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
The paper investigates the expressivity of time-to-first-spike spiking neural networks, showing that each neuron's firing time can be represented in a maxout-like form with many constrained affine pieces. It formalizes causal regions as polyhedral sets defined by fixed causal spike sequences and derives bounds on the number of such regions for both shallow and multilayer networks. Experiments confirm that spiking networks can produce richer input-space partitions than conventional feedforward ReLU networks.
By Manjot Singh, Guido Mont\'ufar, Gitta Kutyniok
arXiv:2607. 14672v1 Announce Type: new Abstract: Continuous-time spiking neural networks (SNNs) provide an event-driven framework for temporal computation, computational neuroscience, and neuromorphic hardware.
By Yusuke Sakemi, Tomoya Takeuchi, Takeo Hosomi, Kazuyuki Aihara
arXiv:2607. 10589v1 Announce Type: cross Abstract: In contrast to most studies on neural network approximation theory that characterize results through a single parameter, such as the total number of network parameters, \cite{shen2020deep} pioneered the characterization of approximation rates as a joint function of the width parameter $N$ and the depth parameter $L$, thereby granting greater architectural flexibility.
By Yanming Lai, Defeng Sun, Yang Wang
arXiv:2608. 19232v1 Announce Type: cross Abstract: Spiking point cloud networks usually scan space in a fixed, input-agnostic order, which leaves the most distinctive resource of spiking computation, the temporal evolution of the membrane potential, unused as a locus of decision-making.
By Akarsh Jain, Arya Pawa, Ayush Debnath, Smera Rawal, Sayeed Shafayet Chowdhury
The paper constructs a width‑4 ReLU network whose iterates simulate any deterministic Turing machine, with polynomial‑time construction and depth per iteration. It shows that reachability for such iterated networks is NP‑complete, NEXP‑complete, or undecidable depending on the time bound, and extends these hardness results to width‑6 networks with common smooth activations and to discretized Neural ODEs in dimension 5.
arXiv:2609. 17477v1 Announce Type: cross Abstract: The absolute capacity of dense associative memory has mainly been analyzed for unbiased patterns.
By Yuto Sakurai, Takeaki Shimokawa, Kazunori Iwata, Kazushi Mimura