The paper demonstrates that for a broad class of spiking neuron models, including the leaky integrate‑and‑fire with subtractive reset, any approximation bound proven for multi‑spike networks can be translated to an equivalent single‑spike network with only a linear change in neuron count, and vice versa. This establishes that single‑spike and multi‑spike neural networks possess identical approximation capabilities for general machine learning tasks. Consequently, existing approximation results for single‑spike networks automatically extend to the multi‑spike case.
By Dominik Dold, Philipp Christian Petersen
arXiv:2504.14015v2 Announce Type: replace-cross
Abstract: We introduce "causal pieces", a novel concept for analysing spiking neural networks (SNNs), inspired by "linear pieces" used to study express...
By Dominik Dold, Philipp Christian Petersen
arXiv:2609. 29756v1 Announce Type: cross Abstract: How much information can a single neuron remember?
By Xinyuan Xie
arXiv:2607. 07778v1 Announce Type: new Abstract: Bubeck, Li and Nagaraj conjectured that, for generic data, any two-layer neural network with $m$ neurons that fits $n$ noisy labels must have Lipschitz constant at least of order $\sqrt{n/m}$, with no restriction on the size of the weights.
By Yitzchak Shmalo
arXiv:2605.12049v2 Announce Type: replace-cross
Abstract: Cortical neurons are complex, multi-timescale processors wired into recurrent circuits, shaped by long evolutionary pressure under stringent...
By Aaron Spieler, Georg Martius, Anna Levina
arXiv:2608.23877v1 Announce Type: new
Abstract: We prove a depth hierarchy for ReLU neural networks in which every additional ReLU layer can save exponentially many neurons. For every $\ell\geq 3$, a...
By Itay Safran