{"slug": "polyhedral-geometry-of-time-to-first-spike-neural-networks", "title": "Polyhedral Geometry of Time-to-First-Spike Neural Networks", "summary": "A new arXiv paper (2609.11227v1) shows that time-to-first-spike spiking neural networks can generate richer partitions of the input space than conventional feedforward ReLU networks. The authors derive upper and lower bounds on the maximal number of causal regions in both shallow and multilayer feedforward spiking networks, formalizing causal regions as polyhedral regions with fixed causal sets, and show each neuron's firing time admits a maxout-like representation with exponentially many highly constrained affine pieces.", "body_md": "arXiv:2609.11227v1 Announce Type: new \nAbstract: 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 the maximal number of causal regions in both shallow and multilayer feedforward spiking networks. Our theoretical and experimental results show that spiking networks can generate richer partitions of the input space than conventional feedforward ReLU networks.", "url": "https://wpnews.pro/news/polyhedral-geometry-of-time-to-first-spike-neural-networks", "canonical_source": "https://www.machinebrief.com/news/polyhedral-geometry-of-time-to-first-spike-neural-networks-i8my", "published_at": "2026-09-11 04:00:00+00:00", "updated_at": "2026-09-11 05:27:25.763247+00:00", "lang": "en", "topics": ["neural-networks", "machine-learning", "ai-research"], "entities": ["arXiv", "ReLU"], "alternates": {"html": "https://wpnews.pro/news/polyhedral-geometry-of-time-to-first-spike-neural-networks", "markdown": "https://wpnews.pro/news/polyhedral-geometry-of-time-to-first-spike-neural-networks.md", "text": "https://wpnews.pro/news/polyhedral-geometry-of-time-to-first-spike-neural-networks.txt", "jsonld": "https://wpnews.pro/news/polyhedral-geometry-of-time-to-first-spike-neural-networks.jsonld"}}