The Origins of Representation Manifolds in Large Language Models

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Conflicts of Interest

Identified Weaknesses

Rating Explanation

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Paper Summary

Paperzilla title

LLMs Think in Shapes: Do Words Have Geometry?

This paper proposes a theory of how large language models (LLMs) represent features as manifolds, geometric shapes in the model's internal representation space. They suggest that cosine similarity between representations reflects the distance between features, and offer some supporting evidence by analyzing text embeddings and activations from models like GPT2-small and text-embedding-large-3.

Possible Conflicts of Interest

None identified

Identified Weaknesses

Limited Model/Data Scope

The study primarily focuses on a few specific models and datasets, limiting the generalizability of findings to other LLMs and domains.

Isometry Challenges

Demonstrating perfect correspondence between cosine similarity and feature distance (isometry) is difficult due to noise and the complexity of semantic similarity, impacting the robustness of the proposed framework.

Manual Metric Selection

The study relies on manually selecting metric spaces for features, which makes scaling the approach to complex features challenging. An automated metric learning method is still unexplored.

Simplified Feature Representation

Reducing complex features like "years" or "colors" to simple metric spaces may be an oversimplification of how LLMs actually represent them. The true representation might be much richer.

Rating Explanation

This paper presents a novel and interesting theoretical framework for understanding feature representation in LLMs. While the empirical validation is preliminary and faces some methodological challenges, the proposed concepts and hypotheses offer a valuable starting point for future research in mechanistic interpretability. The limitations regarding generalizability, difficulty proving isometry, manual metric selection, and potential oversimplification are significant, but do not negate the value of the theoretical contribution, warranting a rating of 4.

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