td><td>Improve</td><td>p-value</td></tr><tr><td>PPO</td><td>4.370±1.180</td><td>-</td><td>-</td></tr><tr><td>CPPO</td><td>4.730±1.231</td><td>8.23%</td><td>0.037</td></tr><tr><td>ChatGPT</td><td>4.760±1.011</td><td>8.92%</td><td>0.013</td></tr><tr><td>Human</td><td>4.900±1.034</td><td>12.13%</td><td>0.001</td></tr></table>
+
+et al., 2022) and ChatGPT. Learning LMs from feedback can be divided into two categories: human or AI feedback. Recent works such as HH-RLHF (Bai et al., 2022a) and InstructGPT (Ouyang et al., 2022) collect human preferences to train a reward model and learn a policy through it. ILF (Scheurer et al., 2023) proposes to learn from natural language feedback, which provides more information per human evaluation. Since human annotation can be expensive, learning from AI feedback (RLAIF) (Bai et al., 2022b; Perez et al., 2022; Ganguli et al., 2022) is proposed, but current methods are only effective for reducing harmless outputs, while helpful outputs still require human feedback.
+
+# 5.2 CONTINUAL LEARNING
+
+Within the realm of continual learning, several noteworthy methodologies emerge, encompassing the regularization-based approach, replay-based techniques, optimization-based strategies, representation-based methodologies, and architecture-based innovations (Wang et al., 2023).
+
+The Regularization-Based Approach (Kirkpatrick et al., 2017; Aljundi et al., 2018; Chaudhry et al., 2018; Li & Hoiem, 2018; Castro et al., 2018) orchestrates the introduction of explicit regularization terms, thereby striving to strike a harmonious balance between the acquisition of new skills and the retention of past knowledge. The Replay-Based Approach aims to preserve and reuse past experiences to enhance model performance, which includes experience replay(Lin, 1992), generative replay or pseudo-rehearsal (Sun et al., 2020) and feature replay(Liu et al., 2020). The Optimization-Based Approach navigates the terrain of continual learning through explicit design and manipulation of optimization programs. This includes techniques such as gradient projection(Lopez-Paz & Ranzato, 2017), and meta-learning(Javed & White, 2019). The Representation-Based Approach leverages the strengths of self-supervised learning (SSL)(Gallardo et al., 2021) and large-scale pre-training(Mehta et al., 2022) to enhance the quality of representations at both the initialization and continual learning stages. The Architecture-Based Approach addresses inter-task interference by fashioning task-specific parameters. This approach can be dissected into three distinct paradigms: parameter allocation(Serra et al., 2018), model decomposition(Ebrahimi et al., 2020), and modular networks(Rusu et al., 2016).
+
+# 6 CONCLUSION
+
+In this work, we propose CPPO, which utilizes learning weights to balance policy learning and knowledge retention, with the aim of improving the PPO algorithm for continual learning from human preferences. CPPO is a task-agnostic and model-agnostic method that does not significantly increase the time and space complexity of PPO. We evaluate CPPO on both the DIL task and three non-continual tasks and show that it outperforms strong continual learning baselines when continually aligning with human preferences. Additionally, CPPO improves the learning efficiency and training stability of PPO. Our experiments demonstrate the potential of our approach for efficient and stable continual learning from human preferences, which can have applications in various domains and tasks.
+
+# ACKNOWLEDGEMENTS
+
+We thank the anonymous reviewers for their valuable suggestions to improve the quality of this work, and we express our sincere gratitude to Dr. Bin Liang for his invaluable guidance and constructive feedback throughout the preparation of this manuscript. This research was supported in part by the National Key Research and Development Program of China (2021ZD0112905), the Major Key Project of PCL (PCL2023A09-4), the National Natural Science Foundation of China (62176076), the Guangdong Provincial Key Laboratory of Novel Security Intelligence Technologies(2022B1212010005), Natural Science Foundation of Guangdong (2023A1515012922), Shenzhen Foundational Research Funding (JCYJ20220818102415032) and the UK Engineering and Physical Sciences Research Council (EP/X019063/1).
+
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+
+# A NOTATIONS
+
+All of the notations used in this paper and their corresponding meanings are listed in Table 9.
+
+Table 9: Notations used in this paper, italic font denotes the CPPO-specific symbols  
+
+<table><tr><td>Notations</td><td>Corresponding Meanings</td></tr><tr><td>i(1,...,I)</td><td>generation of the i-th token</td></tr><tr><td>t(1,...,T)</td><td>t-th task of CL</td></tr><tr><td>x</td><td>a rollout sample</td></tr><tr><td>xi</td><td>i-th token of sample x</td></tr><tr><td>si</td><td>state-i: prompt + x1:i-1</td></tr><tr><td>θ</td><td>parameters of policy learned in task-t</td></tr><tr><td>πt</td><td>policy learned in task-t</td></tr><tr><td>Pπt(x)</td><td>generation probability of x under πt</td></tr><tr><td>J(θ)</td><td>total objective of PPO or CPPO</td></tr><tr><td>LCLIP</td><td>clipped policy learning objective</td></tr><tr><td>LVF</td><td>squared-error value loss</td></tr><tr><td>V(si)</td><td>value estimation by critic</td></tr><tr><td>λ/γ</td><td>reward / value discount coefficients</td></tr><tr><td>Ai</td><td>advantage score of token xi</td></tr><tr><td>R(x)</td><td>reward model score of x</td></tr><tr><td>ri(θ)</td><td>the probability ratio</td></tr><tr><td>ε</td><td>clip hyperparameter</td></tr><tr><td>clip(.,1±ε)</td><td>clip by 1±ε</td></tr><tr><td>c</td><td>coefficient of LVF</td></tr><tr><td>N</td><td>samples number per rollout batch</td></tr><tr><td>k</td><td>the threshold of times of standard variance</td></tr><tr><td>LKR</td><td>knowledge retention penalty</td></tr><tr><td>α(x)</td><td>weight of policy learning</td></tr><tr><td>β(x)</td><td>weight of knowledge retention</td></tr><tr><td>ub,lb</td><td>the upper bound and lower bound of weights</td></tr><tr><td>μ[Pπθ]</td><td>expectation of Pπθ(x)</td></tr><tr><td>μ[R]</td><td>expectation of R(x)</td></tr><tr><td>σ[Pπθ]</td><td>standard variance of Pπθ(x)</td></tr><tr><td>σ[R]</td><td>standard variance of R(x)</td></tr><tr><td>φ(|φ|=2N)</td><td>parameters for weight learning</td></tr><tr><td>Lcoef(φ)</td><td>objective of weight learning</td></tr></table>
+
+# B THE THEORETICAL ANALYSIS OF CPPO
+
+The theoretical objective in Eq. 4 is an intuitive implementation of our basic idea. Based on it, we derive a more practical objective in Eq. 6. Next, we will elaborate the relationship between the two and explain how we were inspired by Eq. 4 and designed Eq. 6.
+
+# Eq. 6 is a generalized version of Eq. 4.
+
+Let  $I_{D_1}(x)$  and  $I_{D_2}(x)$  denote the indicator functions of the sets of  $D_1$  and  $D_2$ , respectively. In Eq. 6,  $\alpha(x)$  and  $\beta(x)$  can be any non-negative real-valued functions defined on the rollout set. We claim that in Eq. 4,  $\alpha(x)$  and  $\beta(x)$  are specialized as  $\alpha(x) = I_{D_1}(x)$ ,  $\beta(x) = I_{D_2}(x)$ . Next, we provide the derivation step by step.
+
+By introducing the actor-critic version, the clipped ratio, the objective Eq. 4. can be written as the objective Eq. 5.
+
+1. We utilize notations  $I_{D_1}(x)$  and  $I_{D_2}(x)$  to rewrite the Eq.4 as  $\max_{\theta} \mathbb{E}_{x \sim \pi_\theta} I_{D_1}(x) \cdot \mathbf{R}(x) - \mathbb{E}_{x \sim \pi_{t-1}} I_{D_2}(x) \cdot D_{KL}(\mathbf{P}_{\pi_\theta}(x) \| \mathbf{P}_{\pi_{t-1}}(x))$ .  
+2. Then we introduce the importance sampling like PPO, the above objective can be written as  $\max_{\theta}\mathbb{E}_{x\sim \pi_{t - 1}}I_{D_1}(x)\cdot \frac{\mathbf{P}_{\pi_\theta}(x)}{\mathbf{P}_{\pi_{\mathbf{t} - 1}}(x)}\mathbf{R}(x) - \mathbb{E}_{x\sim \pi_{t - 1}}I_{D_2}(x)\cdot D_{KL}(\mathbf{P}_{\pi_\theta}(x)\parallel \mathbf{P}_{\pi_{\mathbf{t} - 1}}(x)).$  
+3. In the PPO method, the objective is to maximize the expectation of the advantage function instead of the reward value. By introducing the advantage function instead of the reward, the above objective can be written as  $\max_{\theta} \mathbb{E}_{x \sim \pi_{t-1}} I_{D_1}(x) \cdot \frac{\mathbf{P}_{\pi_\theta}(x)}{\mathbf{P}_{\pi_{t-1}}(x)} \mathbf{A}(x) - \mathbb{E}_{x \sim \pi_{t-1}} I_{D_2}(x) \cdot D_{KL}(\mathbf{P}_{\pi_\theta}(x) \| \mathbf{P}_{\pi_{t-1}}(x))$ .
+
+4. By introducing the knowledge retention penalty, the above objective is written as:  $\max_{\theta}\mathbb{E}_{x\sim \pi_{t - 1}}I_{D_1}(x)\cdot \frac{\mathbf{P}_{\pi_\theta}(x)}{\mathbf{P}_{\pi_{\mathbf{t} - 1}}(x)}\mathbf{A}(x) - \mathbb{E}_{x\sim \pi_{t - 1}}I_{D_2}(x)\cdot L^{KR}(x).$  
+5. In the CL task, the new policy  $\pi_t$  is generally initialized by the old policy  $\pi_{t-1}$ . In CPPO, we treat the  $\pi_{t-1}$  and  $\pi_t$  as the reference model and policy model respectively. Then, we consider the actor-critic version, the clipped ratio, and the entropy bonus used in PPO[32], the above objective can be written as  $\mathbf{J}(\theta)' = L^{I_{D_1} \cdot CLIP + I_{D_2} \cdot KR + VF}(\theta)$ .
+
+# From the objective Eq. 5 to the objective Eq. 6.
+
+Comparing  $\mathbf{J}(\theta)^{\prime}$  with  $\mathbf{J}(\theta) = L^{\alpha \cdot CLIP + \beta \cdot KR + VF}(\theta)$  in Eq. 6,  $\alpha (x)$  and  $\beta (x)$  are specialized as  $I_{D_1}(x)$  and  $I_{D_2}(x)$ . Hence, the objective Eq. 5 can be treated as a special case of Eq. 6.
+
+# C CASE STUDY OF SUMMARY TASK
+
+Table 10 presents a case where CPPO improves the performance on task-1 (r/relationships) after learning task-2 (r/others).
+
+Table 10: Example responses of Reddit TL;DR.  
+
+<table><tr><td>The original POST (the domain is r/relationships): 
+TITLE: [20F] My [22M] SO never wants to spend time with me. 
+POST: My boyfriend and I have been together off &amp; on for three years. We’ve had our fair share of issues, but I love him and I think he loves me. 
+We work opposite shifts, and it really cuts into our time together. Majorly. On the few days we both have off, every other weekend, he chooses to hang out with his friends. He works with his friends on the same schedule, and they are over every single day. 
+I always feel like I have to force him to do anything with me and I’m getting tired of it. I always complain to him that it would be nice if we could spend time together. But, he just says in over reacting. And that I can hang out with him and his friends. The thing is, we haven’t spent a day together just him and I in over a year. I like his friends but I just want a day where we can be together just us. I’m sick of being ignored for his friends, or video games and I don’t know what to do. 
+TL;DR:</td></tr><tr><td>The summary after learning task-1 (r/relationships): 
+CPPO (rPMS: 1.75): My SO never wants to spend time with me. He works with his friends on the same schedule, and they are over every single day. I always feel like I have to force him to do anything with me and I’m getting tired of it.</td></tr><tr><td>The summary after learning task-2 (r/others): 
+CPPO (rPMS: 1.82): My boyfriend prioritizes friends over time with me. Opposite work schedules strain time together. I’m tired of urging for attention. Seeking advice for reconnection. 
+PPO(In order) (rPMS: 1.44): The boyfriend has been with his boyfriend for three years and doesn’t want to spend time with his boyfriend anymore. The boyfriend’s boyfriend has been with him for three years and doesn’t want to spend time with him anymore. 
+PPO (rPMS:1.65): The boyfriend and I have been dating for three years and I love him but he is not interested in going out with his girlfriend.</td></tr></table>
+
+After learning the task-2, the model generates an accurate and concise summary. It more clearly conveys the main issue and emotions in the post, along with the desire for advice. And it also gets a higher rPMS (1.82 v.s. 1.75).
+
+From the three summaries after learning task-2, it can be observed that PPO(In order) seems to exhibit a more noticeable knowledge forgetting, with a seeming lack of understanding of the concept "boyfriend." This is due to the frequent occurrence of "boyfriend" in task-1 (r/relationships) and its almost absence in task-2 (r/others), resulting in a case of catastrophic forgetting. The PPO model still manages to convey the main essence of the text, but it overlooks some crucial details, such as "opposite work schedule" and "prioritizes friends over time with me", hence PPO lags behind CPPO in terms of rPMS value.
+
+# D BASELINES
+
+Supervise fine-tuning (SFT) directly learns the human-labeled summary through the cross-entropy loss.
+
+Online L2Reg penalizes the updating of model parameters through a L2 loss  $L_2^t (\theta) = \sum_i(\theta_t^i -\theta_{t - 1}^i)^2$  This regularization term mitigates the forgetting issue by applying a penalty for every parameter change.
+
+EWC (Kirkpatrick et al., 2017) uses fisher information to measure the parameter importance to old tasks, then slows down the update of the important parameters by L2 regularization.
+
+MAS (Aljundi et al., 2018) computes the importance of the parameters of a neural network in an unsupervised and online manner to restrict the updating of parameters in the next task.
+
+LwF (Li & Hoiem, 2018) is a knowledge-distillation-based method, which computes a smoothed version of the current responses for the new examples at the beginning of each task, minimizing their drift during training.
+
+TFCL (Aljundi et al., 2019) proposes to timely update the importance weights of the parameter regularization by detecting plateaus in the loss surface.
+
+PC (Kaplanis et al., 2019) is inspired by the biologically plausible synaptic model and proposes to consolidate memory directly at the behavioral level by knowledge distillation, aiming to mitigate catastrophic forgetting in the reinforcement learning context.
+
+HN-PPO (Schöpf et al., 2022) Hypernetwork-PPO is a continual model-free RL method employing a hyper network to learn multiple policies in a continual manner by using PPO.
+
+NLPO (Ramamurthy et al., 2022) NLPO learns to mask out less relevant tokens in-context as it trains via top-p sampling, which restricts tokens to the smallest possible set whose cumulative probability is greater than the probability parameter  $p$  (Holtzman et al., 2018).
+
+# E DISCUSSION
+
+# E.1 HYPERPARAMETER SENSITIVE ANALYSIS
+
+Due to the introduction of additional hyperparameters by CPPO, we conducted a sensitivity analysis of CPPO's hyperparameters. We conduct sensitivity analysis on five hyperparameters, including the threshold of times of standard variance  $k$ , the upper bound  $ub$  and lower bound  $lb$  of weights, the learning rate weights-lr of CPPO Heuristic, and the multiplier  $\tau$ . As shown in Table 11, the analysis of experimental results shows that our method is insensitive to the introduction of extra hyperparameters.
+
+Table 11: Hyperparameter sensitivity analysis of CPPO Heuristic and CPPO Learn.  
+
+<table><tr><td>Hyper-Parameters k / ub / lb</td><td>Method</td><td>Task-1 rPMS1(↑)</td><td>rouge (↑)</td><td>AT (↓)</td><td>Task-2 rPMS2(↑)</td><td>rouge (↑)</td><td>SFR (↓)</td></tr><tr><td>0.85 / 2.5 / 0.5</td><td>Heuristic</td><td>3.020 ±0.137</td><td>0.213 ±0.024</td><td>0.035 ±0.023</td><td>2.978 ±0.113</td><td>0.174 ±0.019</td><td>-0.164 ±0.009</td></tr><tr><td>k: 0.85 -&gt; 0.5</td><td>Heuristic</td><td>3.011 ±0.141</td><td>0.209 ±0.026</td><td>0.036 ±0.025</td><td>2.97 ±0.121</td><td>0.171 ±0.018</td><td>-0.162 ±0.011</td></tr><tr><td>k: 0.85 -&gt; 1.0</td><td>Heuristic</td><td>3.017 ±0.132</td><td>0.214 ±0.025</td><td>0.031 ±0.031</td><td>2.891 ±0.117</td><td>0.170 ±0.021</td><td>-0.151 ±0.010</td></tr><tr><td>ub: 2.5 -&gt; 1.5</td><td>Heuristic</td><td>2.982 ±0.124</td><td>0.205 ±0.031</td><td>0.040 ±0.042</td><td>2.809 ±0.124</td><td>0.173 ±0.023</td><td>-0.165 ±0.008</td></tr><tr><td>ub: 2.5 -&gt; 3.0</td><td>Heuristic</td><td>3.012 ±0.123</td><td>0.205 ±0.042</td><td>0.040 ±0.051</td><td>2.941 ±0.115</td><td>0.171 ±0.029</td><td>-0.166 ±0.013</td></tr><tr><td>lb: 0.5 -&gt; 0.1</td><td>Heuristic</td><td>3.011 ±0.162</td><td>0.221 ±0.051</td><td>0.024 ±0.041</td><td>2.809 ±0.115</td><td>0.167 ±0.019</td><td>-0.162 ±0.011</td></tr><tr><td>lb: 0.5 -&gt; 0.0</td><td>Heuristic</td><td>2.997 ±0.152</td><td>0.219 ±0.031</td><td>0.026 ±0.040</td><td>2.941 ±0.141</td><td>0.179 ±0.016</td><td>-0.161 ±0.010</td></tr><tr><td>weights-lr / τ</td><td>Method</td><td>rPMS1(↑)</td><td>rouge (↑)</td><td>AT (↓)</td><td>rPMS2(↑)</td><td>rouge (↑)</td><td>SFR (↓)</td></tr><tr><td>0.01 / 0.1</td><td>Learn</td><td>3.180 ±0.154</td><td>0.220 ±0.040</td><td>0.028 ±0.042</td><td>3.085 ±0.134</td><td>0.164 ±0.024</td><td>-0.161 ±0.008</td></tr><tr><td>weights-lr: 0.01 -&gt; 0.1</td><td>Learn</td><td>3.122 ±0.162</td><td>0.201 ±0.041</td><td>0.044 ±0.041</td><td>2.824 ±0.141</td><td>0.171 ±0.024</td><td>-0.155 ±0.012</td></tr><tr><td>weights-lr: 0.01 -&gt; 0.5</td><td>Learn</td><td>3.141 ±0.131</td><td>0.209 ±0.053</td><td>0.036 ±0.052</td><td>2.934 ±0.125</td><td>0.170 ±0.022</td><td>-0.162 ±0.016</td></tr><tr><td>τ: 0.1 -&gt; 0.01</td><td>Learn</td><td>3.042 ±0.137</td><td>0.211 ±0.046</td><td>0.034 ±0.054</td><td>2.89 ±0.151</td><td>0.168 ±0.026</td><td>-0.161 ±0.020</td></tr><tr><td>τ: 0.1 -&gt; 0.5</td><td>Learn</td><td>3.087 ±0.151</td><td>0.212 ±0.040</td><td>0.033 ±0.062</td><td>2.892 ±0.118</td><td>0.174 ±0.032</td><td>-0.161 ±0.014</td></tr><tr><td>τ: 0.1 -&gt; 1.0</td><td>Learn</td><td>3.072 ±0.148</td><td>0.209 ±0.039</td><td>0.036 ±0.051</td><td>2.967 ±0.129</td><td>0.172 ±0.021</td><td>-0.169 ±0.008</td></tr></table>
+
+# E.2 COMPLEXITY ANALYSIS
+
+In this section, we compare CPPO (learnable weights) with PPO in terms of time and memory occupation. The steps of CPPO are similar to PPO, except for the step of learning balance weights. By considering the time of the rollout step as our reference, we demonstrate that the time required to learn the weights is negligible compared to the overall training process of CPPO and PPO. Figure 5 illustrates the time required for learning balance weights and the time for making rollouts during the training of gpt2-s and gpt2-x1. For gpt2-s training, the ratio between the time spent on learning balance weights (approximately 8s) and the time taken for rollout steps (around 400s) is 1/50. This ratio decreases to 1/200 when training gpt2-x1, due to the fact that the time for learning balance weights remains the same, while the time for making rollouts increases to 1600s. Hence, our method does not significantly increase the time complexity of PPO, especially for training large language models.
+
+![](images/c4086c08bbb031104c33dc9349f68cdfbb7753d61f9ab7d37586de365a277b61.jpg)  
+(a) Time of learning weights
+
+![](images/b48ecc0ac587d38524914493ae48ce799223491e85063300a35893444840bf17.jpg)  
+(b) Time of rollout  
+Figure 5: Time of learning weights and time of making rollout.
+
+For memory occupation, we record the GPU memory allocation, GPU utilization, and the process memory in the training process of PPO and CPPO. Figure 6 illustrates the comparison of the above metrics between PPO and CPPO. CPPO, which learns the balance weights and calculates the knowledge retention loss, leads to higher allocation of GPU memory and process memory compared to PPO. Nevertheless, the improvements in GPU memory and process memory are not particularly substantial.
+
+![](images/56a38f45878a6d05ed23fe89d287ccb410858815d6534357cdbbac30e107f641.jpg)  
+(a) GPU Memory  
+Figure 6: GPU utilization and memory allocation when the algorithm runs for  $15+$  hours. Compared to the PPO method, our CPPO does not significantly utilize extra memory.
+
+![](images/a495f6de28de185b22eb71d028b84a256e96e8447ec5c5470b7199821a2269e2.jpg)  
+(b) GPU Utilization
+
+![](images/1dfcc0ee1bbdd369b4bdbde6bcf9d011b3e3e8345d0d0060df67877cc69319cd.jpg)  
+(c) Process Memory
+
+# F TASKS FOR STATIC LEARNING
+
+We compare PPO and CPPO on 3 static learning tasks, including random walks, sentiment text generation, and summary on CNN Daily Mail.
+
+# F.1 RANDOM WALKS
+
+The task(Chen et al., 2021) involves finding the shortest path on a directed graph. The reward is based on how optimal the path is compared to the shortest possible (bounded in [0, 1]). Paths are represented as strings of letters, with each letter corresponding to a node in the graph. For CPPO or
+
+PPO, a language model was fine-tuned to predict the next token in a sequence of returns-to-go (sum of future rewards), states, and actions.
+
+# F.2 SENTIMENT TEXT GENERATION
+
+This task focuses on generating positive movie reviews by fine-tuning a pre-trained model on the IMDB dataset using a sentiment reward function. We consider the IMDB(Maas et al., 2011) dataset for the task of generating text with positive sentiment. The dataset consists of  $25\mathrm{k}$  training,  $5\mathrm{k}$  validation and  $5\mathrm{k}$  test examples of movie review text with sentiment labels of positive and negative. We utilize a sentiment classifier (Sanh et al., 2019) trained on pairs of text and labels as a reward model, which provides sentiment scores indicating how positive a given piece of text is.
+
+# F.3 SUMMARY ON CNN DAILY MAIL
+
+The dataset for this task comprises 287k training examples, 13k validation examples, and 11k test examples. We utilize meteor(Banerjee & Lavie, 2005) as the reward function. T5 is chosen as the base language model due to its pre-training in a unified text-to-text framework and its ability to handle zero-shot capabilities.
+
+# F.4 EVALUATION ON NON-CONTINUAL LEARNING TASKS
+
+We compare the performance of PPO and CPPO on three static learning tasks, including randomwalks(Chen et al., 2021), sentiment text generation (Ramamurthy et al., 2022) on IMDB(Huang et al., 2021), and summarization on CNN Daily Mail (Hermann et al., 2015). As in the continual learning setting, we initialize our model with a pre-trained model and compute the knowledge retention penalty using both the policy model and the pre-trained model. Experimental results demonstrate that CPPO outperforms PPO in static learning settings. We observe the instability of PPO on the sentiment text generation task, while CPPO can learn stably. As shown in Figure 7, CPPO outperforms the PPO algorithm on all three tasks, which is attributed to CPPO's ability to enhance the learning of high-performance, high-variance, and overfitting samples while slowing down the learning of noisy samples.
+
+![](images/dfa84d1985920548e3e6fd8f473be1c144abacf55be9a58bacd343c754ad35e2.jpg)  
+(a) Randomwalks
+
+![](images/048fcbf5a94dee09a2d642c7a7fa83c33ee16604542008ee10119940cb5bf223.jpg)  
+(b)IMDB  
+Figure 7: Evaluation results on the test data during different training steps. a) The optimality scores in [0, 1], as compared to the shortest path. b) Positive sentiment scores provided by the distilbert trained on the IMDB dataset. c) METEOR (Metric for Evaluation of Translation with Explicit ORdering).
+
+![](images/3779c3a795ac9267eda6714e76f4b818e5c16ea1370669a33219626fbfd05c26.jpg)  
+(c) CNN Daily Mail
+
+# G DETAILS OF IMPLEMENTATION
+
+The algorithm of CPPO is presented in Algorithm 1. Step 3 is for learning an RM continually; step 7 is for computing balance weights; step 9 is for calculating CPPO loss; other steps are the same as the PPO algorithm. Our implementation is based on the open source library trlx<sup>6</sup>. The experiments on the SHP dataset are conducted in 4 Nvidia A100 GPUs with 80 GB of RAM, other experiments are conducted in 2 Nvidia Tesla V100 GPUs with 32 GB of RAM. To conserve GPU memory, we utilize CPU-Offload and Mixed-Precision techniques. We provide all hyperparameters used in both the PPO and CPPO algorithms in Table 12.
+
+Algorithm 1: CPPO  
+input :SFT model  $M_{SFT}$  ,critic model  $C$  ,reward model  $RM$  ,ppo epochs  $N$  ,ppo steps  $S$  ,query streams  $\mathbf{Q}_{\mathbf{t}}(t = 1,2,\dots,T)$  output:Aligend model  $M_T^{\prime}$    
+1 Initialize actor  $M_0\gets M_{SFT}$  .   
+for  $t = 1,2,\ldots ,T$  do update  $RM$  on new feedback by MAS; for epoch  $= 1,2,\ldots ,N$  do make actor  $M_{t - 1}$  generate response  $O_{t - 1}$  on prompts  $Q_{t}$  compute generation probability  $P_{\pi_{t - 1}}(x)$  of  $M_{t - 1}$  on  $O_{t - 1}$  ,reward  $R(x)$  of response  $O_{t - 1}$  by RM, state value evaluation  $v_{t - 1}$  by critic  $C$  and advantage  $A_{t - 1}(x)$  . compute a set of balance weights  $\{(\alpha (x),\beta (x))|x\in O_{t - 1}\}$  . for step  $= 1,2,\ldots ,S$  do compute the CPPO loss by Equation (5); update model  $M_t$  by Adam optimizer ; end   
+end
+
+Table 12: Hyperparameters of different tasks. Italic font denotes the CPPO-specific hyperparameters. For all tasks, we utilize the default PPO hyperparameters released by trlx.  
+CNN Random walks IMDB Reddit   
+seq-length 612 10 1024 550   
+total-steps 17200 10000 4000 25600   
+batch-size 12 100 128 8   
+model (huggingface) google/flan-t5-small CarperAI/randomwalks lvwerra/gpt2-imdb gpt2   
+num-layers-unfrozen 2 -1 2 8   
+optimizer adamw adamw adamw adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw Adamw
+
+![](images/422d0f07981d17c8a3416689abdf33fe99ba5997a0346d1eda8f5afa9bf9aad0.jpg)  
+Figure 8: Cross-domain evaluation of 18 reward models. The i-th row represents the RM trained on domain i, the j-th column represents the RM tested on domain j, and the value indicates the accuracy degradation value, namely,  $Acc_{test}^{j} - Acc_{test}^{i}$ .
+
+# H EVALUATION OF STANFORD HUMAN PREFERENCES BENCHMARK
+
+We have established a novel continual RLHF benchmark using the Stanford Human Preferences Dataset (SHP) (Ethayarajh et al., 2022). We assess CPPO and baselines on this benchmark within the context of a 3-task sequence setting.
+
+# H.1 DOMAIN INIncrementAL LEARNING SETTING
+
+The policy is required to continuously learn from three segments of the SHP dataset. The SHP dataset comprises 18 domains, which we divide into 3 parts based on the maximal errors of the out-of-distribution (OOD) generalization(Shen et al., 2021). We employ the SteamSHP-flan-t5-xl model (Ethayarajh et al., 2022), developed by Stanford, as the reference preference model (rPM) for assessing responses to SHP prompts. The SteamSHP-flan-t5-xl model<sup>7</sup> is trained on the combination of the SHP (all domains) and the HH-RLHF(Bai et al., 2022a) human preference data.
+
+To create more challenging DIL tasks, we individually trained 18 reward models (based on Llama-7b) on 18 domains of SHP data and evaluated each reward model on the test set of the 18 domains, resulting in an accuracy difference matrix of size  $18 \times 18$  as shown in Figure 8. In this matrix, the row coordinates represent the training domains, and the column coordinates represent the evaluation domains. The elements in the matrix represent the relative decrease in performance on the evaluation domain compared to the training domain (both evaluated on test sets from various domains). Based on this accuracy difference matrix, we divided the 18 domains into 3 groups (each has 6 domains). This division ensures that there will be a significant performance decrease, i.e., the largest error of OOD generalization, when evaluated on domains from different groups. For example, the RM trained in the first group (from "explainlikeimfive" to "changemyview") has large errors in the third group (from "legaladvce" to "vet"). Refer to Table 13 for the distribution of samples across various domains.
+
+Table 13: Number of posts in the SHP dataset by subreddit.  
+
+<table><tr><td rowspan="2">Task ID</td><td rowspan="2">subreddit
+ALL</td><td>train</td><td>valid</td><td>test</td><td>total</td><td>% of All</td></tr><tr><td>348718</td><td>18436</td><td>18409</td><td>385563</td><td>100.00%</td></tr><tr><td rowspan="6">Task 1</td><td>explainlikeimfive</td><td>19592</td><td>1014</td><td>1070</td><td>21676</td><td>5.62%</td></tr><tr><td>askanthropology</td><td>3910</td><td>203</td><td>268</td><td>4381</td><td>1.14%</td></tr><tr><td>askcarguys</td><td>3227</td><td>159</td><td>117</td><td>3503</td><td>0.91%</td></tr><tr><td>asksciencefiction</td><td>29382</td><td>1576</td><td>1987</td><td>32945</td><td>8.54%</td></tr><tr><td>asksocialscience</td><td>2706</td><td>147</td><td>188</td><td>3041</td><td>0.79%</td></tr><tr><td>changemyview</td><td>38173</td><td>1637</td><td>1836</td><td>41646</td><td>10.80%</td></tr><tr><td rowspan="6">Task 2</td><td>askacademia</td><td>31450</td><td>2095</td><td>1708</td><td>35253</td><td>9.14%</td></tr><tr><td>askculinary</td><td>45710</td><td>2094</td><td>2563</td><td>50367</td><td>13.06%</td></tr><tr><td>askengineers</td><td>57096</td><td>3154</td><td>2638</td><td>62888</td><td>16.31%</td></tr><tr><td>askphilosophy</td><td>10307</td><td>608</td><td>677</td><td>11592</td><td>3.01%</td></tr><tr><td>askphysics</td><td>7364</td><td>409</td><td>587</td><td>8360</td><td>2.17%</td></tr><tr><td>askscience</td><td>13316</td><td>899</td><td>977</td><td>15192</td><td>3.94%</td></tr><tr><td rowspan="6">Task 3</td><td>legaladvice</td><td>21170</td><td>1106</td><td>1011</td><td>23287</td><td>6.04%</td></tr><tr><td>askbaking</td><td>44007</td><td>2096</td><td>1544</td><td>47647</td><td>12.36%</td></tr><tr><td>askdocs</td><td>6449</td><td>315</td><td>455</td><td>7219</td><td>1.87%</td></tr><tr><td>askhistorians</td><td>3264</td><td>113</td><td>164</td><td>3541</td><td>0.92%</td></tr><tr><td>askhr</td><td>8295</td><td>641</td><td>395</td><td>9331</td><td>2.42%</td></tr><tr><td>askvet</td><td>3300</td><td>170</td><td>224</td><td>3694</td><td>0.96%</td></tr></table>
+
+# H.2 EVALUATION METRIC FOR CONTINUAL LEARNING
+
+Overall performance is commonly assessed using average accuracy (AA)(Chaudhry et al., 2018; Lopez-Paz & Ranzato, 2017) and average incremental accuracy (AIA) (Douillard et al., 2020; Hou et al., 2019). In our evaluation framework, accuracy is replaced by the reference Preference Score, which ranges from 0 to 1. Let  $a_{k,j} \in [0,1]$  represent the reference Preference Score evaluated on the test set of the  $j$ -th task after incremental learning of the  $k$ -th task ( $j \leq k$ ). The two metrics at the $k$-th task are then defined as:
+
+$$
+\mathrm {A A} _ {k} = \frac {1}{k} \sum_ {j = 1} ^ {k} a _ {k, j}, \tag {8}
+$$
+
+$$
+\mathrm {A I A} _ {k} = \frac {1}{k} \sum_ {i = 1} ^ {k} \mathrm {A A} _ {i}, \tag {9}
+$$
+
+where AA signifies the current overall performance, and AIA additionally captures the historical fluctuations.
+
+Memory stability can be evaluated through forgetting measure (FM)(Chaudhry et al., 2018) and backward transfer (BWT) (Lopez-Paz & Ranzato, 2017). Regarding the former, the forgetting of a task is computed as the difference between its best performance achieved in the past and its current performance:
+
+$$
+f _ {j, k} = \max  _ {i \in \{1, \dots , k - 1 \}} \left(a _ {i, j} - a _ {k, j}\right), \forall j <   k. \tag {10}
+$$
+
+FM at the  $k$ -th task is the average forgetting of all old tasks:
+
+$$
+\mathrm {F M} _ {k} = \frac {1}{k - 1} \sum_ {j = 1} ^ {k - 1} f _ {j, k}. \tag {11}
+$$
+
+Regarding the latter, BWT assesses the collective impact of learning the  $k$ -th task on all previous tasks:
+
+$$
+\mathrm {B W T} _ {k} = \frac {1}{k - 1} \sum_ {j = 1} ^ {k - 1} \left(a _ {k, j} - a _ {j, j}\right), \tag {12}
+$$
+
+# H.3 EVALUATION RESULTS
+
+We utilize the Llama-7B as the backbone of the policy model and reward model. When training the reward model, we fine-tune the all of parameters. When training the RLHF model, we only fine-tune the top 8 layers.
+
+The experiments are run for 3 random seeds, the final results are shown in Table 14. We found that using reward and policy models based on Llama-7B, as opposed to training with gpt2-xl as the backbone, significantly improves the training stability. It is related to larger reward models being less susceptible to reward attacks(Gao et al., 2022).
+
+From Table 14, we observe that the Iterated RLHF method has a significant effect in preventing forgetting. Since it re-trains the reward model and policy model from scratch at each task, resulting in higher memory and computational complexity. CPPO, compared to PPO, shows a noticeable improvement in overall performance, and it outperforms PPO in the Memory stability metric. This indicates that CPPO can effectively learning varying human preferences.
+
+Table 14: Performance on DIL setting. The range of SteamSHP score is [0, 1].  
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">Task 1 SteamSHP (↑)</td><td rowspan="2">Task 2 SteamSHP (↑)</td><td rowspan="2">Task 3 SteamSHP (↑)</td><td colspan="2">Overall performance</td><td colspan="2">Memory stability</td></tr><tr><td>AA (↑)</td><td>AIA (↑)</td><td>BWT (↑)</td><td>FM (↓)</td></tr><tr><td>SFT (In order)</td><td>0.806 ±0.0101</td><td>0.836 ±0.0103</td><td>0.853 ±0.0103</td><td>0.832 ±0.0061</td><td>0.837 ±0.0039</td><td>-0.022 ±0.0094</td><td>0.022 ±0.0094</td></tr><tr><td>SFT (multi-tasks)</td><td>0.831 ±0.0266</td><td>0.847 ±0.0145</td><td>0.858 ±0.0114</td><td>0.845 ±0.0147</td><td>0.844 ±0.0082</td><td>-0.006 ±0.0183</td><td>0.009±0.0160</td></tr><tr><td>Iterated RLHF</td><td>0.869 ±0.0583</td><td>0.88 ±0.0490</td><td>0.887 ±0.0421</td><td>0.879 ±0.0488</td><td>0.874 ±0.0433</td><td>-0.0004 ±0.0186</td><td>0.003 ±0.0162</td></tr><tr><td>PPO</td><td>0.853 ±0.0573</td><td>0.879 ±0.0428</td><td>0.889 ±0.0369</td><td>0.874 ±0.0433</td><td>0.877 ±0.0378</td><td>-0.017 ±0.0351</td><td>0.020 ±0.0327</td></tr><tr><td>CPPO (Heuristic)</td><td>0.864 ±0.0557</td><td>0.89 ±0.0448</td><td>0.894 ±0.0350</td><td>0.883 ±0.0429</td><td>0.887 ±0.0391</td><td>-0.015 ±0.0321</td><td>0.018 ±0.0300</td></tr><tr><td>CPPO (Learn)</td><td>0.872 ±0.0544</td><td>0.898 ±0.0450</td><td>0.899 ±0.0342</td><td>0.89 ±0.0424</td><td>0.894 ±0.0389</td><td>-0.013 ±0.0298</td><td>0.016 ±0.0281</td></tr></table>
+
+# I LIMITATION: THE RISK OF OVER-OPTIMIZATION
+
+We have observed that both PPO and CPPO have the potential risk of achieving high rewards while generating poor summaries. This issue is depicted in Figure 9, where the policy model tends to overoptimize against the RM when trained for 100k steps (390 epochs). Over time, the policy becomes excessively focused on maximizing rewards without adequately considering the quality of the generated summaries. To address the risk of optimization, various strategies can be employed. One approach is to train an additional RM to evaluate the policy during training. This allows for evaluating the policy's performance using an external objective metric, providing a more robust measure of the summary quality. Another strategy is to implement early stopping, where the training process is halted based on the quality of the generated summaries or other external metrics. Instead of solely focusing on maximizing rewards, we prioritize the quality of the generated summaries. Training is halted when the summary quality
+
+reaches a certain threshold or shows no further improvement. This approach ensures that the generated summaries not only maximize rewards but also maintain a high level of quality.
+
+![](images/5b0a36e9870f67e95cf4bf2fbddfe40cc21580fe41a150c30e481cbde696cfa3.jpg)  
+Figure 9: Overoptimize against the reward model. After training 100k steps, the RM score (RMS) on the test data has a high bias compared with the rPMS.
+
+Recent research (Gao et al., 2022) has noted an interesting observation regarding larger policy models. It has been found that as the size of the policy models increases, they become less susceptible to over-optimization against the RM. This suggests that scaling up the model size can potentially alleviate the over-optimization issue by introducing more complexity and capacity into the policy model, making it harder for the model to excessively optimize solely for rewards without considering the summary quality.
+
+In summary, mitigating the risk of over-optimization in PPO and CPPO can be achieved through strategies such as training additional reward models, implementing early stopping, and considering larger policy models. These measures aim to strike a balance between achieving high rewards and generating high-quality summaries, ensuring that the models generalize well and produce reliable results even on unseen data.
+
+# J BROADER IMPACT
+
+The broader impact of our proposed CPPO method is significant for both researchers and practitioners in the field of NLP. By addressing the limitations of existing RLHF-based LMs, we enable the continual alignment of these models with human preferences, opening up new possibilities for their widespread adoption and deployment.
+
+One important implication of our work is the reduction of time and computational costs associated with retraining LMs. In many real-world scenarios, complete retraining is impractical due to resource constraints and data privacy. By introducing sample-wise weights and enhancing policy learning while retaining valuable past experiences, CPPO offers a more efficient and practical alternative. This efficiency allows practitioners to keep LMs up-to-date with evolving human preferences without incurring the substantial overhead of retraining, making them more accessible and applicable across a range of applications.
+
+The practical implications of our work extend beyond research and development. Industries that heavily rely on LMs, such as customer service, virtual assistants, and content generation, stand to benefit from the continual alignment provided by CPPO. The improved performance and adaptability of LMs enable more personalized and effective interactions with users, enhancing user satisfaction and overall user experience. Additionally, CPPO's ability to align with human preferences consistently enables the development of more inclusive and fair AI systems that better understand and respect diverse user needs and values.
+
+In summary, our CPPO method has broad implications for the NLP community and beyond. By addressing the challenges associated with RLHF-based LMs, our approach offers a practical and efficient solution for continually aligning with human preferences while reducing retraining costs and preserving data privacy. These advancements promote the wider adoption and responsible use of LMs in various domains, leading to more personalized, inclusive, and trustworthy AI systems.

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