Spiking neural networks (SNNs) are brain-inspired models that enable energy-efficient implementation on neuromorphic hardware. However, the supervised training of SNNs remains a hard problem due to the discontinuity of the spiking neuron model.

Accurate modeling of neuronal action potential (AP) onset timing is crucial for understanding neural coding of danger signals. Traditional leaky integrate-and-fire (LIF) models, while widely used, exhibit high relative error in predicting AP onset latency, especially under strong or rapidly changing stimuli. Inspired by recent experimental findings and quantum theory, we present a quantum-inspired leaky integrate-and-fire (QI-LIF) model that treats AP onset as a probabilistic event, represented by a Gaussian wave packet in time. This approach captures the biological variability and uncertainty inherent in neuronal firing. We systematically compare the relative error of AP onset predictions between the classical LIF and QI-LIF models using synthetic data from hippocampal and sensory neurons subjected to varying stimulus amplitudes. Our results demonstrate that the QI-LIF model significantly reduces prediction error, particularly for high-intensity stimuli, aligning closely with observed biological responses. This work highlights the potential of quantum-inspired computational frameworks in advancing the accuracy of neural modeling and has implications for quantum engineering approaches to brain-inspired computing.

Input: Network parameters θ; Input data x; Label y; Time steps T; Other hyperparameters; Output: Trained network parameters θ . Calculate the output o and the loss L based on o and y . Update θ based on the gradient-based optimizer. We first prove Theorem 1. Then Theorem 2 is similarly proved. We omit repetitive details here.

Spiking neural networks (SNNs) are brain-inspired models that enable energy-efficient implementation on neuromorphic hardware. However, the supervised training of SNNs remains a hard problem due to the discontinuity of the spiking neuron model.

This article proposes a robust brain-inspired audio feature extractor (RBA-FE) model for depression diagnosis, using an improved hierarchical network architecture. Most deep learning models achieve state-of-the-art performance for image-based diagnostic tasks, ignoring the counterpart audio features. In order to tailor the noise challenge, RBA-FE leverages six acoustic features extracted from the raw audio, capturing both spatial characteristics and temporal dependencies. This hybrid attribute helps alleviate the precision limitation in audio feature extraction within other learning models like deep residual shrinkage networks. To deal with the noise issues, our model incorporates an improved spiking neuron model, called adaptive rate smooth leaky integrate-and-fire (ARSLIF). The ARSLIF model emulates the mechanism of ``retuning of cellular signal selectivity" in the brain attention systems, which enhances the model robustness against environmental noises in audio data. Experimental results demonstrate that RBA-FE achieves state-of-the-art accuracy on the MODMA dataset, respectively with 0.8750, 0.8974, 0.8750 and 0.8750 in precision, accuracy, recall and F1 score. Extensive experiments on the AVEC2014 and DAIC-WOZ datasets both show enhancements in noise robustness. It is further indicated by comparison that the ARSLIF neuron model suggest the abnormal firing pattern within the feature extraction on depressive audio data, offering brain-inspired interpretability.

The Spiking Neural Network (SNN) has drawn increasing attention for its energy-efficient, event-driven processing and biological plausibility. To train SNNs via backpropagation, surrogate gradients are used to approximate the non-differentiable spike function, but they only maintain nonzero derivatives within a narrow range of membrane potentials near the firing threshold, referred to as the surrogate gradient support width gamma. We identify a major challenge, termed the dilemma of gamma: a relatively large gamma leads to overactivation, characterized by excessive neuron firing, which in turn increases energy consumption, whereas a small gamma causes vanishing gradients and weakens temporal dependencies. To address this, we propose a temporal Inhibitory Leaky Integrate-and-Fire (ILIF) neuron model, inspired by biological inhibitory mechanisms. This model incorporates interconnected inhibitory units for membrane potential and current, effectively mitigating overactivation while preserving gradient propagation. Theoretical analysis demonstrates ILIF effectiveness in overcoming the gamma dilemma, and extensive experiments on multiple datasets show that ILIF improves energy efficiency by reducing firing rates, stabilizes training, and enhances accuracy. The code is available at github.com/kaisun1/ILIF.

Spiking Neural Networks (SNNs) are valued for their ability to process spatio-temporal information efficiently, offering biological plausibility, low energy consumption, and compatibility with neuromorphic hardware. However, the commonly used Leaky Integrate-and-Fire (LIF) model overlooks neuron heterogeneity and independently processes spatial and temporal information, limiting the expressive power of SNNs. In this paper, we propose the Dual Adaptive Leaky Integrate-and-Fire (DA-LIF) model, which introduces spatial and temporal tuning with independently learnable decays. Evaluations on both static (CIFAR10/100, ImageNet) and neuromorphic datasets (CIFAR10-DVS, DVS128 Gesture) demonstrate superior accuracy with fewer timesteps compared to state-of-the-art methods. Importantly, DA-LIF achieves these improvements with minimal additional parameters, maintaining low energy consumption. Extensive ablation studies further highlight the robustness and effectiveness of the DA-LIF model.

We introduce a new approach for solving forward systems of differential equations using a combination of splitting methods and physics-informed neural networks (PINNs). The proposed method, splitting PINN, effectively addresses the challenge of applying PINNs to forward dynamical systems and demonstrates improved accuracy through its application to neuron models. Specifically, we apply operator splitting to decompose the original neuron model into sub-problems that are then solved using PINNs. Moreover, we develop an $L^1$ scheme for discretizing fractional derivatives in fractional neuron models, leading to improved accuracy and efficiency. The results of this study highlight the potential of splitting PINNs in solving both integer- and fractional-order neuron models, as well as other similar systems in computational science and engineering.

Spiking neural networks (SNNs) are brain-inspired machine learning algorithms with merits such as biological plausibility and unsupervised learning capability. Previous works have shown that converting Artificial Neural Networks (ANNs) into SNNs is a practical and efficient approach for implementing an SNN. However, the basic principle and theoretical groundwork are lacking for training a non-accuracy-loss SNN. This paper establishes a precise mathematical mapping between the biological parameters of the Linear Leaky-Integrate-and-Fire model (LIF)/SNNs and the parameters of ReLU-AN/Deep Neural Networks (DNNs). Such mapping relationship is analytically proven under certain conditions and demonstrated by simulation and real data experiments. It can serve as the theoretical basis for the potential combination of the respective merits of the two categories of neural networks.