arXiv subjects

Pei-Yuan Wu

Publications and source records attributed to Pei-Yuan Wu.

13 recordsLinked to original sources

arXiv2026

RL-STaR: Theoretical Analysis of Reinforcement Learning Frameworks for Self-Taught Reasoner

The reasoning abilities of large language models (LLMs) have improved with chain-of-thought (CoT) prompting, allowing models to solve complex tasks stepwise. However, training CoT capabilities requires detailed reasoning data, which is often scarce. The self-taught reasoner (STaR) framework addresses this by using reinforcement learning to automatically generate reasoning steps, reducing reliance on human-labeled data. Although STaR and its variants have demonstrated empirical success, a theoretical foundation explaining these improvements is lacking. This work provides a theoretical framework for understanding the effectiveness of reinforcement learning on CoT reasoning and STaR. Our contributions are: (1) criteria for the quality of pre-trained models necessary to initiate effective reasoning improvement; (2) an analysis of policy improvement, showing why LLM reasoning improves iteratively with STaR; (3) conditions for convergence to an optimal reasoning policy; and (4) an examination of STaR's robustness, explaining how it can improve reasoning even when incorporating occasional incorrect steps. We also run RL-STaR on GPT-2, Qwen2.5-0.5B and Phi-3-mini, and the measured return curves follow the ones the analysis predicts. This framework bridges empirical findings with theoretical insights, advancing reinforcement learning approaches for reasoning in LLMs.

cs.AI↗

arXiv2026

Explaining Intrinsic Moral Self-Correction with Mechanistic Interpretability

Intrinsic moral self-correction refers to the phenomenon where a language model refines its ethical judgments or aligns its outputs purely through prompting. While effective across diverse tasks, its mechanism remains unclear. We hypothesize intrinsic moral self-correction functions by steering hidden representations along interpretable latent directions. Evaluating six LLMs across four morality-related tasks, we demonstrate that the representation shifts induced by self-correction prompts align with contrastive steering vectors. This alignment transfers even when the steering vectors are constructed from a disjoint corpus. Notably, when applied via activation addition, these prompt-induced shifts can alter model behavior more effectively than the self-correction prompts and the steering vectors. Our findings suggest representation steering is the mechanistic driver of intrinsic moral self-correction.

cs.CL↗

arXiv2026

SpecLoop: An Agentic RTL-to-Specification Framework with Formal Verification Feedback Loop

RTL implementations frequently lack up-to-date or consistent specifications, making comprehension, maintenance, and verification costly and error-prone. While prior work has explored generating specifications from RTL using large language models (LLMs), ensuring that the generated documents faithfully capture design intent remains a major challenge. We present SpecLoop, an agentic framework for RTL-to-specification generation with a formal-verification-driven iterative feedback loop. SpecLoop first generates candidate specifications and then reconstructs RTL from these specifications; it uses formal equivalence checking tools between the reconstructed RTL and the original design to validate functional consistency. When mismatches are detected, counterexamples are fed back to iteratively refine the specifications until equivalence is proven or no further progress can be made. Experiments across multiple LLMs and RTL benchmarks show that incorporating formal verification feedback substantially improves specification correctness and robustness over LLM-only baselines, demonstrating the effectiveness of verification-guided specification generation.

cs.AR↗

arXiv2025

Unveiling the Latent Directions of Reflection in Large Language Models

Reflection, the ability of large language models (LLMs) to evaluate and revise their own reasoning, has been widely used to improve performance on complex reasoning tasks. Yet, most prior works emphasizes designing reflective prompting strategies or reinforcement learning objectives, leaving the inner mechanisms of reflection underexplored. In this paper, we investigate reflection through the lens of latent directions in model activations. We propose a methodology based on activation steering to characterize how instructions with different reflective intentions: no reflection, intrinsic reflection, and triggered reflection. By constructing steering vectors between these reflection levels, we demonstrate that (1) new reflection-inducing instructions can be systematically identified, (2) reflective behavior can be directly enhanced or suppressed through activation interventions, and (3) suppressing reflection is considerably easier than stimulating it. Experiments on GSM8k-adv and Cruxeval-o-adv with Qwen2.5-3B and Gemma3-4B-IT reveal clear stratification across reflection levels, and steering interventions confirm the controllability of reflection. Our findings highlight both opportunities (e.g., reflection-enhancing defenses) and risks (e.g., adversarial inhibition of reflection in jailbreak attacks). This work opens a path toward mechanistic understanding of reflective reasoning in LLMs.

cs.LG↗

arXiv2025

Assessing Large Language Models in Generating RTL Design Specifications

As IC design grows more complex, automating comprehension and documentation of RTL code has become increasingly important. Engineers currently should manually interpret existing RTL code and write specifications, a slow and error-prone process. Although LLMs have been studied for generating RTL from specifications, automated specification generation remains underexplored, largely due to the lack of reliable evaluation methods. To address this gap, we investigate how prompting strategies affect RTL-to-specification quality and introduce metrics for faithfully evaluating generated specs. We also benchmark open-source and commercial LLMs, providing a foundation for more automated and efficient specification workflows in IC design.

cs.AR↗

arXiv2025

A Hierarchical Slice Attention Network for Appendicitis Classification in 3D CT Scans

Timely and accurate diagnosis of appendicitis is critical in clinical settings to prevent serious complications. While CT imaging remains the standard diagnostic tool, the growing number of cases can overwhelm radiologists, potentially causing delays. In this paper, we propose a deep learning model that leverages 3D CT scans for appendicitis classification, incorporating Slice Attention mechanisms guided by external 2D datasets to enhance small lesion detection. Additionally, we introduce a hierarchical classification framework using pre-trained 2D models to differentiate between simple and complicated appendicitis. Our approach improves AUC by 3% for appendicitis and 5.9% for complicated appendicitis, offering a more efficient and reliable diagnostic solution compared to previous work.

cs.CV↗

arXiv2025

CAPM: Fast and Robust Verification on Maxpool-based CNN via Dual Network

This study uses CAPM (Convex Adversarial Polytope for Maxpool-based CNN) to improve the verified bound for general purpose maxpool-based convolutional neural networks (CNNs) under bounded norm adversarial perturbations. The maxpool function is decomposed as a series of ReLU functions to extend the convex relaxation technique to maxpool functions, by which the verified bound can be efficiently computed through a dual network. The experimental results demonstrate that this technique allows the state-of-the-art verification precision for maxpool-based CNNs and involves a much lower computational cost than current verification methods, such as DeepZ, DeepPoly and PRIMA. This method is also applicable to large-scale CNNs, which previous studies show to be often computationally prohibitively expensive. Under certain circumstances, CAPM is 40-times, 20-times or twice as fast and give a significantly higher verification bound (CAPM 98% vs. PRIMA 76%/DeepPoly 73%/DeepZ 8%) as compared to PRIMA/DeepPoly/DeepZ. Furthermore, we additionally present the time complexity of our algorithm as $O(W^2NK)$, where $W$ is the maximum width of the neural network, $N$ is the number of neurons, and $K$ is the size of the maxpool layer's kernel.

cs.CV↗

arXiv2025

A Theoretical Framework for OOD Robustness in Transformers using Gevrey Classes

We study the robustness of Transformer language models under semantic out-of-distribution (OOD) shifts, where training and test data lie in disjoint latent spaces. Using Wasserstein-1 distance and Gevrey-class smoothness, we derive sub-exponential upper bounds on prediction error. Our theoretical framework explains how smoothness governs generalization under distributional drift. We validate these findings through controlled experiments on arithmetic and Chain-of-Thought tasks with latent permutations and scalings. Results show empirical degradation aligns with our bounds, highlighting the geometric and functional principles underlying OOD generalization in Transformers.

cs.LG↗

arXiv2025

Leveraging Unlabeled Data Sharing through Kernel Function Approximation in Offline Reinforcement Learning

Offline reinforcement learning (RL) learns policies from a fixed dataset, but often requires large amounts of data. The challenge arises when labeled datasets are expensive, especially when rewards have to be provided by human labelers for large datasets. In contrast, unlabelled data tends to be less expensive. This situation highlights the importance of finding effective ways to use unlabelled data in offline RL, especially when labelled data is limited or expensive to obtain. In this paper, we present the algorithm to utilize the unlabeled data in the offline RL method with kernel function approximation and give the theoretical guarantee. We present various eigenvalue decay conditions of $\mathcal{H}_k$ which determine the complexity of the algorithm. In summary, our work provides a promising approach for exploiting the advantages offered by unlabeled data in offline RL, whilst maintaining theoretical assurances.

cs.LG↗

arXiv2025

Unraveling Arithmetic in Large Language Models: The Role of Algebraic Structures

Large language models (LLMs) have demonstrated remarkable mathematical capabilities, largely driven by chain-of-thought (CoT) prompting, which decomposes complex reasoning into step-by-step solutions. This approach has enabled significant advancements, as evidenced by performance on benchmarks like GSM8K and MATH. However, the mechanisms underlying LLMs' ability to perform arithmetic in a single step of CoT remain poorly understood. Existing studies debate whether LLMs encode numerical values or rely on symbolic reasoning, while others explore attention and multi-layered processing in arithmetic tasks. In this work, we propose that LLMs learn arithmetic by capturing algebraic structures, such as commutativity and identity properties. Since these structures are observable through input-output relationships, they can generalize to unseen data. We empirically demonstrate that LLMs can learn algebraic structures using a custom dataset of arithmetic problems, as well as providing theoretical evidence showing that, under specific configurations of weights and biases, the transformer-based LLMs can generate embeddings that remain invariant to both permutations of input tokens and the presence of identity elements. Our findings indicate that leveraging algebraic structures can enhance the LLMs' arithmetic capabilities, offering insights into improving their arithmetic performance.

cs.LG↗

arXiv2023

Sample Complexity of Kernel-Based Q-Learning

Modern reinforcement learning (RL) often faces an enormous state-action space. Existing analytical results are typically for settings with a small number of state-actions, or simple models such as linearly modeled Q-functions. To derive statistically efficient RL policies handling large state-action spaces, with more general Q-functions, some recent works have considered nonlinear function approximation using kernel ridge regression. In this work, we derive sample complexities for kernel based Q-learning when a generative model exists. We propose a nonparametric Q-learning algorithm which finds an $ε$-optimal policy in an arbitrarily large scale discounted MDP. The sample complexity of the proposed algorithm is order optimal with respect to $ε$ and the complexity of the kernel (in terms of its information gain). To the best of our knowledge, this is the first result showing a finite sample complexity under such a general model.

cs.LG↗

arXiv2021

AutoGAN-based Dimension Reduction for Privacy Preservation

Protecting sensitive information against data exploiting attacks is an emerging research area in data mining. Over the past, several different methods have been introduced to protect individual privacy from such attacks while maximizing data-utility of the application. However, these existing techniques are not sufficient to effectively protect data owner privacy, especially in the scenarios that utilize visualizable data (e.g. images, videos) or the applications that require heavy computations for implementation. To address these problems, we propose a new dimension reduction-based method for privacy preservation. Our method generates dimension-reduced data for performing machine learning tasks and prevents a strong adversary from reconstructing the original data. We first introduce a theoretical approach to evaluate dimension reduction-based privacy preserving mechanisms, then propose a non-linear dimension reduction framework motivated by state-of-the-art neural network structures for privacy preservation. We conducted experiments over three different face image datasets (AT&T, YaleB, and CelebA), and the results show that when the number of dimensions is reduced to seven, we can achieve the accuracies of 79%, 80%, and 73% respectively and the reconstructed images are not recognizable to naked human eyes.

cs.CR↗

arXiv2020

NTIRE 2020 Challenge on NonHomogeneous Dehazing

This paper reviews the NTIRE 2020 Challenge on NonHomogeneous Dehazing of images (restoration of rich details in hazy image). We focus on the proposed solutions and their results evaluated on NH-Haze, a novel dataset consisting of 55 pairs of real haze free and nonhomogeneous hazy images recorded outdoor. NH-Haze is the first realistic nonhomogeneous haze dataset that provides ground truth images. The nonhomogeneous haze has been produced using a professional haze generator that imitates the real conditions of haze scenes. 168 participants registered in the challenge and 27 teams competed in the final testing phase. The proposed solutions gauge the state-of-the-art in image dehazing.

cs.CV↗