# Formal derivation of Mesh Neural Networks with their Forward-Only gradient Propagation

## TL;DR

This paper introduces Mesh Neural Networks (MNNs), a new architecture enabling flexible neuron connectivity and direct gradient computation without backpropagation, potentially improving efficiency for large-scale sparse neural networks.

## Contribution

It formally derives the MNN architecture and error propagation method using tensor algebra, offering a novel approach to neural network training without backward passes.

## Key findings

- MNNs can be trained using forward-only gradient propagation.
- The architecture is suitable for large-scale sparse neural networks.
- MNNs show potential for improved training efficiency.

## Abstract

This paper proposes the Mesh Neural Network (MNN), a novel architecture which allows neurons to be connected in any topology, to efficiently route information. In MNNs, information is propagated between neurons throughout a state transition function. State and error gradients are then directly computed from state updates without backward computation. The MNN architecture and the error propagation schema is formalized and derived in tensor algebra. The proposed computational model can fully supply a gradient descent process, and is potentially suitable for very large scale sparse NNs, due to its expressivity and training efficiency, with respect to NNs based on back-propagation and computational graphs.