The Origins of Representation Manifolds in Large Language Models
This work addresses a foundational problem in mechanistic interpretability for AI researchers, offering a novel theoretical framework that could enhance feature understanding in neural networks.
The paper tackles the problem of understanding how features are represented in large language models by proposing that features are encoded as manifolds, where cosine similarity in representation space reflects the intrinsic geometry of features, and validates this theory on text embeddings and token activations.
There is a large ongoing scientific effort in mechanistic interpretability to map embeddings and internal representations of AI systems into human-understandable concepts. A key element of this effort is the linear representation hypothesis, which posits that neural representations are sparse linear combinations of `almost-orthogonal' direction vectors, reflecting the presence or absence of different features. This model underpins the use of sparse autoencoders to recover features from representations. Moving towards a fuller model of features, in which neural representations could encode not just the presence but also a potentially continuous and multidimensional value for a feature, has been a subject of intense recent discourse. We describe why and how a feature might be represented as a manifold, demonstrating in particular that cosine similarity in representation space may encode the intrinsic geometry of a feature through shortest, on-manifold paths, potentially answering the question of how distance in representation space and relatedness in concept space could be connected. The critical assumptions and predictions of the theory are validated on text embeddings and token activations of large language models.