Pengxiao Lin

Zheng-An Chen, Pengxiao Lin, Zhi-Qin John Xu et al.

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.

Zhongwang Zhang, Pengxiao Lin, Zhiwei Wang et al.

Transformers have shown impressive capabilities across various tasks, but their performance on compositional problems remains a topic of debate. In this work, we investigate the mechanisms of how transformers behave on unseen compositional tasks. We discover that the parameter initialization scale plays a critical role in determining whether the model learns inferential (reasoning-based) solutions, which capture the underlying compositional primitives, or symmetric (memory-based) solutions, which simply memorize mappings without understanding the compositional structure. By analyzing the information flow and vector representations within the model, we reveal the distinct mechanisms underlying these solution types. We further find that inferential (reasoning-based) solutions exhibit low complexity bias, which we hypothesize is a key factor enabling them to learn individual mappings for single anchors. We validate our conclusions on various real-world datasets. Our findings provide valuable insights into the role of initialization scale in tuning the reasoning and memorizing ability and we propose the initialization rate $γ$ to be a convenient tunable hyper-parameter in common deep learning frameworks, where $1/d_{\mathrm{in}}^γ$ is the standard deviation of parameters of the layer with $d_{\mathrm{in}}$ input neurons.

Zhongwang Zhang, Pengxiao Lin, Zhiwei Wang et al.

Transformers have demonstrated impressive capabilities across various tasks, yet their performance on compositional problems remains a subject of debate. In this study, we investigate the internal mechanisms underlying Transformers' behavior in compositional tasks. We find that complexity control strategies significantly influence whether the model learns primitive-level rules that generalize out-of-distribution (reasoning-based solutions) or relies solely on memorized mappings (memory-based solutions). By applying masking strategies to the model's information circuits and employing multiple complexity metrics, we reveal distinct internal working mechanisms associated with different solution types. Further analysis reveals that reasoning-based solutions exhibit a lower complexity bias, which aligns with the well-studied neuron condensation phenomenon. This lower complexity bias is hypothesized to be the key factor enabling these solutions to learn reasoning rules. We validate these conclusions across multiple real-world datasets, including image generation and natural language processing tasks, confirming the broad applicability of our findings.

Liangkai Hang, Junjie Yao, Zhiwei Bai et al.

The reasoning ability of large language models (LLMs) has been rapidly advancing in recent years, attracting interest in more fundamental approaches that can reliably enhance their generalizability. This work demonstrates that model complexity control, conveniently implementable by adjusting the initialization rate and weight decay coefficient, improves the scaling law of LLMs consistently over varying model sizes and data sizes. This gain is further illustrated by comparing the benchmark performance of 2.4B models pretrained on 1T tokens with different complexity hyperparameters. Instead of fixing the initialization std, we found that a constant initialization rate (the exponent of std) enables the scaling law to descend faster in both model and data sizes. These results indicate that complexity control is a promising direction for the continual advancement of LLMs.

Pengxiao Lin, Zhongwang Zhang, Zhi-Qin John Xu

Since the inception of Large Language Models (LLMs), the quest to efficiently train them for superior reasoning capabilities has been a pivotal challenge. The dominant training paradigm for LLMs is based on next token prediction (NTP). Alternative methodologies, called Critical Token Prediction (CTP), focused exclusively on specific critical tokens (such as the answer in Q\&A dataset), aiming to reduce the overfitting of extraneous information and noise. Contrary to initial assumptions, our research reveals that despite NTP's exposure to noise during training, it surpasses CTP in reasoning ability. We attribute this counterintuitive outcome to the regularizing influence of noise on the training dynamics. Our empirical analysis shows that NTP-trained models exhibit enhanced generalization and robustness across various benchmark reasoning datasets, demonstrating greater resilience to perturbations and achieving flatter loss minima. These findings illuminate that NTP is instrumental in fostering reasoning abilities during pretraining, whereas CTP is more effective for finetuning, thereby enriching our comprehension of optimal training strategies in LLM development.

Pengxiao Lin, Zheng-An Chen, Zhi-Qin John Xu

Despite remarkable advances, large language models often fail at compositional reasoning tasks, a phenomenon exemplified by the ``curse of two-hop reasoning''. This paper introduces the Identity Bridge, a simple yet powerful mechanism that resolves this compositionality gap by supervising the model on a zero-hop identity task. We demonstrate empirically that this addition enables models to successfully perform out-of-distribution two-hop reasoning, a task they otherwise completely fail. To explain this phenomenon, we provide a theoretical analysis using a simplified Emb-MLP model, proving that identity supervision reshapes the model's latent geometry. We show this alignment is induced by an implicit nuclear-norm regularization during optimization, which favors low-rank solutions that share structure across tasks. For complex tasks, we use small initialization or weight decay to enhance the regularization effect, which enhances the latent space alignment effect and slows down the generalization decay. Finally, we extend our investigation to large-scale models, observing that they still achieve two-hop reasoning through the latent memory, which provides crucial inspiration for enhancing their implicit reasoning abilities.

Tianyi Chen, Pengxiao Lin, Zhiwei Wang et al.

State Space Models (SSMs) have emerged as promising alternatives to attention mechanisms, with the Mamba architecture demonstrating impressive performance and linear complexity for processing long sequences. However, the fundamental differences between Mamba and Transformer architectures remain incompletely understood. In this work, we use carefully designed synthetic tasks to reveal Mamba's inherent limitations. Through experiments, we identify that Mamba's nonlinear convolution introduces an asymmetry bias that significantly impairs its ability to recognize symmetrical patterns and relationships. Using composite function and inverse sequence matching tasks, we demonstrate that Mamba strongly favors compositional solutions over symmetrical ones and struggles with tasks requiring the matching of reversed sequences. We show these limitations stem not from the SSM module itself but from the nonlinear convolution preceding it, which fuses token information asymmetrically. These insights provide a new understanding of Mamba's constraints and suggest concrete architectural improvements for future sequence models.