Fu-Chieh Chang

Tzu-Lin Kuo, Feng-Ting Liao, Mu-Wei Hsieh et al.

In real-world applications with Large Language Models (LLMs), external retrieval mechanisms - such as Search-Augmented Generation (SAG), tool utilization, and Retrieval-Augmented Generation (RAG) - are often employed to enhance the quality of augmented generations in dialogues. These approaches often come with multi-turn dialogue, where each interaction is enriched by relevant information retrieved from external sources. Existing benchmarks either assess LLMs' chat abilities in multi-turn dialogues or their use of retrieval for augmented responses in single-turn settings. However, there is a gap in evaluating LLMs' ability to leverage retrieval for more precise responses across multiple turns. To address this limitation, we introduce RAD-Bench (Retrieval Augmented Dialogue), a benchmark designed to evaluate LLMs' capabilities in multi-turn dialogues following retrievals, essential for their deployment in context-rich applications. RAD-Bench evaluates two key abilities of LLMs: Retrieval Synthesis and Retrieval Reasoning. These are measured using discriminative questions and retrieved contexts, and corresponding reference answers, assessing how effectively LLMs integrate and reason with context to maintain and enhance conversation quality over multiple turns. Our evaluation results on commonly used LLMs reveal that model performance deteriorates as additional layers of conditions or constraints are applied across conversation turns, even when accurate retrieved contexts are provided. The data and code are available at https://github.com/mtkresearch/RAD-Bench

Fu-Chieh Chang, Yu-Wei Tseng, Ya-Wen Yu et al.

Recently, successful applications of reinforcement learning to chip placement have emerged. Pretrained models are necessary to improve efficiency and effectiveness. Currently, the weights of objective metrics (e.g., wirelength, congestion, and timing) are fixed during pretraining. However, fixed-weighed models cannot generate the diversity of placements required for engineers to accommodate changing requirements as they arise. This paper proposes flexible multiple-objective reinforcement learning (MORL) to support objective functions with inference-time variable weights using just a single pretrained model. Our macro placement results show that MORL can generate the Pareto frontier of multiple objectives effectively.

Sing-Yuan Yeh, Fu-Chieh Chang, Chang-Wei Yueh et al.

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.

Yu-Ting Lee, Fu-Chieh Chang, Hui-Ying Shih et al.

Intrinsic self-correction refers to the phenomenon where a language model refines its own outputs purely through prompting, without external feedback or parameter updates. While this approach improves performance across diverse tasks, its internal mechanism remains poorly understood. We analyze intrinsic self-correction from a representation-level perspective. We formalize and introduce the notion of a prompt-induced shift, which is the change in hidden representations caused by a self-correction prompt. Across 5 open-source LLMs, prompt-induced shifts in text detoxification and text toxification align with latent directions constructed from contrastive pairs. In detoxification, the shifts align with the non-toxic direction; in toxification, they align with the toxic direction. These results suggest that intrinsic self-correction functions as representation steering along interpretable latent directions, beyond what standard metrics such as task scores or model confidence capture. Our analysis offers an interpretability-based account of intrinsic self-correction and contributes to a more systematic understanding of LLM prompting.

Yen-Ru Lai, Fu-Chieh Chang, Pei-Yuan Wu

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.

Yu-Ting Lee, Samuel Yen-Chi Chen, Fu-Chieh Chang

Reinforcement learning is one of the most challenging learning paradigms where efficacy and efficiency gains are extremely valuable. Hierarchical reinforcement learning is a variant that leverages temporal abstraction to structure decision-making. While parametrized quantum computations have shown success in non-hierarchical reinforcement learning, whether these advantages adapt to hierarchical decision-making remains a critical open question. In this work, we develop a hybrid hierarchical agent based on the option-critic architecture. This hybrid agent substitutes classical components with variational quantum circuits for feature extractors, option-value functions, termination functions, and intra-option policies. Evaluated on standard benchmarking environments, results show that a hybrid agent utilizing a quantum feature extractor can outperform classical baselines while saving up to 66\% trainable parameters. We also identify an architectural bottleneck that quantum option-value estimation severely degrades performance. Further ablation studies reveal how architectural choices of the quantum circuits affect performance. Our work establishes design principles for parameter-efficient hybrid hierarchical agents.

Yu Wang, Fu-Chieh Chang, Pei-Yuan Wu

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.

Fu-Chieh Chang, You-Chen Lin, Pei-Yuan Wu

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.

Fu-Chieh Chang, Yu-Ting Lee, Hui-Ying Shih et al.

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; This framework aims to bridge empirical findings with theoretical insights, advancing reinforcement learning approaches for reasoning in LLMs.

Fu-Chieh Chang, Yu-Ting Lee, Pei-Yuan Wu

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 work 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 with Qwen2.5-3B and Gemma3-4B 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.

Jia-Hau Bai, Chi-Ting Liu, Yu Wang et al.

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.

Fu-Chieh Chang, Hao-Jen Wang, Chun-Nan Chou et al.

Performing supervised learning from the data synthesized by using Generative Adversarial Networks (GANs), dubbed GAN-synthetic data, has two important applications. First, GANs may generate more labeled training data, which may help improve classification accuracy. Second, in scenarios where real data cannot be released outside certain premises for privacy and/or security reasons, using GAN- synthetic data to conduct training is a plausible alternative. This paper proposes a generalization bound to guarantee the generalization capability of a classifier learning from GAN-synthetic data. This generalization bound helps developers gauge the generalization gap between learning from synthetic data and testing on real data, and can therefore provide the clues to improve the generalization capability.

Chun-Nan Chou, Chuen-Kai Shie, Fu-Chieh Chang et al.

Deep learning owes its success to three key factors: scale of data, enhanced models to learn representations from data, and scale of computation. This book chapter presented the importance of the data-driven approach to learn good representations from both big data and small data. In terms of big data, it has been widely accepted in the research community that the more data the better for both representation and classification improvement. The question is then how to learn representations from big data, and how to perform representation learning when data is scarce. We addressed the first question by presenting CNN model enhancements in the aspects of representation, optimization, and generalization. To address the small data challenge, we showed transfer representation learning to be effective. Transfer representation learning transfers the learned representation from a source domain where abundant training data is available to a target domain where training data is scarce. Transfer representation learning gave the OM and melanoma diagnosis modules of our XPRIZE Tricorder device (which finished $2^{nd}$ out of $310$ competing teams) a significant boost in diagnosis accuracy.