Space as Time Through Neuron Position Learning

2025-11-03

AI Summary

Existing spiking neural networks (SNNs) lack the spatiotemporal coupling inherent in biological neural systems—where communication delays are physically determined by inter-neuronal distances. To address this, we propose a learnable neuronal positioning framework for SNNs that jointly optimizes spatial embedding and differentiable synaptic delays, enforcing strict Euclidean distance–dependent delay constraints. This biologically grounded mechanism spontaneously induces modular small-world topology and functional specialization without explicit architectural constraints. By incorporating distance-dependent connection costs and performing end-to-end gradient-based optimization, our model significantly enhances temporal awareness, biological plausibility, and structural interpretability on sequential classification tasks. The approach establishes a novel paradigm for brain-inspired networks that simultaneously achieve high computational efficiency and neuroscientific fidelity.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Machine Learning: Bio-inspired Learning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Biological neural networks exist in physical space where distance determines communication delays: a fundamental space-time coupling 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, small-world topologies with modular structure emerging under distance-dependent connection costs. Remarkably, we observe unprompted functional specialization aligned with spatial clustering without explictly 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.

Problem

• Unifying spatial embeddings with learnable synaptic delays
• Modeling biological space-time coupling in neural networks
• Developing neuron position learning for temporal classification tasks

Innovation

• Learns neuron positions to model communication delays
• Derives gradients for spatial organization through training
• Enables spontaneous modular specialization without explicit constraints