Xingcheng Xu

Xingcheng Xu, Zihao Pan, Haipeng Zhang et al.

Large language models (LLMs) have achieved remarkable proficiency on solving diverse problems. However, their generalization ability is not always satisfying and the generalization problem is common for generative transformer models in general. Researchers take basic mathematical tasks like n-digit addition or multiplication as important perspectives for investigating their generalization behaviors. It is observed that when training models on n-digit operations (e.g., additions) in which both input operands are n-digit in length, models generalize successfully on unseen n-digit inputs (in-distribution (ID) generalization), but fail miserably on longer, unseen cases (out-of-distribution (OOD) generalization). We bring this unexplained performance drop into attention and ask whether there is systematic OOD generalization. Towards understanding LLMs, we train various smaller language models which may share the same underlying mechanism. We discover that the strong ID generalization stems from structured representations, while behind the unsatisfying OOD performance, the models still exhibit clear learned algebraic structures. Specifically, these models map unseen OOD inputs to outputs with learned equivalence relations in the ID domain, which we call the equivalence generalization. These findings deepen our knowledge regarding the generalizability of generative models including LLMs, and provide insights into potential avenues for improvement.

Xingcheng Xu

This paper proposes a novel deep generative model, called BSDE-Gen, which combines the flexibility of backward stochastic differential equations (BSDEs) with the power of deep neural networks for generating high-dimensional complex target data, particularly in the field of image generation. The incorporation of stochasticity and uncertainty in the generative modeling process makes BSDE-Gen an effective and natural approach for generating high-dimensional data. The paper provides a theoretical framework for BSDE-Gen, describes its model architecture, presents the maximum mean discrepancy (MMD) loss function used for training, and reports experimental results.

Xingcheng Xu, Zibo Zhao, Haipeng Zhang et al.

Transformer-based models excel in various tasks but their generalization capabilities, especially in arithmetic reasoning, remain incompletely understood. Arithmetic tasks provide a controlled framework to explore these capabilities, yet performance anomalies persist, such as inconsistent effectiveness in multiplication and erratic generalization in modular addition (e.g., modulo 100 vs. 101). This paper develops a unified theoretical framework for understanding the generalization behaviors of transformers in arithmetic tasks, focusing on length generalization. Through detailed analysis of addition, multiplication, and modular operations, we reveal that translation invariance in addition aligns with relative positional encoding for robust generalization, while base mismatch in modular operations disrupts this alignment. Experiments across GPT-family models validate our framework, confirming its ability to predict generalization behaviors. Our work highlights the importance of task structure and training data distribution for achieving data-efficient and structure-aware training, providing a systematic approach to understanding of length generalization in transformers.

Zibo Zhao, Yuanting Zha, Haipeng Zhang et al.

Self-reflection capabilities emerge in Large Language Models after RL post-training, with multi-turn RL achieving substantial gains over SFT counterparts. Yet the mechanism of how a unified optimization objective gives rise to functionally distinct capabilities of generating solutions and evaluating when to revise them remains opaque. To address this question, we introduce the Gradient Attribution Property to characterize how reward gradients distribute across policy components, formalized through the Two-Stage Decision-Sampling (DS) Hypothesis, which decomposes the policy into sampling ($π_{sample}$) for generation and decision ($π_{d}$) for verification. We prove that surrogate rewards exhibit Balanced Gradient Attribution, while SFT and KL penalties exhibit Unbalanced Gradient Attribution, with length-weighting creating asymmetric regularization that constrains $π_{sample}$ while leaving $π_{d}$ under-optimized, providing an theoretical explanation of why RL succeeds where SFT fails. We also empirically validate our theoretical predictions on arithmetic reasoning demonstrates that RL's superior generalization stems primarily from improved decision-making ($π_{d}$) rather than sampling capabilities, providing a first-principles mechanistic explanation for self-correction in thinking models.

Xingcheng Xu

We introduce a novel model called GAMMT (Generative Ambiguity Models using Multiple Transformers) for sequential data that is based on sets of probabilities. Unlike conventional models, our approach acknowledges that the data generation process of a sequence is not deterministic, but rather ambiguous and influenced by a set of probabilities. To capture this ambiguity, GAMMT employs multiple parallel transformers that are linked by a selection mechanism, allowing for the approximation of ambiguous probabilities. The generative nature of our approach also enables multiple representations of input tokens and sequences. While our models have not yet undergone experimental validation, we believe that our model has great potential to achieve high quality and diversity in modeling sequences with uncertain data generation processes.