FAdam: Adam is a natural gradient optimizer using diagonal empirical Fisher information

Dongseong Hwang

Keywords: Optimizer, Adam, Natural gradient descent, Second order optimization, Information geometry, Riemannian geometry, Differential geometry, Tensor calculus, Deep learning, Fisher Information, Hessian, Curvature

TL;DR: This paper thoroughly analyzes the Adam optimizer, connects it to natural gradient descent, and proposes an improved version called FAdam. FAdam outperforms Adam in text, speech and image domain tasks, including achieving SoTA in speech recognition.

Abstract: This paper establishes a mathematical foundation for the Adam optimizer, elucidating its connection to natural gradient descent through Riemannian and information geometry. We rigorously analyze the diagonal empirical Fisher information matrix (FIM) in Adam, clarifying all detailed approximations and advocating for the use of log probability functions as loss, which should be based on discrete distributions, due to the limitations of empirical FIM. Our analysis uncovers flaws in the original Adam algorithm, leading to proposed corrections such as enhanced momentum calculations, adjusted bias corrections, and gradient clipping. We refine the weight decay term based on our theoretical framework. Our modified algorithm, Fisher Adam (FAdam), demonstrates superior performance across diverse domains including LLM, ASR, and VQ-VAE, achieving SoTA results in ASR.

Primary Area: optimization

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Submission Number: 7668