arXiv subjects

Zheng-An Chen

Publications and source records attributed to Zheng-An Chen.

6 recordsLinked to original sources

arXiv2026

Unveiling the Mechanisms of Multi-Hop Reasoning in Transformers via Identity Bridge

Large Language Models (LLMs) excel at multi-hop reasoning in distribution, yet fail on unseen compositions, a phenomenon known as the curse of two-hop reasoning. In this work, we argue that this phenomenon can be attributed to a missing supervision on the bridge entity. We formalize this gap by introducing identity bridge, a minimal supervision that enforces a identity mapping on bridge tokens. Under this supervision, even a one-layer transformer with uniform attention (Emb-MLP) can achieve out-of-distribution (OOD) two-hop generalization. We provide a theoretical analysis demonstrating that identity bridge induces an implicit regularization effect, leading the model to establish a direct subject-to-answer association. From an empirical perspective, the performance of standard GPT-2 models aligns closely with simple Emb--MLP models across varying levels of problem complexity. Finally, analyses of fine-tuned mainstream LLMs indicate that correct two-hop predictions consistently coincide with the establishment of a subject-to-answer relationship, extending our findings to realistic settings.

cs.LG↗

arXiv2026

Focus and Dilution: The Multi-stage Learning Process of Attention

Transformer-based models have achieved remarkable success across a wide range of domains, yet our understanding of their training dynamics remains limited. In this work, we identify a recurrent focus-dilution cycle in attention learning and provide a rigorous explanation in a one-layer Transformer setting for Markovian data via gradient-flow analysis. Using stage-wise linearization around critical points, we show that a single focus-dilution cycle can be decomposed into a sequence of distinct stages. First, embedding and projection rapidly condense to a rank-one structure, while attention parameters remain effectively frozen. Then, the attention parameters begin to increase, inducing a frequency-driven focus toward high-frequency tokens. As attention continues to evolve, it generates next-order perturbations in embeddings, leading to a mass-redistribution mechanism that progressively dilutes this focus. Finally, small asymmetries among low-frequency tokens lift a degenerate critical point, opening new embedding directions and initiating the next cycle. Experiments on synthetic Markovian data as well as WikiText and TinyStories corroborate the predicted stages and cyclical dynamics.

cs.LG↗

arXiv2025

From Condensation to Rank Collapse: A Two-Stage Analysis of Transformer Training Dynamics

Although transformer-based models have shown exceptional empirical performance, the fundamental principles governing their training dynamics are inadequately characterized beyond configuration-specific studies. Inspired by empirical evidence showing improved reasoning capabilities under small initialization scales in language models, we employ the gradient flow analytical framework established in [Zhou et al. NeurIPS 2022] to systematically investigate linearized Transformer training dynamics. Our theoretical analysis dissects the dynamics of attention modules into two distinct stages. In the first stage, asymmetric weight perturbations from random initialization sustain non-degenerate gradient dynamics in parameter matrices, facilitating systematic escape from small initialization regimes. Subsequently, these matrices undergo condensation, progressively aligning toward the target orientation. In the second stage, the previously static key-query matrices actively participate in training, driving the normalized matrices toward asymptotic rank collapse. This two-stage framework generalizes classical directional convergence results.

cs.LG↗

arXiv2025

Semi-Discrete in Time Method for Time-Dependent Equations by Random Neural Basis

Neural network-based solvers for partial differential equations (PDEs) have attracted considerable attention, yet they often face challenges in accuracy and computational efficiency. In this work, we focus on time-dependent PDEs and observe that coupling space and time in a single network can increase the difficulty of approximation. To address this, we propose a semi-discrete in time method (SDTM) which leverages classical numerical time integrators and random neural basis (RNB). Additional adaptive operations are introduced to enhance the network's ability to capture features across scales to ensure uniform approximation accuracy for multi-scale PDEs. Numerical experiments demonstrate the framework's effectiveness and confirm the convergence of the temporal integrator as well as the network's approximation performance.

math.NA↗

arXiv2024

On Multi-Stage Loss Dynamics in Neural Networks: Mechanisms of Plateau and Descent Stages

The multi-stage phenomenon in the training loss curves of neural networks has been widely observed, reflecting the non-linearity and complexity inherent in the training process. In this work, we investigate the training dynamics of neural networks (NNs), with particular emphasis on the small initialization regime, identifying three distinct stages observed in the loss curve during training: the initial plateau stage, the initial descent stage, and the secondary plateau stage. Through rigorous analysis, we reveal the underlying challenges contributing to slow training during the plateau stages. While the proof and estimate for the emergence of the initial plateau were established in our previous work, the behaviors of the initial descent and secondary plateau stages had not been explored before. Here, we provide a more detailed proof for the initial plateau, followed by a comprehensive analysis of the initial descent stage dynamics. Furthermore, we examine the factors facilitating the network's ability to overcome the prolonged secondary plateau, supported by both experimental evidence and heuristic reasoning. Finally, to clarify the link between global training trends and local parameter adjustments, we use the Wasserstein distance to track the fine-scale evolution of weight amplitude distribution.

cs.LG↗

arXiv2024

On the dynamics of three-layer neural networks: initial condensation

Empirical and theoretical works show that the input weights of two-layer neural networks, when initialized with small values, converge towards isolated orientations. This phenomenon, referred to as condensation, indicates that the gradient descent methods tend to spontaneously reduce the complexity of neural networks during the training process. In this work, we elucidate the mechanisms behind the condensation phenomena occurring in the training of three-layer neural networks and distinguish it from the training of two-layer neural networks. Through rigorous theoretical analysis, we establish the blow-up property of effective dynamics and present a sufficient condition for the occurrence of condensation, findings that are substantiated by experimental results. Additionally, we explore the association between condensation and the low-rank bias observed in deep matrix factorization.

cs.LG↗