# An Introduction to Probabilistic Spiking Neural Networks: Probabilistic Models, Learning Rules, and Applications

arXiv: https://arxiv.org/abs/1910.01059 · HTML: https://mlsanity.com/paper/1910.01059/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Oct 2019.

## Built on by (most cited first, 26 of 26)

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- [Learning to Time-Decode in Spiking Neural Networks Through the Information Bottleneck](https://mlsanity.com/paper/2106.01177/) (2021)
- [Bayesian Continual Learning via Spiking Neural Networks](https://mlsanity.com/paper/2208.13723/) (2022)
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- [Spiking Generative Adversarial Networks With a Neural Network Discriminator: Local Training, Bayesian Models, and Continual Meta-Learning](https://mlsanity.com/paper/2111.01750/) (2021)
- [Knowing When to Stop: Delay-Adaptive Spiking Neural Network Classifiers with Reliability Guarantees](https://mlsanity.com/paper/2305.11322/) (2023)
- [Fast On-Device Adaptation for Spiking Neural Networks via Online-Within-Online Meta-Learning](https://mlsanity.com/paper/2103.03901/) (2021)
- [Bayesian Inference on Binary Spiking Networks Leveraging Nanoscale Device Stochasticity](https://mlsanity.com/paper/2302.01302/) (2023)
- [Neuromorphic Event-Driven Semantic Communication in Microgrids](https://mlsanity.com/paper/2402.18390/) (2024)
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- [Neuromorphic Wireless Device-Edge Co-Inference via the Directed Information Bottleneck](https://mlsanity.com/paper/2404.01804/) (2024)
- [Stochastic Quantum Spiking Neural Networks with Quantum Memory and Local Learning](https://mlsanity.com/paper/2506.21324/) (2025)
- [Multi-Sample Online Learning for Spiking Neural Networks based on Generalized Expectation Maximization](https://mlsanity.com/paper/2102.03280/) (2021)
- [A Construction Kit for Efficient Low Power Neural Network Accelerator Designs](https://mlsanity.com/paper/2106.12810/) (2021)
- [Learning Spiking Neural Network from Easy to Hard task](https://mlsanity.com/paper/2309.04737/) (2023)
- [A Neuromorphic Approach to Obstacle Avoidance in Robot Manipulation](https://mlsanity.com/paper/2404.05858/) (2024)
- [Neuromorphic Wireless Split Computing with Resonate-and-Fire Neurons](https://mlsanity.com/paper/2506.20015/) (2025)
- [Training of Spiking Neural Networks with Expectation-Propagation](https://mlsanity.com/paper/2506.23757/) (2025)
- [Quantization Meets Spikes: Nearly Lossless Conversion at the First Timestep via Polarity Multi-Spike Mapping](https://mlsanity.com/paper/2508.14520/) (2025)

## Abstract (arXiv)

Spiking neural networks (SNNs) are distributed trainable systems whose computing elements, or neurons, are characterized by internal analog dynamics and by digital and sparse synaptic communications. The sparsity of the synaptic spiking inputs and the corresponding event-driven nature of neural processing can be leveraged by energy-efficient hardware implementations, which can offer significant energy reductions as compared to conventional artificial neural networks (ANNs). The design of training algorithms lags behind the hardware implementations. Most existing training algorithms for SNNs have been designed either for biological plausibility or through conversion from pretrained ANNs via rate encoding. This article provides an introduction to SNNs by focusing on a probabilistic signal processing methodology that enables the direct derivation of learning rules by leveraging the unique time-encoding capabilities of SNNs. We adopt discrete-time probabilistic models for networked spiking neurons and derive supervised and unsupervised learning rules from first principles via variational inference. Examples and open research problems are also provided.