Adaptive Step Sizes and Implicit Regularization: Decoding the Generalization Landscape of Gradient Optimizers
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2025
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| _version_ | 1866901231092367360 |
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| author | Revista, Zen IA, 10 |
| author_facet | Revista, Zen IA, 10 |
| contents | The remarkable success of deep learning in a myriad of applications is often attributed to the efficacy of gradient-based optimization algorithms. Among these, adaptive step size methods like Adam, RMSprop, and Adagrad have become ubiquitous due to their ability to navigate complex loss landscapes efficiently. While these optimizers excel at rapid convergence to low training error, their generalization performance, particularly in overparameterized regimes, often presents a puzzling dichotomy compared to simpler methods like Stochastic Gradient Descent (SGD) with momentum. This paper delves into the intricate interplay between adaptive step sizes and implicit regularization, a phenomenon where optimization algorithms, by their very dynamics, induce properties in the learned model that promote generalization without explicit regularization terms. We provide a comprehensive theoretical and empirical analysis of how the adaptive scaling of gradients inherently shapes the effective loss landscape and influences the selection of solutions in high-dimensional parameter spaces. Our investigation reveals that adaptive optimizers can exhibit a distinct implicit regularization signature, often favoring flatter minima or specific parameter geometries that may not always align with optimal generalization. We explore the conditions under which adaptive methods either enhance or hinder generalization, offering insights into their underlying mechanisms and proposing a framework for understanding their generalization landscape. By decoding these dynamics, this research aims to bridge the gap between empirical observations and theoretical understanding, paving the way for the design of more robust and generalizable deep learning models. |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17822474 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Adaptive Step Sizes and Implicit Regularization: Decoding the Generalization Landscape of Gradient Optimizers Revista, Zen IA, 10 The remarkable success of deep learning in a myriad of applications is often attributed to the efficacy of gradient-based optimization algorithms. Among these, adaptive step size methods like Adam, RMSprop, and Adagrad have become ubiquitous due to their ability to navigate complex loss landscapes efficiently. While these optimizers excel at rapid convergence to low training error, their generalization performance, particularly in overparameterized regimes, often presents a puzzling dichotomy compared to simpler methods like Stochastic Gradient Descent (SGD) with momentum. This paper delves into the intricate interplay between adaptive step sizes and implicit regularization, a phenomenon where optimization algorithms, by their very dynamics, induce properties in the learned model that promote generalization without explicit regularization terms. We provide a comprehensive theoretical and empirical analysis of how the adaptive scaling of gradients inherently shapes the effective loss landscape and influences the selection of solutions in high-dimensional parameter spaces. Our investigation reveals that adaptive optimizers can exhibit a distinct implicit regularization signature, often favoring flatter minima or specific parameter geometries that may not always align with optimal generalization. We explore the conditions under which adaptive methods either enhance or hinder generalization, offering insights into their underlying mechanisms and proposing a framework for understanding their generalization landscape. By decoding these dynamics, this research aims to bridge the gap between empirical observations and theoretical understanding, paving the way for the design of more robust and generalizable deep learning models. |
| title | Adaptive Step Sizes and Implicit Regularization: Decoding the Generalization Landscape of Gradient Optimizers |
| url | https://doi.org/10.5281/zenodo.17822474 |