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 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.

Neural Information Processing Systems http://nips.cc/

Spiking neural networks (SNNs) are biologically inspired, event-driven models that are suitable for processing temporal data and offer energy-efficient computation when implemented on neuromorphic hardware. In SNNs, richer neuronal dynamic allows capturing more complex temporal dependencies, with delays playing a crucial role by allowing past inputs to directly influence present spiking behavior. We propose a general framework for incorporating delays into SNNs through additional state variables. The proposed mechanism enables each neuron to access a finite temporal input history. The framework is agnostic to neuron models and hence can be seamlessly integrated into standard spiking neuron models such as LIF and adLIF. We analyze how the duration of the delays and the learnable parameters associated with them affect the performance. We investigate the trade-offs in the network architecture due to additional state variables introduced by the delay mechanism. Experiments on the Spiking Heidelberg Digits (SHD) dataset show that the proposed mechanism matches the performance of existing delay-based SNNs while remaining computationally efficient. Moreover, the results illustrate that the incorporation of delays may substantially improve performance in smaller networks.

Neural Information Processing Systems http://nips.cc/

Research in spike-based computation has been impeded by the lack of efficient supervised learning algorithm for spiking neural networks.

Spike-based temporal messaging enables SNNs to efficiently process both purely temporal and spatio-temporal time-series or event-driven data. Combining SNNs with Gated Recurrent Units (GRUs), a variant of recurrent neural networks, gives rise to a robust framework for sequential data processing; however, traditional RNNs often lose local details when handling long sequences. Previous approaches, such as SpikGRU, fail to capture fine-grained local dependencies in event-based spatio-temporal data. In this paper, we introduce the Convolutional Spiking GRU (CS-GRU) cell, which leverages convolutional operations to preserve local structure and dependencies while integrating the temporal precision of spiking neurons with the efficient gating mechanisms of GRUs. This versatile architecture excels on both temporal datasets (NTIDIGITS, SHD) and spatio-temporal benchmarks (MNIST, DVSGesture, CIFAR10DVS). Our experiments show that CS-GRU outperforms state-of-the-art GRU variants by an average of 4.35%, achieving over 90% accuracy on sequential tasks and up to 99.31% on MNIST. It is worth noting that our solution achieves 69% higher efficiency compared to SpikGRU. The code is available at: https://github.com/YesmineAbdennadher/CS-GRU.

Characterizing the cellular properties of neurons is fundamental to understanding their function in the brain. In this quest, the generation of bio-realistic models is central towards integrating multimodal cellular data sets and establishing causal relationships. However, current modeling approaches remain constrained by the limited availability and intrinsic variability of experimental neuronal data. The deterministic formalism of bio-realistic models currently precludes accounting for the natural variability observed experimentally. While deep learning is becoming increasingly relevant in this space, it fails to capture the full biophysical complexity of neurons, their nonlinear voltage dynamics, and variability. To address these shortcomings, we introduce NOBLE, a neural operator framework that learns a mapping from a continuous frequency-modulated embedding of interpretable neuron features to the somatic voltage response induced by current injection. Trained on synthetic data generated from bio-realistic neuron models, NOBLE predicts distributions of neural dynamics accounting for the intrinsic experimental variability. Unlike conventional bio-realistic neuron models, interpolating within the embedding space offers models whose dynamics are consistent with experimentally observed responses. NOBLE enables the efficient generation of synthetic neurons that closely resemble experimental data and exhibit trial-to-trial variability, offering a $4200\times$ speedup over the numerical solver. NOBLE is the first scaled-up deep learning framework that validates its generalization with real experimental data. To this end, NOBLE captures fundamental neural properties in a unique and emergent manner that opens the door to a better understanding of cellular composition and computations, neuromorphic architectures, large-scale brain circuits, and general neuroAI applications.

Spiking Neural Networks (SNNs) have emerged as energy-efficient alternatives to traditional artificial neural networks, leveraging asynchronous and biologically inspired neuron dynamics. Among existing neuron models, the Leaky Integrate-and-Fire (LIF) neuron has become widely adopted in deep SNNs due to its simplicity and computational efficiency. However, this efficiency comes at the expense of expressiveness, as LIF dynamics are constrained to linear decay at each timestep. In contrast, more complex models, such as the Quadratic Integrate-and-Fire (QIF) neuron, exhibit richer, nonlinear dynamics but have seen limited adoption due to their training instability. On that note, we propose the first discretization of the QIF neuron model tailored for high-performance deep spiking neural networks and provide an in-depth analysis of its dynamics. To ensure training stability, we derive an analytical formulation for surrogate gradient windows directly from our discretizations' parameter set, minimizing gradient mismatch. We evaluate our method on CIFAR-10, CIFAR-100, ImageNet, and CIFAR-10 DVS, demonstrating its ability to outperform state-of-the-art LIF-based methods. These results establish our discretization of the QIF neuron as a compelling alternative to LIF neurons for deep SNNs, combining richer dynamics with practical scalability.