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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 sho","title":"Decomposing Representation Space into Interpretable Subspaces with Unsupervised Learning","url":"https://arxiv.org/abs/2508.01916","vendor":"arxiv_cs_ai"},"summary":"arXiv:2508.01916v3 Announce Type: replace-cross \nAbstract: 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. 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