Polyhedral Geometry of Time-to-First-Spike Neural Networks
We study the expressivity of spiking neural networks, which provide a natural framework for asynchronous, event-driven computation complementary to conventional feedforward neural networks. We consider the time-to-first-spike model in a setting for which the input-output map is continuous and piecewise linear, with affine pieces governed by causal feasibility constraints that determine which presynaptic spikes occur before a neuron fires. We first show that each neuron's firing time admits a maxout-like representation with exponentially many, highly constrained affine pieces. We then formalize causal regions as polyhedral regions with fixed causal sets and derive upper and lower bounds on...
| Authors | Manjot Singh, Guido Montúfar, Gitta Kutyniok |
|---|---|
| Primary category | cs.LG |
| Published | 10 September 2026 |
| Last updated at source | 10 September 2026 |
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