Decomposing Representation Space into Interpretable Subspaces with Unsupervised Learning

TL;DR

This paper introduces a novel unsupervised method called neighbor distance minimization (NDM) to decompose neural representation spaces into interpretable subspaces, revealing their organization and relation to model circuits.

Contribution

The authors propose NDM, an unsupervised approach to identify interpretable subspaces in neural models, demonstrating its effectiveness on GPT-2 and larger models.

Findings

Subspaces are often interpretable and encode shared abstract concepts.

Strong connection between subspaces and known circuit variables in GPT-2.

Scalability of the method to 2B parameter models for understanding context and knowledge routing.

Abstract

Understanding internal representations of neural models is a core interest of mechanistic interpretability. Due to its large dimensionality, the representation space can encode various aspects about inputs. To what extent are different aspects organized and encoded in separate subspaces? Is it possible to find these ``natural'' subspaces in a purely unsupervised way? Somewhat surprisingly, we can indeed achieve this and find interpretable subspaces by a seemingly unrelated training objective. Our method, neighbor distance minimization (NDM), learns non-basis-aligned subspaces in an unsupervised manner. Qualitative analysis shows subspaces are interpretable in many cases, and encoded information in obtained subspaces tends to share the same abstract concept across different inputs, making such subspaces similar to ``variables'' used by the model. We also conduct quantitative experiments using known circuits in GPT-2; results show a strong connection between subspaces and circuit variables. We also provide evidence showing scalability to 2B models by finding separate subspaces mediating context and parametric knowledge routing. Viewed more broadly, our findings offer a new perspective on understanding model internals and building circuits.