🤖 AI Summary
This work investigates whether semantic factors in neural network representation spaces can be unsupervisedly decomposed into interpretable, orthogonal subspaces. We propose Neighborhood Distance Minimization (NDM), the first fully unsupervised method—without basis alignment assumptions—to learn class-variable-directed, interpretable subspaces, revealing structured, “functional-circuit”-like organization within model internals. Qualitative analysis and quantitative validation against known GPT-2 circuits confirm strong correlations between discovered subspaces and specific semantic variables (e.g., grammatical roles, factual knowledge). Furthermore, we successfully separate contextual representation from knowledge routing in a 2-billion-parameter GPT-2 model, demonstrating the method’s scalability and practical utility. Our approach advances interpretability by enabling decomposition of high-dimensional representations into semantically meaningful, disentangled subspaces without supervision or architectural constraints.
📝 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.