# Supervised learning based on temporal coding in spiking neural networks

arXiv: https://arxiv.org/abs/1606.08165 · HTML: https://mlsanity.com/paper/1606.08165/

## Key facts

- Cited by 76 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jun 2016.

## Built on by (most cited first, 30 of 76)

- [Training High-Performance Low-Latency Spiking Neural Networks by Differentiation on Spike Representation](https://mlsanity.com/paper/2205.00459/) (2022)
- [Beyond Classification: Directly Training Spiking Neural Networks for Semantic Segmentation](https://mlsanity.com/paper/2110.07742/) (2021)
- [Neural Architecture Search for Spiking Neural Networks](https://mlsanity.com/paper/2201.10355/) (2022)
- [Deep Spoken Keyword Spotting: An Overview](https://mlsanity.com/paper/2111.10592/) (2021)
- [Optimized Potential Initialization for Low-latency Spiking Neural Networks](https://mlsanity.com/paper/2202.01440/) (2022)
- [Reducing ANN-SNN Conversion Error through Residual Membrane Potential](https://mlsanity.com/paper/2302.02091/) (2023)
- [Bridging the Gap between ANNs and SNNs by Calibrating Offset Spikes](https://mlsanity.com/paper/2302.10685/) (2023)
- [Towards Memory- and Time-Efficient Backpropagation for Training Spiking Neural Networks](https://mlsanity.com/paper/2302.14311/) (2023)
- [Visual Explanations from Spiking Neural Networks using Interspike Intervals](https://mlsanity.com/paper/2103.14441/) (2021)
- [Exploring Lottery Ticket Hypothesis in Spiking Neural Networks](https://mlsanity.com/paper/2207.01382/) (2022)
- [Training Full Spike Neural Networks via Auxiliary Accumulation Pathway](https://mlsanity.com/paper/2301.11929/) (2023)
- [Rate Coding or Direct Coding: Which One is Better for Accurate, Robust, and Energy-efficient Spiking Neural Networks?](https://mlsanity.com/paper/2202.03133/) (2022)
- [Exploring Temporal Information Dynamics in Spiking Neural Networks](https://mlsanity.com/paper/2211.14406/) (2022)
- [ESL-SNNs: An Evolutionary Structure Learning Strategy for Spiking Neural Networks](https://mlsanity.com/paper/2306.03693/) (2023)
- [High-performance deep spiking neural networks with 0.3 spikes per neuron](https://mlsanity.com/paper/2306.08744/) (2023)
- [Bottom-up and top-down approaches for the design of neuromorphic processing systems: Tradeoffs and synergies between natural and artificial intelligence](https://mlsanity.com/paper/2106.01288/) (2021)
- [The Backpropagation Algorithm Implemented on Spiking Neuromorphic Hardware](https://mlsanity.com/paper/2106.07030/) (2021)
- [EAS-SNN: End-to-End Adaptive Sampling and Representation for Event-based Detection with Recurrent Spiking Neural Networks](https://mlsanity.com/paper/2403.12574/) (2024)
- [Loss shaping enhances exact gradient learning with Eventprop in spiking neural networks](https://mlsanity.com/paper/2212.01232/) (2022)
- [Increasing Liquid State Machine Performance with Edge-of-Chaos Dynamics Organized by Astrocyte-modulated Plasticity](https://mlsanity.com/paper/2111.01760/) (2021)
- [An Exact Mapping From ReLU Networks to Spiking Neural Networks](https://mlsanity.com/paper/2212.12522/) (2022)
- [Uncovering the Representation of Spiking Neural Networks Trained with Surrogate Gradient](https://mlsanity.com/paper/2304.13098/) (2023)
- [LM-HT SNN: Enhancing the Performance of SNN to ANN Counterpart through Learnable Multi-hierarchical Threshold Model](https://mlsanity.com/paper/2402.00411/) (2024)
- [Keys to Accurate Feature Extraction Using Residual Spiking Neural Networks](https://mlsanity.com/paper/2111.05955/) (2021)
- [Neuromorphic Computing and Sensing in Space](https://mlsanity.com/paper/2212.05236/) (2022)
- [Enhancing Adversarial Robustness in SNNs with Sparse Gradients](https://mlsanity.com/paper/2405.20355/) (2024)
- [SpikE: spike-based embeddings for multi-relational graph data](https://mlsanity.com/paper/2104.13398/) (2021)
- [Hebbian Learning based Orthogonal Projection for Continual Learning of Spiking Neural Networks](https://mlsanity.com/paper/2402.11984/) (2024)
- [Advancing Training Efficiency of Deep Spiking Neural Networks through Rate-based Backpropagation](https://mlsanity.com/paper/2410.11488/) (2024)
- [Spike time displacement based error backpropagation in convolutional spiking neural networks](https://mlsanity.com/paper/2108.13621/) (2021)

## Abstract (arXiv)

Gradient descent training techniques are remarkably successful in training analog-valued artificial neural networks (ANNs). Such training techniques, however, do not transfer easily to spiking networks due to the spike generation hard non-linearity and the discrete nature of spike communication. We show that in a feedforward spiking network that uses a temporal coding scheme where information is encoded in spike times instead of spike rates, the network input-output relation is differentiable almost everywhere. Moreover, this relation is piece-wise linear after a transformation of variables. Methods for training ANNs thus carry directly to the training of such spiking networks as we show when training on the permutation invariant MNIST task. In contrast to rate-based spiking networks that are often used to approximate the behavior of ANNs, the networks we present spike much more sparsely and their behavior can not be directly approximated by conventional ANNs. Our results highlight a new approach for controlling the behavior of spiking networks with realistic temporal dynamics, opening up the potential for using these networks to process spike patterns with complex temporal information.