Space as Time Through Neuron Position Learning

TL;DR

This paper introduces a neuron position learning algorithm that couples space and time in neural networks, leading to emergent modular structures and functional specialization, inspired by biological neural systems.

Contribution

It unifies spatial embeddings and synaptic delays through a novel position learning method, revealing how space influences network organization and function.

Findings

Networks self-organize into local, clustered topologies

Emergence of modular, efficient wiring structures

Functional specialization aligns with spatial clustering

Abstract

Biological neural networks exist in physical space where distance influences communication delays: a fundamental coupling between space and time absent in most artificial neural networks. While recent work has separately explored spatial embeddings and learnable synaptic delays in spiking neural networks, we unify these approaches through a novel neuron position learning algorithm where delays relate to the Euclidean distances between neurons. We derive gradients with respect to neuron positions and demonstrate that this biologically-motivated constraint acts as an inductive bias: networks trained on temporal classification tasks spontaneously self-organize into local, clustered topologies and a modular, efficiently wired structure emerges if connection costs are distance-dependent. Remarkably, we observe functional specialization aligned with spatial clustering without explicitly enforcing it. These findings lay the groundwork for networks in which space and time are intrinsically coupled, offering new avenues for mechanistic interpretability, biologically inspired modelling, and efficient implementations.