Multi-Scale Manifold Alignment for Interpreting Large Language Models: A Unified Information-Geometric Framework
This work addresses the challenge of understanding and controlling information flow in LLMs for researchers and practitioners, though it is incremental as it builds on existing manifold and alignment concepts.
The paper tackles the problem of interpreting large language models by decomposing their representations into multi-scale manifolds and aligning them with an information-geometric framework, resulting in improved alignment metrics such as relative KL reduction and mutual information gains with statistical significance across models like GPT-2, BERT, RoBERTa, and T5.
We present Multi-Scale Manifold Alignment(MSMA), an information-geometric framework that decomposes LLM representations into local, intermediate, and global manifolds and learns cross-scale mappings that preserve geometry and information. Across GPT-2, BERT, RoBERTa, and T5, we observe consistent hierarchical patterns and find that MSMA improves alignment metrics under multiple estimators (e.g., relative KL reduction and MI gains with statistical significance across seeds). Controlled interventions at different scales yield distinct and architecture-dependent effects on lexical diversity, sentence structure, and discourse coherence. While our theoretical analysis relies on idealized assumptions, the empirical results suggest that multi-objective alignment offers a practical lens for analyzing cross-scale information flow and guiding representation-level control.