SPATIAL SPIKING NEURAL NETWORKS VIA AUTOGRAD-ENABLED EXACT EVENT-GRADIENTS

Neurons have been observed to adapt, maintain or learn, not just synaptic weights, but also axonal conduction delays. Recently developments in SNNs for ML have focussed on bringing such delay tuning to neural models, however, here, the focus has been on achieving good ML-task performance given the tuning of arbitrary delay values. In contrast, in biological networks, delays arise from the spatial embedding of neurons, and the physical distance action potentials have to travel. In this work, we introduce Spatial Spiking Neural Networks (SpSNNs) using a novel mathematical modelling framework. Neurons are embedded in a low-dimensional Euclidean space, and axonal delays are determined by inter-neuronal distance, while synaptic weights and neuron positions are optimized jointly during learning.

We evaluated SpSNNs on two neuromorphic temporal processing tasks. Networks with spatially derived delays achieved equal or higher classification accuracy compared to networks with freely learned delays, despite a substantial reduction in the number of trainable parameters. Performance was maximal for networks embedded in two or three spatial dimensions, whereas higher-dimensional embeddings did not yield further improvements.

We further examined robustness to synaptic sparsification using a dynamic pruning procedure. Spatially embedded networks maintained stable performance even at high sparsity levels, whereas networks with unconstrained delays showed less robustness towards sparsification. These results suggest that spatial provides an effective structural regularization for temporal computation in spiking networks. Hereby, our methods allow for studying the interaction between the geometry of conductance delays and neural computation, with potential applications in both theoretical neuroscience and neuromorphic systems.