Zicheng Xu

Jun Tan, Qing Guo, Zicheng Xu et al.

Counterfactual explanations (CEs) are essential for actionable recourse, yet their reliability is often compromised in low-density regions, where classifiers exhibit high variance. Unlike existing methods that rely on expensive ensemble intersections to define stability, we propose \textit{DensityFlow}, a generative framework that constructs robust CEs by adhering to the high-confidence data manifold. Specifically, we model the counterfactual generation as continuous-time dynamics parameterized by Neural ODE, guided by a differentiable density score to actively avoid uncertain, low-density areas. This density score is learned via Noise Contrastive Estimation, effectively leveraging a $(K{+}1)$-way discriminator to estimate density ratios. For black-box settings, we introduce a local proxy distillation mechanism that aligns a lightweight surrogate with the target model strictly within the trajectory of CE generation, enabling efficient gradient-based optimization with minimal queries. Experiments demonstrate that \textit{DensityFlow} achieves superior validity under model multiplicity while significantly reducing query costs compared to ensemble-based baselines. Our implementation is available at https://github.com/G-AILab/DensityFlow.

Tian Ye, Zicheng Xu, Yuanzhi Li et al.

Recent advances in language models have demonstrated their capability to solve mathematical reasoning problems, achieving near-perfect accuracy on grade-school level math benchmarks like GSM8K. In this paper, we formally study how language models solve these problems. We design a series of controlled experiments to address several fundamental questions: (1) Can language models truly develop reasoning skills, or do they simply memorize templates? (2) What is the model's hidden (mental) reasoning process? (3) Do models solve math questions using skills similar to or different from humans? (4) Do models trained on GSM8K-like datasets develop reasoning skills beyond those necessary for solving GSM8K problems? (5) What mental process causes models to make reasoning mistakes? (6) How large or deep must a model be to effectively solve GSM8K-level math questions? Our study uncovers many hidden mechanisms by which language models solve mathematical questions, providing insights that extend beyond current understandings of LLMs.

Tian Ye, Zicheng Xu, Yuanzhi Li et al.

Language models have demonstrated remarkable performance in solving reasoning tasks; however, even the strongest models still occasionally make reasoning mistakes. Recently, there has been active research aimed at improving reasoning accuracy, particularly by using pretrained language models to "self-correct" their mistakes via multi-round prompting. In this paper, we follow this line of work but focus on understanding the usefulness of incorporating "error-correction" data directly into the pretraining stage. This data consists of erroneous solution steps immediately followed by their corrections. Using a synthetic math dataset, we show promising results: this type of pretrain data can help language models achieve higher reasoning accuracy directly (i.e., through simple auto-regression, without multi-round prompting) compared to pretraining on the same amount of error-free data. We also delve into many details, such as (1) how this approach differs from beam search, (2) how such data can be prepared, (3) whether masking is needed on the erroneous tokens, (4) the amount of error required, (5) whether such data can be deferred to the fine-tuning stage, and many others.

Zicheng Xu, Guanchu Wang, Yu-Neng Chuang et al.

Large Reasoning Models (LRMs) demonstrate strong performance on complex reasoning tasks, yet they often suffer from overthinking, producing excessively long chain-of-thought (CoT) traces that increase inference cost and may degrade accuracy. Our analysis reveals a clear anti-correlation between reasoning length and accuracy, where across multiple stochastic decodes, the short reasoning paths consistently achieve the highest correctness, while longer ones accumulate errors and repetitions. These short optimal reasoning paths can be found ideally through full enumeration of the reasoning space. However, the tree-structured reasoning space grows exponentially with sequence length, rendering exhaustive exploration infeasible. To address this, we propose DTS, a model-agnostic decoding framework that sketches the reasoning space by selectively branching at high-entropy tokens and applies early stopping to select the shortest completed reasoning path. This approach approximates the optimal solution that enhances both efficiency and accuracy, without requiring additional training or supervision. Experiments on AIME2024 and AIME2025 datasets with DeepSeek-R1-Distill-Qwen-7B and 1.5B show that DTS improves accuracy by up to 8%, reduces average reasoning length by 23%, and decreases repetition frequency by 12%, demonstrating DTS's ability for scalable and efficient LRM reasoning.

Feng Luo, Yu-Neng Chuang, Guanchu Wang et al.

On-policy distillation (OPD) trains student models under their own induced distribution while leveraging supervision from stronger teachers. We identify a failure mode of OPD: as training progresses, on-policy rollouts can undergo abrupt length inflation, causing truncated trajectories to dominate the training data. This truncation collapse coincides with abrupt repetition saturation and induces biased gradient signals, leading to severe training instability and sharp degradation in validation performance. We attribute this problem to the interaction between student-induced data collection and the distillation objective, which implicitly favors long and repetitive rollouts. To address this issue, we propose StableOPD, a stabilized OPD framework that combines a reference-based divergence constraint with rollout mixture distillation. These together mitigate repetition-induced length inflation and further stabilize OPD training. Across multiple math reasoning datasets, our approach prevents truncation collapse, stabilizes training dynamics, and improves performance by 7.2% on average.

Jiacan Yu, Siyi Chen, Mingrui Liu et al.

Joint-Embedding Predictive Architecture (JEPA) is increasingly used for visual representation learning and as a component in model-based RL, but its behavior remains poorly understood. We provide a theoretical characterization of a simple, practical JEPA variant that has an auxiliary regression head trained jointly with latent dynamics. We prove a No Unhealthy Representation Collapse theorem: in deterministic MDPs, if training drives both the latent-transition consistency loss and the auxiliary regression loss to zero, then any pair of non-equivalent observations, i.e., those that do not have the same transition dynamics or auxiliary value, must map to distinct latent representations. Thus, the auxiliary task anchors which distinctions the representation must preserve. Controlled ablations in a counting environment corroborate the theory and show that training the JEPA model jointly with the auxiliary head generates a richer representation than training them separately. Our work indicates a path to improve JEPA encoders: training them with an auxiliary function that, together with the transition dynamics, encodes the right equivalence relations.

Zicheng Xu, Guanchu Wang, Guangyao Zheng et al.

Although Large Language Models (LLMs) perform well in general fields, they exhibit a confidence distortion problem on multi-choice question-answering (MCQA), particularly as the number of answer choices increases. Specifically, on MCQA with many choices, LLMs suffer from under-confidence in correct predictions and over-confidence in incorrect ones, leading to a substantially degraded performance. To solve this problem, we propose Self-ensemble in this work. Our method splits the choices into several groups and ensembles LLM predictions across these groups to reach a final decision. The advantage of Self-ensemble is its plug-and-play nature, where it can be integrated into existing LLM architecture based on a designed attention mask and positional encoding, without requiring labeled datasets for parameter tuning. Experimental results on three LLMs and datasets demonstrate that Self-ensemble comprehensively addresses the confidence distortion problem of LLMs, outperforming standard inference as well as baseline methods.