Towards Practical Second-Order Optimizers in Deep Learning: Insights from Fisher Information Analysis
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918003684147200 |
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| author | Gomes, Damien Martins |
| author_facet | Gomes, Damien Martins |
| contents | First-order optimization methods remain the standard for training deep neural networks (DNNs). Optimizers like Adam incorporate limited curvature information by preconditioning the stochastic gradient with a diagonal matrix. Despite the widespread adoption of first-order methods, second-order optimization algorithms often exhibit superior convergence compared to methods like Adam and SGD. However, their practicality in training DNNs is still limited by a significantly higher per-iteration computational cost compared to first-order methods. In this thesis, we present AdaFisher, a novel adaptive second-order optimizer that leverages a diagonal block-Kronecker approximation of the Fisher information matrix to adaptively precondition gradients. AdaFisher aims to bridge the gap between the improved convergence and generalization of second-order methods and the computational efficiency needed for training DNNs. Despite the traditionally slower speed of second-order optimizers, AdaFisher is effective for tasks such as image classification and language modeling, exhibiting remarkable stability and robustness during hyperparameter tuning. We demonstrate that AdaFisher outperforms state-of-the-art optimizers in both accuracy and convergence speed. The code is available from https://github.com/AtlasAnalyticsLab/AdaFisher. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_20096 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Towards Practical Second-Order Optimizers in Deep Learning: Insights from Fisher Information Analysis Gomes, Damien Martins Machine Learning Optimization and Control First-order optimization methods remain the standard for training deep neural networks (DNNs). Optimizers like Adam incorporate limited curvature information by preconditioning the stochastic gradient with a diagonal matrix. Despite the widespread adoption of first-order methods, second-order optimization algorithms often exhibit superior convergence compared to methods like Adam and SGD. However, their practicality in training DNNs is still limited by a significantly higher per-iteration computational cost compared to first-order methods. In this thesis, we present AdaFisher, a novel adaptive second-order optimizer that leverages a diagonal block-Kronecker approximation of the Fisher information matrix to adaptively precondition gradients. AdaFisher aims to bridge the gap between the improved convergence and generalization of second-order methods and the computational efficiency needed for training DNNs. Despite the traditionally slower speed of second-order optimizers, AdaFisher is effective for tasks such as image classification and language modeling, exhibiting remarkable stability and robustness during hyperparameter tuning. We demonstrate that AdaFisher outperforms state-of-the-art optimizers in both accuracy and convergence speed. The code is available from https://github.com/AtlasAnalyticsLab/AdaFisher. |
| title | Towards Practical Second-Order Optimizers in Deep Learning: Insights from Fisher Information Analysis |
| topic | Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2504.20096 |