Wanxiang Che

Dingzirui Wang, Xuanliang Zhang, Keyan Xu et al.

Contextual information at inference time, such as demonstrations, retrieved knowledge, or interaction history, can substantially improve large language models (LLMs) without parameter updates, yet its theoretical role remains poorly understood beyond specific settings such as in-context learning (ICL). We present a unified theoretical framework for analyzing the effect of arbitrary contextual information in Transformer-based LLMs. Our analysis characterizes contextual influence through output error dynamics. In a single-layer Transformer, we prove that the context-conditioned error vector decomposes additively into the baseline error vector and a contextual correction vector. This yields necessary geometric conditions for error reduction: the contextual correction must align with the negative baseline error and satisfy a norm constraint. We further show that the contextual correction norm admits an explicit upper bound determined by context-query relevance and complementarity. These results extend to multi-context and multi-layer Transformers. Experiments across ICL, retrieval-augmented generation, and memory evolution validate our theory and motivate a principled context selection strategy that improves performance by $0.6\%$.

Xuanliang Zhang, Dingzirui Wang, Keyan Xu et al.

While Large Language Models (LLMs) are increasingly deployed for table-related tasks, the internal mechanisms enabling them to process linearized two-dimensional structured tables remain opaque. In this work, we investigate the process of table understanding by dissecting the atomic task of cell location. Through activation patching and complementary interpretability techniques, we delineate the table understanding mechanism into a sequential three-stage pipeline: Semantic Binding, Coordinate Localization, and Information Extraction. We demonstrate that models locate the target cell via an ordinal mechanism that counts discrete delimiters to resolve coordinates. Furthermore, column indices are encoded within a linear subspace that allows for precise steering of model focus through vector arithmetic. Finally, we reveal that models generalize to multi-cell location tasks by multiplexing the identical attention heads identified during atomic location. Our findings provide a comprehensive explanation of table understanding within Transformer architectures.