# Multi-Scale Manifold Alignment for Interpreting Large Language Models: A Unified Information-Geometric Framework

arXiv: https://arxiv.org/abs/2505.20333 · HTML: https://mlsanity.com/paper/2505.20333/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 23 references that are in the map.
- First posted on arXiv 24 May 2025.

## Builds on (most cited first, 16 of 16)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Deep contextualized word representations](https://mlsanity.com/paper/1802.05365/) (2018)
- [BERT Rediscovers the Classical NLP Pipeline](https://mlsanity.com/paper/1905.05950/) (2019)
- [What Does BERT Look At? An Analysis of BERT's Attention](https://mlsanity.com/paper/1906.04341/) (2019)
- [Analyzing Multi-Head Self-Attention: Specialized Heads Do the Heavy Lifting, the Rest Can Be Pruned](https://mlsanity.com/paper/1905.09418/) (2019)
- [Are Sixteen Heads Really Better than One?](https://mlsanity.com/paper/1905.10650/) (2019)
- [A Primer in BERTology: What we know about how BERT works](https://mlsanity.com/paper/2002.12327/) (2020)
- [How Contextual are Contextualized Word Representations? Comparing the Geometry of BERT, ELMo, and GPT-2 Embeddings](https://mlsanity.com/paper/1909.00512/) (2019)
- [Linguistic Knowledge and Transferability of Contextual Representations](https://mlsanity.com/paper/1903.08855/) (2019)
- [A Multiscale Visualization of Attention in the Transformer Model](https://mlsanity.com/paper/1906.05714/) (2019)
- [Visualizing and Measuring the Geometry of BERT](https://mlsanity.com/paper/1906.02715/) (2019)

## Built on by (most cited first, 1 of 1)

- [LLM as Attention-Informed NTM and Topic Modeling as long-input Generation: Interpretability and long-Context Capability](https://mlsanity.com/paper/2510.03174/) (2025)

## Abstract (arXiv)

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.