Gradient Descent as a Perceptron Algorithm: Understanding Dynamics and Implicit Acceleration
arXiv:2512.11587v2 Announce Type: replace Abstract: Even for the gradient descent (GD) method applied to neural network training, understanding its optimization dynamics, including convergence rate, iterate trajectories, function value oscillations, and especially its implicit acceleration, remains a challenging problem. We analyze nonlinear models with the logistic loss and show that the steps of GD reduce to those of generalized perceptron algorithms (Rosenblatt, 1958), providing a new perspective on the dynamics. This reduction yields significantly simpler algorithmic steps, which we analyz
This research provides a more fundamental understanding of gradient descent dynamics, linking it to established perceptron algorithms, which is crucial as machine learning models become increasingly complex.
A deeper theoretical understanding of core AI algorithms like gradient descent can lead to significant improvements in training efficiency, stability, and the development of new, more performant architectures.
This research offers a new analytical framework for understanding the implicit acceleration and optimization dynamics of neural networks, potentially simplifying current approaches to model optimization.
- · AI researchers
- · Machine learning framework developers
- · Companies with large-scale neural network training needs
- · Developers relying solely on empirical tuning
Improved understanding of neural network training mechanisms will inform more efficient algorithm design.
The simplification of algorithmic steps could lead to breakthroughs in resource-constrained AI deployments.
These theoretical advancements might enable the creation of AI systems with fundamentally new learning paradigms, accelerating the development of advanced AI agents.
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Read at arXiv cs.LG