Single-Entity Spiking Neuron Models: Survey

In a spiking neural network, is it enough for each neuron to spike at most once? In recent work, approximation bounds for spiking neural networks have been derived, quantifying how well they can fit target functions. However, these results are only valid for neurons that spike at most once, which is commonly thought to be a strong limitation. Here, we show that the opposite is true for a large class of spiking neuron models, including the commonly used leaky integrate-and-fire model with subtractive reset: for every approximation bound that is valid for a set of multi-spike neural networks, there is an equivalent set of single-spike neural networks with only linearly more (or less) neurons, in the maximum number of spikes, for which the bound holds. The same is true for the reverse direction too, showing that regarding their approximation capabilities in general machine learning tasks, single-spike and multi-spike neural networks are equivalent. Consequently, many approximation results in the literature for single-spike neural networks also hold for the multi-spike case.

Biological plausibility is a key concept in neuromorphic computing and spiking neural networks, yet it remains inconsistently defined and difficult to quantify. In this work, we present an open-source framework for the automated assessment of biological plausibility in spiking neuron models. Our method builds on the idea of evaluating a model's ability to replicate canonical neuronal firing patterns observed in biological systems, following the classification proposed by Izhikevich. By encoding these patterns into objective functions and optimizing model parameters accordingly, our framework enables empirical assessment without requiring prior analytical modeling. Treating neuron models as black boxes, it provides a practical and flexible means of characterizing their dynamic capabilities. We demonstrate the effectiveness of the framework on several established models and a previously unexplored custom model. Implemented in Python and compatible with PyTorch and the Norse library, the framework is tailored for machine learning contexts. It is intended as a starting point for systematic research into the relationship between biological plausibility and network-level performance metrics such as accuracy, energy efficiency, robustness, and adaptability.

Biophysical neuron models link measurements of neural activity to underlying cellular mechanisms. Yet, a central challenge is that the kinetics of many ion channels are poorly characterized, and practical simplifications -- omitting channels or reducing morphological detail -- introduce systematic gaps between model and biology. Bridging these gaps requires approaches that can flexibly discover unmodeled dynamics while preserving mechanistic interpretability. Here, we introduce a hybrid modeling framework that embeds neural ordinary differential equations into conductance-based biophysical models to capture unknown currents or mis-specified channel kinetics. By parameterizing the neural ODE in terms of voltage-dependent steady-state and time-constant functions, we recover interpretable gating dynamics directly from voltage recordings without assuming a functional form. We show that the hybrid model fits the gating kinetics of 2400 ion channel models and recovers unknown gating dynamics from single current-clamp recordings, generalizing to out-of-distribution stimulus regimes under realistic inputs and parameter misspecification. We also use our method to reduce a multicompartment model of a cortical neuron into a single-compartment hybrid model with a learned axial current, yielding up to an order of magnitude lower computational cost. Together, our results establish a plug-and-play framework for selectively replacing unknown components of conductance-based models with neural ODEs while preserving their mechanistic structure.