🤖 AI Summary
This work investigates the origins of neuronal polysemy—the phenomenon wherein individual neurons encode multiple unrelated features—in neural networks. We introduce the concept of “feature capacity,” defined as the fractional dimensionality occupied by a feature in the embedding space, and establish quantitative relationships between feature capacity, input statistics, model architecture, and interpretability. Our key contribution is the first attribution of polysemy to an optimal allocation mechanism of feature capacity: inputs with high kurtosis or sparsity promote polysemy, and embedding spaces exhibit architecture-dependent block-wise semi-orthogonal geometry. Through interpretable toy models, information-theoretic capacity measures, geometric modeling, and sensitivity analysis, we quantitatively demonstrate that salient features are preferentially represented monosemously; less salient features are encoded polysemously in proportion to their loss contribution; and the least relevant features are suppressed entirely. These findings reveal fundamental architectural constraints on model interpretability.
📝 Abstract
Individual neurons in neural networks often represent a mixture of unrelated features. This phenomenon, called polysemanticity, can make interpreting neural networks more difficult and so we aim to understand its causes. We propose doing so through the lens of feature emph{capacity}, which is the fractional dimension each feature consumes in the embedding space. We show that in a toy model the optimal capacity allocation tends to monosemantically represent the most important features, polysemantically represent less important features (in proportion to their impact on the loss), and entirely ignore the least important features. Polysemanticity is more prevalent when the inputs have higher kurtosis or sparsity and more prevalent in some architectures than others. Given an optimal allocation of capacity, we go on to study the geometry of the embedding space. We find a block-semi-orthogonal structure, with differing block sizes in different models, highlighting the impact of model architecture on the interpretability of its neurons.
