# Spike-based causal inference for weight alignment

arXiv: https://arxiv.org/abs/1910.01689 · HTML: https://mlsanity.com/paper/1910.01689/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Oct 2019.

## Built on by (most cited first, 10 of 10)

- [Credit Assignment in Neural Networks through Deep Feedback Control](https://mlsanity.com/paper/2106.07887/) (2021)
- [Latent Equilibrium: A unified learning theory for arbitrarily fast computation with arbitrarily slow neurons](https://mlsanity.com/paper/2110.14549/) (2021)
- [Meta-Learning Biologically Plausible Plasticity Rules with Random Feedback Pathways](https://mlsanity.com/paper/2210.16414/) (2022)
- [Constrained Parameter Inference as a Principle for Learning](https://mlsanity.com/paper/2203.13203/) (2022)
- [Training Deep Architectures Without End-to-End Backpropagation: A Survey on the Provably Optimal Methods](https://mlsanity.com/paper/2101.03419/) (2021)
- [BioGrad: Biologically Plausible Gradient-Based Learning for Spiking Neural Networks](https://mlsanity.com/paper/2110.14092/) (2021)
- [A Goal-Driven Approach to Systems Neuroscience](https://mlsanity.com/paper/2311.02704/) (2023)
- [Spike-based alignment learning solves the weight transport problem](https://mlsanity.com/paper/2503.02642/) (2025)
- [Forward Only Learning for Orthogonal Neural Networks of any Depth](https://mlsanity.com/paper/2512.20668/) (2025)
- [A Variational Latent Equilibrium for Learning in Neuronal Circuits](https://mlsanity.com/paper/2603.09600/) (2026)

## Abstract (arXiv)

In artificial neural networks trained with gradient descent, the weights used for processing stimuli are also used during backward passes to calculate gradients. For the real brain to approximate gradients, gradient information would have to be propagated separately, such that one set of synaptic weights is used for processing and another set is used for backward passes. This produces the so-called "weight transport problem" for biological models of learning, where the backward weights used to calculate gradients need to mirror the forward weights used to process stimuli. This weight transport problem has been considered so hard that popular proposals for biological learning assume that the backward weights are simply random, as in the feedback alignment algorithm. However, such random weights do not appear to work well for large networks. Here we show how the discontinuity introduced in a spiking system can lead to a solution to this problem. The resulting algorithm is a special case of an estimator used for causal inference in econometrics, regression discontinuity design. We show empirically that this algorithm rapidly makes the backward weights approximate the forward weights. As the backward weights become correct, this improves learning performance over feedback alignment on tasks such as Fashion-MNIST, SVHN, CIFAR-10 and VOC. Our results demonstrate that a simple learning rule in a spiking network can allow neurons to produce the right backward connections and thus solve the weight transport problem.