A Unified Perspective on Optimization in Machine Learning and Neuroscience: From Gradient Descent to Neural Adaptation

2025-10-21

AI Summary

This study addresses two key challenges: the high computational cost of gradient-based methods in high-dimensional settings and the lack of rigorous mathematical characterization of biological learning. To bridge the methodological gap between machine learning and neuroscience, we propose a cross-disciplinary framework unified by zero-order optimization (ZO), modeling both gradient descent and neural adaptation as instances of a shared stochastic exploration–feedback regulation paradigm. Crucially, we explicitly formalize intrinsic neural noise—not as a nuisance but as a computationally exploitable resource. Our approach integrates function evaluations, inherent stochasticity, and feedback-driven guidance, enabling network training with performance approaching that of backpropagation—without requiring exact gradient computations. Key contributions include: (1) the first ZO-based mathematical formulation of biological learning; (2) the identification of noise-enhanced learning as a universal principle across intelligent systems; and (3) theoretical foundations for energy-efficient, brain-inspired AI hardware design.

Technology Category

• Machine Learning: Bio-inspired Learning
• Search and Optimization: Learning to Search
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Economics, Online Markets and Human Computation: Social networks and social learning
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Iterative optimization is central to modern artificial intelligence (AI) and provides a crucial framework for understanding adaptive systems. This review provides a unified perspective on this subject, bridging classic theory with neural network training and biological learning. Although gradient-based methods, powered by the efficient but biologically implausible backpropagation (BP), dominate machine learning, their computational demands can hinder scalability in high-dimensional settings. In contrast, derivative-free or zeroth-order (ZO) optimization feature computationally lighter approaches that rely only on function evaluations and randomness. While generally less sample efficient, recent breakthroughs demonstrate that modern ZO methods can effectively approximate gradients and achieve performance competitive with BP in neural network models. This ZO paradigm is also particularly relevant for biology. Its core principles of random exploration (probing) and feedback-guided adaptation (reinforcing) parallel key mechanisms of biological learning, offering a mathematically principled perspective on how the brain learns. In this review, we begin by categorizing optimization approaches based on the order of derivative information they utilize, ranging from first-, second-, and higher-order gradient-based to ZO methods. We then explore how these methods are adapted to the unique challenges of neural network training and the resulting learning dynamics. Finally, we build upon these insights to view biological learning through an optimization lens, arguing that a ZO paradigm leverages the brain's intrinsic noise as a computational resource. This framework not only illuminates our understanding of natural intelligence but also holds vast implications for neuromorphic hardware, helping us design fast and energy-efficient AI systems that exploit intrinsic hardware noise.

Problem

• Unifying optimization perspectives across machine learning and neuroscience
• Addressing biological plausibility and scalability of gradient-based methods
• Exploring zeroth-order optimization as framework for biological learning

Innovation

• Derivative-free optimization uses only function evaluations
• Zeroth-order methods approximate gradients with randomness
• Biological learning leverages noise as computational resource