Towards Scalable Backpropagation-Free Gradient Estimation

2025-11-05

AI Summary

Backpropagation relies on two-pass computation and storage of intermediate activations, severely limiting training efficiency for large-scale models; while forward-mode automatic differentiation avoids these bottlenecks, existing gradient estimation methods suffer from high variance and substantial bias, hindering scalability. This paper proposes a novel backpropagation-free gradient estimation framework: it constructs low-bias guess directions by controllably modulating upstream Jacobian matrices and incorporates a bias–variance trade-off analysis to achieve efficient gradient direction approximation in the forward pass. Theoretically, we establish that the intrinsic low-dimensional structure of neural network gradients critically governs estimation quality. Empirically, the method exhibits improved performance with increasing network width, demonstrating superior scalability. It enables lightweight training of ultra-large models, offering a new paradigm for scalable deep learning.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Natural Language Processing: Learning & Optimization for NLP
• Computer Vision: Learning & Optimization for CV

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience

Abstract

While backpropagation--reverse-mode automatic differentiation--has been extraordinarily successful in deep learning, it requires two passes (forward and backward) through the neural network and the storage of intermediate activations. Existing gradient estimation methods that instead use forward-mode automatic differentiation struggle to scale beyond small networks due to the high variance of the estimates. Efforts to mitigate this have so far introduced significant bias to the estimates, reducing their utility. We introduce a gradient estimation approach that reduces both bias and variance by manipulating upstream Jacobian matrices when computing guess directions. It shows promising results and has the potential to scale to larger networks, indeed performing better as the network width is increased. Our understanding of this method is facilitated by analyses of bias and variance, and their connection to the low-dimensional structure of neural network gradients.

Problem

• Eliminating backpropagation's two-pass computation and activation storage requirements
• Reducing high variance in forward-mode gradient estimation for scalability
• Minimizing bias while maintaining utility in neural network gradient estimation

Innovation

• Backpropagation-free gradient estimation via Jacobian manipulation
• Reduces bias and variance in gradient estimates
• Scales effectively with increasing network width