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Yisen Wang

Publications and source records attributed to Yisen Wang.

At least 37 records · Page 2Linked to original sources
arXiv2026

Automated Formal Proofs of Combinatorial Identities via Wilf-Zeilberger Guidance and LLMs

Automating formal proofs of combinatorial identities is challenging for LLM-based provers, as long-horizon proof planning is required and unconstrained search quickly explodes. Symbolic methods such as the Wilf-Zeilberger (WZ) method can achieve a mechanized proof of combinatorial identities by constructing special auxiliary functions and demonstrating that they satisfy specific recurrence relations. We propose WZ-LLM, a neuro-symbolic framework that turns WZ proof plans into executable proof sketches in Lean 4 and uses an LLM-based prover to discharge the resulting machine-checkable subgoals. We also train a dedicated WZ-Prover via a Lean-kernel-verified bootstrapping loop with expert-verified iteration, followed by DAPO-based refinement. Experiments show that WZ-LLM achieves a 34% proof success rate on LCI-Test (100 classic combinatorial identities), outperforming strong baselines such as DeepSeek-V3 and Goedel-Prover-V2, and delivering consistent gains on CombiBench and PutnamBench-Comb. These results indicate that our framework provides two complementary strengths: improved direct proving for identities beyond the scope of WZ, and substantially higher end-to-end success when WZ sketches guide a specialized prover.

cs.LG↗
arXiv2026

A Unified Theory of Sparse Dictionary Learning in Mechanistic Interpretability: Piecewise Biconvexity and Spurious Minima

As AI models achieve remarkable capabilities across diverse domains, understanding what representations they learn and how they encode concepts has become increasingly important for both scientific progress and trustworthy deployment. Recent works in mechanistic interpretability have widely reported that neural networks represent meaningful concepts as linear directions in their representation spaces and often encode diverse concepts in superposition. Various sparse dictionary learning (SDL) methods, including sparse autoencoders, transcoders, and crosscoders, are utilized to address this by training auxiliary models with sparsity constraints to disentangle these superposed concepts into monosemantic features. These methods are the backbone of modern mechanistic interpretability, yet in practice they consistently produce polysemantic features, feature absorption, and dead neurons, with very limited theoretical understanding of why these phenomena occur. Existing theoretical work is limited to tied-weight sparse autoencoders, leaving the broader family of SDL methods without formal grounding. We develop the first unified theoretical framework that casts all major SDL variants as a single piecewise biconvex optimization problem, and characterize its global solution set, non-identifiability, and spurious optima. This analysis yields principled explanations for feature absorption and dead neurons. To expose these pathologies under full ground-truth access, we introduce the Linear Representation Bench. Guided by our theory, we propose feature anchoring, a novel technique that restores SDL identifiability, substantially improving feature recovery across synthetic benchmarks and real neural representations.

cs.LG↗
arXiv2026

TrustLDM: Benchmarking Trustworthiness in Language Diffusion Models

The rapid development of Language Diffusion Models (LDMs) challenges the dominant position of auto-regressive competitors in language processing. However, their flexible, any-order decoding strategies not only enable fast decoding speed but also potentially bring new trustworthiness challenges. To better understand the risks behind their pipelines, we introduce a comprehensive trustworthiness benchmark tailored to LDMs (TrustLDM), evaluating safety, privacy, and fairness across different LDM architectures with multiple categories of static post contexts. Our empirical results show that although LDMs generally exhibit strong trustworthiness with only the user prompts, their alignment behavior degrades noticeably when the malicious post contexts are attached to the masked responses. We further observe that longer contexts do not necessarily induce stronger effects, and both decoding order and generation length affect the evaluation outcomes. Finally, we propose TrustLDM-Auto, an automatic evaluation framework that leverages LDM decoding flexibility to systematically identify vulnerable configurations, revealing substantial trustworthiness weaknesses across all evaluated models and dimensions. Our work may potentially help the community build more trustworthy LDMs. Our code is available at https://github.com/PKU-ML/TrustLDM.

cs.CL↗
arXiv2026

Towards provable probabilistic safety for scalable embodied AI systems

Embodied AI systems, comprising AI models and physical plants, are increasingly prevalent across various applications. Due to the rarity of system failures, ensuring their safety in complex operating environments remains a major challenge, which severely hinders their large-scale deployment in safety-critical domains, such as autonomous vehicles, medical devices, and robotics. While achieving provable deterministic safety-verifying system safety across all possible scenarios-remains theoretically ideal, the rarity and complexity of corner cases make this approach impractical for scalable embodied AI systems. Instead, empirical safety evaluation is employed as an alternative, but the absence of provable guarantees imposes significant limitations. To address these issues, we argue for a paradigm shift to provable probabilistic safety that integrates provable guarantees with progressive achievement toward a probabilistic safety boundary on overall system performance. The new paradigm better leverages statistical methods to enhance feasibility and scalability, and a well-defined probabilistic safety boundary enables embodied AI systems to be deployed at scale. In this Perspective, we outline a roadmap for provable probabilistic safety, along with corresponding challenges and potential solutions. By bridging the gap between theoretical safety assurance and practical deployment, this Perspective offers a pathway toward safer, large-scale adoption of embodied AI systems in safety-critical applications.

eess.SY↗
arXiv2026

On the Adversarial Transferability of Generalized "Skip Connections"

Skip connection is an essential ingredient for modern deep models to be deeper and more powerful. Despite their huge success in normal scenarios (state-of-the-art classification performance on natural examples), we investigate and identify an interesting property of skip connections under adversarial scenarios, namely, the use of skip connections allows easier generation of highly transferable adversarial examples. Specifically, in ResNet-like models (with skip connections), we find that biasing backpropagation to favor gradients from skip connections--while suppressing those from residual modules via a decay factor--allows one to craft adversarial examples with high transferability. Based on this insight, we propose the Skip Gradient Method (SGM). Although starting from ResNet-like models in vision domains, we further extend SGM to more advanced architectures, including Vision Transformers (ViTs), models with varying-length paths, and other domains such as natural language processing. We conduct comprehensive transfer-based attacks against diverse model families, including ResNets, Transformers, Inceptions, Neural Architecture Search-based models, and Large Language Models (LLMs). The results demonstrate that employing SGM can greatly improve the transferability of crafted attacks in almost all cases. Furthermore, we demonstrate that SGM can still be effective under more challenging settings such as ensemble-based attacks, targeted attacks, and against defense equipped models. At last, we provide theoretical explanations and empirical insights on how SGM works. Our findings not only motivate new adversarial research into the architectural characteristics of models but also open up further challenges for secure model architecture design. Our code is available at https://github.com/mo666666/SGM.

cs.LG↗
arXiv2026

Finding and Reactivating Post-Trained LLMs' Hidden Safety Mechanisms

Despite the impressive performance of general-purpose large language models (LLMs), they often require fine-tuning or post-training to excel at specific tasks. For instance, large reasoning models (LRMs), such as the DeepSeek-R1 series, demonstrate strong reasoning capabilities after post-training different general large language models on diverse chain-of-thought (CoT) datasets. However, this additional training frequently comes at the cost of reduced safety, as the fine-tuned or post-trained models tend to exhibit more harmful behaviors compared with the regular LLMs before post-training or fine-tuning, potentially leading to harmful outcomes due to their enhanced capabilities. Taking LRMs as an example, we first investigate the underlying cause of this safety degradation in this paper. Our analysis reveals that post-training can mask the original safety mechanisms of the base LLM, while over-amplifying representations related to their post-training ability. But luckily, we also find that LRMs' safety mechanisms still exist instead of being removed during their post-training. Based on these findings, we propose a lightweight and cost-effective solution called SafeReAct that restores the suppressed safety behaviors by aligning with LoRA adapters on a few layers. Experiments on four state-of-the-art LRMs show that our method significantly improves safety on harmful prompts without compromising reasoning performance. Besides LRMs, additional results on other domain-specific LLMs, like medical models, further confirm the generality and effectiveness of our approach.

cs.CL↗
arXiv2026

Difficult Examples Hurt Unsupervised Contrastive Learning: A Theoretical Perspective

Unsupervised contrastive learning has shown significant performance improvements in recent years, often approaching or even rivaling supervised learning in various tasks. However, its learning mechanism is fundamentally different from supervised learning. Previous works have shown that difficult examples (well-recognized in supervised learning as examples around the decision boundary), which are essential in supervised learning, contribute minimally in unsupervised settings. In this paper, perhaps surprisingly, we find that the direct removal of difficult examples, although reduces the sample size, can boost the downstream classification performance of contrastive learning. To uncover the reasons behind this, we develop a theoretical framework modeling the similarity between different pairs of samples. Guided by this framework, we conduct a thorough theoretical analysis revealing that the presence of difficult examples negatively affects the generalization of contrastive learning. Furthermore, we demonstrate that the removal of these examples, and techniques such as margin tuning and temperature scaling can enhance its generalization bounds, thereby improving performance. Empirically, we propose a simple and efficient mechanism for selecting difficult examples and validate the effectiveness of the aforementioned methods, which substantiates the reliability of our proposed theoretical framework.

cs.LG↗
arXiv2026

On the Limits of Sparse Autoencoders: A Theoretical Framework and Reweighted Remedy

Sparse autoencoders (SAEs) have recently emerged as a powerful tool for interpreting the features learned by large language models (LLMs). By reconstructing features with sparsely activated networks, SAEs aim to recover complex superposed polysemantic features into interpretable monosemantic ones. Despite their wide applications, it remains unclear under what conditions SAEs can fully recover the ground truth monosemantic features from the superposed polysemantic ones. In this paper, we provide the first theoretical analysis with a closed-form solution for SAEs, revealing that they generally fail to fully recover the ground truth monosemantic features unless the ground truth features are extremely sparse. To improve the feature recovery of SAEs in general cases, we propose a reweighting strategy targeting at enhancing the reconstruction of the ground truth monosemantic features instead of the observed polysemantic ones. We further establish a theoretical weight selection principle for our proposed weighted SAE (WSAE). Experiments across multiple settings validate our theoretical findings and demonstrate that our WSAE significantly improves feature monosemanticity and interpretability.

cs.LG↗
arXiv2026

SAE as a Crystal Ball: Interpretable Features Predict Cross-domain Transferability of LLMs without Training

In recent years, pre-trained large language models have achieved remarkable success across diverse tasks. Besides the pivotal role of self-supervised pre-training, their effectiveness in downstream applications also depends critically on the post-training process, which adapts models to task-specific data and objectives. However, this process inevitably introduces model shifts that can influence performance in different domains, and how such shifts transfer remains poorly understood. To open up the black box, we propose the SAE-based Transferability Score (STS), a new metric that leverages sparse autoencoders (SAEs) to forecast post-training transferability. Taking supervised fine-tuning as an example, STS identifies shifted dimensions in SAE representations and calculates their correlations with downstream domains, enabling reliable estimation of transferability \textit{before} fine-tuning. Extensive experiments across multiple models and domains show that STS accurately predicts the transferability of supervised fine-tuning, achieving Pearson correlation coefficients above 0.7 with actual performance changes. Beyond this, we take an initial step toward extending STS to reinforcement learning. We believe that STS can serve as an {\color{black} interpretable} tool for guiding post-training strategies in LLMs. Code is available at https://github.com/PKU-ML/STS.

cs.AI↗
arXiv2026

Rethinking Personalization in Large Language Models at the Token Level

With large language models (LLMs) now performing strongly across diverse tasks, there is growing demand for them to personalize outputs for individual users. Personalization is typically framed as an additional layer on top of a base NLP task, requiring model responses to meet user-specific needs while still accomplishing the underlying task. From a token-level perspective, different tokens in a response contribute to personalization to varying degrees. Tokens with higher personalization relevance should therefore receive greater emphasis when developing personalized LLMs. However, accurately estimating such personalization degrees remains challenging. To address this challenge, we propose PerContrast, a self-contrast method that estimates each output token's dependence on user-specific information through causal intervention. Building on this mechanism, we develop the PerCE loss, which adaptively upweights tokens with higher estimated personalization degrees during training via a bootstrap procedure, enabling the model to alternate between estimating and optimizing these tokens. Experiments on multiple LLMs demonstrate that PerCE substantially improves personalization performance with minimal additional cost, achieving average gains of over 10% and up to 68.04% on the LongLaMP dataset, along with strong cross-task and cross-scenario transferability. These results highlight the importance of token-level personalization modeling and establish token-aware training as a simple yet effective paradigm for advancing personalized LLMs.

cs.CL↗
arXiv2026

Autoregressive Models Rival Diffusion Models at ANY-ORDER Generation

Diffusion language models enable any-order generation and bidirectional conditioning, offering appealing flexibility for tasks such as infilling, rewriting, and self-correction. However, their formulation-predicting one part of a sequence from another within a single-step dependency-limits modeling depth and often yields lower sample quality and stability than autoregressive (AR) models. To address this, we revisit autoregressive modeling as a foundation and reformulate diffusion-style training into a structured multi-group prediction process. We propose Any-order Any-subset Autoregressive modeling (A3), a generalized framework that extends the standard AR factorization to arbitrary token groups and generation orders. A3 preserves the probabilistic rigor and multi-layer dependency modeling of AR while inheriting diffusion models' flexibility for parallel and bidirectional generation. We implement A3 through a two-stream attention architecture and a progressive adaptation strategy that transitions pretrained AR models toward any-order prediction. Experiments on question answering, commonsense reasoning, and story infilling demonstrate that A3 outperforms diffusion-based models while maintaining flexible decoding. This work offers a unified approach for a flexible, efficient, and novel language modeling paradigm.

cs.CL↗
arXiv2026

Leveraging Flatness to Improve Information-Theoretic Generalization Bounds for SGD

Information-theoretic (IT) generalization bounds have been used to study the generalization of learning algorithms. These bounds are intrinsically data- and algorithm-dependent so that one can exploit the properties of data and algorithm to derive tighter bounds. However, we observe that although the flatness bias is crucial for SGD's generalization, these bounds fail to capture the improved generalization under better flatness and are also numerically loose. This is caused by the inadequate leverage of SGD's flatness bias in existing IT bounds. This paper derives a more flatness-leveraging IT bound for the flatness-favoring SGD. The bound indicates the learned models generalize better if the large-variance directions of the final weight covariance have small local curvatures in the loss landscape. Experiments on deep neural networks show our bound not only correctly reflects the better generalization when flatness is improved, but is also numerically much tighter. This is achieved by a flexible technique called "omniscient trajectory". When applied to Gradient Descent's minimax excess risk on convex-Lipschitz-Bounded problems, it improves representative IT bounds' $Ω(1)$ rates to $O(1/\sqrt{n})$. It also implies a by-pass of memorization-generalization trade-offs.

cs.LG↗
arXiv2025

Decoding Large Language Diffusion Models with Foreseeing Movement

Large Language Diffusion Models (LLDMs) benefit from a flexible decoding mechanism that enables parallelized inference and controllable generations over autoregressive models. Yet such flexibility introduces a critical challenge: inference performance becomes highly sensitive to the decoding order of tokens. Existing heuristic methods, however, focus mainly on local effects while overlooking long-term impacts. To address this limitation, we propose the Foreseeing Decoding Method (FDM), a novel approach that integrates both local and global considerations to unlock the full potential, employing a search-based strategy to enable effective optimization in discrete spaces. Furthermore, by analyzing the consistency of chosen tokens in the full decoding process, we develop a variant, FDM with Acceleration (FDM-A), which restricts deep exploration to critical steps identified as the exploration and balance circumantences. Extensive experiments across diverse benchmarks and model architectures validate the scalability of FDM and demonstrate the superior efficiency-performance trade-off achieved by FDM-A. Our work might potentially provide a principled step toward more powerful decoding methods for LLDMs.

cs.LG↗
arXiv2025

Monet: Reasoning in Latent Visual Space Beyond Images and Language

"Thinking with images" has emerged as an effective paradigm for advancing visual reasoning, extending beyond text-only chains of thought by injecting visual evidence into intermediate reasoning steps. However, existing methods fall short of human-like abstract visual thinking, as their flexibility is fundamentally limited by external tools. In this work, we introduce Monet, a training framework that enables multimodal large language models (MLLMs) to reason directly within the latent visual space by generating continuous embeddings that function as intermediate visual thoughts. We identify two core challenges in training MLLMs for latent visual reasoning: high computational cost in latent-vision alignment and insufficient supervision over latent embeddings, and address them with a three-stage distillation-based supervised fine-tuning (SFT) pipeline. We further reveal a limitation of applying GRPO to latent reasoning: it primarily enhances text-based reasoning rather than latent reasoning. To overcome this, we propose VLPO (Visual-latent Policy Optimization), a reinforcement learning method that explicitly incorporates latent embeddings into policy gradient updates. To support SFT, we construct Monet-SFT-125K, a high-quality text-image interleaved CoT dataset containing 125K real-world, chart, OCR, and geometry CoTs. Our model, Monet-7B, shows consistent gains across real-world perception and reasoning benchmarks and exhibits strong out-of-distribution generalization on challenging abstract visual reasoning tasks. We also empirically analyze the role of each training component and discuss our early unsuccessful attempts, providing insights for future developments in visual latent reasoning. Our model, data, and code are available at https://github.com/NOVAglow646/Monet.

cs.CV↗
arXiv2025

An Augmentation Overlap Theory of Contrastive Learning

Recently, self-supervised contrastive learning has achieved great success on various tasks. However, its underlying working mechanism is yet unclear. In this paper, we first provide the tightest bounds based on the widely adopted assumption of conditional independence. Further, we relax the conditional independence assumption to a more practical assumption of augmentation overlap and derive the asymptotically closed bounds for the downstream performance. Our proposed augmentation overlap theory hinges on the insight that the support of different intra-class samples will become more overlapped under aggressive data augmentations, thus simply aligning the positive samples (augmented views of the same sample) could make contrastive learning cluster intra-class samples together. Moreover, from the newly derived augmentation overlap perspective, we develop an unsupervised metric for the representation evaluation of contrastive learning, which aligns well with the downstream performance almost without relying on additional modules. Code is available at https://github.com/PKU-ML/GARC.

cs.LG↗
arXiv2025

Parallel BiLSTM-Transformer networks for forecasting chaotic dynamics

The nonlinear nature of chaotic systems results in extreme sensitivity to initial conditions and highly intricate dynamical behaviors, posing fundamental challenges for accurately predicting their evolution. To overcome the limitation that conventional approaches fail to capture both local features and global dependencies in chaotic time series simultaneously, this study proposes a parallel predictive framework integrating Transformer and Bidirectional Long Short-Term Memory (BiLSTM) networks. The hybrid model employs a dual-branch architecture, where the Transformer branch mainly captures long-range dependencies while the BiLSTM branch focuses on extracting local temporal features. The complementary representations from the two branches are fused in a dedicated feature-fusion layer to enhance predictive accuracy. As illustrating examples, the model's performance is systematically evaluated on two representative tasks in the Lorenz system. The first is autonomous evolution prediction, in which the model recursively extrapolates system trajectories from the time-delay embeddings of the state vector to evaluate long-term tracking accuracy and stability. The second is inference of unmeasured variable, where the model reconstructs the unobserved states from the time-delay embeddings of partial observations to assess its state-completion capability. The results consistently indicate that the proposed hybrid framework outperforms both single-branch architectures across tasks, demonstrating its robustness and effectiveness in chaotic system prediction.

cs.LG↗
arXiv2025

Language Ranker: A Lightweight Ranking framework for LLM Decoding

Conventional research on large language models (LLMs) has primarily focused on refining output distributions, while paying less attention to the decoding process that transforms these distributions into final responses. Recent advances, such as scaling the computation of inference time with reward models, have underscored the importance of decoding, but these methods often suffer from high computational costs and limited applicability. In this paper, we revisit LLM generation through the lens of recommender systems, conceptualizing the decoding process as analogous to the ranking stage in recommendation pipelines. From this perspective, we observe that both traditional decoding methods and reward models exhibit clear limitations such as redundancy. Motivated by this insight, we propose Language Ranker, a novel framework that introduces a lightweight module to rerank candidate responses using features extracted by the base model. Experiments across a wide range of tasks show that Language Ranker achieves performance comparable to large-scale reward models, while requiring only <0.5M additional parameters, significantly reducing the computational overhead during both training and inference stages. This highlights the efficiency and effectiveness of our method, showcasing its potential to fully unlock the capabilities of LLMs.

cs.CL↗
arXiv2025

LANPO: Bootstrapping Language and Numerical Feedback for Reinforcement Learning in LLMs

Reinforcement learning in large language models (LLMs) often relies on scalar rewards, a practice that discards valuable textual rationale buried in the rollouts, forcing the model to explore \textit{de novo} with each attempt and hindering sample efficiency. While LLMs can uniquely learn from language feedback provided in-context, naively integrating on-line experiences into RL training presents a paradox: feedback from the same problem risks information leakage and memorization, while feedback from different problems often leads to behavior collapse due to irrelevant context. To resolve this tension, we propose \textbf{Language-And-Numerical Policy Optimization (LANPO)}, a framework that cleanly separates the roles of feedback: language guides exploration, while numerical rewards drive optimization. LANPO builds a dynamic experience pool from past trials and introduces two principles to ensure feedback is effective: \emph{Reward-Agnostic Reflection} for safe intra-sample self-correction and \emph{Relevant Abstraction} to distill generalizable lessons from inter-sample experiences. Across mathematical reasoning benchmarks, LANPO enables 7B and 14B models to significantly outperform strong baselines trained with GRPO in test accuracy. Our work provides a robust method for integrating historical experiences into the LLM RL loop, creating more effective and data-efficient learning agents.

cs.LG↗