Polysemy of Synthetic Neurons Towards a New Type of Explanatory Categorical Vector Spaces

TL;DR

This paper introduces a geometric framework for understanding synthetic neurons as categorical vector spaces with non-orthogonal bases, offering a new perspective on their polysemy in language models.

Contribution

It proposes a novel geometric model representing neurons as categorical vector spaces, enabling better interpretation of their polysemantic behavior.

Findings

Defines neurons as categorical vector spaces with non-orthogonal bases

Introduces intra-neuronal attention to identify critical categorical zones

Suggests this approach improves understanding of neuron polysemy in language models

Abstract

The polysemantic nature of synthetic neurons in artificial intelligence language models is currently understood as the result of a necessary superposition of distributed features within the latent space. We propose an alternative approach, geometrically defining a neuron in layer n as a categorical vector space with a non-orthogonal basis, composed of categorical sub-dimensions extracted from preceding neurons in layer n-1. This categorical vector space is structured by the activation space of each neuron and enables, via an intra-neuronal attention process, the identification and utilization of a critical categorical zone for the efficiency of the language model - more homogeneous and located at the intersection of these different categorical sub-dimensions.