# Accurate online training of dynamical spiking neural networks through Forward Propagation Through Time

**Authors:** Bojian Yin, Federico Corradi, Sander M. Bohte  
**arXiv:** [2112.11231](https://arxiv.org/abs/2112.11231)  
**Date:** 2021-12-20  
**Summary page:** https://www.summarizepaper.com/en/paper/2112.11231v1/

## Key points

- Event-driven and sparse communication between spiking neurons in the brain is promising for energy-efficient AI.
- Recurrent networks of spiking neurons can achieve competitive performance compared to standard neural networks.
- Learning algorithms like error-backpropagation through time (BPTT) have limitations such as high memory requirements, slow training speed, and incompatibility with online learning.
- Online approximations to BPTT with lower computational and memory complexity have been proposed but still suffer from limitations.
- Forward Propagation Through Time (FPTT) is introduced as an alternative to BPTT for spiking neural networks (SNNs), aiming to minimize dynamically regularized risk on the loss.
- FPTT allows for online computation with fixed complexity relative to sequence length.
- The Liquid-Time-Constant neuron model is introduced, incorporating dynamic and input-driven internal time constants similar to gating operations in LSTMs.
- Integration of Liquid Spiking Neurons into SNNs trained with FPTT improves performance on long sequences and enables online learning while reducing memory complexity.
- Large-scale convolutional SNNs trained with FPTT using Liquid-Time-Constant neurons achieve state-of-the-art performance on benchmarks like S-MNIST, R-MNIST, and DVS GESTURE.
- Large feedforward SNNs can be successfully trained online to near state-of-the-art performance achieved with offline BPTT on benchmarks like Fashion MNIST and DVS CIFAR10.
- FPTT combined with the Liquid Time Constant neuron model allows for efficient training of SNNs in a memory-friendly online fashion on long sequences.

## Summary

The event-driven and sparse nature of communication between spiking neurons in the brain holds great promise for flexible and energy-efficient artificial intelligence (AI). Recent advancements in learning algorithms have shown that recurrent networks of spiking neurons can be trained effectively to achieve competitive performance compared to standard recurrent neural networks. However, these learning algorithms, which use error-backpropagation through time (BPTT), have limitations such as high memory requirements, slow training speed, and incompatibility with online learning. To address these limitations, online approximations to BPTT with lower computational and memory complexity have been proposed. These approximations, such as e-prop and OSTL, still suffer from memory limitations and do not outperform standard BPTT training. In this study, a recently developed alternative to BPTT called Forward Propagation Through Time (FPTT) is introduced for application in spiking neural networks (SNNs). Unlike BPTT, FPTT aims to minimize an ongoing dynamically regularized risk on the loss. This allows FPTT to be computed in an online fashion with fixed complexity relative to the sequence length. To further enhance the performance of SNNs trained with FPTT, a novel dynamic spiking neuron model called the Liquid-Time-Constant neuron is introduced. This neuron model incorporates internal time constants that are dynamic and input-driven in a learned manner, similar to the gating operation in Long Short-Term Memory networks (LSTMs). The integration of Liquid Spiking Neurons into SNNs trained with FPTT results in improved performance compared to various SNNs trained with BPTT on long sequences. Additionally, this approach enables online learning and significantly reduces memory complexity. The effectiveness of this approach is demonstrated on classical benchmarks such as the adding task and the DVS gesture benchmark. Furthermore, large-scale convolutional SNNs trained with FPTT using Liquid-Time-Constant neurons achieve state-of-the-art performance on several standard benchmarks, including S-MNIST, R-MNIST, and DVS GESTURE. This study also shows that large feedforward SNNs can be trained successfully in an online manner to near state-of-the art performance achieved with offline BPTT on benchmarks such as Fashion MNIST and DVS CIFAR10. Overall, the application of FPTT in SNNs combined with the novel Liquid Time Constant neuron model allows for efficient training of SNNs in a memory friendly online fashion on long sequences. This approach has the potential to scale up SNNs to complex neural architectures and opens up new possibilities for flexible and energy efficient AI systems.