# Fast and energy-efficient neuromorphic deep learning with first-spike times

arXiv: https://arxiv.org/abs/1912.11443 · HTML: https://mlsanity.com/paper/1912.11443/

## Key facts

- Cited by 52 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Dec 2019.

## Built on by (most cited first, 30 of 52)

- [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)
- [Latent Equilibrium: A unified learning theory for arbitrarily fast computation with arbitrarily slow neurons](https://mlsanity.com/paper/2110.14549/) (2021)
- [Loss shaping enhances exact gradient learning with Eventprop in spiking neural networks](https://mlsanity.com/paper/2212.01232/) (2022)
- [An Exact Mapping From ReLU Networks to Spiking Neural Networks](https://mlsanity.com/paper/2212.12522/) (2022)
- [The Yin-Yang dataset](https://mlsanity.com/paper/2102.08211/) (2021)
- [Neuromorphic Computing and Sensing in Space](https://mlsanity.com/paper/2212.05236/) (2022)
- [Backpropagation through space, time, and the brain](https://mlsanity.com/paper/2403.16933/) (2024)
- [DelGrad: Exact event-based gradients for training delays and weights on spiking neuromorphic hardware](https://mlsanity.com/paper/2404.19165/) (2024)
- [Spiking Neural Networks and Bio-Inspired Supervised Deep Learning: A Survey](https://mlsanity.com/paper/2307.16235/) (2023)
- [Continual Learning with Neuromorphic Computing: Foundations, Methods, and Emerging Applications](https://mlsanity.com/paper/2410.09218/) (2024)
- [Simple and complex spiking neurons: perspectives and analysis in a simple STDP scenario](https://mlsanity.com/paper/2207.04881/) (2022)
- [SparseProp: Efficient Event-Based Simulation and Training of Sparse Recurrent Spiking Neural Networks](https://mlsanity.com/paper/2312.17216/) (2023)
- [Spike-inspired Rank Coding for Fast and Accurate Recurrent Neural Networks](https://mlsanity.com/paper/2110.02865/) (2021)
- [Stable Learning Using Spiking Neural Networks Equipped With Affine Encoders and Decoders](https://mlsanity.com/paper/2404.04549/) (2024)
- [Random Quantum Neural Networks (RQNN) for Noisy Image Recognition](https://mlsanity.com/paper/2203.01764/) (2022)
- [Relational representation learning with spike trains](https://mlsanity.com/paper/2205.09140/) (2022)
- [EXODUS: Stable and Efficient Training of Spiking Neural Networks](https://mlsanity.com/paper/2205.10242/) (2022)
- [Addressing the speed-accuracy simulation trade-off for adaptive spiking neurons](https://mlsanity.com/paper/2311.11390/) (2023)
- [The Role of Temporal Hierarchy in Spiking Neural Networks](https://mlsanity.com/paper/2407.18838/) (2024)
- [Biologically-inspired Semi-supervised Semantic Segmentation for Biomedical Imaging](https://mlsanity.com/paper/2412.03192/) (2024)
- [Time to Spike? Understanding the Representational Power of Spiking Neural Networks in Discrete Time](https://mlsanity.com/paper/2505.18023/) (2025)
- [Timing-Based Backpropagation in Spiking Neural Networks Without Single-Spike Restrictions](https://mlsanity.com/paper/2211.16113/) (2022)
- [Sparse-firing regularization methods for spiking neural networks with time-to-first spike coding](https://mlsanity.com/paper/2307.13007/) (2023)
- [Towards biologically plausible Dreaming and Planning in recurrent spiking networks](https://mlsanity.com/paper/2205.10044/) (2022)
- [Neuro-symbolic computing with spiking neural networks](https://mlsanity.com/paper/2208.02576/) (2022)
- [Spyx: A Library for Just-In-Time Compiled Optimization of Spiking Neural Networks](https://mlsanity.com/paper/2402.18994/) (2024)
- [Causal pieces: analysing and improving spiking neural networks piece by piece](https://mlsanity.com/paper/2504.14015/) (2025)
- [Training event-based neural networks with exact gradients via Differentiable ODE Solving in JAX](https://mlsanity.com/paper/2603.08146/) (2026)

## Abstract (arXiv)

For a biological agent operating under environmental pressure, energy consumption and reaction times are of critical importance. Similarly, engineered systems are optimized for short time-to-solution and low energy-to-solution characteristics. At the level of neuronal implementation, this implies achieving the desired results with as few and as early spikes as possible. With time-to-first-spike coding both of these goals are inherently emerging features of learning. Here, we describe a rigorous derivation of a learning rule for such first-spike times in networks of leaky integrate-and-fire neurons, relying solely on input and output spike times, and show how this mechanism can implement error backpropagation in hierarchical spiking networks. Furthermore, we emulate our framework on the BrainScaleS-2 neuromorphic system and demonstrate its capability of harnessing the system's speed and energy characteristics. Finally, we examine how our approach generalizes to other neuromorphic platforms by studying how its performance is affected by typical distortive effects induced by neuromorphic substrates.