# Spike-based alignment learning solves the weight transport problem

arXiv: https://arxiv.org/abs/2503.02642 · HTML: https://mlsanity.com/paper/2503.02642/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 123 references that are in the map.
- First posted on arXiv 4 Mar 2025.

## Builds on (most cited first, 30 of 46)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Equilibrium Propagation: Bridging the Gap Between Energy-Based Models and Backpropagation](https://mlsanity.com/paper/1602.05179/) (2016)
- [Direct Feedback Alignment Provides Learning in Deep Neural Networks](https://mlsanity.com/paper/1609.01596/) (2016)
- [Difference Target Propagation](https://mlsanity.com/paper/1412.7525/) (2014)
- [Assessing the Scalability of Biologically-Motivated Deep Learning Algorithms and Architectures](https://mlsanity.com/paper/1807.04587/) (2018)
- [Dendritic cortical microcircuits approximate the backpropagation algorithm](https://mlsanity.com/paper/1810.11393/) (2018)
- [Deep Learning without Weight Transport](https://mlsanity.com/paper/1904.05391/) (2019)
- [How Auto-Encoders Could Provide Credit Assignment in Deep Networks via Target Propagation](https://mlsanity.com/paper/1407.7906/) (2014)
- [Predictive Coding: a Theoretical and Experimental Review](https://mlsanity.com/paper/2107.12979/) (2021)
- [Towards deep learning with segregated dendrites](https://mlsanity.com/paper/1610.00161/) (2016)
- [How Important is Weight Symmetry in Backpropagation?](https://mlsanity.com/paper/1510.05067/) (2015)
- [A Theoretical Framework for Target Propagation](https://mlsanity.com/paper/2006.14331/) (2020)
- [A scalable multi-core architecture with heterogeneous memory structures for Dynamic Neuromorphic Asynchronous Processors (DYNAPs)](https://mlsanity.com/paper/1708.04198/) (2017)
- [Fast and energy-efficient neuromorphic deep learning with first-spike times](https://mlsanity.com/paper/1912.11443/) (2019)
- [The BrainScaleS-2 accelerated neuromorphic system with hybrid plasticity](https://mlsanity.com/paper/2201.11063/) (2022)
- [Biologically-plausible learning algorithms can scale to large datasets](https://mlsanity.com/paper/1811.03567/) (2018)
- [Towards Scaling Difference Target Propagation by Learning Backprop Targets](https://mlsanity.com/paper/2201.13415/) (2022)
- [Feedback alignment in deep convolutional networks](https://mlsanity.com/paper/1812.06488/) (2018)
- [Credit Assignment in Neural Networks through Deep Feedback Control](https://mlsanity.com/paper/2106.07887/) (2021)
- [Learning to solve the credit assignment problem](https://mlsanity.com/paper/1906.00889/) (2019)
- [DYNAP-SE2: a scalable multi-core dynamic neuromorphic asynchronous spiking neural network processor](https://mlsanity.com/paper/2310.00564/) (2023)
- [Versatile emulation of spiking neural networks on an accelerated neuromorphic substrate](https://mlsanity.com/paper/1912.12980/) (2019)
- [Latent Equilibrium: A unified learning theory for arbitrarily fast computation with arbitrarily slow neurons](https://mlsanity.com/paper/2110.14549/) (2021)
- [Event-Driven Contrastive Divergence for Spiking Neuromorphic Systems](https://mlsanity.com/paper/1311.0966/) (2013)
- [Dendritic predictive coding: A theory of cortical computation with spiking neurons](https://mlsanity.com/paper/2205.05303/) (2022)
- [The implications of perception as probabilistic inference for correlated neural variability during behavior](https://mlsanity.com/paper/1409.0257/) (2014)
- [Spike-based causal inference for weight alignment](https://mlsanity.com/paper/1910.01689/) (2019)
- [Backpropagation through space, time, and the brain](https://mlsanity.com/paper/2403.16933/) (2024)
- [Accelerated physical emulation of Bayesian inference in spiking neural networks](https://mlsanity.com/paper/1807.02389/) (2018)

## Built on by (most cited first, 1 of 1)

- [A Variational Latent Equilibrium for Learning in Neuronal Circuits](https://mlsanity.com/paper/2603.09600/) (2026)

## Abstract (arXiv)

In both machine learning and in computational neuroscience, plasticity in functional neural networks is frequently expressed as gradient descent on a cost. Often, this imposes symmetry constraints that are difficult to reconcile with local computation, as is required for biological networks or neuromorphic hardware. For example, wake-sleep learning in networks characterized by Boltzmann distributions assumes symmetric connectivity. Similarly, the error backpropagation algorithm is notoriously plagued by the weight transport problem between the representation and the error stream. Existing solutions such as feedback alignment circumvent the problem by deferring to the robustness of these algorithms to weight asymmetry. However, they scale poorly with network size and depth. We introduce spike-based alignment learning (SAL), a complementary learning rule for spiking neural networks, which uses spike timing statistics to extract and correct the asymmetry between effective reciprocal connections. Apart from being spike-based and fully local, our proposed mechanism takes advantage of noise. Based on an interplay between Hebbian and anti-Hebbian plasticity, synapses can thereby recover the true local gradient. This also alleviates discrepancies that arise from neuron and synapse variability -- an omnipresent property of physical neuronal networks. We demonstrate the efficacy of our mechanism using different spiking network models. First, SAL can significantly improve convergence to the target distribution in probabilistic spiking networks versus Hebbian plasticity alone. Second, in neuronal hierarchies based on cortical microcircuits, SAL effectively aligns feedback weights to the forward pathway, thus allowing the backpropagation of correct feedback errors. Third, our approach enables competitive performance in deep networks using only local plasticity for weight transport.