# Direct Feedback Alignment with Sparse Connections for Local Learning

## TL;DR

This paper introduces a sparse, biologically plausible feedback alignment method for training deep neural networks that significantly reduces data movement and computation compared to backpropagation, with competitive accuracy.

## Contribution

It proposes a novel sparse feedback alignment algorithm that improves efficiency and hardware suitability while maintaining competitive performance.

## Key findings

- Orders of magnitude reduction in data movement.
- Twofold increase in multiply-and-accumulate efficiency.
- Competitive accuracy with backpropagation when training only the fully connected layers.

## Abstract

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 $2\times$ 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.