Katharina Flügel

Katharina Flügel, Daniel Coquelin, Marie Weiel et al.

Backpropagation has long been criticized for being biologically implausible due to its reliance on concepts that are not viable in natural learning processes. Two core issues are the weight transport and update locking problems caused by the forward-backward dependencies, which limit biological plausibility, computational efficiency, and parallelization. Although several alternatives have been proposed to increase biological plausibility, they often come at the cost of reduced predictive performance. This paper proposes an alternative approach to training feed-forward neural networks addressing these issues by using approximate gradient information. We introduce Feed-Forward with delayed Feedback (F$^3$), which approximates gradients using fixed random feedback paths and delayed error information from the previous epoch to balance biological plausibility with predictive performance. We evaluate F$^3$ across multiple tasks and architectures, including both fully-connected and Transformer networks. Our results demonstrate that, compared to similarly plausible approaches, F$^3$ significantly improves predictive performance, narrowing the gap to backpropagation by up to 56% for classification and 96% for regression. This work is a step towards more biologically plausible learning algorithms while opening up new avenues for energy-efficient and parallelizable neural network training.

Katharina Flügel, Daniel Coquelin, Marie Weiel et al.

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.

Daniel Coquelin, Katharina Flügel, Marie Weiel et al.

This study explores the learning dynamics of neural networks by analyzing the singular value decomposition (SVD) of their weights throughout training. Our investigation reveals that an orthogonal basis within each multidimensional weight's SVD representation stabilizes during training. Building upon this, we introduce Orthogonality-Informed Adaptive Low-Rank (OIALR) training, a novel training method exploiting the intrinsic orthogonality of neural networks. OIALR seamlessly integrates into existing training workflows with minimal accuracy loss, as demonstrated by benchmarking on various datasets and well-established network architectures. With appropriate hyperparameter tuning, OIALR can surpass conventional training setups, including those of state-of-the-art models.