Polyhedral Geometry of Time-to-First-Spike Neural Networks — Paper

Abstract

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.

Authors 3

Manjot Singh, Guido Mont\'ufar, Gitta Kutyniok

Specification

Official page: arxiv.org/abs/2609.11227
Source:arXiv (Atom API + RSS)T1observed 1 h agohigh
Arxiv announce type: new
Source:arXiv (Atom API + RSS)T1observed 1 h agohigh
arXiv id: 2609.11227
Source:arXiv (Atom API + RSS)T1observed 1 h agohigh
Categories: cs.LG, math.CO
Source:arXiv (Atom API + RSS)T1observed 1 h agohigh
PDF: arxiv.org/pdf/2609.11227
Source:arXiv (Atom API + RSS)T1observed 1 h agohigh
Primary category: cs.LG
Source:arXiv (Atom API + RSS)T1observed 1 h agohigh
Published: 11 Sept 2026
Source:arXiv (Atom API + RSS)T1observed 1 h agohigh

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9

Source tiers

T19

Freshest observation

1 h ago

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None

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Authors: Manjot Singh, Guido Mont\'ufar, Gitta Kutyniok

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Claim history for Primary category
Value	Valid from → to	Status	Source	Confidence	Extractor
cs.LG	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Claims are temporal and append-only: a new observation closes the previous claim (valid_to) instead of overwriting it. Conflicting claims from different sources are kept side by side and flagged — never averaged. Methodology →

11 Sept 2026
New paperPaperPolyhedral Geometry of Time-to-First-Spike Neural Networks
New paper: Polyhedral Geometry of Time-to-First-Spike Neural Networks
arxiv
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Source documents
Source	Document	Type	Tier	Last observed	Snapshots
arXiv (Atom API + RSS)	rss.arxiv.org/rss/cs.LG	feed	T1· Official	1 h ago	1

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