Towards Practical Second-Order Optimizers in Deep Learning: Insights from Fisher Information Analysis

Damien Martins Gomes

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arXiv · 2504.20096

Towards Practical Second-Order Optimizers in Deep Learning: Insights from Fisher Information Analysis

Damien Martins Gomes

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Abstract

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.

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Damien Martins Gomes. 2025-04-26. Towards Practical Second-Order Optimizers in Deep Learning: Insights from Fisher Information Analysis. https://arxiv.org/abs/2504.20096

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