# A Gradient-based yet Spike-Timing-Dependent Solution to the Feedback Learning Problem in Neural Microcircuits

arXiv: https://arxiv.org/abs/2609.08070 · HTML: https://mlsanity.com/paper/2609.08070/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 58 references that are in the map.
- First posted on arXiv 8 Sep 2026.

## Builds on (most cited first, 15 of 15)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [EEGNet: A Compact Convolutional Network for EEG-based Brain-Computer Interfaces](https://mlsanity.com/paper/1611.08024/) (2016)
- [Surrogate Gradient Learning in Spiking Neural Networks](https://mlsanity.com/paper/1901.09948/) (2019)
- [Spatio-Temporal Backpropagation for Training High-performance Spiking Neural Networks](https://mlsanity.com/paper/1706.02609/) (2017)
- [Long short-term memory and learning-to-learn in networks of spiking neurons](https://mlsanity.com/paper/1803.09574/) (2018)
- [The Heidelberg spiking datasets for the systematic evaluation of spiking neural networks](https://mlsanity.com/paper/1910.07407/) (2019)
- [Accurate online training of dynamical spiking neural networks through Forward Propagation Through Time](https://mlsanity.com/paper/2112.11231/) (2021)
- [Scalable Event-by-event Processing of Neuromorphic Sensory Signals With Deep State-Space Models](https://mlsanity.com/paper/2404.18508/) (2024)
- [Increasing Liquid State Machine Performance with Edge-of-Chaos Dynamics Organized by Astrocyte-modulated Plasticity](https://mlsanity.com/paper/2111.01760/) (2021)
- [LibEER: A Comprehensive Benchmark and Algorithm Library for EEG-based Emotion Recognition](https://mlsanity.com/paper/2410.09767/) (2024)
- [PLSM: A Parallelized Liquid State Machine for Unintentional Action Detection](https://mlsanity.com/paper/2105.09909/) (2021)
- [Algorithm-hardware co-design of neuromorphic networks with dual memory pathways](https://mlsanity.com/paper/2512.07602/) (2025)
- [Current Opinions on Memristor-Accelerated Machine Learning Hardware](https://mlsanity.com/paper/2501.12644/) (2025)

## Abstract (arXiv)

The brain uses discrete spikes for dynamic computation, yet, how neural microcircuits (NMCs) solve temporal credit assignment using local spike timing remains a fundamental open question. Dominant spiking neural network (SNN) approaches circumvent this by approximating backpropagation through surrogate gradients, decoupling learning from biological spike timing. Here, we reformulate temporal credit assignment as a state separation problem: extracting task-required components induced by historical perturbations directly from the current neural state. This enables an online feedback learning framework for NMCs through a gradient tunneling (GT) algorithm and the lead-lag expansion technique that derives credit assignment from local synaptic spike timing, while remaining compatible with ANN-SNN hybrid architectures. Experimentally, GT-trained NMCs excel at long-timescale evidence integration and noise-robust memory retention, and perform comparably to leading SNN online learning methods on real-world benchmarks with far fewer parameters. The proposed framework addresses the two-decade-old NMC feedback learning problem and suggests a computationally plausible explanation for the brain's learning mechanisms.