# Direct Feedback Alignment with Sparse Connections for Local Learning

arXiv: https://arxiv.org/abs/1903.02083 · HTML: https://mlsanity.com/paper/1903.02083/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jan 2019.

## Built on by (most cited first, 26 of 26)

- [Credit Assignment in Neural Networks through Deep Feedback Control](https://mlsanity.com/paper/2106.07887/) (2021)
- [Is Bio-Inspired Learning Better than Backprop? Benchmarking Bio Learning vs. Backprop](https://mlsanity.com/paper/2212.04614/) (2022)
- [Learning efficient backprojections across cortical hierarchies in real time](https://mlsanity.com/paper/2212.10249/) (2022)
- [Low-Variance Forward Gradients using Direct Feedback Alignment and Momentum](https://mlsanity.com/paper/2212.07282/) (2022)
- [Fixed-Weight Difference Target Propagation](https://mlsanity.com/paper/2212.10352/) (2022)
- [LLS: Local Learning Rule for Deep Neural Networks Inspired by Neural Activity Synchronization](https://mlsanity.com/paper/2405.15868/) (2024)
- [Counter-Current Learning: A Biologically Plausible Dual Network Approach for Deep Learning](https://mlsanity.com/paper/2409.19841/) (2024)
- [TESS: A Scalable Temporally and Spatially Local Learning Rule for Spiking Neural Networks](https://mlsanity.com/paper/2502.01837/) (2025)
- [Target Propagation via Regularized Inversion](https://mlsanity.com/paper/2112.01453/) (2021)
- [Adaptive Spatial Goodness Encoding: Advancing and Scaling Forward-Forward Learning Without Backpropagation](https://mlsanity.com/paper/2509.12394/) (2025)
- [Hyperspherical Forward-Forward with Prototypical Representations](https://mlsanity.com/paper/2605.00082/) (2026)
- [A Robust Backpropagation-Free Framework for Images](https://mlsanity.com/paper/2206.01820/) (2022)
- [Brain-like Flexible Visual Inference by Harnessing Feedback-Feedforward Alignment](https://mlsanity.com/paper/2310.20599/) (2023)
- [Representation Learning in a Decomposed Encoder Design for Bio-inspired Hebbian Learning](https://mlsanity.com/paper/2401.08603/) (2023)
- [Training Large Neural Networks With Low-Dimensional Error Feedback](https://mlsanity.com/paper/2502.20580/) (2025)
- [Accelerated Predictive Coding Networks via Direct Kolen-Pollack Feedback Alignment](https://mlsanity.com/paper/2602.15571/) (2026)
- [Covariance-Aware Goodness for Scalable Forward-Forward Learning](https://mlsanity.com/paper/2605.04346/) (2026)
- [Feedback Alignment Meets Low-Rank Manifolds: A Structured Recipe for Local Learning](https://mlsanity.com/paper/2510.25594/) (2025)
- [Conditioned Direct Feedback Alignment via Activity and Error Geometry](https://mlsanity.com/paper/2607.18574/) (2026)
- [Learning with augmented target information: An alternative theory of Feedback Alignment](https://mlsanity.com/paper/2304.01406/) (2023)
- [Random Feedback Alignment Algorithms to train Neural Networks: Why do they Align?](https://mlsanity.com/paper/2306.02325/) (2023)
- [Forward Direct Feedback Alignment for Online Gradient Estimates of Spiking Neural Networks](https://mlsanity.com/paper/2403.08804/) (2024)
- [Dopamine-driven synaptic credit assignment in neural networks](https://mlsanity.com/paper/2510.22178/) (2025)
- [Forward Only Learning for Orthogonal Neural Networks of any Depth](https://mlsanity.com/paper/2512.20668/) (2025)
- [SAL: Selective Adaptive Learning for Backpropagation-Free Training with Sparsification](https://mlsanity.com/paper/2601.21561/) (2026)
- [What Accuracy and Gradient Cosine Miss: Evaluating Feedback Alignment via Scale Stability, Reference Validity, and Depth Utility](https://mlsanity.com/paper/2606.21126/) (2026)

## Abstract (arXiv)

Recent advances in deep neural networks (DNNs) owe their success to training algorithms that use backpropagation and gradient-descent. Backpropagation, while highly effective on von Neumann architectures, becomes inefficient when scaling to large networks. Commonly referred to as the weight transport problem, each neuron's dependence on the weights and errors located deeper in the network require exhaustive data movement which presents a key problem in enhancing the performance and energy-efficiency of machine-learning hardware. In this work, we propose a bio-plausible alternative to backpropagation drawing from advances in feedback alignment algorithms in which the error computation at a single synapse reduces to the product of three scalar values. Using a sparse feedback matrix, we show that a neuron needs only a fraction of the information previously used by the feedback alignment algorithms. Consequently, memory and compute can be partitioned and distributed whichever way produces the most efficient forward pass so long as a single error can be delivered to each neuron. Our results show orders of magnitude improvement in data movement and 2× improvement in multiply-and-accumulate operations over backpropagation. Like previous work, we observe that any variant of feedback alignment suffers significant losses in classification accuracy on deep convolutional neural networks. By transferring trained convolutional layers and training the fully connected layers using direct feedback alignment, we demonstrate that direct feedback alignment can obtain results competitive with backpropagation. Furthermore, we observe that using an extremely sparse feedback matrix, rather than a dense one, results in a small accuracy drop while yielding hardware advantages. All the code and results are available under https://github.com/bcrafton/ssdfa.