arXiv subjects

Zhiquan Tan

Publications and source records attributed to Zhiquan Tan.

At least 19 recordsLinked to original sources

arXiv2026

Self-Supervised On-Policy Distillation for Reasoning Language Models

GRPO-style RLVR trains reasoning models from multiple on-policy attempts per prompt, but typically uses these attempts only through terminal rewards. We show that a mixed group contains a richer process signal: a correct completion is a self-generated witness of how the current policy can solve the problem, while a wrong completion provides on-policy prefixes where the policy needs correction. We introduce \emph{Self-Supervised On-Policy Distillation} (SSOPD), which distills a teacher distribution conditioned on the shortest correct completion into prefixes of the longest wrong completion. This converts intra-group correct--wrong contrast into dense process supervision without external solution traces. A stopping-time view motivates the shortest-correct / longest-wrong rule as a finite-group approximation to editing persistent failures toward fast-success actions, and a prompt-level frontier weight concentrates the auxiliary loss where correct and wrong branches coexist. Across AIME 2024, AIME 2025, and HMMT 2025, SSOPD improves over GRPO in all nine model-benchmark settings. On Qwen3-8B, it reaches a macro Avg@12 of 65.6, outperforming GRPO by 1.6 points and the solution-conditioned OPSD baseline by 0.8 points. Code will be released at https://github.com/tzq1999/SSOPD.

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arXiv2026

From Intent to Evidence: A Categorical Approach for Structural Evaluation of Deep Research Agents

Deep Research Agents (DRAs) aim to answer complex questions by searching the web, checking evidence, and synthesizing conclusions across heterogeneous sources. We introduce a category-theoretic framework for evaluating and improving such agents. The framework treats deep research as a structured mapping from user intent to evidence-grounded conclusions, making retrieval traces, cross-source alignment, and final synthesis explicit. Guided by this view, we derive a mechanism-aware benchmark of 296 bilingual questions. The benchmark targets four structural skills central to real research: following multi-hop evidence chains, verifying claims across sources, re-ordering fragmented information, and rejecting unsupported assumptions. We evaluate 16 frontier systems with human verification and find that these structural tasks remain highly challenging: the best system reaches only 19.9% average accuracy. The results show that strong agents can sometimes reorganize evidence and detect false premises, but still struggle with long-horizon synthesis and intersection-heavy verification. Beyond evaluation, the same theory also leads to practical system improvements. We instantiate theory-guided interventions such as tracked search, which preserves retrieval traces, and category tools, which add explicit verification and synthesis steps. These interventions yield measurable gains in API-based deep research systems. Our work therefore provides both a challenging benchmark and concrete design guidance for building more reliable research agents.

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arXiv2026

PAINT: Partial-Solution Adaptive Interpolated Training for Self-Distilled Reasoners

Improving large language model (LLM) reasoning requires supervision that is both aligned with the model's own test-time states and informative at the token level. Reinforcement learning with verifiable rewards provides on-policy exploration but offers sparse, high-variance credit; supervised fine-tuning and distillation provide dense targets but often train on fixed trajectories or rely on stronger teachers. Recent privileged on-policy self-distillation explores a middle ground by scoring student rollouts with the same model under verified solution context. We revisit this setting through a contextual re-scoring lens: for reasoning, the important choices are not only whether privileged context is available, but how much of it should be revealed and where its distribution should shape the student. We propose PAINT (Partial-solution Adaptive INterpolated Training), which masks the verified solution according to rollout-reference overlap and applies a small energy-space interpolation on a sparse set of entropy-mismatch token positions. Across competition-level math benchmarks, PAINT consistently improves over a strong prior on-policy self-distillation baseline at all three Qwen3 scales. On Qwen3-8B, it raises macro Avg@12 by 2.1 points over this prior baseline and 2.9 points over GRPO.

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arXiv2026

Inference-Cost-Aware Dynamic Tree Construction for Efficient Inference in Large Language Models

Large Language Models (LLMs) face significant inference latency challenges stemming from their autoregressive design and large size. To address this, speculative decoding emerges as a solution, enabling the simultaneous generation and validation of multiple tokens. While recent approaches like EAGLE-2 and EAGLE-3 improve speculative decoding using dynamic tree structures, they often neglect the impact of crucial system variables such as GPU devices and batch sizes. Therefore, we introduce a new dynamic tree decoding approach called CAST that takes into account inference costs, including factors such as GPU configurations and batch sizes, to dynamically refine the tree structure. Through comprehensive experimentation across six diverse tasks and utilizing six distinct LLMs, our methodology demonstrates remarkable results, achieving speeds up to 5.2 times faster than conventional decoding methods. Moreover, it generally outperforms existing state-of-the-art techniques from 5 % to 20%. The code is available at https://github.com/EAGLE-Research/sglang-eagle4.

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arXiv2025

A Theoretical Lens for RL-Tuned Language Models via Energy-Based Models

Large language models (LLMs) trained via KL-regularized reinforcement learning demonstrate strong instruction following, self-correction, and reasoning abilities. Yet their theoretical underpinnings remain limited. We exploit the closed-form energy-based model (EBM) structure of the optimal KL-regularized policy to provide a unified variational analysis of LLMs. For instruction-tuned models, under natural assumptions on reward potentials and pretraining symmetry, we prove that the transition kernel satisfies detailed balance with respect to a scalar potential encoding response quality. This yields monotonic KL convergence to a high-quality stationary distribution, bounded hitting times to superior states, and exponential mixing governed by the spectral gap. For reasoning models trained with verifiable rewards (RLVR), we show the objective is equivalent to expected KL minimization toward an optimal reasoning distribution, with the suboptimality gap reducing to the Bernoulli KL between target and current accuracies along the natural gradient flow. This helps explain empirical entropy-accuracy trade-offs.

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arXiv2025

Generalized Category Discovery via Reciprocal Learning and Class-Wise Distribution Regularization

Generalized Category Discovery (GCD) aims to identify unlabeled samples by leveraging the base knowledge from labeled ones, where the unlabeled set consists of both base and novel classes. Since clustering methods are time-consuming at inference, parametric-based approaches have become more popular. However, recent parametric-based methods suffer from inferior base discrimination due to unreliable self-supervision. To address this issue, we propose a Reciprocal Learning Framework (RLF) that introduces an auxiliary branch devoted to base classification. During training, the main branch filters the pseudo-base samples to the auxiliary branch. In response, the auxiliary branch provides more reliable soft labels for the main branch, leading to a virtuous cycle. Furthermore, we introduce Class-wise Distribution Regularization (CDR) to mitigate the learning bias towards base classes. CDR essentially increases the prediction confidence of the unlabeled data and boosts the novel class performance. Combined with both components, our proposed method, RLCD, achieves superior performance in all classes with negligible extra computation. Comprehensive experiments across seven GCD datasets validate its superiority. Our codes are available at https://github.com/APORduo/RLCD.

cs.CV↗

arXiv2025

RelationMatch: Matching In-batch Relationships for Semi-supervised Learning

Semi-supervised learning has emerged as a pivotal approach for leveraging scarce labeled data alongside abundant unlabeled data. Despite significant progress, prevailing SSL methods predominantly enforce consistency between different augmented views of individual samples, thereby overlooking the rich relational structure inherent within a mini-batch. In this paper, we present RelationMatch, a novel SSL framework that explicitly enforces in-batch relational consistency through a Matrix Cross-Entropy (MCE) loss function. The proposed MCE loss is rigorously derived from both matrix analysis and information geometry perspectives, ensuring theoretical soundness and practical efficacy. Extensive empirical evaluations on standard benchmarks, including a notable 15.21% accuracy improvement over FlexMatch on STL-10, demonstrate that RelationMatch not only advances state-of-the-art performance but also provides a principled foundation for incorporating relational cues in SSL.

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arXiv2025

Exploring Information-Theoretic Metrics Associated with Neural Collapse in Supervised Training

In this paper, we introduce matrix entropy as an analytical tool for studying supervised learning, investigating the information content of data representations and classification head vectors, as well as the dynamic interactions between them during the supervised learning process. Our experimental results reveal that matrix entropy effectively captures the variations in information content of data representations and classification head vectors as neural networks approach Neural Collapse during supervised training, while also serving as a robust metric for measuring similarity among data samples. Leveraging this property, we propose Cross-Model Alignment (CMA) loss to optimize the fine-tuning of pretrained models. To characterize the dynamics of neural networks nearing the Neural Collapse state, we introduce two novel metrics: the Matrix Mutual Information Ratio (MIR) and the Matrix Entropy Difference Ratio (HDR), which quantitatively assess the interactions between data representations and classification heads in supervised learning, with theoretical optimal values derived under the Neural Collapse state. Our experiments demonstrate that MIR and HDR effectively explain various phenomena in neural networks, including the dynamics of standard supervised training, linear mode connectivity. Moreover, we use MIR and HDR to analyze the dynamics of grokking, which is a fascinating phenomenon in supervised learning where a model unexpectedly exhibits generalization long after achieving training data fit.

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arXiv2025

Information-Theoretic Perspectives on Optimizers

The interplay of optimizers and architectures in neural networks is complicated and hard to understand why some optimizers work better on some specific architectures. In this paper, we find that the traditionally used sharpness metric does not fully explain the intricate interplay and introduces information-theoretic metrics called entropy gap to better help analyze. It is found that both sharpness and entropy gap affect the performance, including the optimization dynamic and generalization. We further use information-theoretic tools to understand a recently proposed optimizer called Lion and find ways to improve it.

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arXiv2024

Multiplexed Streaming Codes for Messages with Different Decoding Delays in Channel with Burst and Random Erasures

In a real-time transmission scenario, messages are transmitted through a channel that is subject to packet loss. The destination must recover the messages within the required deadline. In this paper, we consider a setup where two different types of messages with distinct decoding deadlines are transmitted through a channel model that introduces either one burst erasure of length at most $B$, or $N$ random erasures in any fixed-sized sliding window. The message with a short decoding deadline $T_{\mathrm{u}}$ is referred to as an urgent message, while the other one with a decoding deadline $T_{\mathrm{v}}$ ($T_{\mathrm{v}} > T_{\mathrm{u}}$) is referred to as a less urgent message. We consider the scenario where $T_{\mathrm{v}} > T_{\mathrm{u}} + B$ and propose a non-trivial achievable region $\mathcal{R}$ for the aforementioned channel model. We propose a novel merging approach to encode two message streams of different urgency levels into a single flow and present explicit constructions for encoding, contributing to the establishment of the achievability of region $\mathcal{R}$. Our comprehensive analysis demonstrates that this region encompasses the rate pairs of existing encoding schemes and coincides with the capacity region in burst channel scenarios. Lastly, we investigate the property of the achievable region $\mathcal{R}$, proving that it is the largest one obtained from all the rate pairs under the merging method.

cs.IT↗

arXiv2024

Diff-eRank: A Novel Rank-Based Metric for Evaluating Large Language Models

Large Language Models (LLMs) have transformed natural language processing and extended their powerful capabilities to multi-modal domains. As LLMs continue to advance, it is crucial to develop diverse and appropriate metrics for their evaluation. In this paper, we introduce a novel rank-based metric, Diff-eRank, grounded in information theory and geometry principles. Diff-eRank assesses LLMs by analyzing their hidden representations, providing a quantitative measure of how efficiently they eliminate redundant information during training. We demonstrate the applicability of Diff-eRank in both single-modal (e.g., language) and multi-modal settings. For language models, our results show that Diff-eRank increases with model size and correlates well with conventional metrics such as loss and accuracy. In the multi-modal context, we propose an alignment evaluation method based on the eRank, and verify that contemporary multi-modal LLMs exhibit strong alignment performance based on our method. Our code is publicly available at https://github.com/waltonfuture/Diff-eRank.

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arXiv2024

ATLAS: Adapter-Based Multi-Modal Continual Learning with a Two-Stage Learning Strategy

While vision-and-language models significantly advance in many fields, the challenge of continual learning is unsolved. Parameter-efficient modules like adapters and prompts present a promising way to alleviate catastrophic forgetting. However, existing works usually learn individual adapters for each task, which may result in redundant knowledge among adapters. Moreover, they continue to use the original pre-trained model to initialize the downstream model, leading to negligible changes in the model's generalization compared to the original model. In addition, there is still a lack of research investigating the consequences of integrating a multi-modal model into the updating procedure for both uni-modal and multi-modal tasks and the subsequent impacts it has on downstream tasks. In this paper, we propose an adapter-based two-stage learning paradigm, a multi-modal continual learning scheme that consists of experience-based learning and novel knowledge expansion, which helps the model fully use experience knowledge and compensate for novel knowledge. Extensive experiments demonstrate that our method is proficient for continual learning. It expands the distribution of representation upstream while also minimizing the negative impact of forgetting previous tasks. Additionally, it enhances the generalization capability for downstream tasks. Furthermore, we incorporate both multi-modal and uni-modal tasks into upstream continual learning. We observe that learning from upstream tasks can help with downstream tasks. Our code will be available at: https://github.com/lihong2303/ATLAS.

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arXiv2024

Matrix Information Theory for Self-Supervised Learning

The maximum entropy encoding framework provides a unified perspective for many non-contrastive learning methods like SimSiam, Barlow Twins, and MEC. Inspired by this framework, we introduce Matrix-SSL, a novel approach that leverages matrix information theory to interpret the maximum entropy encoding loss as matrix uniformity loss. Furthermore, Matrix-SSL enhances the maximum entropy encoding method by seamlessly incorporating matrix alignment loss, directly aligning covariance matrices in different branches. Experimental results reveal that Matrix-SSL outperforms state-of-the-art methods on the ImageNet dataset under linear evaluation settings and on MS-COCO for transfer learning tasks. Specifically, when performing transfer learning tasks on MS-COCO, our method outperforms previous SOTA methods such as MoCo v2 and BYOL up to 3.3% with only 400 epochs compared to 800 epochs pre-training. We also try to introduce representation learning into the language modeling regime by fine-tuning a 7B model using matrix cross-entropy loss, with a margin of 3.1% on the GSM8K dataset over the standard cross-entropy loss. Code available at https://github.com/yifanzhang-pro/Matrix-SSL.

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arXiv2024

Can I understand what I create? Self-Knowledge Evaluation of Large Language Models

Large language models (LLMs) have achieved remarkable progress in linguistic tasks, necessitating robust evaluation frameworks to understand their capabilities and limitations. Inspired by Feynman's principle of understanding through creation, we introduce a self-knowledge evaluation framework that is easy to implement, evaluating models on their ability to comprehend and respond to self-generated questions. Our findings, based on testing multiple models across diverse tasks, reveal significant gaps in the model's self-knowledge ability. Further analysis indicates these gaps may be due to misalignment with human attention mechanisms. Additionally, fine-tuning on self-generated math task may enhance the model's math performance, highlighting the potential of the framework for efficient and insightful model evaluation and may also contribute to the improvement of LLMs.

cs.CL↗

arXiv2024

Unveiling the Dynamics of Information Interplay in Supervised Learning

In this paper, we use matrix information theory as an analytical tool to analyze the dynamics of the information interplay between data representations and classification head vectors in the supervised learning process. Specifically, inspired by the theory of Neural Collapse, we introduce matrix mutual information ratio (MIR) and matrix entropy difference ratio (HDR) to assess the interactions of data representation and class classification heads in supervised learning, and we determine the theoretical optimal values for MIR and HDR when Neural Collapse happens. Our experiments show that MIR and HDR can effectively explain many phenomena occurring in neural networks, for example, the standard supervised training dynamics, linear mode connectivity, and the performance of label smoothing and pruning. Additionally, we use MIR and HDR to gain insights into the dynamics of grokking, which is an intriguing phenomenon observed in supervised training, where the model demonstrates generalization capabilities long after it has learned to fit the training data. Furthermore, we introduce MIR and HDR as loss terms in supervised and semi-supervised learning to optimize the information interactions among samples and classification heads. The empirical results provide evidence of the method's effectiveness, demonstrating that the utilization of MIR and HDR not only aids in comprehending the dynamics throughout the training process but can also enhances the training procedure itself.

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arXiv2024

OTMatch: Improving Semi-Supervised Learning with Optimal Transport

Semi-supervised learning has made remarkable strides by effectively utilizing a limited amount of labeled data while capitalizing on the abundant information present in unlabeled data. However, current algorithms often prioritize aligning image predictions with specific classes generated through self-training techniques, thereby neglecting the inherent relationships that exist within these classes. In this paper, we present a new approach called OTMatch, which leverages semantic relationships among classes by employing an optimal transport loss function to match distributions. We conduct experiments on many standard vision and language datasets. The empirical results show improvements in our method above baseline, this demonstrates the effectiveness and superiority of our approach in harnessing semantic relationships to enhance learning performance in a semi-supervised setting.

cs.CV↗

arXiv2024

Information Flow in Self-Supervised Learning

In this paper, we conduct a comprehensive analysis of two dual-branch (Siamese architecture) self-supervised learning approaches, namely Barlow Twins and spectral contrastive learning, through the lens of matrix mutual information. We prove that the loss functions of these methods implicitly optimize both matrix mutual information and matrix joint entropy. This insight prompts us to further explore the category of single-branch algorithms, specifically MAE and U-MAE, for which mutual information and joint entropy become the entropy. Building on this intuition, we introduce the Matrix Variational Masked Auto-Encoder (M-MAE), a novel method that leverages the matrix-based estimation of entropy as a regularizer and subsumes U-MAE as a special case. The empirical evaluations underscore the effectiveness of M-MAE compared with the state-of-the-art methods, including a 3.9% improvement in linear probing ViT-Base, and a 1% improvement in fine-tuning ViT-Large, both on ImageNet.

cs.CV↗

arXiv2024

Provable Contrastive Continual Learning

Continual learning requires learning incremental tasks with dynamic data distributions. So far, it has been observed that employing a combination of contrastive loss and distillation loss for training in continual learning yields strong performance. To the best of our knowledge, however, this contrastive continual learning framework lacks convincing theoretical explanations. In this work, we fill this gap by establishing theoretical performance guarantees, which reveal how the performance of the model is bounded by training losses of previous tasks in the contrastive continual learning framework. Our theoretical explanations further support the idea that pre-training can benefit continual learning. Inspired by our theoretical analysis of these guarantees, we propose a novel contrastive continual learning algorithm called CILA, which uses adaptive distillation coefficients for different tasks. These distillation coefficients are easily computed by the ratio between average distillation losses and average contrastive losses from previous tasks. Our method shows great improvement on standard benchmarks and achieves new state-of-the-art performance.

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