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

Michael Pichat, William Pogrund, Paloma Pichat, Judicael Poumay, Armanouche Gasparian, Samuel Demarchi, Martin Corbet, Alois Georgeon, Michael Veillet-Guillem

TL;DR

This work proposes an intra-neuronal, geometric model for polysemy in language models: each neuron in layer $n$ hosts a non-orthogonal categorical vector space whose basis consists of categorical sub-dimensions clipped from predecessor neurons in layer $n-1$. Activation levels modulate tokens’ coordinates within this space, yielding a spectrum from polysemous to monosemous representations, with high-activation tokens converging across sub-dimensions. Empirical analysis on GPT2-XL demonstrates a consistent link between activation strength and dimensional proximity to sub-dimensions, and a PCA analysis reveals partial convergence among sub-dimensions alongside divergence patterns, supporting the proposed framework. The authors argue this intra-neuronal perspective complements existing inter-neuronal explanations and opens pathways toward neuro-symbolic architectures that tightly couple synthetic cognition with symbolic reasoning, with implications for explainability and controllable fine-tuning. Overall, the paper advances a novel geometric account of polysemy and lays groundwork for integrating cognitive theories with practical AI design.

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.

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

TL;DR

This work proposes an intra-neuronal, geometric model for polysemy in language models: each neuron in layer hosts a non-orthogonal categorical vector space whose basis consists of categorical sub-dimensions clipped from predecessor neurons in layer . Activation levels modulate tokens’ coordinates within this space, yielding a spectrum from polysemous to monosemous representations, with high-activation tokens converging across sub-dimensions. Empirical analysis on GPT2-XL demonstrates a consistent link between activation strength and dimensional proximity to sub-dimensions, and a PCA analysis reveals partial convergence among sub-dimensions alongside divergence patterns, supporting the proposed framework. The authors argue this intra-neuronal perspective complements existing inter-neuronal explanations and opens pathways toward neuro-symbolic architectures that tightly couple synthetic cognition with symbolic reasoning, with implications for explainability and controllable fine-tuning. Overall, the paper advances a novel geometric account of polysemy and lays groundwork for integrating cognitive theories with practical AI design.

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.
Paper Structure (18 sections, 1 equation, 4 figures, 2 tables)

This paper contains 18 sections, 1 equation, 4 figures, 2 tables.

Table of Contents

  1. Theoretical Context
  2. Neuronal Activations and the Structure of the Vector Space and Semantic Encoding
  3. Polysemy of Neurons and Superposition
  4. Superposition and Quasi-Orthogonality
  5. Dimensional Representations of Concepts in Human Cognition
  6. Synthesis of Our Previous Work: Activation / Categorization Homomorphism & Extraction of Categorical Sub-Dimensions
  7. Problematic
  8. Methodology
  9. Methodological Framework
  10. Model and Statistical Units Used
  11. Statistical Processing
  12. Results
  13. Relationship Between Activation and Dimensional Proximity: Group Comparisons
  14. Structure of Categorical Sub-Dimensions
  15. Discussion of Results
  16. ...and 3 more sections

Figures (4)

  • Figure : Graph n°1 : Comparison of mean activations between categorical clusters from hierarchical classification on tokens' embeddings (layer 0).
  • Figure : Graph n°2: Correlation circle (PCA) on the average neuron associated with layer 1.
  • Figure : Graph n°3: Correlation circles (PCA) for different neurons in layer 1.
  • Figure : Graph n°4: Projection of tokens on factorial axes, with activations (layer 1).