arXiv subjects

Guhan Chen

Publications and source records attributed to Guhan Chen.

9 recordsLinked to original sources

arXiv2026

DIAG: Diagnostic Iterative Alignment and Generation for Data-Efficient Mathematical Preference Distillation

Iterative preference optimization is essential for aligning Large Language Models on mathematical reasoning tasks, yet its efficiency is often throttled by signal scarcity: as the model improves, static problem sets become increasingly mismatched to the model's evolving competence, producing rollouts that are either too easy or too hard and therefore non-informative, which leads to a scarcity of valid preference pairs. We propose DIAG, a Diagnostic Iterative Alignment and Generation framework that adaptively reshapes the practice distribution to increase informative supervision and focus training near the student's current competence boundary. DIAG consists of two phases: (1) diagnosing valid preference-pair yield to calibrate the exploration-exploitation trade-off and allocate topic quotas via an Empirical Bayes shrinkage estimator, thereby prioritizing high-yield concepts; and (2) generating targeted practice, where a teacher synthesizes variants from the student's failure traces. We further provide a theoretical view interpreting DIAG as a teacher-mediated approximation to KL-regularized reweighting of the practice distribution toward the student's competence boundary, where valid preference-pair yield is maximized. Experiments show that DIAG boosts yield across iterations and delivers stronger reasoning performance under an iso-effective training budget, demonstrating that it can distill more informative preference supervision for mathematical reasoning.

cs.CL↗

arXiv2026

Curvature-Adaptive Consistency Flow Matching: Autonomous Trajectory Optimization via Reinforcement Learning

Consistency distillation has significantly accelerated diffusion-model inference, but its sampling dynamics remain underexplored. We reveal an asymmetry: although Logit-Normal sampling priors work well for standard iterative generation, consistency distillation exhibits a different difficulty profile (e.g., U-shaped), with optimization bottlenecks concentrated at the boundary stages rather than intermediate steps. To address the limitations of static sampling under evolving learning demands, we propose Curvature-Adaptive Consistency Flow Matching (CACFM). By formulating distillation as a dynamic decision process, CACFM uses a lightweight reinforcement learning agent to probe Probability Flow ODE trajectories and construct an efficiency-oriented curriculum that prioritizes critical regions without manual scheduling. Combined with Flow-adapted DMD and adversarial consistency objectives, our RL-based scheduler achieves state-of-the-art results on large-scale models such as FLUX and SDXL, mitigating structural deformities and preserving high-frequency details in extreme few-step regimes.

cs.CV↗

arXiv2026

MathAgent: Adversarial Evolution of Constraint Graphs for Mathematical Reasoning Data Synthesis

Synthesizing high-quality mathematical reasoning data without human priors remains a significant challenge. Current approaches typically rely on seed data mutation or simple prompt engineering, often suffering from mode collapse and limited logical complexity. This paper proposes a hierarchical synthesis framework that formulates data synthesis as an unsupervised optimization problem over a constraint graph followed by semantic instantiation, rather than treating it as a direct text generation task. We introduce a Legislator-Executor paradigm: The Legislator adversarially evolves structured generation blueprints encoding the constraints of the problem, while the Executor instantiates these specifications into diverse natural language scenarios. This decoupling of skeleton design from linguistic realization enables a prioritized focus on constructing complex and diverse logical structures, thereby guiding high-quality data synthesis. Experiments conducted on a total of 10 models across the Qwen, Llama, Mistral, and Gemma series demonstrate that our method achieves notable results: models fine-tuned on 1K synthesized samples outperform widely-used datasets of comparable scale (LIMO, s1K) across eight mathematical benchmarks, exhibiting superior out-of-distribution generalization.

cs.CL↗

arXiv2026

Mining or Synthesis? Rethinking Exploration Efficiency in Iterative Alignment of Mathematical Reasoning

Iterative Direct Preference Optimization (DPO) has emerged as a widely used paradigm for aligning Large Language Models on reasoning tasks. Existing approaches typically rely on Best-of-N sampling ($N\geq8$) to mine positive trajectories from the distribution tail. In this work, we show that in mathematical reasoning, increasing $N$ yields diminishing returns while increasing verifier-induced false-positive risk and the distribution shift required for policy updates. To address this, we introduce PACE (Proximal Alignment via Corrective Exploration), a generation-based corrective framework that replaces exhaustive mining with low-budget exploration ($2\leq N\leq3$). Rather than searching for increasingly rare positive samples, PACE synthesizes high-fidelity preference pairs from failed explorations through corrective hindsight refinement and verification-guided filtering. Empirically, PACE matches or exceeds the performance of DPO-R1 ($N=16$) while using about $1/5$ of the compute, and remains robust under 20\% label corruption, where high-$N$ baselines exhibit substantially higher noise exploitation.

cs.CL↗

arXiv2025

Tool-Augmented Policy Optimization: Synergizing Reasoning and Adaptive Tool Use with Reinforcement Learning

Recent advances in large language models (LLMs) have popularized test-time scaling, where models generate additional reasoning tokens before producing final answers. These approaches have demonstrated significant performance improvements on benchmarks involving mathematical reasoning. However, language models relying solely on direct inference still struggle with tasks demanding up-to-date knowledge or computational tools such as calculators and code interpreters for complex arithmetic operations. To overcome these limitations, we propose Tool-Augmented Policy Optimization (TAPO), a novel reinforcement learning framework that systematically integrates multi-hop reasoning with adaptive tool-calling capabilities. Our approach employs a modified version of Dynamic Sampling Policy Optimization (DAPO), a recently developed RL paradigm, which we adapt specifically for tool invocation scenarios, enabling models to dynamically interleave complex reasoning with on-demand tool usage (including search APIs and Python interpreters). To support this research, we introduce two new datasets: TAPO-easy-60K and TAPO-hard-18K, specifically designed to train and evaluate both fact-based reasoning and mathematical calculation capabilities. Our experiments on Qwen2.5-3B and Qwen2.5-7B models demonstrate the effectiveness of our approach, with both models achieving state-of-the-art performance on tasks requiring external knowledge and mathematical computation among methods with comparable parameters. Notably, TAPO achieves more efficient tool utilization than baseline methods while preventing excessive calls caused by reward hacking. These results highlight the significant potential of combining advanced reasoning with tool usage to enhance model performance in knowledge-intensive and computationally demanding tasks.

cs.AI↗

arXiv2025

Divergence of Empirical Neural Tangent Kernel in Classification Problems

This paper demonstrates that in classification problems, fully connected neural networks (FCNs) and residual neural networks (ResNets) cannot be approximated by kernel logistic regression based on the Neural Tangent Kernel (NTK) under overtraining (i.e., when training time approaches infinity). Specifically, when using the cross-entropy loss, regardless of how large the network width is (as long as it is finite), the empirical NTK diverges from the NTK on the training samples as training time increases. To establish this result, we first demonstrate the strictly positive definiteness of the NTKs for multi-layer FCNs and ResNets. Then, we prove that during training, % with the cross-entropy loss, the neural network parameters diverge if the smallest eigenvalue of the empirical NTK matrix (Gram matrix) with respect to training samples is bounded below by a positive constant. This behavior contrasts sharply with the lazy training regime commonly observed in regression problems. Consequently, using a proof by contradiction, we show that the empirical NTK does not uniformly converge to the NTK across all times on the training samples as the network width increases. We validate our theoretical results through experiments on both synthetic data and the MNIST classification task. This finding implies that NTK theory is not applicable in this context, with significant theoretical implications for understanding neural networks in classification problems.

cs.LG↗

arXiv2024

On the Impacts of the Random Initialization in the Neural Tangent Kernel Theory

This paper aims to discuss the impact of random initialization of neural networks in the neural tangent kernel (NTK) theory, which is ignored by most recent works in the NTK theory. It is well known that as the network's width tends to infinity, the neural network with random initialization converges to a Gaussian process $f^{\mathrm{GP}}$, which takes values in $L^{2}(\mathcal{X})$, where $\mathcal{X}$ is the domain of the data. In contrast, to adopt the traditional theory of kernel regression, most recent works introduced a special mirrored architecture and a mirrored (random) initialization to ensure the network's output is identically zero at initialization. Therefore, it remains a question whether the conventional setting and mirrored initialization would make wide neural networks exhibit different generalization capabilities. In this paper, we first show that the training dynamics of the gradient flow of neural networks with random initialization converge uniformly to that of the corresponding NTK regression with random initialization $f^{\mathrm{GP}}$. We then show that $\mathbf{P}(f^{\mathrm{GP}} \in [\mathcal{H}^{\mathrm{NT}}]^{s}) = 1$ for any $s < \frac{3}{d+1}$ and $\mathbf{P}(f^{\mathrm{GP}} \in [\mathcal{H}^{\mathrm{NT}}]^{s}) = 0$ for any $s \geq \frac{3}{d+1}$, where $[\mathcal{H}^{\mathrm{NT}}]^{s}$ is the real interpolation space of the RKHS $\mathcal{H}^{\mathrm{NT}}$ associated with the NTK. Consequently, the generalization error of the wide neural network trained by gradient descent is $Ω(n^{-\frac{3}{d+3}})$, and it still suffers from the curse of dimensionality. On one hand, the result highlights the benefits of mirror initialization. On the other hand, it implies that NTK theory may not fully explain the superior performance of neural networks.

stat.ML↗

arXiv2024

Branch Scaling Manifests as Implicit Architectural Regularization for Improving Generalization in Overparameterized ResNets

Scaling factors in residual branches have emerged as a prevalent method for boosting neural network performance, especially in normalization-free architectures. While prior work has primarily examined scaling effects from an optimization perspective, this paper investigates their role in residual architectures through the lens of generalization theory. Specifically, we establish that wide residual networks (ResNets) with constant scaling factors become asymptotically unlearnable as depth increases. In contrast, when the scaling factor exhibits rapid depth-wise decay combined with early stopping, over-parameterized ResNets achieve minimax-optimal generalization rates. To establish this, we demonstrate that the generalization capability of wide ResNets can be approximated by kernel regression associated with the Neural Tangent Kernel (NTK). Our theoretical findings are validated through experiments on synthetic data and real-world classification tasks, including MNIST and CIFAR-100.

cs.LG↗

arXiv2023

On the Eigenvalue Decay Rates of a Class of Neural-Network Related Kernel Functions Defined on General Domains

In this paper, we provide a strategy to determine the eigenvalue decay rate (EDR) of a large class of kernel functions defined on a general domain rather than $\mathbb S^{d}$. This class of kernel functions include but are not limited to the neural tangent kernel associated with neural networks with different depths and various activation functions. After proving that the dynamics of training the wide neural networks uniformly approximated that of the neural tangent kernel regression on general domains, we can further illustrate the minimax optimality of the wide neural network provided that the underground truth function $f\in [\mathcal H_{\mathrm{NTK}}]^{s}$, an interpolation space associated with the RKHS $\mathcal{H}_{\mathrm{NTK}}$ of NTK. We also showed that the overfitted neural network can not generalize well. We believe our approach for determining the EDR of kernels might be also of independent interests.

stat.ML↗