Spatial Spiking Neural Networks Enable Efficient and Robust Temporal Computation

The efficiency of modern machine intelligence depends on high accuracy with minimal computational cost. In spiking neural networks (SNNs), synaptic delays are crucial for encoding temporal structure, yet existing models treat them as fully trainable, unconstrained parameters, leading to large memory footprints, higher computational demand, and a departure from biological plausibility. In the brain, however, delays arise from physical distances between neurons embedded in space. Building on this principle, we introduce Spatial Spiking Neural Networks (SpSNNs), a framework in which neurons learn coordinates in a finite-dimensional Euclidean space and delays emerge from inter-neuron distances. This replaces per-synapse delay learning with position learning, substantially reducing parameter count while retaining temporal expressiveness. Across the Yin-Yang and Spiking Heidelberg Digits benchmarks, SpSNNs outperform SNNs with unconstrained delays despite using far fewer parameters. Performance consistently peaks in 2D and 3D networks rather than infinite-dimensional delay spaces, revealing a geometric regularization effect. Moreover, dynamically sparsified SpSNNs maintain full accuracy even at 90% sparsity, matching standard delay-trained SNNs while using up to 18x fewer parameters. Because learned spatial layouts map naturally onto hardware geometries, SpSNNs lend themselves to efficient neuromorphic implementation. Methodologically, SpSNNs compute exact delay gradients via automatic differentiation with custom-derived rules, supporting arbitrary neuron models and architectures. Altogether, SpSNNs provide a principled platform for exploring spatial structure in temporal computation and offer a hardware-friendly substrate for scalable, energy-efficient neuromorphic intelligence.