Beyond Backpropagation: Optimization with Multi-Tangent Forward Gradients

• URL: http://arxiv.org/abs/2410.17764v1
• Date: Wed, 23 Oct 2024 11:02:59 GMT
• Title: Beyond Backpropagation: Optimization with Multi-Tangent Forward Gradients
• Authors: Katharina Flügel, Daniel Coquelin, Marie Weiel, Achim Streit, Markus Götz,
• Abstract summary: Forward gradients are an approach to approximate the gradients from directional derivatives along random tangents computed by forward-mode automatic differentiation. This paper provides an in-depth analysis of multi-tangent forward gradients and introduces an improved approach to combining the forward gradients from multiple tangents based on projections.
• Score: 0.08388591755871733
• License:
• Abstract: The gradients used to train neural networks are typically computed using backpropagation. While an efficient way to obtain exact gradients, backpropagation is computationally expensive, hinders parallelization, and is biologically implausible. Forward gradients are an approach to approximate the gradients from directional derivatives along random tangents computed by forward-mode automatic differentiation. So far, research has focused on using a single tangent per step. This paper provides an in-depth analysis of multi-tangent forward gradients and introduces an improved approach to combining the forward gradients from multiple tangents based on orthogonal projections. We demonstrate that increasing the number of tangents improves both approximation quality and optimization performance across various tasks.

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