Gradient Manifolds: Navigating Complex Loss Landscapes for Enhanced AI Generalization
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| Auteurs principaux: | , |
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| Format: | Recurso digital |
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Zenodo
2025
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| _version_ | 1866901252664721408 |
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| author | Revista, Zen IA, 10 |
| author_facet | Revista, Zen IA, 10 |
| contents | The optimization of deep learning models often involves navigating highly non-convex and high-dimensional loss landscapes, which poses significant challenges for achieving robust generalization. Traditional gradient-based optimization methods are prone to getting stuck in sharp local minima or saddle points, leading to suboptimal performance on unseen data. This paper introduces the concept of gradient manifolds as a novel framework for understanding and traversing these complex loss landscapes. We posit that the effective search space for model parameters can be constrained to a lower-dimensional manifold defined by the local geometry of the loss function's gradient. By focusing on the intrinsic structure of these manifolds, our approach aims to guide optimization towards flatter, more generalizable minima, thereby enhancing the model's capacity to perform well on new, diverse datasets. We explore the theoretical underpinnings of gradient manifolds, propose practical algorithms for their exploration, and present a series of experiments demonstrating their effectiveness in improving generalization across various deep learning architectures and tasks. Our findings suggest that leveraging the manifold structure inherent in gradient information can significantly improve the stability of training and lead to models with superior generalization capabilities, offering a promising direction for future research in robust AI optimization. |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17816010 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Gradient Manifolds: Navigating Complex Loss Landscapes for Enhanced AI Generalization Revista, Zen IA, 10 The optimization of deep learning models often involves navigating highly non-convex and high-dimensional loss landscapes, which poses significant challenges for achieving robust generalization. Traditional gradient-based optimization methods are prone to getting stuck in sharp local minima or saddle points, leading to suboptimal performance on unseen data. This paper introduces the concept of gradient manifolds as a novel framework for understanding and traversing these complex loss landscapes. We posit that the effective search space for model parameters can be constrained to a lower-dimensional manifold defined by the local geometry of the loss function's gradient. By focusing on the intrinsic structure of these manifolds, our approach aims to guide optimization towards flatter, more generalizable minima, thereby enhancing the model's capacity to perform well on new, diverse datasets. We explore the theoretical underpinnings of gradient manifolds, propose practical algorithms for their exploration, and present a series of experiments demonstrating their effectiveness in improving generalization across various deep learning architectures and tasks. Our findings suggest that leveraging the manifold structure inherent in gradient information can significantly improve the stability of training and lead to models with superior generalization capabilities, offering a promising direction for future research in robust AI optimization. |
| title | Gradient Manifolds: Navigating Complex Loss Landscapes for Enhanced AI Generalization |
| url | https://doi.org/10.5281/zenodo.17816010 |