Daily Papers

On-policy Self-distillation (OPSD) has proven effective for post-training large language models by constructing a teacher conditioned on privileged references. However, existing approaches keep the teacher fixed either throughout training by consistently exposing it to the full reference, or within each response by adaptively varying partial reference exposure only across responses. In this paper, we argue that neither of them is sufficient. Instead, every token needs its own teacher, as the teacher preference can vary token by token within the same response. Through a teacher-intervention pilot study, we validate that the teacher preference differs across tokens, and reveal that a preferred teacher can be identified for each token through majority voting and KL-based selection. Motivated by these findings, we propose Multi-teacher Adaptive On-policy Self-Distillation (MTA-OPSD), the first token-level adaptive OPSD method. Our method constructs a multi-teacher pool consisting of candidate teachers, and enables every token to adaptively select its preferred teacher during training. Experiments with Qwen3 models on mathematical reasoning tasks show that MTA-OPSD consistently outperforms existing OPSD approaches with an average gain of up to +5.9 over the base model, highlighting the importance of adapting teacher supervision at the token level. The code is available at https://github.com/xingzhejun/MTA-OPSD.

Distilling pretrained softmax attention Transformers into more efficient hybrid architectures that interleave softmax and linear attention layers is a promising approach for improving the inference efficiency of LLMs without requiring expensive pretraining from scratch. A critical factor in the conversion process is layer selection, i.e., deciding on which layers to convert to linear attention variants. This paper describes a simple and efficient recipe for layer selection that uses layer importance scores derived from a small amount of training on generic text data. Once the layers have been selected we use a recent pipeline for the distillation process itself \citep[RADLADS;][]{goldstein2025radlads}, which consists of attention weight transfer, hidden state alignment, KL-based distribution matching, followed by a small amount of finetuning. We find that this approach is more effective than existing approaches for layer selection, including heuristics that uniformly interleave linear attentions based on a fixed ratio, as well as more involved approaches that rely on specialized diagnostic datasets.

Structured pruning of large language models (LLMs) offers substantial efficiency improvements by removing entire hidden units, yet current approaches often suffer from significant performance degradation, particularly in zero-shot settings, and necessitate costly recovery techniques such as supervised fine-tuning (SFT) or adapter insertion. To address these critical shortcomings, we introduce NIRVANA, a novel pruning method explicitly designed to balance immediate zero-shot accuracy preservation with robust fine-tuning capability. Leveraging a first-order saliency criterion derived from the Neural Tangent Kernel under Adam optimization dynamics, NIRVANA provides a theoretically grounded pruning strategy that respects essential model training behaviors. To further address the unique challenges posed by structured pruning, NIRVANA incorporates an adaptive sparsity allocation mechanism across layers and modules (attention vs. MLP), which adjusts pruning intensity between modules in a globally balanced manner. Additionally, to mitigate the high sensitivity of pruning decisions to calibration data quality, we propose a simple yet effective KL divergence-based calibration data selection strategy, ensuring more reliable and task-agnostic pruning outcomes. Comprehensive experiments conducted on Llama3, Qwen, and T5 models demonstrate that NIRVANA outperforms existing structured pruning methods under equivalent sparsity constraints, providing a theoretically sound and practical approach to LLM compression. The code is available at https://github.com/iDEA-iSAIL-Lab-UIUC/NIRVANA.

Sparse on-policy distillation (OPD) allocates teacher supervision to a small subset of tokens in student-generated trajectories. However, useful teacher guidance can yield a noisy update when its gradient is estimated from a sampled next token. We study this estimation problem at a fixed prefix in information geometry and propose an information-efficiency ratio (IER) based on a signal-to-noise decomposition. IER characterizes relative gradient estimation error under an optimal scalar baseline. A candidate-set approximation enables token selection based on IER and its combination with existing usefulness scores, while retaining the sampled reverse-KL training objective. On mathematical and medical reasoning tasks, adding IER improves existing selectors in multiple settings, with sparse configurations matching or exceeding full OPD without token selection at small token budgets of 0.1\%--1\%. These results support accounting for both usefulness and gradient-estimation reliability when allocating sparse supervision. Our code is available at https://github.com/BruceSheng1202/IER-OPD.

Large Language Models (LLMs) face significant computational bottlenecks during inference due to the quadratic complexity of self-attention mechanisms, particularly as context lengths increase. We introduce SpecAttn, a novel training-free approach that seamlessly integrates with existing speculative decoding techniques to enable efficient sparse attention in pre-trained transformers. Our key insight is to exploit the attention weights already computed by the draft model during speculative decoding to identify important tokens for the target model, eliminating redundant computation while maintaining output quality. SpecAttn employs three core techniques: KL divergence-based layer alignment between draft and target models, a GPU-optimized sorting-free algorithm for top-p token selection from draft attention patterns, and dynamic key-value cache pruning guided by these predictions. By leveraging the computational work already performed in standard speculative decoding pipelines, SpecAttn achieves over 75% reduction in key-value cache accesses with a mere 15.29% increase in perplexity on the PG-19 dataset, significantly outperforming existing sparse attention methods. Our approach demonstrates that speculative execution can be enhanced to provide approximate verification without significant performance degradation.

On-policy distillation has recently emerged as a promising alternative to standard sequence-level imitation, training a student by scoring its own rollouts with a teacher model. However, we observe ``Off-policy Teacher Decay'' problem in this paradigm: for the later tokens, with student's earlier trajectory as context that is off-policy to the teacher, the teacher's ability to produce a corrective score would decay, and may fall back to token-completion behavior learned in the pre-training stage. We empirically verify this problem, and we propose Early Stopping Rollout (ESR) to fix it: a simple yet effective distillation strategy that simply restricts the rollout generation to the first response tokens. We show that ESR both surpasses the full rollout OPD performance across model size, family, tasks and training regime, and exhibit much higher GPU efficiency and training stability, especially under cross model family scenarios. We further investigate the mechanism behind this surprising performance and discovered "Cascading Alignment" and "Sub-mode Commitment" effect of ESR that may explain why it works effectively and even sometimes exceeding the teacher model performance. Besides, we show that this position-based token selection strategy cannot be fully explainable by KL divergence and entropy signals.

Agentic reinforcement learning has advanced large language models (LLMs) to reason through long chain-of-thought trajectories while interleaving external tool use. Existing approaches assume a fixed inventory of tools, limiting LLM agents' adaptability to new or evolving toolsets. We present AutoTool, a framework that equips LLM agents with dynamic tool-selection capabilities throughout their reasoning trajectories. We first construct a 200k dataset with explicit tool-selection rationales across 1,000+ tools and 100+ tasks spanning mathematics, science, code generation, and multimodal reasoning. Building on this data foundation, AutoTool employs a dual-phase optimization pipeline: (i) supervised and RL-based trajectory stabilization for coherent reasoning, and (ii) KL-regularized Plackett-Luce ranking to refine consistent multi-step tool selection. Across ten diverse benchmarks, we train two base models, Qwen3-8B and Qwen2.5-VL-7B, with AutoTool. With fewer parameters, AutoTool consistently outperforms advanced LLM agents and tool-integration methods, yielding average gains of 6.4% in math & science reasoning, 4.5% in search-based QA, 7.7% in code generation, and 6.9% in multimodal understanding. In addition, AutoTool exhibits stronger generalization by dynamically leveraging unseen tools from evolving toolsets during inference.

Alignment is crucial for text-to-image (T2I) models to ensure that generated images faithfully capture user intent while maintaining safety and fairness. Direct Preference Optimization (DPO), prominent in large language models (LLMs), is extending its influence to T2I systems. This paper introduces DPO-Kernels for T2I models, a novel extension enhancing alignment across three dimensions: (i) Hybrid Loss, integrating embedding-based objectives with traditional probability-based loss for improved optimization; (ii) Kernelized Representations, employing Radial Basis Function (RBF), Polynomial, and Wavelet kernels for richer feature transformations and better separation between safe and unsafe inputs; and (iii) Divergence Selection, expanding beyond DPO's default Kullback-Leibler (KL) regularizer by incorporating Wasserstein and R'enyi divergences for enhanced stability and robustness. We introduce DETONATE, the first large-scale benchmark of its kind, comprising approximately 100K curated image pairs categorized as chosen and rejected. DETONATE encapsulates three axes of social bias and discrimination: Race, Gender, and Disability. Prompts are sourced from hate speech datasets, with images generated by leading T2I models including Stable Diffusion 3.5 Large, Stable Diffusion XL, and Midjourney. Additionally, we propose the Alignment Quality Index (AQI), a novel geometric measure quantifying latent-space separability of safe/unsafe image activations, revealing hidden vulnerabilities. Empirically, we demonstrate that DPO-Kernels maintain strong generalization bounds via Heavy-Tailed Self-Regularization (HT-SR). DETONATE and complete code are publicly released.

Jev-style decision models return categorical probability distributions over predefined options without generating free-form text, enabling software systems to act on their outputs directly. In this work, we investigate the extent to which general-purpose LLMs already possess this capability out of the box, and when fine-tuning is actually necessary. We present LLM-as-Jev, an architecture-preserving framework that extracts calibrated decisions directly from next-token probabilities over bracketed numeric identifiers. LLM-as-Jev provides both a training-free inference recipe and a fine-tuning objective that optimizes candidate selection via a tree-factorized listwise loss while anchoring auxiliary predictions to the base model using KL divergence penalties. Evaluating on Qwen3.5-4B and Qwen3-0.6B, we find that modern LLMs are inherently effective decision models: without training, the 4B model matches community Jev-style models built on the same backbone, outperforms letter-logit readouts, supports arbitrary option counts, and natively handles multimodal decisions over images. Fine-tuning provides targeted rather than universal benefits -- substantially improving weaker models and specific tasks (such as many-option intent routing), but offering diminishing returns for strong backbones. Crucially, our KL anchors prevent behavioral degradation in conversational text generation, with LoRA delivering the strongest performance on capable models.

Large language models (LLMs) often exhibit systematic preferences for certain answer choices when responding to multiple-choice questions-a behavior known as selection bias. This bias reduces the accuracy and reliability of LLM outputs, limiting their usefulness in decision-critical applications. While prior work has focused on adjusting model inputs or outputs to mitigate this issue, our work takes a fundamentally different approach by identifying and removing the internal sources of bias. We introduce two methods: Bias Node Pruning (BNP), which prunes parameters that contribute to selection bias, and Auxiliary Option Injection (AOI), which introduces an additional answer choice to reduce bias in both white-box and black-box settings. To address the shortcomings of existing evaluation metrics, we propose Choice Kullback-Leibler Divergence (CKLD), a new metric that captures distributional imbalances in model predictions. Experiments on three LLMs across multiple datasets demonstrate that our methods consistently improve answer accuracy while reducing selection bias, providing a robust solution for both open- and closed-source models.

High-dimensional datasets require effective feature selection to improve predictive performance, interpretability, and robustness. We propose and evaluate feature selection methods for tabular datasets based on Kolmogorov-Arnold networks (KANs), which parameterize feature transformations through splines, enabling direct access to interpretable importance measures. We introduce four KAN-based selectors (KAN-L1, KAN-L2, KAN-SI, KAN-KO) and compare them against classical baselines (LASSO, Random Forest, Mutual Information, SVM-RFE) across multiple classification and regression tabular dataset benchmarks. Average (over three retention levels: 20\%, 40\%, and 60\%) F1 scores and R^2 score results reveal that KAN-based selectors, particularly KAN-L2, KAN-L1, KAN-SI, and KAN-KO, are competitive with and sometimes superior to classical baselines in structured and synthetic datasets. However, KAN-L1 is often too aggressive in regression, removing useful features, while KAN-L2 underperforms in classification, where simple coefficient shrinkage misses complex feature interactions. KAN-L2 and KAN-SI provide robust performance on noisy regression datasets and heterogeneous datasets, aligning closely with ensemble predictors. In classification tasks, KAN selectors such as KAN-L1, KAN-KO, and KAN-SI sometimes surpass the other selectors by eliminating redundancy, particularly in high-dimensional multi-class data. Overall, our findings demonstrate that KAN-based feature selection provides a powerful and interpretable alternative to traditional methods, capable of uncovering nonlinear and multivariate feature relevance beyond sparsity or impurity-based measures.

We study the data selection problem, whose aim is to select a small representative subset of data that can be used to efficiently train a machine learning model. We present a new data selection approach based on k-means clustering and sensitivity sampling. Assuming access to an embedding representation of the data with respect to which the model loss is H\"older continuous, our approach provably allows selecting a set of ``typical'' k + 1/varepsilon^2 elements whose average loss corresponds to the average loss of the whole dataset, up to a multiplicative (1pmvarepsilon) factor and an additive varepsilon lambda Phi_k, where Phi_k represents the k-means cost for the input embeddings and lambda is the H\"older constant. We furthermore demonstrate the performance and scalability of our approach on fine-tuning foundation models and show that it outperforms state-of-the-art methods. We also show how it can be applied on linear regression, leading to a new sampling strategy that surprisingly matches the performances of leverage score sampling, while being conceptually simpler and more scalable.

Kullback-Leiber divergence has been widely used in Knowledge Distillation (KD) to compress Large Language Models (LLMs). Contrary to prior assertions that reverse Kullback-Leibler (RKL) divergence is mode-seeking and thus preferable over the mean-seeking forward Kullback-Leibler (FKL) divergence, this study empirically and theoretically demonstrates that neither mode-seeking nor mean-seeking properties manifest in KD for LLMs. Instead, RKL and FKL are found to share the same optimization objective and both converge after a sufficient number of epochs. However, due to practical constraints, LLMs are seldom trained for such an extensive number of epochs. Meanwhile, we further find that RKL focuses on the tail part of the distributions, while FKL focuses on the head part at the beginning epochs. Consequently, we propose a simple yet effective Adaptive Kullback-Leiber (AKL) divergence method, which adaptively allocates weights to combine FKL and RKL. Metric-based and GPT-4-based evaluations demonstrate that the proposed AKL outperforms the baselines across various tasks and improves the diversity and quality of generated responses.

Speculative decoding accelerates autoregressive large language model (LLM) inference by using a lightweight draft model to propose candidate tokens that are then verified in parallel by the target model. The speedup is significantly determined by the acceptance rate, yet standard training minimizes Kullback-Leibler (KL) divergence as a proxy objective. While KL divergence and acceptance rate share the same global optimum, small draft models, having limited capacity, typically converge to suboptimal solutions where minimizing KL does not guarantee maximizing acceptance rate. To address this issue, we propose LK losses, special training objectives that directly target acceptance rate. Comprehensive experiments across four draft architectures and six target models, ranging from 8B to 685B parameters, demonstrate consistent improvements in acceptance metrics across all configurations compared to the standard KL-based training. We evaluate our approach on general, coding and math domains and report gains of up to 8-10% in average acceptance length. LK losses are easy to implement, introduce no computational overhead and can be directly integrated into any existing speculator training framework, making them a compelling alternative to the existing draft training objectives.

A simple and effective method for the alignment of generative models is the best-of-n policy, where n samples are drawn from a base policy, and ranked based on a reward function, and the highest ranking one is selected. A commonly used analytical expression in the literature claims that the KL divergence between the best-of-n policy and the base policy is equal to log (n) - (n-1)/n. We disprove the validity of this claim, and show that it is an upper bound on the actual KL divergence. We also explore the tightness of this upper bound in different regimes. Finally, we propose a new estimator for the KL divergence and empirically show that it provides a tight approximation through a few examples.

Selecting the best response from multiple small-model samples using a stronger scorer is a simple inference-time strategy, but fails when the small model has already committed to incorrect reasoning paths. PRM guided search avoids this by scoring candidate continuations during generation, but requires a reward model trained with step-level labels. We propose Chunk-Level Guided Generation, a training-free alternative that uses an off-the-shelf large language model as a process scorer. At each step, a small model samples k fixed-length candidate chunks, while the larger model scores the candidates using likelihoods without generating any text. The selected chunk is committed before the next step, steering generation before errors can propagate. We instantiate this framework with two selection rules: Likelihood-Guided Selection (LGS), which selects the chunk with the highest length-normalized large-model log-probability, and Contrastive-Guided Selection (CGS), which subtracts the small model's log-probability to favor chunks where the large model's preference diverges from the small model's. We show that scoring variable-length reasoning steps with large-model likelihoods is unreliable due to a systematic length bias that persists even after length normalization, and that fixed-length chunks avoid this confound. On GSM8K, MATH, Minerva Math, AMC23, and AIME24 with Qwen2.5-1.5B guided by Qwen2.5-32B and Llama-3.2-1B guided by Llama-3.1-70B, CGS outperforms majority voting by up to 28 pp and, under matched guidance budgets, matches or outperforms Qwen2.5-Math-PRM-72B guided search on most benchmarks without reward-model training. With Qwen2.5-7B guided by Qwen2.5-72B, CGS reaches 81.8% on MATH and 63.6% on Minerva Math at k=16, surpassing majority voting by 4--6 pp. Finally, Chunk-Level Guided Generation produces substantially shorter reasoning traces than PRM guided search.

Selecting a suitable training dataset is crucial for both general-domain (e.g., GPT-3) and domain-specific (e.g., Codex) language models (LMs). We formalize this data selection problem as selecting a subset of a large raw unlabeled dataset to match a desired target distribution, given some unlabeled target samples. Due to the large scale and dimensionality of the raw text data, existing methods use simple heuristics to select data that are similar to a high-quality reference corpus (e.g., Wikipedia), or leverage experts to manually curate data. Instead, we extend the classic importance resampling approach used in low-dimensions for LM data selection. Crucially, we work in a reduced feature space to make importance weight estimation tractable over the space of text. To determine an appropriate feature space, we first show that KL reduction, a data metric that measures the proximity between selected data and the target in a feature space, has high correlation with average accuracy on 8 downstream tasks (r=0.89) when computed with simple n-gram features. From this observation, we present Data Selection with Importance Resampling (DSIR), an efficient and scalable algorithm that estimates importance weights in a reduced feature space (e.g., n-gram features in our instantiation) and selects data with importance resampling according to these weights. When training general-domain models (target is Wikipedia + books), DSIR improves over random selection and heuristic filtering baselines by 2--2.5% on the GLUE benchmark. When performing continued pretraining towards a specific domain, DSIR performs comparably to expert curated data across 8 target distributions.

Combining the answers a large language model (LLM) samples for a question into one decision is a test-time information fusion problem, usually solved by majority voting. Voting is unreliable on difficult questions, where the sampled answers share correlated errors, so the wrong answer can win and drawing more samples makes the decision worse. Selecting a candidate by reading a correctness signal from the model's hidden states is a promising alternative, but its accuracy varies across models and tasks, and no measure indicates when it can be trusted. In this paper, we propose CASE (Correctness-Axis SElection), a dynamic selection combiner that trains a linear gate on the answer-token hidden state and selects the highest-scoring candidate. Its main contribution is decodability, a leakage-free measure of how well the gate ranks a question's correct candidates above its incorrect ones, which predicts whether hidden-state selection will outperform voting. A conventional probe appears accurate only because of question-identity leakage, which vanishes under question-grouped evaluation. On held-out data, decodability predicts the accuracy gain of selection over voting with a Pearson correlation r=0.75 and a decision threshold near AUC=0.60. Across general and medical LLMs, CASE improves over voting by up to 19 points on medium-difficulty questions and 16.8 points on hard questions. Decodability depends on the aligned knowledge a model must recall, not on its scale, and its prediction transfers to an unseen scientific domain within 3.8 points. It thus provides a practical criterion, measurable in advance for a given model and task, for choosing between learned selection and majority voting.

Generative reward models with parallel sampling have enabled effective test-time scaling for reasoning tasks. Current approaches employ pointwise scoring of individual solutions or pairwise comparisons. However, pointwise methods underutilize LLMs' comparative abilities, while pairwise methods scale inefficiently with larger sampling budgets. We introduce GenSelect, where the LLM uses long reasoning to select the best solution among N candidates. This leverages LLMs' comparative strengths while scaling efficiently across parallel sampling budgets. For math reasoning, we demonstrate that reasoning models, such as QwQ and DeepSeek-R1-0528, excel at GenSelect, outperforming existing scoring approaches with simple prompting.

The lottery ticket hypothesis posits the existence of ``winning tickets'' within a randomly initialized neural network. Do winning tickets exist for LLMs in fine-tuning scenarios? How can we find such winning tickets? In this paper, we propose KS-Lottery, a method to identify a small subset of LLM parameters highly effective in multilingual fine-tuning. Our key idea is to use Kolmogorov-Smirnov Test to analyze the distribution shift of parameters before and after fine-tuning. We further theoretically prove that KS-Lottery can find the certified winning tickets in the embedding layer, fine-tuning on the found parameters is guaranteed to perform as well as full fine-tuning. Comparing KS-Lottery with other parameter-efficient tuning algorithms on translation tasks, the experimental results show that KS-Lottery finds a much smaller set of parameters for fine-tuning while achieving the comparable performance as full fine-tuning LLM. Surprisingly, we find that fine-tuning 18 tokens' embedding of LLaMA suffices to reach the fine-tuning translation performance. Code and model will be released to the public.

Selecting the best code solution from multiple generated ones is an essential task in code generation, which can be achieved by using some reliable validators (e.g., developer-written test cases) for assistance. Since reliable test cases are not always available and can be expensive to build in practice, researchers propose to automatically generate test cases to assess code solutions. However, when both code solutions and test cases are plausible and not reliable, selecting the best solution becomes challenging. Although some heuristic strategies have been proposed to tackle this problem, they lack a strong theoretical guarantee and it is still an open question whether an optimal selection strategy exists. Our work contributes in two ways. First, we show that within a Bayesian framework, the optimal selection strategy can be defined based on the posterior probability of the observed passing states between solutions and tests. The problem of identifying the best solution is then framed as an integer programming problem. Second, we propose an efficient approach for approximating this optimal (yet uncomputable) strategy, where the approximation error is bounded by the correctness of prior knowledge. We then incorporate effective prior knowledge to tailor code generation tasks. Both theoretical and empirical studies confirm that existing heuristics are limited in selecting the best solutions with plausible test cases. Our proposed approximated optimal strategy B4 significantly surpasses existing heuristics in selecting code solutions generated by large language models (LLMs) with LLM-generated tests, achieving a relative performance improvement by up to 50% over the strongest heuristic and 246% over the random selection in the most challenging scenarios. Our code is publicly available at https://github.com/ZJU-CTAG/B4.

Masked diffusion models have demonstrated competitive results on various tasks including language generation. However, due to its iterative refinement process, the inference is often bottlenecked by slow and static sampling speed. To overcome this problem, we introduce `KL-Adaptive Stability Sampling' (KLASS), a fast yet effective sampling method that exploits token-level KL divergence to identify stable, high-confidence predictions. By unmasking multiple tokens in each iteration without any additional model training, our approach speeds up generation significantly while maintaining sample quality. On reasoning benchmarks, KLASS achieves up to 2.78times wall-clock speedups while improving performance over standard greedy decoding, attaining state-of-the-art results among diffusion-based samplers. We further validate KLASS across diverse domains, including text, image, and molecular generation, showing its effectiveness as a broadly applicable sampler across different models.

Modern Text-to-SQL systems often follow generate-execute-select pipelines, generating multiple candidate queries then selecting the best one. Listwise selection, by jointly comparing multiple candidates, has been widely adopted, but fine-tuning listwise selectors is costly. We thus propose a fine-tuning-free listwise selector. We replace two major fine-tuning objectives with inference-time strategies: (1) learning selection criteria as ordering and (2) mitigating positional bias. First, we build reusable structured memories instead of learning selection behavior as model parameters. Given a question, MaP-SQL retrieves memories distilled from training data that encode how natural language maps to schema elements, SQL operations, and expected outputs. These memories serve as explicit decision criteria for evaluating candidates in a listwise manner. Second, to mitigate ordering bias of listwise selectors, we aggregate rankings across multiple input permutations, with inference cost optimized by execution results and pointwise scoring. Our approach improves selection accuracy while maintaining efficiency and compatibility with existing large language models. Across Text-to-SQL benchmarks, it produces more stable selection without fine-tuning and fewer unnecessary comparisons than existing methods. On BIRD-dev, it outperforms the previous state-of-the-art selector-based method R^3-SQL by 2.02 execution accuracy points on average using the same candidate sets, with 2.92x fewer tokens.

Speculative decoding reduces the inference latency of a target large language model via utilizing a smaller and faster draft model. Its performance depends on a hyperparameter K -- the candidate length, i.e., the number of candidate tokens for the target model to verify in each round. However, previous methods often use simple heuristics to choose K, which may result in sub-optimal performance. We study the choice of the candidate length K and formulate it as a Markov Decision Process. We theoretically show that the optimal policy of this Markov decision process takes the form of a threshold policy, i.e., the current speculation should stop and be verified when the probability of getting a rejection exceeds a threshold value. Motivated by this theory, we propose SpecDec++, an enhanced version of speculative decoding that adaptively determines the candidate length on the fly. We augment the draft model with a trained acceptance prediction head to predict the conditional acceptance probability of the candidate tokens. SpecDec++ will stop the current speculation when the predicted probability that at least one token gets rejected exceeds a threshold. We implement SpecDec++ and apply it to the llama-2-chat 7B & 70B model pair. Our adaptive method achieves a 2.04x speedup on the Alpaca dataset (an additional 7.2% improvement over the baseline speculative decoding). On the GSM8K and HumanEval datasets, our method achieves a 2.26x speedup (9.4% improvement) and 2.23x speedup (11.1% improvement), respectively.

Long-context LLMs demand accurate inference at low latency, yet decoding becomes primarily constrained by KV cache as context grows. Prior pruning methods are largely context-agnostic: their token selection ignores step-wise relevance and local semantics, which undermines quality. Moreover, their irregular accesses and selection overheads yield only limited wall-clock speedups. To address this, we propose CHESS, an algorithm-system co-design KV-cache management system. Algorithmically, CHESS introduces a context-aware, hierarchical selection policy that dynamically reconstructs a coherent context for the current decoding. System-wise, coarse granularity selection eliminates expensive data movement, fully realizing practical acceleration from theoretical sparsity. Extensive evaluations demonstrate that CHESS surpasses Full-KV quality using only 1\% of the KV cache, delivers low-latency stable inference with up to 4.56times higher throughput, and consistently outperforms other strong baselines. Code is available at https://anonymous.4open.science/r/CHESS-9958/{https://anonymous.4open.science/r/CHESS/}.

Keyphrase Generation (KPG) is a longstanding task in NLP with widespread applications. The advent of sequence-to-sequence (seq2seq) pre-trained language models (PLMs) has ushered in a transformative era for KPG, yielding promising performance improvements. However, many design decisions remain unexplored and are often made arbitrarily. This paper undertakes a systematic analysis of the influence of model selection and decoding strategies on PLM-based KPG. We begin by elucidating why seq2seq PLMs are apt for KPG, anchored by an attention-driven hypothesis. We then establish that conventional wisdom for selecting seq2seq PLMs lacks depth: (1) merely increasing model size or performing task-specific adaptation is not parameter-efficient; (2) although combining in-domain pre-training with task adaptation benefits KPG, it does partially hinder generalization. Regarding decoding, we demonstrate that while greedy search achieves strong F1 scores, it lags in recall compared with sampling-based methods. Based on these insights, we propose DeSel, a likelihood-based decode-select algorithm for seq2seq PLMs. DeSel improves greedy search by an average of 4.7% semantic F1 across five datasets. Our collective findings pave the way for deeper future investigations into PLM-based KPG.

Large Language Models (LLMs) are increasingly deployed in discovery domains such as math and science. The usual approach is to present the problem to the model and use its answer as the proposed solution. However, beyond this best guess, discovery can be enhanced by increasing test-time compute. In a process called pass@k, the model is allowed to explore the solution space and generate diverse candidate solutions. Unfortunately, the standard approach to post-training LLMs through Reinforcement Learning (RL) may limit pass@k: the model's output distribution narrows around high-reward outputs, causing the solution coverage to collapse. The alternative is to use Evolution Strategies (ES), a population-based, gradient-free post-training method that optimizes directly in weight space through random perturbations. As this paper shows, ES achieves consistently higher pass@k than RL and produces a broader output distribution with greater solution coverage. This coverage in turn makes it possible to achieve better results in e.g. standard math benchmarks. Thus, ES provides a better foundation for post-training in discovery problems and other domains where diverse solution coverage is critical.

Decoding sits between a language model and everything we do with it, yet it is still treated as a heuristic knob-tuning exercise. We argue decoding should be understood as a principled optimisation layer: at each token, we solve a regularised problem over the probability simplex that trades off model score against structural preferences and constraints. This single template recovers greedy decoding, Softmax sampling, Top-K, Top-P, and Sparsemax-style sparsity as special cases, and explains their common structure through optimality conditions. More importantly, the framework makes it easy to invent new decoders without folklore. We demonstrate this by designing Best-of-K (BoK), a KL-anchored coverage objective aimed at multi-sample pipelines (self-consistency, reranking, verifier selection). BoK targets the probability of covering good alternatives within a fixed K-sample budget and improves empirical performance. We show that such samples can improve accuracy by, for example, +18.6% for Qwen2.5-Math-7B on MATH500 at high sampling temperatures.

Beam search is the default decoding strategy for many sequence generation tasks in NLP. The set of approximate K-best items returned by the algorithm is a useful summary of the distribution for many applications; however, the candidates typically exhibit high overlap and may give a highly biased estimate for expectations under our model. These problems can be addressed by instead using stochastic decoding strategies. In this work, we propose a new method for turning beam search into a stochastic process: Conditional Poisson stochastic beam search. Rather than taking the maximizing set at each iteration, we sample K candidates without replacement according to the conditional Poisson sampling design. We view this as a more natural alternative to Kool et. al. 2019's stochastic beam search (SBS). Furthermore, we show how samples generated under the CPSBS design can be used to build consistent estimators and sample diverse sets from sequence models. In our experiments, we observe CPSBS produces lower variance and more efficient estimators than SBS, even showing improvements in high entropy settings.

Supervised fine-tuning (SFT) followed by reinforcement learning (RL) has become a standard post-training paradigm for large language models. This paradigm provides a cold-start for RL exploration, avoiding the inefficiency of pure RL where on-policy sampling yields insufficient positive samples. However, in practice, existing approaches often use a small amount of data for SFT initialization compared to the RL phase, which can cause the model to fit the limited samples and shift away from its pre-trained distribution. This distribution shift impedes the model's ability to effectively explore during subsequent RL training. To address this challenge, we propose that in low-data regimes, SFT should prioritize activating task-relevant capabilities rather than memorizing specific content. Along this line, we propose EKSFT (Entropy-KL Selective Fine-Tuning), which selectively masks tokens that exhibit either high entropy or high KL divergence from a reference model. By excluding these high-uncertainty, distribution-shifting tokens from imitation, EKSFT injects task-specific knowledge while preserving the integrity of the model's pre-trained distribution. Empirical evaluations on mathematical reasoning benchmarks demonstrate that EKSFT consistently outperforms standard SFT. Further RL fine-tuning from the EKSFT model yields consistently better post-RL performance, indicating improved exploration for the RL stage. Our codes and datasets are available at https://github.com/MINE-USTC/EKSFT.

Growing efforts to improve knowledge distillation (KD) in large language models (LLMs) replace dense teacher supervision with selective distillation, which uses a subset of token positions, vocabulary classes, or training samples for supervision. However, it remains unclear which importance signals, selection policies, and their interplay are most effective. In this work, we revisit where and how to distill in autoregressive LLMs. We disentangle selective KD along the position, class, and sample axes and systematically compare importance signals and selection policies. Then, guided by this analysis, we identify underexplored opportunities and introduce student-entropy-guided position selection (SE-KD). Across a suite of benchmarks, SE-KD often improves accuracy, downstream task adherence, and memory efficiency over dense distillation. Extending this approach across the class and sample axes (SE-KD 3X) yields complementary efficiency gains that make offline teacher caching feasible. In practice, this reduces wall time by 70% and peak memory by 18%, while cutting storage usage by 80% over prior methods without sacrificing performance.

Web-based applications such as chatbots, search engines and news recommendations continue to grow in scale and complexity with the recent surge in the adoption of LLMs. Online model selection has thus garnered increasing attention due to the need to choose the best model among a diverse set while balancing task reward and exploration cost. Organizations faces decisions like whether to employ a costly API-based LLM or a locally finetuned small LLM, weighing cost against performance. Traditional selection methods often evaluate every candidate model before choosing one, which are becoming impractical given the rising costs of training and finetuning LLMs. Moreover, it is undesirable to allocate excessive resources towards exploring poor-performing models. While some recent works leverage online bandit algorithm to manage such exploration-exploitation trade-off in model selection, they tend to overlook the increasing-then-converging trend in model performances as the model is iteratively finetuned, leading to less accurate predictions and suboptimal model selections. In this paper, we propose a time-increasing bandit algorithm TI-UCB, which effectively predicts the increase of model performances due to finetuning and efficiently balances exploration and exploitation in model selection. To further capture the converging points of models, we develop a change detection mechanism by comparing consecutive increase predictions. We theoretically prove that our algorithm achieves a logarithmic regret upper bound in a typical increasing bandit setting, which implies a fast convergence rate. The advantage of our method is also empirically validated through extensive experiments on classification model selection and online selection of LLMs. Our results highlight the importance of utilizing increasing-then-converging pattern for more efficient and economic model selection in the deployment of LLMs.

Large language models (LLMs) have shown impressive in-context learning (ICL) ability in code generation. LLMs take a prompt consisting of requirement-code examples and a new requirement as input, and output new programs. Existing studies have found that ICL is highly dominated by the examples and thus arises research on example selection. However, existing approaches randomly select examples or only consider the textual similarity of requirements to retrieve, leading to sub-optimal performance. In this paper, we propose a novel learning-based selection approach named LAIL (LLM-Aware In-context Learning) for code generation. Given a candidate example, we exploit LLMs themselves to estimate it by considering the generation probabilities of ground-truth programs given a requirement and the example. We then label candidate examples as positive or negative through the probability feedback. Based on the labeled data, we import a contrastive learning objective to train an effective retriever that acquires the preference of LLMs in code generation. We apply LAIL to three LLMs and evaluate it on three representative datasets (e.g., MBJP, MBPP, and MBCPP). LATA outperforms the state-of-the-art baselines by 11.58%, 6.89%, and 5.07% on CodeGen, and 4.38%, 2.85%, and 2.74% on GPT-3.5 in terms of Pass@1, respectively.

The ever-growing ecosystem of LLMs has posed a challenge in selecting the most appropriate pre-trained model to fine-tune amidst a sea of options. Given constrained resources, fine-tuning all models and making selections afterward is unrealistic. In this work, we formulate this resource-constrained selection task into predicting fine-tuning performance and illustrate its natural connection with scaling laws. Unlike pre-training, We find that the fine-tuning scaling curve includes not just the well-known "power phase" but also the previously unobserved "pre-power phase". We also explain why existing scaling laws fail to capture this phase transition phenomenon both theoretically and empirically. To address this, we introduce the concept of "pre-learned data size" into our rectified scaling law, which overcomes theoretical limitations and fits experimental results much better. By leveraging our law, we propose a novel LLM selection algorithm that selects the near-optimal model with hundreds of times less resource consumption, while other methods may provide negatively correlated selection.

Sparse attention visits few keys, yet finding them can still require scoring every key with every indexer head. We introduce DoSA (Dots Sparse Attention), a lossless method for making this computation conditional while preserving exact token selection. Its central observation is that Top-K selection requires sufficient evidence to reject a candidate, not necessarily its full score. A seed set supplies a lower bound on the winning threshold. Nonnegative head projections and joint residual bounds upper-bound positive contributions, while activation-informed aggregation bounds the magnitude subtracted by negative heads. The certificate directs full scoring toward candidates that remain eligible; exact-score filtering further reduces writeback and selection work. We establish the certificate and its exact-selection conditions, and analyze how geometry and selection margins govern its effectiveness. Our GPU implementation accelerates the complete Indexer by up to 2.74 times over SGLang and 1.69 times over LiteTopK across English, Chinese, and code workloads. End-to-end evaluation on GLM-5.2 and DeepSeek-V3.2 achieves up to 1.94 times and 1.50 times time-to-first-token speedups over the two baselines, respectively.

Similarity search finds application in specialized database systems handling complex data such as images or videos, which are typically represented by high-dimensional features and require specific indexing structures. This paper tackles the problem of better utilizing GPUs for this task. While GPUs excel at data-parallel tasks, prior approaches are bottlenecked by algorithms that expose less parallelism, such as k-min selection, or make poor use of the memory hierarchy. We propose a design for k-selection that operates at up to 55% of theoretical peak performance, enabling a nearest neighbor implementation that is 8.5x faster than prior GPU state of the art. We apply it in different similarity search scenarios, by proposing optimized design for brute-force, approximate and compressed-domain search based on product quantization. In all these setups, we outperform the state of the art by large margins. Our implementation enables the construction of a high accuracy k-NN graph on 95 million images from the Yfcc100M dataset in 35 minutes, and of a graph connecting 1 billion vectors in less than 12 hours on 4 Maxwell Titan X GPUs. We have open-sourced our approach for the sake of comparison and reproducibility.

The ability to achieve long-term goals is a key challenge in the current development of large language models (LLMs). To address this, pre-trained LLMs can be fine-tuned with reinforcement learning (RL) to explore solutions that optimize a given goal. However, exploration with LLMs is difficult, as a balance has to be struck between discovering new solutions and staying close enough to the pre-trained model, so as not to degrade basic capabilities. This is typically controlled with a Kullback-Leibler (KL) penalty. In this paper, we investigate the exploration dynamics of a small language model on a simple arithmetic task. We show how varying degrees of pre-training influence exploration and demonstrate the importance of "critical tokens" which have a dramatic impact on the final outcome. Consequently, we introduce a simple modification to the KL penalty that favors exploration on critical tokens, increasing the efficiency of the RL fine-tuning stage.

BoN improves model outputs by sampling several candidates and selecting one with a proxy score, but it assumes that complete candidates can be evaluated reliably. Many vision-language tasks instead provide only partial verification: a finding, span, value, region, or relation may be checkable even when no dependable whole-response verifier exists. Moreover, the same claim may recur across candidates with opposing stances, allowing one observation to support part of the pool and contradict another. We introduce Best-of-Evidence (BoE), an inference-time selection framework that keeps the BoN candidate pool fixed, represents reusable claims with a signed candidate--factor graph, and allocates a limited budget to evidence actions that can change the final choice. BoE formalizes selection under partial verification and provides a practical score-based controller, with the zero-budget case recovering the underlying BoN decision. Theoretically, we show that residual evidence capacity limits any evidence-driven improvement and that shared factor queries can achieve an O(log K) versus Θ(K) query separation in a factor-code model. Common-ledger experiments on four medical VQA settings show that BoE can improve fixed-pool selection and rescue some BoN failures when evidence is reliable, contrastive, and decision-relevant, while also revealing the channel-quality and candidate-generation limits that prevent universal gains.

Selecting high-quality and diverse training samples from extensive datasets plays a crucial role in reducing training overhead and enhancing the performance of Large Language Models (LLMs). However, existing studies fall short in assessing the overall value of selected data, focusing primarily on individual quality, and struggle to strike an effective balance between ensuring diversity and minimizing data point traversals. Therefore, this paper introduces a novel choice-based sample selection framework that shifts the focus from evaluating individual sample quality to comparing the contribution value of different samples when incorporated into the subset. Thanks to the advanced language understanding capabilities of LLMs, we utilize LLMs to evaluate the value of each option during the selection process. Furthermore, we design a greedy sampling process where samples are incrementally added to the subset, thereby improving efficiency by eliminating the need for exhaustive traversal of the entire dataset with the limited budget. Extensive experiments demonstrate that selected data from our method not only surpass the performance of the full dataset but also achieves competitive results with state-of-the-art (SOTA) studies, while requiring fewer selections. Moreover, we validate our approach on a larger medical dataset, highlighting its practical applicability in real-world applications.

Mid-training has become an important stage in modern LLM development, using large-scale curated mixtures to strengthen capabilities before final post-training. Its data selection problem is distinct: the data are optimized under a pretraining-style objective at near-pretraining scale, but are curated toward downstream capabilities and drawn from heterogeneous sources with different formats and training roles. As a result, effective selection requires both scalability and source-adaptive semantic criteria. Existing model-based methods scale well, but provide only implicit quality signals. Semantic selection methods offer stronger judgments, but usually assume fixed rubrics or standardized data formats. To address this mismatch, we propose MIRA, a source-aware filtering framework based on self-anchored rubric discovery. The key idea is to make rubric construction part of data selection: MIRA first discovers what should be evaluated for each source group, then distills those judgments into scalable student scorers for full-corpus filtering. On code-oriented mid-training with 21 sources and 5 source groups, MIRA outperforms selection baselines across nine code benchmarks and matches the full-corpus run while using only half the tokens.

Let p denote a generative language model. Let r denote a reward model that returns a scalar that captures the degree at which a draw from p is preferred. The goal of language model alignment is to alter p to a new distribution phi that results in a higher expected reward while keeping phi close to p. A popular alignment method is the KL-constrained reinforcement learning (RL), which chooses a distribution phi_Delta that maximizes E_{phi_{Delta}} r(y) subject to a relative entropy constraint KL(phi_Delta || p) leq Delta. Another simple alignment method is best-of-N, where N samples are drawn from p and one with highest reward is selected. In this paper, we offer a closed-form characterization of the optimal KL-constrained RL solution. We demonstrate that any alignment method that achieves a comparable trade-off between KL divergence and reward must approximate the optimal KL-constrained RL solution in terms of relative entropy. To further analyze the properties of alignment methods, we introduce two simplifying assumptions: we let the language model be memoryless, and the reward model be linear. Although these assumptions may not reflect complex real-world scenarios, they enable a precise characterization of the asymptotic behavior of both the best-of-N alignment, and the KL-constrained RL method, in terms of information-theoretic quantities. We prove that the reward of the optimal KL-constrained RL solution satisfies a large deviation principle, and we fully characterize its rate function. We also show that the rate of growth of the scaled cumulants of the reward is characterized by a proper Renyi cross entropy. Finally, we show that best-of-N is asymptotically equivalent to KL-constrained RL solution by proving that their expected rewards are asymptotically equal, and concluding that the two distributions must be close in KL divergence.

In real-world NLP applications, Large Language Models (LLMs) offer promising solutions due to their extensive training on vast datasets. However, the large size and high computation demands of LLMs limit their practicality in many applications, especially when further fine-tuning is required. To address these limitations, smaller models are typically preferred for deployment. However, their training is hindered by the scarcity of labeled data. In contrast, unlabeled data is often readily which can be leveraged by using LLMs to generate pseudo-labels for training smaller models. This enables the smaller models (student) to acquire knowledge from LLMs(teacher) while reducing computational costs. This process introduces challenges, such as potential noisy pseudo-labels. Selecting high-quality and informative data is therefore critical to enhance model performance while improving the efficiency of data utilization. To address this, we propose LLKD that enables Learning with Less computational resources and less data for Knowledge Distillation from LLMs. LLKD is an adaptive sample selection method that incorporates signals from both the teacher and student. Specifically, it prioritizes samples where the teacher demonstrates high confidence in its labeling, indicating reliable labels, and where the student exhibits a high information need, identifying challenging samples that require further learning. Our comprehensive experiments show that LLKD achieves superior performance across various datasets with higher data efficiency.

Recent discoveries on neural network pruning reveal that, with a carefully chosen layerwise sparsity, a simple magnitude-based pruning achieves state-of-the-art tradeoff between sparsity and performance. However, without a clear consensus on "how to choose," the layerwise sparsities are mostly selected algorithm-by-algorithm, often resorting to handcrafted heuristics or an extensive hyperparameter search. To fill this gap, we propose a novel importance score for global pruning, coined layer-adaptive magnitude-based pruning (LAMP) score; the score is a rescaled version of weight magnitude that incorporates the model-level ell_2 distortion incurred by pruning, and does not require any hyperparameter tuning or heavy computation. Under various image classification setups, LAMP consistently outperforms popular existing schemes for layerwise sparsity selection. Furthermore, we observe that LAMP continues to outperform baselines even in weight-rewinding setups, while the connectivity-oriented layerwise sparsity (the strongest baseline overall) performs worse than a simple global magnitude-based pruning in this case. Code: https://github.com/jaeho-lee/layer-adaptive-sparsity

Knowledge distillation (KD) is a widely used framework for training compact, task-specific models by leveraging the knowledge of teacher models. However, its application to active learning (AL), which aims to minimize annotation costs through iterative sample selection, remains underexplored. This gap stems from the fact that KD typically assumes access to sufficient labeled data, whereas AL operates in data-scarce scenarios where task-specific teacher models are often unavailable. In this paper, we introduce ActiveKD, a framework that integrates AL with KD by leveraging the zero- and few-shot capabilities of large vision-language models (VLMs). A key aspect of ActiveKD is the structured prediction bias of VLMs -- i.e., their predictions form clusters in the probability space. We regard this structure as an inductive bias of the teacher model, capturing generalizable output patterns beneficial to student learning. To exploit this bias, we propose Probabilistic CoreSet (PCoreSet), a selection strategy that maximizes coverage in the probability space rather than the feature space. PCoreSet strategically selects categorically diverse unlabeled samples, facilitating more efficient transfer of teacher knowledge under limited annotation budgets. Evaluations on 11 datasets show that PCoreSet consistently outperforms existing selection methods within the ActiveKD framework, advancing research at the intersection of AL and KD.

The rapid advancement in large language models (LLMs) has brought forth a diverse range of models with varying capabilities that excel in different tasks and domains. However, selecting the optimal LLM for user queries often involves a challenging trade-off between accuracy and cost, a problem exacerbated by the diverse demands of individual queries. In this work, we present a novel framework that formulates the LLM selection process as a multi-armed bandit problem, enabling dynamic and intelligent routing of queries to the most appropriate model. Our approach incorporates a preference-conditioned dynamic routing mechanism, allowing users to specify their preferences at inference time, thereby offering a customizable balance between performance and cost. Additionally, our selection policy is designed to generalize to unseen LLMs, ensuring adaptability to new models as they emerge. Experimental results demonstrate that our method achieves significant improvements in both accuracy and cost-effectiveness across various LLM platforms, showcasing the potential of our framework to adaptively optimize LLM selection in real-world scenarios.

In this work, we present a modular and interpretable framework that uses Large Language Models (LLMs) to automate candidate assessment in recruitment. The system integrates diverse sources, including job descriptions, CVs, interview transcripts, and HR feedback; to generate structured evaluation reports that mirror expert judgment. Unlike traditional ATS tools that rely on keyword matching or shallow scoring, our approach employs role-specific, LLM-generated rubrics and a multi-agent architecture to perform fine-grained, criteria-driven evaluations. The framework outputs detailed assessment reports, candidate comparisons, and ranked recommendations that are transparent, auditable, and suitable for real-world hiring workflows. Beyond rubric-based analysis, we introduce an LLM-Driven Active Listwise Tournament mechanism for candidate ranking. Instead of noisy pairwise comparisons or inconsistent independent scoring, the LLM ranks small candidate subsets (mini-tournaments), and these listwise permutations are aggregated using a Plackett-Luce model. An active-learning loop selects the most informative subsets, producing globally coherent and sample-efficient rankings. This adaptation of listwise LLM preference modeling (previously explored in financial asset ranking) provides a principled and highly interpretable methodology for large-scale candidate ranking in talent acquisition.

Recent advances in large language model (LLM) post-training have leveraged two distinct paradigms to enhance reasoning capabilities: reinforcement learning (RL) and knowledge distillation (KD). While RL enables the emergence of complex reasoning behaviors, it often suffers from low sample efficiency when the initial policy struggles to explore high-reward trajectories. Conversely, KD improves learning efficiency via mimicking the teacher model but tends to generalize poorly to out-of-domain scenarios. In this work, we present KDRL, a unified post-training framework that jointly optimizes a reasoning model through teacher supervision (KD) and self-exploration (RL). Specifically, KDRL leverages policy gradient optimization to simultaneously minimize the reverse Kullback-Leibler divergence (RKL) between the student and teacher distributions while maximizing the expected rule-based rewards. We first formulate a unified objective that integrates GRPO and KD, and systematically explore how different KL approximations, KL coefficients, and reward-guided KD strategies affect the overall post-training dynamics and performance. Empirical results on multiple reasoning benchmarks demonstrate that KDRL outperforms GRPO and various KD baselines while achieving a favorable balance between performance and reasoning token efficiency. These findings indicate that integrating KD and RL serves as an effective and efficient strategy to train reasoning LLMs.

One-shot coreset selection aims to select a representative subset of the training data, given a pruning rate, that can later be used to train future models while retaining high accuracy. State-of-the-art coreset selection methods pick the highest importance examples based on an importance metric and are found to perform well at low pruning rates. However, at high pruning rates, they suffer from a catastrophic accuracy drop, performing worse than even random sampling. This paper explores the reasons behind this accuracy drop both theoretically and empirically. We first propose a novel metric to measure the coverage of a dataset on a specific distribution by extending the classical geometric set cover problem to a distribution cover problem. This metric helps explain why coresets selected by SOTA methods at high pruning rates perform poorly compared to random sampling because of worse data coverage. We then propose a novel one-shot coreset selection method, Coverage-centric Coreset Selection (CCS), that jointly considers overall data coverage upon a distribution as well as the importance of each example. We evaluate CCS on five datasets and show that, at high pruning rates (e.g., 90%), it achieves significantly better accuracy than previous SOTA methods (e.g., at least 19.56% higher on CIFAR10) as well as random selection (e.g., 7.04% higher on CIFAR10) and comparable accuracy at low pruning rates. We make our code publicly available at https://github.com/haizhongzheng/Coverage-centric-coreset-selection.

Gradient-based data selection offers a principled framework for estimating sample utility in large language model (LLM) fine-tuning, but existing methods are mostly designed for offline settings. They are therefore less suited to online fine-tuning, where data arrives sequentially, sample utility is step-dependent, and the effective update geometry is shaped by adaptive optimizers. We propose an optimizer-aware framework for gradient-based online data selection and reweighting in LLM fine-tuning. Our key idea is to view online selection not as static sample ranking, but as shaping the next target-oriented update under the optimizer state. We formulate this as an optimizer-aware update-matching problem, establish its connection to second-order target utility, and show why subset-level construction must account for interactions and redundancy among selected samples. Based on this view, we develop a two-stage Filter-then-Weight algorithm that first filters geometrically useful candidates and then optimizes their coefficients. To make the framework practical for LLMs, we introduce a factorized outer-product gradient representation and optimized matrix computations for long-context data. Experiments show that our method consistently improves convergence and downstream performance over existing online data selection baselines under the same data budget.

A selector that allocates work across opaque components must evaluate them without being told how they performed. We study the least communication that suffices. Each parent maintains an allocation vector over its children and updates it from outcomes by proportional redistribution. Each child reads the sign of its own allocation change, one bit per round it is selected, so no evaluation message crosses the parent-child boundary. (1) The update preserves the simplex with strict positivity. (2) Conditional on being selected, a child's sign is exactly the root outcome at every depth, a sufficient statistic. The conditioning is necessary. (3) Under interiority a single selector has a unique interior equilibrium, exact and closed-form for N=2, with almost sure convergence under decreasing steps. For general N an equi-ratio condition gives an explicit affine equilibrium. (4) The linearised mean flow has real, strictly negative tangent eigenvalues with explicit bounds for all N >= 2. (5) The mean flow converges globally. An explicit potential, up to normalisation the KL divergence between the failure and slack distributions, decreases at a rate equal to the variance of the equi-ratio statistic. Without interiority the rule drops exactly the children below the surviving support's threshold. (6) The update law composes along a single active path, since ancestors select a node's active rounds but do not alter a realised signal. No joint convergence theorem for a hierarchy whose levels adapt simultaneously is claimed. (7) The one-bit interface admits exactly four deterministic memoryless distortions, and at a single selector passing the bit on unchanged delivers strictly higher mean quality upward than negation or constant transmission. Illustrations on synthetic hierarchies up to 16,384 leaves and three real datasets (3.4 billion comparisons, no mismatches) are consistent with the theory.

This paper presents our winning submission to the AI Mathematical Olympiad - Progress Prize 2 (AIMO-2) competition. Our recipe for building state-of-the-art mathematical reasoning models relies on three key pillars. First, we create a large-scale dataset comprising 540K unique high-quality math problems, including olympiad-level problems, and their 3.2M long-reasoning solutions. Second, we develop a novel method to integrate code execution with long reasoning models through iterative training, generation, and quality filtering, resulting in 1.7M high-quality Tool-Integrated Reasoning solutions. Third, we create a pipeline to train models to select the most promising solution from many candidates. We show that such generative solution selection (GenSelect) can significantly improve upon majority voting baseline. Combining these ideas, we train a series of models that achieve state-of-the-art results on mathematical reasoning benchmarks. To facilitate further research, we release our code, models, and the complete OpenMathReasoning dataset under a commercially permissive license.

Some security-development settings require local models that map an objective to an ordered, checkable plan. We present a low-rank decomposition adapter and release a case-disjoint corpus with 24 authored decompositions and 83 derived next-step examples across 24 satellite-security cases. To prevent reference-plan leakage, prompts contain one objective and eight shuffled SPARTA candidates. The evaluation candidate sets are constructed with oracle inclusion of every reference technique, so this study measures selection from a controlled set, not retrieval. On six fixed cases and five decoding seeds, mean scores vary across adapters and prompted Qwen2.5 baselines; a separate greedy check over three adapter training seeds shows non-negligible training variance. A 24-fold greedy leave-one-case-out control at the two compact sizes likewise shows tradeoffs: at 1.5B, adapter precision is 0.583 against 0.480 for two-shot prompting, while recall is 0.586 against 0.660. Case-resampling intervals for adapter precision relative to the strongest prompted baseline cross zero at 1.5B and 7B. The adapter is also substantially more format-compliant, which prevents attributing all score differences to selection. Autoregressive next-step accuracy is 0.08, 0.06, and 0.29 at 0.5B, 1.5B, and 7B. We therefore offer the formulation, leakage-controlled dataset, reproducibility package, and descriptive analysis as a proof of concept, not evidence of a reliable stand-alone decomposition system or a general adapter advantage. A separate diagnostic tests contract reuse.

Reinforcement learning (RL) is frequently employed in fine-tuning large language models (LMs), such as GPT-3, to penalize them for undesirable features of generated sequences, such as offensiveness, social bias, harmfulness or falsehood. The RL formulation involves treating the LM as a policy and updating it to maximise the expected value of a reward function which captures human preferences, such as non-offensiveness. In this paper, we analyze challenges associated with treating a language model as an RL policy and show how avoiding those challenges requires moving beyond the RL paradigm. We start by observing that the standard RL approach is flawed as an objective for fine-tuning LMs because it leads to distribution collapse: turning the LM into a degenerate distribution. Then, we analyze KL-regularised RL, a widely used recipe for fine-tuning LMs, which additionally constrains the fine-tuned LM to stay close to its original distribution in terms of Kullback-Leibler (KL) divergence. We show that KL-regularised RL is equivalent to variational inference: approximating a Bayesian posterior which specifies how to update a prior LM to conform with evidence provided by the reward function. We argue that this Bayesian inference view of KL-regularised RL is more insightful than the typically employed RL perspective. The Bayesian inference view explains how KL-regularised RL avoids the distribution collapse problem and offers a first-principles derivation for its objective. While this objective happens to be equivalent to RL (with a particular choice of parametric reward), there exist other objectives for fine-tuning LMs which are no longer equivalent to RL. That observation leads to a more general point: RL is not an adequate formal framework for problems such as fine-tuning language models. These problems are best viewed as Bayesian inference: approximating a pre-defined target distribution.

The reasoning performance of large language models (LLMs) can be substantially improved by training them with reinforcement learning (RL). The RL objective for LLM training involves a regularization term, which is the reverse Kullback-Leibler (KL) divergence between the trained policy and the reference policy. Since computing the KL divergence exactly is intractable, various estimators are used in practice to estimate it from on-policy samples. Despite its wide adoption, including in several open-source libraries, there is no systematic study analyzing the numerous ways of incorporating KL estimators in the objective and their effect on the downstream performance of RL-trained models. Recent works show that prevailing practices for incorporating KL regularization do not provide correct gradients for stated objectives, creating a discrepancy between the objective and its implementation. In this paper, we further analyze these practices and study the gradients of several estimators configurations, revealing how design choices shape gradient bias. We substantiate these findings with empirical observations by RL fine-tuning Qwen2.5-7B, Llama-3.1-8B-Instruct and Qwen3-4B-Instruct-2507 with different configurations and evaluating their performance on both in- and out-of-distribution tasks. Through our analysis, we observe that, in on-policy settings: (1) estimator configurations with biased gradients can result in training instabilities; and (2) using estimator configurations resulting in unbiased gradients leads to better performance on in-domain as well as out-of-domain tasks. We also investigate the performance resulting from different KL configurations in off-policy settings and observe that KL regularization can help stabilize off-policy RL training resulting from asynchronous setups.

Pretrained language models (LMs) perform well on many tasks even when learning from a few examples, but prior work uses many held-out examples to tune various aspects of learning, such as hyperparameters, training objectives, and natural language templates ("prompts"). Here, we evaluate the few-shot ability of LMs when such held-out examples are unavailable, a setting we call true few-shot learning. We test two model selection criteria, cross-validation and minimum description length, for choosing LM prompts and hyperparameters in the true few-shot setting. On average, both marginally outperform random selection and greatly underperform selection based on held-out examples. Moreover, selection criteria often prefer models that perform significantly worse than randomly-selected ones. We find similar results even when taking into account our uncertainty in a model's true performance during selection, as well as when varying the amount of computation and number of examples used for selection. Overall, our findings suggest that prior work significantly overestimated the true few-shot ability of LMs given the difficulty of few-shot model selection.

Reinforcement Learning with Verifiable Rewards (RLVR) has become the standard paradigm for LLM mathematical reasoning, with Group Relative Policy Optimization (GRPO) serving as the dominant algorithm. We identify two overlooked inefficiencies inherent in GRPO. First, a fixed KL coefficient overly restricts policy exploration at moments when the model needs to diverge significantly from the reference policy. Second, uniform question sampling overlooks that moderately difficult problems produce the most informative gradient signals. We propose FG-ExPO, short for Frontier-Guided Exploration-Prioritized Policy Optimization, which integrates two lightweight components. Accuracy-Conditioned KL Scaling (AKL) adjusts the KL penalty strength through a smooth nonlinear function of batch average accuracy, loosening the constraint when the model performs poorly and strengthening it when the model achieves satisfactory results. Gaussian Curriculum Sampling (GCS) assigns sampling weights to questions following a Gaussian distribution centered at a moderate accuracy level around 0.5, focusing model training on its learning frontier. We conduct evaluations on DeepSeek-R1-Distill-Qwen-1.5B and Qwen3-8B-Base across six mainstream mathematical reasoning benchmarks. Experimental results demonstrate that FG-ExPO consistently outperforms vanilla GRPO. It delivers an absolute improvement of 13.34 on the AIME 2025 pass@32 metric, rising from 63.33 percent to 76.67 percent, and obtains an average pass@32 gain of 2.66 on the 8B model. The substantially larger performance gains observed on pass@32 compared to pass@1 verify that FG-ExPO enlarges the model's effective exploration space under a fixed inference budget.

Large language models (LLMs) have shown remarkable promise but remain challenging to continually improve through traditional finetuning, particularly when integrating capabilities from other specialized LLMs. Popular methods like ensemble and weight merging require substantial memory and struggle to adapt to changing data environments. Recent efforts have transferred knowledge from multiple LLMs into a single target model; however, they suffer from interference and degraded performance among tasks, largely due to limited flexibility in candidate selection and training pipelines. To address these issues, we propose a framework that adaptively selects and aggregates knowledge from diverse LLMs to build a single, stronger model, avoiding the high memory overhead of ensemble and inflexible weight merging. Specifically, we design an adaptive selection network that identifies the most relevant source LLMs based on their scores, thereby reducing knowledge interference. We further propose a dynamic weighted fusion strategy that accounts for the inherent strengths of candidate LLMs, along with a feedback-driven loss function that prevents the selector from converging on a single subset of sources. Experimental results demonstrate that our method can enable a more stable and scalable knowledge aggregation process while reducing knowledge interference by up to 50% compared to existing approaches. Code is avaliable at https://github.com/ZLKong/LLM_Integration

Decoder hidden states from different layers of large language models (LLMs) often encode complementary information. However, existing speculative decoding methods typically rely on a small set of target-model layers chosen using fixed, position-based heuristics. Selecting an optimal subset of layers is inherently a combinatorial problem, making exhaustive evaluation infeasible even for moderately deep models. In this work, we present a principled framework for multi-layer hidden-state selection for speculative decoding based on two complementary criteria: informativeness, measured through matrix-entropy analysis, and diversity, quantified using centered kernel alignment (CKA). We investigate layer-wise Shannon entropy, aggregate entropy under hidden-state concatenation, and pairwise CKA dynamics across depth, revealing distinct geometric and informational compartments within decoder representations. Motivated by these findings, we propose entropy and CKA-based layer selection algorithms that favor hidden-state sets that are both highly informative and minimally redundant. As part of this framework, we introduce token-entropy filtering, which removes hidden states associated with low predictive-entropy tokens, thereby improving the quality of layer-selection statistics. In EAGLE3-style speculative decoding, our selected sets outperform fixed baseline choices, including the default [2, N//2, N-3] rule, while providing a clearer explanation of why some defaults can remain competitive. Our results provide a practical recipe for multi-layer hidden-state selection for speculative decoding, insights into the geometry and information in LLM decoder states, and a foundation for extending similar analysis to related applications.

This paper considers the problem of combinatorial multi-armed bandits with semi-bandit feedback and a cardinality constraint on the super-arm size. Existing algorithms for solving this problem typically involve two key sub-routines: (1) a parameter estimation routine that sequentially estimates a set of base-arm parameters, and (2) a super-arm selection policy for selecting a subset of base arms deemed optimal based on these parameters. State-of-the-art algorithms assume access to an exact oracle for super-arm selection with unbounded computational power. At each instance, this oracle evaluates a list of score functions, the number of which grows as low as linearly and as high as exponentially with the number of arms. This can be prohibitive in the regime of a large number of arms. This paper introduces a novel realistic alternative to the perfect oracle. This algorithm uses a combination of group-testing for selecting the super arms and quantized Thompson sampling for parameter estimation. Under a general separability assumption on the reward function, the proposed algorithm reduces the complexity of the super-arm-selection oracle to be logarithmic in the number of base arms while achieving the same regret order as the state-of-the-art algorithms that use exact oracles. This translates to at least an exponential reduction in complexity compared to the oracle-based approaches.

On-policy learning has been argued to reduce catastrophic forgetting, produce sparser parameter updates, and improve generalisation. However, existing comparisons between supervised fine-tuning and reinforcement learning vary many factors simultaneously, making the contribution of rollout policy difficult to isolate. We study the effect of rollout policy in a controlled strong-to-weak distillation setting, by independently varying rollout policy, token-level KL direction, and learning rate across the Llama3 and Qwen2.5 model families and reasoning tasks spanning scientific, medical, and arithmetic domains. Our analysis reveals a nuanced picture of distillation dynamics in which rollout policy does not necessarily play a central role. Instead, token-level KL direction more clearly shapes task performance and output coverage, while learning rate governs forgetting and update sparsity. Analysis of KL gradients and experiments along a continuous student-teacher rollout-policy spectrum explain this pattern: forward KL is remarkably robust to rollout policy, with its performance stable and strong despite changes to the rollout policy, whereas reverse KL is substantially more sensitive and favours student-generated rollouts. On-policy data nevertheless improves generalisation to harder variants of the Countdown arithmetic task under both KL directions, although this advantage does not reliably persist after subsequent RLVR. Our broader conclusions remain robust to removing gradient clipping, using sampled KL estimators, and training on tasks requiring longer reasoning chains. Overall, our results challenge the view that on-policy rollouts are inherently preferable and show that their value depends critically on the objective, evaluation setting, and optimisation hyperparameters.

Leveraging Large Language Models (LLMs) for recommendation has recently garnered considerable attention, where fine-tuning plays a key role in LLMs' adaptation. However, the cost of fine-tuning LLMs on rapidly expanding recommendation data limits their practical application. To address this challenge, few-shot fine-tuning offers a promising approach to quickly adapt LLMs to new recommendation data. We propose the task of data pruning for efficient LLM-based recommendation, aimed at identifying representative samples tailored for LLMs' few-shot fine-tuning. While coreset selection is closely related to the proposed task, existing coreset selection methods often rely on suboptimal heuristic metrics or entail costly optimization on large-scale recommendation data. To tackle these issues, we introduce two objectives for the data pruning task in the context of LLM-based recommendation: 1) high accuracy aims to identify the influential samples that can lead to high overall performance; and 2) high efficiency underlines the low costs of the data pruning process. To pursue the two objectives, we propose a novel data pruning method based on two scores, i.e., influence score and effort score, to efficiently identify the influential samples. Particularly, the influence score is introduced to accurately estimate the influence of sample removal on the overall performance. To achieve low costs of the data pruning process, we use a small-sized surrogate model to replace LLMs to obtain the influence score. Considering the potential gap between the surrogate model and LLMs, we further propose an effort score to prioritize some hard samples specifically for LLMs. Empirical results on three real-world datasets validate the effectiveness of our proposed method. In particular, the proposed method uses only 2% samples to surpass the full data fine-tuning, reducing time costs by 97%.

Recent research suggests that tree search algorithms (e.g. Monte Carlo Tree Search) can dramatically boost LLM performance on complex mathematical reasoning tasks. However, they often require more than 10 times the computational resources of greedy decoding due to wasteful search strategies, making them difficult to be deployed in practical applications. This study introduces a novel guided tree search algorithm with dynamic node selection and node-level exploration budget (maximum number of children) calculation to tackle this issue. By considering the search progress towards the final answer (history) and the guidance from a value network (future) trained without any step-wise annotations, our algorithm iteratively selects the most promising tree node before expanding it within the boundaries of the allocated computational budget. Experiments conducted on the GSM8K and TabMWP datasets demonstrate that our approach not only offers competitive performance but also enjoys significantly lower computational costs compared to baseline methods.

The core learning signal used in language model distillation is the standard Kullback-Leibler (KL) divergence between the student and teacher distributions. Traditional KL divergence tends to be dominated by the next tokens with the highest probabilities, i.e., the teacher's modes, thereby diminishing the influence of less probable yet potentially informative components of the output distribution. We propose a new tail-aware divergence that decouples the contribution of the teacher model's top-K predicted probabilities from that of lower-probability predictions, while maintaining the same computational profile as the KL Divergence. Our decoupled approach reduces the impact of the teacher modes and, consequently, increases the contribution of the tail of the distribution. Experimental results demonstrate that our modified distillation method yields competitive performance in both pre-training and supervised distillation of decoder models across various datasets. Furthermore, the distillation process is efficient and can be performed with a modest academic budget for large datasets, eliminating the need for industry-scale computing.

Verifier-based selection improves LLM performance by generating multiple candidate solutions and using a verifier to select the most promising one. However, existing methods typically treat verification only as a ranking step and discard its feedback once a fixed candidate pool has been evaluated. In this paper, we ask whether verification can also improve the candidate set itself. To this end, we introduce LLM-as-an-Improver and propose Verify--Repair--Reselect (VRR), which uses verification feedback to generate and reselect improved candidates. VRR retains the initial winner while conditionally generating three complementary alternatives: repaired versions of the winner and runner-up, and a solution based on a new approach. It filters invalid and duplicate candidates using only inference-time information and then reselects the final answer under the original evaluation criteria. Across diverse models and code-generation and reasoning benchmarks, VRR improves over fixed-pool verifier-based selection in many settings and can recover correct solutions even when all candidates in the initial pool are incorrect. These results highlight a broader role for LLMs as improvers: verification feedback can not only select among existing solutions but also construct stronger candidates beyond the initial pool.

Knowledge distillation (KD) has been widely adopted to compress large language models (LLMs). Existing KD methods investigate various divergence measures including the Kullback-Leibler (KL), reverse Kullback-Leibler (RKL), and Jensen-Shannon (JS) divergences. However, due to limitations inherent in their assumptions and definitions, these measures fail to deliver effective supervision when few distribution overlap exists between the teacher and the student. In this paper, we show that the aforementioned KL, RKL, and JS divergences respectively suffer from issues of mode-averaging, mode-collapsing, and mode-underestimation, which deteriorates logits-based KD for diverse NLP tasks. We propose the Sinkhorn Knowledge Distillation (SinKD) that exploits the Sinkhorn distance to ensure a nuanced and precise assessment of the disparity between teacher and student distributions. Besides, profit by properties of the Sinkhorn metric, we can get rid of sample-wise KD that restricts the perception of divergence in each teacher-student sample pair. Instead, we propose a batch-wise reformulation to capture geometric intricacies of distributions across samples in the high-dimensional space. Comprehensive evaluation on GLUE and SuperGLUE, in terms of comparability, validity, and generalizability, highlights our superiority over state-of-the-art methods on all kinds of LLMs with encoder-only, encoder-decoder, and decoder-only architectures.

Finetuning large language models on instruction data is crucial for enhancing pre-trained knowledge and improving instruction-following capabilities. As instruction datasets proliferate, selecting optimal data for effective training becomes increasingly important. This work addresses the question: How can we determine the optimal subset of data for effective training? While existing research often emphasizes local criteria like instance quality for subset selection, we argue that a global approach focused on data diversity is more critical. Our method employs k-means clustering to ensure the selected subset effectively represents the full dataset. We propose an iterative refinement method inspired by active learning techniques to resample instances from clusters, reassessing each cluster's importance and sampling weight in every training iteration. This approach reduces the effect of outliers and automatically filters out clusters containing low-quality data. Through extensive evaluation across natural language reasoning, general world knowledge, code and math reasoning tasks, and by fine-tuning models from various families, we observe consistent improvements, achieving a 7% increase over random selection and a 3.8% improvement over state-of-the-art sampling methods. Our work highlights the significance of diversity-first sampling when finetuning LLMs to enhance performance across a broad array of evaluation tasks. Our code is available at https://github.com/for-ai/iterative-data-selection.

Best-of-N selection is a key technique for improving the reasoning performance of Large Language Models (LLMs) through increased test-time computation. Current state-of-the-art methods often employ computationally intensive reward models for response evaluation and selection. Reward-free alternatives, like self-consistency and universal self-consistency, are limited in their ability to handle open-ended generation tasks or scale effectively. To address these limitations, we propose self-certainty, a novel and efficient metric that leverages the inherent probability distribution of LLM outputs to estimate response quality without requiring external reward models. We hypothesize that higher distributional self-certainty, aggregated across multiple samples, correlates with improved response accuracy, as it reflects greater confidence in the generated output. Through extensive experiments on various reasoning tasks, we demonstrate that self-certainty (1) scales effectively with increasing sample size N, akin to reward models but without the computational overhead; (2) complements chain-of-thought, improving reasoning performance beyond greedy decoding; and (3) generalizes to open-ended tasks where traditional self-consistency methods fall short. Our findings establish self-certainty as a practical and efficient way for improving LLM reasoning capabilities. The code is available at https://github.com/backprop07/Self-Certainty

Recent Reinforcement Learning (RL) algorithms making use of Kullback-Leibler (KL) regularization as a core component have shown outstanding performance. Yet, only little is understood theoretically about why KL regularization helps, so far. We study KL regularization within an approximate value iteration scheme and show that it implicitly averages q-values. Leveraging this insight, we provide a very strong performance bound, the very first to combine two desirable aspects: a linear dependency to the horizon (instead of quadratic) and an error propagation term involving an averaging effect of the estimation errors (instead of an accumulation effect). We also study the more general case of an additional entropy regularizer. The resulting abstract scheme encompasses many existing RL algorithms. Some of our assumptions do not hold with neural networks, so we complement this theoretical analysis with an extensive empirical study.

Machine learning especially deep neural networks have achieved great success but many of them often rely on a number of labeled samples for supervision. As sufficient labeled training data are not always ready due to e.g., continuously emerging prediction targets and costly sample annotation in real world applications, machine learning with sample shortage is now being widely investigated. Among all these studies, many prefer to utilize auxiliary information including those in the form of Knowledge Graph (KG) to reduce the reliance on labeled samples. In this survey, we have comprehensively reviewed over 90 papers about KG-aware research for two major sample shortage settings -- zero-shot learning (ZSL) where some classes to be predicted have no labeled samples, and few-shot learning (FSL) where some classes to be predicted have only a small number of labeled samples that are available. We first introduce KGs used in ZSL and FSL as well as their construction methods, and then systematically categorize and summarize KG-aware ZSL and FSL methods, dividing them into different paradigms such as the mapping-based, the data augmentation, the propagation-based and the optimization-based. We next present different applications, including not only KG augmented prediction tasks such as image classification, question answering, text classification and knowledge extraction, but also KG completion tasks, and some typical evaluation resources for each task. We eventually discuss some challenges and open problems from different perspectives.

Many policy optimization approaches in reinforcement learning incorporate a Kullback-Leilbler (KL) divergence to the previous policy, to prevent the policy from changing too quickly. This idea was initially proposed in a seminal paper on Conservative Policy Iteration, with approximations given by algorithms like TRPO and Munchausen Value Iteration (MVI). We continue this line of work by investigating a generalized KL divergence -- called the Tsallis KL divergence -- which use the q-logarithm in the definition. The approach is a strict generalization, as q = 1 corresponds to the standard KL divergence; q > 1 provides a range of new options. We characterize the types of policies learned under the Tsallis KL, and motivate when q >1 could be beneficial. To obtain a practical algorithm that incorporates Tsallis KL regularization, we extend MVI, which is one of the simplest approaches to incorporate KL regularization. We show that this generalized MVI(q) obtains significant improvements over the standard MVI(q = 1) across 35 Atari games.

The controllable generation of diffusion models aims to steer the model to generate samples that optimize some given objective functions. It is desirable for a variety of applications including image generation, molecule generation, and DNA/sequence generation. Reinforcement Learning (RL) based fine-tuning of the base model is a popular approach but it can overfit the reward function while requiring significant resources. We frame controllable generation as a problem of finding a distribution that optimizes a KL-regularized objective function. We present SLCD -- Supervised Learning based Controllable Diffusion, which iteratively generates online data and trains a small classifier to guide the generation of the diffusion model. Similar to the standard classifier-guided diffusion, SLCD's key computation primitive is classification and does not involve any complex concepts from RL or control. Via a reduction to no-regret online learning analysis, we show that under KL divergence, the output from SLCD provably converges to the optimal solution of the KL-regularized objective. Further, we empirically demonstrate that SLCD can generate high quality samples with nearly the same inference time as the base model in both image generation with continuous diffusion and biological sequence generation with discrete diffusion. Our code is available at https://github.com/Owen-Oertell/slcd

The kernel thinning (KT) algorithm of Dwivedi and Mackey (2021) compresses a probability distribution more effectively than independent sampling by targeting a reproducing kernel Hilbert space (RKHS) and leveraging a less smooth square-root kernel. Here we provide four improvements. First, we show that KT applied directly to the target RKHS yields tighter, dimension-free guarantees for any kernel, any distribution, and any fixed function in the RKHS. Second, we show that, for analytic kernels like Gaussian, inverse multiquadric, and sinc, target KT admits maximum mean discrepancy (MMD) guarantees comparable to or better than those of square-root KT without making explicit use of a square-root kernel. Third, we prove that KT with a fractional power kernel yields better-than-Monte-Carlo MMD guarantees for non-smooth kernels, like Laplace and Mat\'ern, that do not have square-roots. Fourth, we establish that KT applied to a sum of the target and power kernels (a procedure we call KT+) simultaneously inherits the improved MMD guarantees of power KT and the tighter individual function guarantees of target KT. In our experiments with target KT and KT+, we witness significant improvements in integration error even in 100 dimensions and when compressing challenging differential equation posteriors.

In online algorithm selection (OAS), instances of an algorithmic problem class are presented to an agent one after another, and the agent has to quickly select a presumably best algorithm from a fixed set of candidate algorithms. For decision problems such as satisfiability (SAT), quality typically refers to the algorithm's runtime. As the latter is known to exhibit a heavy-tail distribution, an algorithm is normally stopped when exceeding a predefined upper time limit. As a consequence, machine learning methods used to optimize an algorithm selection strategy in a data-driven manner need to deal with right-censored samples, a problem that has received little attention in the literature so far. In this work, we revisit multi-armed bandit algorithms for OAS and discuss their capability of dealing with the problem. Moreover, we adapt them towards runtime-oriented losses, allowing for partially censored data while keeping a space- and time-complexity independent of the time horizon. In an extensive experimental evaluation on an adapted version of the ASlib benchmark, we demonstrate that theoretically well-founded methods based on Thompson sampling perform specifically strong and improve in comparison to existing methods.

We propose a goodness-of-fit measure for probability densities modeling observations with varying dimensionality, such as text documents of differing lengths or variable-length sequences. The proposed measure is an instance of the kernel Stein discrepancy (KSD), which has been used to construct goodness-of-fit tests for unnormalized densities. The KSD is defined by its Stein operator: current operators used in testing apply to fixed-dimensional spaces. As our main contribution, we extend the KSD to the variable-dimension setting by identifying appropriate Stein operators, and propose a novel KSD goodness-of-fit test. As with the previous variants, the proposed KSD does not require the density to be normalized, allowing the evaluation of a large class of models. Our test is shown to perform well in practice on discrete sequential data benchmarks.

AI research agents are demonstrating great potential to accelerate scientific progress by automating the design, implementation, and training of machine learning models. We focus on methods for improving agents' performance on MLE-bench, a challenging benchmark where agents compete in Kaggle competitions to solve real-world machine learning problems. We formalize AI research agents as search policies that navigate a space of candidate solutions, iteratively modifying them using operators. By designing and systematically varying different operator sets and search policies (Greedy, MCTS, Evolutionary), we show that their interplay is critical for achieving high performance. Our best pairing of search strategy and operator set achieves a state-of-the-art result on MLE-bench lite, increasing the success rate of achieving a Kaggle medal from 39.6% to 47.7%. Our investigation underscores the importance of jointly considering the search strategy, operator design, and evaluation methodology in advancing automated machine learning.

Decision trees are a crucial class of models offering robust predictive performance and inherent interpretability across various domains, including healthcare, finance, and logistics. However, current tree induction methods often face limitations such as suboptimal solutions from greedy methods or prohibitive computational costs and limited applicability of exact optimization approaches. To address these challenges, we propose an evolutionary optimization method for decision tree induction based on genetic programming (GP). Our key innovation is the integration of semantic priors and domain-specific knowledge about the search space into the optimization algorithm. To this end, we introduce LLEGO, a framework that incorporates semantic priors into genetic search operators through the use of Large Language Models (LLMs), thereby enhancing search efficiency and targeting regions of the search space that yield decision trees with superior generalization performance. This is operationalized through novel genetic operators that work with structured natural language prompts, effectively utilizing LLMs as conditional generative models and sources of semantic knowledge. Specifically, we introduce fitness-guided crossover to exploit high-performing regions, and diversity-guided mutation for efficient global exploration of the search space. These operators are controlled by corresponding hyperparameters that enable a more nuanced balance between exploration and exploitation across the search space. Empirically, we demonstrate across various benchmarks that LLEGO evolves superior-performing trees compared to existing tree induction methods, and exhibits significantly more efficient search performance compared to conventional GP approaches.

Speculative decoding accelerates language model inference by using a fast drafter to propose candidate tokens that are then verified by a larger target model. Existing theory largely studies the stochastic, distribution-preserving setting, where the goal is to exactly sample from the target distribution. In contrast, many practical systems use greedy decoding, relaxed acceptance rules, or tree-based candidate sets, where success is governed by local ranking and threshold events rather than exact distributional equality. We develop a theory for these regimes. We identify that many common acceptance criteria have rejection regions that can be characterized as lower level sets of the target distribution. For these, we characterize the exact KL divergence required for rejection yielding exact certificates and sharp margin-based bounds for strict greedy decoding, additive and multiplicative relaxed acceptance, top-(m) relaxed criteria, and entropy-thresholded acceptance. We then extend the framework to greedy tree decoding, deriving exact and margin-only certificates for when the target greedy token remains covered by the drafter's top-(m) candidates. Finally, we evaluate the resulting certificates on Qwen3 models, showing that relaxed and tree-based criteria substantially enlarge the region of certified acceptance, especially on decoding steps with low target model distribution margin. These results complement existing distribution-preserving analyses of speculative decoding by characterizing the deterministic local acceptance events common in practical inference systems.

Parallel drafting reduces the drafting overhead of speculative decoding for large language models (LLMs), but its gains remain limited by the accepted prefix length. Even when the correct token is present in the candidate pool, a single early selection error prevents subsequent predictions from being used. We propose DRelay, which uses global information from the entire draft block to perform prefix-aware selective repair of candidate selections before target-model verification. DRelay bases its decisions on candidate correlations and the selected path: a global reader extracts predictive information across positions for each candidate. While a causal selector combines candidate-level information extracted by the global read with the tokens selected at preceding positions to determine whether the native choice at the current position is consistent with the global evidence and the selected prefix. It then decides whether to retain or replace the token, thereby repairing early errors and extending the accepted prefix. We further jointly train the draft backbone and the selector, combining candidate-support learning with a repair objective, while weighting the repair loss according to each block position's potential contribution to the consecutive accepted prefix. Across eight diverse benchmarks on an H800 GPU, DRelay consistently improves both average acceptance length and end-to-end decoding performance over DFlash, Domino, and DSpark. Under SGLang serving, DRelay improves average end-to-end speedup over DFlash, Domino, and DSpark by 14.7%-16.8%, 8.7%-9.3%, and 8.1%-9.3%, respectively.

Recent advances have demonstrated that integrating reinforcement learning with rule-based rewards can significantly enhance the reasoning capabilities of large language models, even without supervised fine-tuning. However, prevalent reinforcement learning algorithms such as GRPO and its variants like DAPO, suffer from a coarse granularity issue when computing the advantage. Specifically, they compute rollout-level advantages that assign identical values to every token within a sequence, failing to capture token-specific contributions and hindering effective learning. To address this limitation, we propose Key-token Advantage Estimation (KTAE) - a novel algorithm that estimates fine-grained, token-level advantages without introducing additional models. KTAE leverages the correctness of sampled rollouts and applies statistical analysis to quantify the importance of individual tokens within a sequence to the final outcome. This quantified token-level importance is then combined with the rollout-level advantage to obtain a more fine-grained token-level advantage estimation. Empirical results show that models trained with GRPO+KTAE and DAPO+KTAE outperform baseline methods across five mathematical reasoning benchmarks. Notably, they achieve higher accuracy with shorter responses and even surpass R1-Distill-Qwen-1.5B using the same base model.

Data selection for fine-tuning Large Language Models (LLMs) aims to select a high-quality subset from a given candidate dataset to train a Pending Fine-tune Model (PFM) into a Selective-Enhanced Model (SEM). It can improve the model performance and accelerate the training process. Although a few surveys have investigated related works of data selection, there is a lack of comprehensive comparison between existing methods due to their various experimental settings. To address this issue, we first propose a three-stage scheme for data selection and comprehensively review existing works according to this scheme. Then, we design a unified comparing method with ratio-based efficiency indicators and ranking-based feasibility indicators to overcome the difficulty of comparing various models with diverse experimental settings. After an in-depth comparative analysis, we find that the more targeted method with data-specific and model-specific quality labels has higher efficiency, but the introduction of additional noise information should be avoided when designing selection algorithms. Finally, we summarize the trends in data selection and highlight the short-term and long-term challenges to guide future research.

Determinantal point processes (DPPs) are a useful probabilistic model for selecting a small diverse subset out of a large collection of items, with applications in summarization, stochastic optimization, active learning and more. Given a kernel function and a subset size k, our goal is to sample k out of n items with probability proportional to the determinant of the kernel matrix induced by the subset (a.k.a. k-DPP). Existing k-DPP sampling algorithms require an expensive preprocessing step which involves multiple passes over all n items, making it infeasible for large datasets. A naïve heuristic addressing this problem is to uniformly subsample a fraction of the data and perform k-DPP sampling only on those items, however this method offers no guarantee that the produced sample will even approximately resemble the target distribution over the original dataset. In this paper, we develop an algorithm which adaptively builds a sufficiently large uniform sample of data that is then used to efficiently generate a smaller set of k items, while ensuring that this set is drawn exactly from the target distribution defined on all n items. We show empirically that our algorithm produces a k-DPP sample after observing only a small fraction of all elements, leading to several orders of magnitude faster performance compared to the state-of-the-art.

Large-scale kernel ridge regression (KRR) is limited by the need to store a large kernel matrix K_t. To avoid storing the entire matrix K_t, Nystrom methods subsample a subset of columns of the kernel matrix, and efficiently find an approximate KRR solution on the reconstructed matrix. The chosen subsampling distribution in turn affects the statistical and computational tradeoffs. For KRR problems, recent works show that a sampling distribution proportional to the ridge leverage scores (RLSs) provides strong reconstruction guarantees for the approximation. While exact RLSs are as difficult to compute as a KRR solution, we may be able to approximate them well enough. In this paper, we study KRR problems in a sequential setting and introduce the INK-ESTIMATE algorithm, that incrementally computes the RLSs estimates. INK-ESTIMATE maintains a small sketch of K_t, that at each step is used to compute an intermediate estimate of the RLSs. First, our sketch update does not require access to previously seen columns, and therefore a single pass over the kernel matrix is sufficient. Second, the algorithm requires a fixed, small space budget to run dependent only on the effective dimension of the kernel matrix. Finally, our sketch provides strong approximation guarantees on the distance between the true kernel matrix and its approximation, and on the statistical risk of the approximate KRR solution at any time, because all our guarantees hold at any intermediate step.

Recent Large Language Model (LLM)-based AutoML systems demonstrate impressive capabilities but face significant limitations such as constrained exploration strategies and a severe execution bottleneck. Exploration is hindered by one-shot methods lacking diversity and Monte Carlo Tree Search (MCTS) approaches that fail to recombine strong partial solutions. The execution bottleneck arises from lengthy code validation cycles that stifle iterative refinement. To overcome these challenges, we introduce KompeteAI, a novel AutoML framework with dynamic solution space exploration. Unlike previous MCTS methods that treat ideas in isolation, KompeteAI introduces a merging stage that composes top candidates. We further expand the hypothesis space by integrating Retrieval-Augmented Generation (RAG), sourcing ideas from Kaggle notebooks and arXiv papers to incorporate real-world strategies. KompeteAI also addresses the execution bottleneck via a predictive scoring model and an accelerated debugging method, assessing solution potential using early stage metrics to avoid costly full-code execution. This approach accelerates pipeline evaluation 6.9 times. KompeteAI outperforms leading methods (e.g., RD-agent, AIDE, and Ml-Master) by an average of 3\% on the primary AutoML benchmark, MLE-Bench. Additionally, we propose Kompete-bench to address limitations in MLE-Bench, where KompeteAI also achieves state-of-the-art results

In reinforcement learning and imitation learning, an object of central importance is the state distribution induced by the policy. It plays a crucial role in the policy gradient theorem, and references to it--along with the related state-action distribution--can be found all across the literature. Despite its importance, the state distribution is mostly discussed indirectly and theoretically, rather than being modeled explicitly. The reason being an absence of appropriate density estimation tools. In this work, we investigate applications of a normalizing flow-based model for the aforementioned distributions. In particular, we use a pair of flows coupled through the optimality point of the Donsker-Varadhan representation of the Kullback-Leibler (KL) divergence, for distribution matching based imitation learning. Our algorithm, Coupled Flow Imitation Learning (CFIL), achieves state-of-the-art performance on benchmark tasks with a single expert trajectory and extends naturally to a variety of other settings, including the subsampled and state-only regimes.

This paper introduces the Open Ko-LLM Leaderboard and the Ko-H5 Benchmark as vital tools for evaluating Large Language Models (LLMs) in Korean. Incorporating private test sets while mirroring the English Open LLM Leaderboard, we establish a robust evaluation framework that has been well integrated in the Korean LLM community. We perform data leakage analysis that shows the benefit of private test sets along with a correlation study within the Ko-H5 benchmark and temporal analyses of the Ko-H5 score. Moreover, we present empirical support for the need to expand beyond set benchmarks. We hope the Open Ko-LLM Leaderboard sets precedent for expanding LLM evaluation to foster more linguistic diversity.

Code Large Language Models (CodeLLMs) have ushered in a new era of code generation advancements. However, selecting the best solutions from among all possible CodeLLM solutions remains a challenge. Previous methods frequently overlooked the intricate functional similarities and interactions between clusters, resulting in suboptimal results. In this work, we introduce SRank, a novel reranking strategy for selecting the best solution from code generation that focuses on modeling inter-cluster relationship. By quantifying the functional overlap between clusters, our approach provides a better ranking strategy of code solutions. Empirical results show that our method achieves a remarkable results on pass@1 score. For instance, on the Human-Eval benchmark, we achieve 69.66\% in pass@1 with Codex002, 75.31\% for WizardCoder, 53.99\% for StarCoder and 60.55\% for CodeGen, which surpass the state-of-the-arts solution ranking methods, such as CodeT and Coder-Reviewer on the same CodeLLM with significant margin (approx 6.1% improvement on average). Comparing to the random sampling method, we can achieve an average improvement of approx 23.07% on Human-Eval and 17.64\% on MBPP. Even in scenarios with limited test inputs, our approach demonstrates robustness and superiority, marking a new state-of-the-arts in code generation reranking.

Coreset selection picks a representative subset of the labeled training set to make training cheaper. However, it is usually evaluated by downstream accuracy at a fixed subset size, ignoring both the time spent selecting the subset and the training recipe behind each reported number. We introduce an end-to-end benchmark that standardizes downstream training and charges selection and training to the same auditable wall-clock budget, spanning 4 datasets from CIFAR-10 to ImageNet-1K, 11 selectors, 5 fractions, and 3 seeds, with over 1,500 released runs. Repeated-sampling work has shown that budget-aware evaluation already favors random strategies. Our two budget studies test whether that verdict survives when every selector is granted its most favorable operating point. Across eight wall-clock budget anchors on each of CIFAR-10 and Tiny ImageNet, no anchor is won by a sophisticated selector: every winner is class-balanced random sampling, repeated random sampling, or full-data training. In fixed-budget duels on ImageNet-1K, training on all data for fewer epochs beats every selection strategy we probe while also costing the least. A per-dataset cost audit shows that selection cost is dominated at every scale by a fixed full-dataset scan, so it cannot be amortized away by selecting a smaller fraction, and its absolute size does not extrapolate from one dataset to another. We further quantify when selection does pay back through subset reuse, and document 9 correctness fixes to a widely used codebase, one of which shifts a standard Herding baseline by nearly 6 points. Selection time is not free preprocessing, and an evaluation that ignores it measures the wrong quantity.

The Combined Algorithm Selection and Hyperparameter optimization (CASH) is one of the most fundamental problems in Automatic Machine Learning (AutoML). The existing Bayesian optimization (BO) based solutions turn the CASH problem into a Hyperparameter Optimization (HPO) problem by combining the hyperparameters of all machine learning (ML) algorithms, and use BO methods to solve it. As a result, these methods suffer from the low-efficiency problem due to the huge hyperparameter space in CASH. To alleviate this issue, we propose the alternating optimization framework, where the HPO problem for each ML algorithm and the algorithm selection problem are optimized alternately. In this framework, the BO methods are used to solve the HPO problem for each ML algorithm separately, incorporating a much smaller hyperparameter space for BO methods. Furthermore, we introduce Rising Bandits, a CASH-oriented Multi-Armed Bandits (MAB) variant, to model the algorithm selection in CASH. This framework can take the advantages of both BO in solving the HPO problem with a relatively small hyperparameter space and the MABs in accelerating the algorithm selection. Moreover, we further develop an efficient online algorithm to solve the Rising Bandits with provably theoretical guarantees. The extensive experiments on 30 OpenML datasets demonstrate the superiority of the proposed approach over the competitive baselines.

Multi-path reasoning methods such as self-consistency (SC) sample K reasoning paths and choose the most frequent answer. However, their gains quickly plateau as K increases, and existing methods do not predict when this saturation will occur. We formalize multi-path LLM reasoning as a diversity combining problem from wireless communications: each path is a noisy channel observation, and the pairwise correlation of path correctness caps the design-effect effective sample size of the vote at a finite ceiling. Generalized least squares (GLS) analysis shows that, under exchangeability, the optimal symmetric linear combiner of latent embeddings is uniform, supporting majority vote as the natural default in standard SC while leaving room for weighting or pruning under heterogeneous prompt-template branches. Across 5 models and 12 benchmarks, prompt-template diversity reduces path correlation in 55 of 57 valid cells, with the strongest effect on open-ended QA. We derive an Adaptive-K rule that uses a four-path pilot to select K^*, retaining 96--103% of MV@K{=}32 accuracy across Math, QA, and NLU.

Machine learning is increasingly used to guide branch-and-cut (B&C) for mixed-integer linear programming by learning score-based policies for selecting branching variables and cutting planes. Many approaches train on local signals from lookahead heuristics such as strong branching, and linear programming (LP) bound improvement for cut selection. Training and evaluation of the learned models often focus on local score accuracy. We show that such local score-based methods can lead to search trees exponentially larger than optimal tree sizes, by identifying two sources of this gap. The first is that these widely used expert signals can be misaligned with overall tree size. LP bound improvement can select a root cut set that yields an exponentially larger strong branching tree than selecting cuts by a simple proxy score, and strong branching itself can be exponentially suboptimal (Dey et al., 2024). The second is that small discrepancies can be amplified by the branch-and-bound recursion. An arbitrarily small perturbation of the right-hand sides in a root cut set can change the minimum tree size from a single node to exponentially many. For branching, arbitrarily small score discrepancies, and differences only in tie-breaking, can produce trees of exponentially different sizes, and even a small number of decision differences along a trajectory can incur exponential growth. These results show that branch-and-cut policies trained and learned using local expert scores do not guarantee small trees, thus motivating the study of data-driven methods that produce policies better aligned with tree size rather than only accuracy on expert scores.

Instruction fine-tuning of large language models (LLMs) often involves selecting a subset of instruction training data from a large candidate pool, using a small query set from the target task. Despite growing interest, the literature on targeted instruction selection remains fragmented and opaque: methods vary widely in selection budgets, often omit zero-shot baselines, and frequently entangle the contributions of key components. As a result, practitioners lack actionable guidance on selecting instructions for their target tasks. In this work, we aim to bring clarity to this landscape by disentangling and systematically analyzing the two core ingredients: data representation and selection algorithms. Our framework enables controlled comparisons across models, tasks, and budgets. We find that only gradient-based data representations choose subsets whose similarity to the query consistently predicts performance across datasets and models. While no single method dominates, gradient-based representations paired with a greedy round-robin selection algorithm tend to perform best on average at low budgets, but these benefits diminish at larger budgets. Finally, we unify several existing selection algorithms as forms of approximate distance minimization between the selected subset and the query set, and support this view with new generalization bounds. More broadly, our findings provide critical insights and a foundation for more principled data selection in LLM fine-tuning. The code is available at https://github.com/dcml-lab/targeted-instruction-selection.

Generations from large language models (LLMs) can be improved by sampling and scoring multiple solutions to select a final answer. Current "sample and select" methods such as self-consistency (SC) rely on majority voting to score answers. However, when tasks have many distinct and valid answers, selection by voting requires a large number of samples. This makes SC prohibitively expensive for interactive tasks that involve generating multiple actions (answers) sequentially. After establishing that majority voting fails to provide consistent gains on such tasks, we demonstrate how to increase success rates by softening the scoring criterion. We introduce Soft Self-Consistency (SOFT-SC), which replaces SC's discontinuous scoring with a continuous score computed from model likelihoods, allowing for selection even when actions are sparsely distributed. SOFT-SC improves both performance and efficiency on long-horizon interactive tasks, requiring half as many samples as SC for comparable or better performance. For a fixed number of samples, SOFT-SC leads to a 1.3% increase over SC in absolute success rate on writing bash programs, a 6.6% increase on online shopping (WebShop), and a 4.7% increase for an interactive household game (ALFWorld). Finally, we show that SOFT-SC can be applied to both open-source and black-box models.

In tackling the challenges of large language model (LLM) performance for Text-to-SQL tasks, we introduce CHASE-SQL, a new framework that employs innovative strategies, using test-time compute in multi-agent modeling to improve candidate generation and selection. CHASE-SQL leverages LLMs' intrinsic knowledge to generate diverse and high-quality SQL candidates using different LLM generators with: (1) a divide-and-conquer method that decomposes complex queries into manageable sub-queries in a single LLM call; (2) chain-of-thought reasoning based on query execution plans, reflecting the steps a database engine takes during execution; and (3) a unique instance-aware synthetic example generation technique, which offers specific few-shot demonstrations tailored to test questions.To identify the best candidate, a selection agent is employed to rank the candidates through pairwise comparisons with a fine-tuned binary-candidates selection LLM. This selection approach has been demonstrated to be more robust over alternatives. The proposed generators-selector framework not only enhances the quality and diversity of SQL queries but also outperforms previous methods. Overall, our proposed CHASE-SQL achieves the state-of-the-art execution accuracy of 73.0% and 73.01% on the test set and development set of the notable BIRD Text-to-SQL dataset benchmark, rendering CHASE-SQL the top submission of the leaderboard (at the time of paper submission).

Many evaluation measures are used to evaluate social biases in masked language models (MLMs). However, we find that these previously proposed evaluation measures are lacking robustness in scenarios with limited datasets. This is because these measures are obtained by comparing the pseudo-log-likelihood (PLL) scores of the stereotypical and anti-stereotypical samples using an indicator function. The disadvantage is the limited mining of the PLL score sets without capturing its distributional information. In this paper, we represent a PLL score set as a Gaussian distribution and use Kullback Leibler (KL) divergence and Jensen Shannon (JS) divergence to construct evaluation measures for the distributions of stereotypical and anti-stereotypical PLL scores. Experimental results on the publicly available datasets StereoSet (SS) and CrowS-Pairs (CP) show that our proposed measures are significantly more robust and interpretable than those proposed previously.

The multilayer perceptron (MLP), a fundamental paradigm in current artificial intelligence, is widely applied in fields such as computer vision and natural language processing. However, the recently proposed Kolmogorov-Arnold Network (KAN), based on nonlinear additive connections, has been proven to achieve performance comparable to MLPs with significantly fewer parameters. Despite this potential, the use of a single activation function space results in reduced performance of KAN and related works across different tasks. To address this issue, we propose an activation space Selectable KAN (S-KAN). S-KAN employs an adaptive strategy to choose the possible activation mode for data at each feedforward KAN node. Our approach outperforms baseline methods in seven representative function fitting tasks and significantly surpasses MLP methods with the same level of parameters. Furthermore, we extend the structure of S-KAN and propose an activation space selectable Convolutional KAN (S-ConvKAN), which achieves leading results on four general image classification datasets. Our method mitigates the performance variability of the original KAN across different tasks and demonstrates through extensive experiments that feedforward KANs with selectable activations can achieve or even exceed the performance of MLP-based methods. This work contributes to the understanding of the data-centric design of new AI paradigms and provides a foundational reference for innovations in KAN-based network architectures.

The correct use of model evaluation, model selection, and algorithm selection techniques is vital in academic machine learning research as well as in many industrial settings. This article reviews different techniques that can be used for each of these three subtasks and discusses the main advantages and disadvantages of each technique with references to theoretical and empirical studies. Further, recommendations are given to encourage best yet feasible practices in research and applications of machine learning. Common methods such as the holdout method for model evaluation and selection are covered, which are not recommended when working with small datasets. Different flavors of the bootstrap technique are introduced for estimating the uncertainty of performance estimates, as an alternative to confidence intervals via normal approximation if bootstrapping is computationally feasible. Common cross-validation techniques such as leave-one-out cross-validation and k-fold cross-validation are reviewed, the bias-variance trade-off for choosing k is discussed, and practical tips for the optimal choice of k are given based on empirical evidence. Different statistical tests for algorithm comparisons are presented, and strategies for dealing with multiple comparisons such as omnibus tests and multiple-comparison corrections are discussed. Finally, alternative methods for algorithm selection, such as the combined F-test 5x2 cross-validation and nested cross-validation, are recommended for comparing machine learning algorithms when datasets are small.

We introduce the Korean Canonical Legal Benchmark (KCL), a benchmark designed to assess language models' legal reasoning capabilities independently of domain-specific knowledge. KCL provides question-level supporting precedents, enabling a more faithful disentanglement of reasoning ability from parameterized knowledge. KCL consists of two components: (1) KCL-MCQA, multiple-choice problems of 283 questions with 1,103 aligned precedents, and (2) KCL-Essay, open-ended generation problems of 169 questions with 550 aligned precedents and 2,739 instance-level rubrics for automated evaluation. Our systematic evaluation of 30+ models shows large remaining gaps, particularly in KCL-Essay, and that reasoning-specialized models consistently outperform their general-purpose counterparts. We release all resources, including the benchmark dataset and evaluation code, at https://github.com/lbox-kr/kcl.

Large language models (LLMs) are commonly aligned with human preferences using reinforcement learning from human feedback (RLHF). In this method, LLM policies are generally optimized through reward maximization with Kullback-Leibler (KL) divergence regularization of the reference policy. However, KL and its f-divergence variants only compare token probabilities at identical indices, failing to capture semantic similarity. We propose Wasserstein Policy Regularization (WPR), a semantic-aware regularization for the RLHF framework based on the entropy-regularized Wasserstein distance, which incorporates the geometry of the token space. The dual formulation of the distance expresses the regularization as penalty terms applied to the reward via optimal dual variables, which yield a tractable objective compatible with standard RL algorithms. Empirically, our method outperforms KL- and f-divergence-based baselines, demonstrating the benefits of semantic-aware policy distances for alignment. Our code is available at https://github.com/aailab-kaist/WPR.

Compression reports summarize how far a compressed language model moved from the dense one, usually by a KL divergence; a deployment that relies on the dense model's outputs needs to know how many of its decisions changed. We show that total variation, not KL, answers this directly. Across 802 compressed and perturbed copies of 19 open models on five corpora and nine mechanically unrelated perturbation families, the rate at which the arg-max token changes (the flip rate) tracks total variation at a ratio with median 1.05, with no fitted constant. KL converts into flips only through its square root and a factor that varies fourfold across models and corpora, because KL averages over tokens before the root is taken; first-order statistics averaged per token, such as Hellinger distance, avoid this, but reports rarely give them. As a result, of two compressors reported on different models and corpora whose flip rates differ by at least 10%, KL assigns the smaller divergence to the one that changes more decisions in 11% of cases, total variation in 1%. Two pre-registered tests mark the limits: on a held-out code corpus the ratio held for all eight models while three predictions about KL each failed for half of them or more, and on three new models with real kernels it stayed in its band for 37 of 38 checkpoints but fell below one on code for two models. In vLLM speculative decoding, total variation measured under teacher forcing predicts greedy draft acceptance with a mean relative error of 1.1--2.4%, without the task-specific calibration that KL needs.

We present a new implementation of the LLM-driven genetic algorithm {\it funsearch}, whose aim is to generate examples of interest to mathematicians and which has already had some success in problems in extremal combinatorics. Our implementation is designed to be useful in practice for working mathematicians; it does not require expertise in machine learning or access to high-performance computing resources. Applying {\it funsearch} to a new problem involves modifying a small segment of Python code and selecting a large language model (LLM) from one of many third-party providers. We benchmarked our implementation on three different problems, obtaining metrics that may inform applications of {\it funsearch} to new problems. Our results demonstrate that {\it funsearch} successfully learns in a variety of combinatorial and number-theoretic settings, and in some contexts learns principles that generalize beyond the problem originally trained on.

One of the major limits of kernel ridge regression (KRR) is that storing and manipulating the kernel matrix K_n for n samples requires O(n^2) space, which rapidly becomes unfeasible for large n. Nystrom approximations reduce the space complexity to O(nm) by sampling m columns from K_n. Uniform sampling preserves KRR accuracy (up to epsilon) only when m is proportional to the maximum degree of freedom of K_n, which may require O(n) columns for datasets with high coherence. Sampling columns according to their ridge leverage scores (RLS) gives accurate Nystrom approximations with m proportional to the effective dimension, but computing exact RLS also requires O(n^2) space. (Calandriello et al. 2016) propose INK-Estimate, an algorithm that processes the dataset incrementally and updates RLS, effective dimension, and Nystrom approximations on-the-fly. Its space complexity scales with the effective dimension but introduces a dependency on the largest eigenvalue of K_n, which in the worst case is O(n). In this paper we introduce SQUEAK, a new algorithm that builds on INK-Estimate but uses unnormalized RLS. As a consequence, the algorithm is simpler, does not need to estimate the effective dimension for normalization, and achieves a space complexity that is only a constant factor worse than exact RLS sampling.

Benchmarks of machine learning models often include many datasets, making evaluation expensive. For efficiency, it is preferable to perform evaluations on small, representative datasets instead. The selection of such subsets typically relies on heuristics and is rarely analyzed for the robustness of the resulting model rankings. We introduce a framework to perform the task of selecting datasets subsets with an evaluation of how different selection strategies preserve the global model rankings. Our framework includes bootstrap aggregation, which provides valid confidence intervals, allowing a principled comparison of selection strategies. We consider clustering, design criteria (A/D-optimality), random baselines, and greedy farthest-first (FAFI). For the latter, we derive upper bounds on selection quality in terms of ranking errors as a function of the number of selected datasets. Empirically, in time series classification (TSC, 112 datasets) and in a supplementary natural language processing benchmark derived from MTEB (57 tasks), several selection strategies improve rank preservation compared with random subsets, including simple FAFI. In contrast, in recommender systems (30 datasets), the improvement of strategies over random selection is small and typically statistically insignificant. For TSC, our best-performing strategy achieves a Spearman correlation of 0.95 with the full benchmark model rankings using only five selected datasets. Additional experiments indicate that the effectiveness of selection approaches depends on both the quality of dataset representations and the scale of the benchmarking regime.

With the development of large language models (LLMs), the ability to handle longer contexts has become a key capability for Web applications such as cross-document understanding and LLM-powered search systems. However, this progress faces two major challenges: performance degradation due to sequence lengths out-of-distribution, and excessively long inference times caused by the quadratic computational complexity of attention. These issues hinder the application of LLMs in long-context scenarios. In this paper, we propose Dynamic Token-Level KV Cache Selection (TokenSelect), a model-agnostic, training-free method for efficient and accurate long-context inference. TokenSelect builds upon the observation of non-contiguous attention sparsity, using Query-Key dot products to measure per-head KV Cache criticality at token-level. By per-head soft voting mechanism, TokenSelect selectively involves a small number of critical KV cache tokens in the attention calculation without sacrificing accuracy. To further accelerate TokenSelect, we designed the Selection Cache based on observations of consecutive Query similarity and implemented efficient dot product kernel, significantly reducing the overhead of token selection. A comprehensive evaluation of TokenSelect demonstrates up to 23.84x speedup in attention computation and up to 2.28x acceleration in end-to-end latency, while providing superior performance compared to state-of-the-art long-context inference methods.

Asynchronous reinforcement learning (RL) for large language model (LLM) agents trains one policy on trajectories generated by another: rollouts come from stale checkpoints, and the inference engine's probabilities differ from the trainer's even at identical parameters. Standard remedies either clip importance ratios, which biases the update, or, as in GRPO, sample a group of responses per prompt, which is costly when episodes are long. We propose KL-Regularized Policy Optimization (KLPO), a framework that anchors the KL regularizer at the sampler. The regularized improvement step then has a closed-form Gibbs solution, and KLPO fits its log-ratio optimality condition by least squares on the sampler's own trajectories, so the sampler probability enters through a log-ratio and no importance weights are needed. Profiling out the regression intercept replaces the intractable log-partition function with the signal's sampler mean plus a sampler-to-trainer KL divergence. For token-level policy mirror descent targets, we show that the resulting gradient can be computed from terminal returns without a critic, via sampler-centered scores or a single trajectory residual, even under stochastic tool outputs. We further prove that independent Monte Carlo estimates of the KL term keep these gradients unbiased, derive the exact KL gap of cheaper top-K and binary approximations, and show that SPPO, GPO, REBEL, and BPO arise as special cases of KLPO. The result is a critic-free update that uses one rollout per prompt and requires neither a learned normalizer nor a group of responses.

Long contexts have become standard in pretrained LLMs, yet they remain expensive to run: prefill compute grows quadratically with sequence length, and every decode step re-reads a key-value cache that grows linearly with it. Sparse attention cuts these costs by attending only to a relevant subset of past tokens, but selecting that subset is itself expensive. We present SpotAttention, a lightweight selector that attaches to a frozen pretrained transformer and learns by KL distillation to estimate its attention distribution. The selector picks the top-K keys each query attends to, and because its estimate is a calibrated distribution, a dual top-p rule reads the per-query, per-layer budget directly from it. Across Qwen3 (dense, 4B-32B) and Qwen3.5 (hybrid linear/full attention, 4B-9B), SpotAttention matches dense accuracy at contexts up to 128K tokens, eight times the training length. Decode at L=128K runs 3.9x faster than FlashAttention and 1.8x faster than Twilight, the strongest training-free baseline. Quantizing the selector's K-cache to INT4 or FP4 microscale shrinks it 3.5x at no accuracy cost.

The rapid progress in machine learning (ML) has brought forth many large language models (LLMs) that excel in various tasks and areas. These LLMs come with different abilities and costs in terms of computation or pricing. Since the demand for each query can vary, e.g., because of the queried domain or its complexity, defaulting to one LLM in an application is not usually the best choice, whether it is the biggest, priciest, or even the one with the best average test performance. Consequently, picking the right LLM that is both accurate and cost-effective for an application is necessary yet remains a challenge. In this paper, we introduce MetaLLM, a framework that dynamically and intelligently routes each query to the optimal LLM (among several available LLMs) for classification and multi-choice question-answering tasks, achieving significantly improved accuracy and cost-effectiveness. By framing the selection problem as a multi-armed bandit, MetaLLM balances prediction accuracy and cost efficiency under uncertainty. Our experiments, conducted on popular LLM platforms such as OpenAI and Together AI, as well as open-source LLM, showcase MetaLLM's efficacy in real-world scenarios, laying the groundwork for future extensions.

Retrieve-and-rerank is a popular retrieval pipeline because of its ability to make slow but effective rerankers efficient enough at query time by reducing the number of comparisons. Recent works in neural rerankers take advantage of large language models for their capability in reasoning between queries and passages and have achieved state-of-the-art retrieval effectiveness. However, such rerankers are resource-intensive, even after heavy optimization. In this work, we introduce Rank-K, a listwise passage reranking model that leverages the reasoning capability of the reasoning language model at query time that provides test time scalability to serve hard queries. We show that Rank-K improves retrieval effectiveness by 23\% over the RankZephyr, the state-of-the-art listwise reranker, when reranking a BM25 initial ranked list and 19\% when reranking strong retrieval results by SPLADE-v3. Since Rank-K is inherently a multilingual model, we found that it ranks passages based on queries in different languages as effectively as it does in monolingual retrieval.

We consider the problem of subset selection where one is given multiple rankings of items and the goal is to select the highest ``quality'' subset. Score functions from the multiwinner voting literature have been used to aggregate rankings into quality scores for subsets. We study this setting of subset selection problems when, in addition, rankings may contain systemic or unconscious biases toward a group of items. For a general model of input rankings and biases, we show that requiring the selected subset to satisfy group fairness constraints can improve the quality of the selection with respect to unbiased rankings. Importantly, we show that for fairness constraints to be effective, different multiwinner score functions may require a drastically different number of rankings: While for some functions, fairness constraints need an exponential number of rankings to recover a close-to-optimal solution, for others, this dependency is only polynomial. This result relies on a novel notion of ``smoothness'' of submodular functions in this setting that quantifies how well a function can ``correctly'' assess the quality of items in the presence of bias. The results in this paper can be used to guide the choice of multiwinner score functions for the subset selection setting considered here; we additionally provide a tool to empirically enable this.

Human evaluation is the gold-standard for evaluating text generation models. It is also expensive, and to fit budgetary constraints, a random subset of the test data is often chosen in practice. The randomly selected data may not accurately represent test performance, making this approach economically inefficient for model comparison. Thus, in this work, we develop a suite of selectors to get the most informative datapoints for human evaluation while taking the evaluation costs into account. We show that selectors based on variance in automated metric scores, diversity in model outputs, or Item Response Theory outperform random selection. We further develop an approach to distill these selectors to the scenario where the model outputs are not yet available. In particular, we introduce source-based estimators, which predict item usefulness for human evaluation just based on the source texts. We demonstrate the efficacy of our selectors in two common NLG tasks, machine translation and summarization, and show that up to only ~50% of the test data is needed to produce the same evaluation result as the entire data. Our implementations are published in the subset2evaluate package.

Recently, large vision-language models (LVLMs) have rapidly gained popularity for their strong generation and reasoning capabilities given diverse multimodal inputs. However, these models incur significant computational and memory overhead during inference, which greatly hinders the efficient deployment in practical scenarios. The extensive key-value (KV) cache, necessitated by the lengthy input and output sequences, notably contributes to the high inference cost. Based on this, recent works have investigated ways to reduce the KV cache size for higher efficiency. Although effective, they generally overlook the distinct importance distributions of KV vectors across layers and maintain the same cache size for each layer during the next token prediction. This results in the significant contextual information loss for certain layers, leading to notable performance decline. To address this, we present PrefixKV. It reframes the challenge of determining KV cache sizes for all layers into the task of searching for the optimal global prefix configuration. With an adaptive layer-wise KV retention recipe based on binary search, the maximum contextual information can thus be preserved in each layer, facilitating the generation. Extensive experiments demonstrate that our method achieves the state-of-the-art performance compared with others. It exhibits superior inference efficiency and generation quality trade-offs, showing promising potential for practical applications. Code is available at https://github.com/THU-MIG/PrefixKV.

Today, large language models (LLMs) are taught to use new tools by providing a few demonstrations of the tool's usage. Unfortunately, demonstrations are hard to acquire, and can result in undesirable biased usage if the wrong demonstration is chosen. Even in the rare scenario that demonstrations are readily available, there is no principled selection protocol to determine how many and which ones to provide. As tasks grow more complex, the selection search grows combinatorially and invariably becomes intractable. Our work provides an alternative to demonstrations: tool documentation. We advocate the use of tool documentation, descriptions for the individual tool usage, over demonstrations. We substantiate our claim through three main empirical findings on 6 tasks across both vision and language modalities. First, on existing benchmarks, zero-shot prompts with only tool documentation are sufficient for eliciting proper tool usage, achieving performance on par with few-shot prompts. Second, on a newly collected realistic tool-use dataset with hundreds of available tool APIs, we show that tool documentation is significantly more valuable than demonstrations, with zero-shot documentation significantly outperforming few-shot without documentation. Third, we highlight the benefits of tool documentations by tackling image generation and video tracking using just-released unseen state-of-the-art models as tools. Finally, we highlight the possibility of using tool documentation to automatically enable new applications: by using nothing more than the documentation of GroundingDino, Stable Diffusion, XMem, and SAM, LLMs can re-invent the functionalities of the just-released Grounded-SAM and Track Anything models.

As large language models (LLMs) become increasingly versatile, numerous large scale benchmarks have been developed to thoroughly assess their capabilities. These benchmarks typically consist of diverse datasets and prompts to evaluate different aspects of LLM performance. However, comprehensive evaluations on hundreds or thousands of prompts incur tremendous costs in terms of computation, money, and time. In this work, we investigate strategies to improve evaluation efficiency by selecting a subset of examples from each benchmark using a learned policy. Our approach models the dependencies across test examples, allowing accurate prediction of the evaluation outcomes for the remaining examples based on the outcomes of the selected ones. Consequently, we only need to acquire the actual evaluation outcomes for the selected subset. We rigorously explore various subset selection policies and introduce a novel RL-based policy that leverages the captured dependencies. Empirical results demonstrate that our approach significantly reduces the number of evaluation prompts required while maintaining accurate performance estimates compared to previous methods.

Large pretrained language models (LMs) have shown impressive In-Context Learning (ICL) ability, where the model learns to do an unseen task via a prompt consisting of input-output examples as the demonstration, without any parameter updates. The performance of ICL is highly dominated by the quality of the selected in-context examples. However, previous selection methods are mostly based on simple heuristics, leading to sub-optimal performance. In this work, we formulate in-context example selection as a subset selection problem. We propose CEIL (Compositional Exemplars for In-context Learning), which is instantiated by Determinantal Point Processes (DPPs) to model the interaction between the given input and in-context examples, and optimized through a carefully-designed contrastive learning objective to obtain preference from LMs. We validate CEIL on 12 classification and generation datasets from 7 distinct NLP tasks, including sentiment analysis, paraphrase detection, natural language inference, commonsense reasoning, open-domain question answering, code generation, and semantic parsing. Extensive experiments demonstrate not only the state-of-the-art performance but also the transferability and compositionality of CEIL, shedding new light on effective and efficient in-context learning. Our code is released at https://github.com/HKUNLP/icl-ceil.

Knowledge distillation is central to LLM post-training, yet its design space remains poorly understood, especially alongside reinforcement learning (RL). We show that the prevailing paradigms, off-policy distillation and on-policy distillation (OPD), implicitly couple two orthogonal choices: prefix source and token-level KL direction. This follows from decomposing sequence-level KL over autoregressive response distributions: forward KL pairs teacher prefixes with token-level forward KL, and reverse KL pairs student prefixes with token-level reverse KL. We argue this coupling is not intrinsic: decoupling the two axes yields four valid objectives. We establish gradient-level identities showing forward KL gives SFT-style cross-entropy matching with teacher soft targets, whereas reverse KL gives an RL-style policy-gradient objective with a dense teacher-student log-ratio reward, connecting them to off-policy SFT, DAgger-style on-policy SFT, offline-RL-style distillation, and OPD. We conduct an extensive controlled study on math reasoning, evaluating the four objectives both as standalone methods and as initializations for subsequent RL. The results reveal three tradeoffs: KL direction induces an accuracy-entropy tradeoff, prefix source a quality-compute tradeoff, and training length an accuracy-stability tradeoff. Motivated by these findings, we propose KL mixing and an entropy-gated length curriculum. KL mixing shows long-sequence distillation requires substantial forward-KL weight to prevent entropy collapse and length inflation without sacrificing accuracy. The entropy-gated length curriculum improves Avg@k and Pass@k by 3.6 and up to 5.8 points, and cuts average response length by roughly 3x versus fixed long-horizon training. Our results provide a framework and practical methods for designing reasoning distillation objectives that balance accuracy, diversity, compute, and RL behavior.

This work delved into the realm of automatic text generation, exploring a variety of techniques ranging from traditional deterministic approaches to more modern stochastic methods. Through analysis of greedy search, beam search, top-k sampling, top-p sampling, contrastive searching, and locally typical searching, this work has provided valuable insights into the strengths, weaknesses, and potential applications of each method. Each text-generating method is evaluated using several standard metrics and a comparative study has been made on the performance of the approaches. Finally, some future directions of research in the field of automatic text generation are also identified.

This paper studies using foundational large language models (LLMs) to make decisions during hyperparameter optimization (HPO). Empirical evaluations demonstrate that in settings with constrained search budgets, LLMs can perform comparably or better than traditional HPO methods like random search and Bayesian optimization on standard benchmarks. Furthermore, we propose to treat the code specifying our model as a hyperparameter, which the LLM outputs, going beyond the capabilities of existing HPO approaches. Our findings suggest that LLMs are a promising tool for improving efficiency in the traditional decision-making problem of hyperparameter optimization.

Autoregressive sampling from large language models has led to state-of-the-art results in several natural language tasks. However, autoregressive sampling generates tokens one at a time making it slow, and even prohibitive in certain tasks. One way to speed up sampling is speculative decoding: use a small model to sample a draft (block or sequence of tokens), and then score all tokens in the draft by the large language model in parallel. A subset of the tokens in the draft are accepted (and the rest rejected) based on a statistical method to guarantee that the final output follows the distribution of the large model. In this work, we provide a principled understanding of speculative decoding through the lens of optimal transport (OT) with membership cost. This framework can be viewed as an extension of the well-known maximal-coupling problem. This new formulation enables us to generalize the speculative decoding method to allow for a set of k candidates at the token-level, which leads to an improved optimal membership cost. We show that the optimal draft selection algorithm (transport plan) can be computed via linear programming, whose best-known runtime is exponential in k. We then propose a valid draft selection algorithm whose acceptance probability is (1-1/e)-optimal multiplicatively. Moreover, it can be computed in time almost linear with size of domain of a single token. Using this new draft selection algorithm, we develop a new autoregressive sampling algorithm called SpecTr, which provides speedup in decoding while ensuring that there is no quality degradation in the decoded output. We experimentally demonstrate that for state-of-the-art large language models, the proposed approach achieves a wall clock speedup of 2.13X, a further 1.37X speedup over speculative decoding on standard benchmarks.

In-context learning is the paradigm that adapts large language models to downstream tasks by providing a few examples. Few-shot selection -- selecting appropriate examples for each test instance separately -- is important for in-context learning. In this paper, we propose Skill-KNN, a skill-based few-shot selection method for in-context learning. The key advantages of Skill-KNN include: (1) it addresses the problem that existing methods based on pre-trained embeddings can be easily biased by surface natural language features that are not important for the target task; (2) it does not require training or fine-tuning of any models, making it suitable for frequently expanding or changing example banks. The key insight is to optimize the inputs fed into the embedding model, rather than tuning the model itself. Technically, Skill-KNN generates the skill-based descriptions for each test case and candidate example by utilizing a pre-processing few-shot prompting, thus eliminating unimportant surface features. Experimental results across five cross-domain semantic parsing datasets and six backbone models show that Skill-KNN significantly outperforms existing methods.

In the field of large language models (LLMs), Knowledge Distillation (KD) is a critical technique for transferring capabilities from teacher models to student models. However, existing KD methods face limitations and challenges in distillation of LLMs, including efficiency and insufficient measurement capabilities of traditional KL divergence. It is shown that LLMs can serve as an implicit reward function, which we define as a supplement to KL divergence. In this work, we propose Direct Preference Knowledge Distillation (DPKD) for LLMs. DPKD utilizes distribution divergence to represent the preference loss and implicit reward function. We re-formulate KD of LLMs into two stages: first optimizing and objective consisting of implicit reward and reverse KL divergence and then improving the preference probability of teacher outputs over student outputs. We conducted experiments and analysis on various datasets with LLM parameters ranging from 120M to 13B and demonstrate the broad applicability and effectiveness of our DPKD approach. Meanwhile, we prove the value and effectiveness of the introduced implicit reward and output preference in KD through experiments and theoretical analysis. The DPKD method outperforms the baseline method in both output response precision and exact match percentage. Code and data are available at https://aka.ms/dpkd.

The unprecedented performance of large language models (LLMs) necessitates improvements in evaluations. Rather than merely exploring the breadth of LLM abilities, we believe meticulous and thoughtful designs are essential to thorough, unbiased, and applicable evaluations. Given the importance of world knowledge to LLMs, we construct a Knowledge-oriented LLM Assessment benchmark (KoLA), in which we carefully design three crucial factors: (1) For ability modeling, we mimic human cognition to form a four-level taxonomy of knowledge-related abilities, covering 19 tasks. (2) For data, to ensure fair comparisons, we use both Wikipedia, a corpus prevalently pre-trained by LLMs, along with continuously collected emerging corpora, aiming to evaluate the capacity to handle unseen data and evolving knowledge. (3) For evaluation criteria, we adopt a contrastive system, including overall standard scores for better numerical comparability across tasks and models and a unique self-contrast metric for automatically evaluating knowledge hallucination. We evaluate 21 open-source and commercial LLMs and obtain some intriguing findings. The KoLA dataset and open-participation leaderboard are publicly released at https://kola.xlore.cn and will be continuously updated to provide references for developing LLMs and knowledge-related systems.