arXiv:2602.05600v2 Announce Type: replace Abstract: Stochastic Gradient Descent (SGD) introduces anisotropic noise that is correlated with the local curvature of the loss landscape, thereby biasing optimization toward flat minima. Prior work often assumes an equivalence between the Fisher Information Matrix and the Hessian for negative log-likelihood losses, leading to the claim that the SGD noise covariance $\mathbf{C}$ is proportional to the Hessian $\mathbf{H}$. We show that this assumption holds only under restrictive conditions that are typically violated in deep neural networks. Using th
This paper refines the understanding of SGD noise behavior in deep learning, a fundamental aspect of training complex AI models, building on prior work and noting limitations in common assumptions.
A strategic reader should care because a more accurate understanding of SGD dynamics can lead to more efficient and robust AI training, potentially impacting the scalability and performance of future AI systems.
The previous assumption that SGD noise covariance is proportional to the Hessian in deep neural networks is now shown to hold only under restrictive conditions, implying a need for more nuanced optimization strategies.
- · AI researchers
- · Deep learning framework developers
- · Companies building large AI models
- · Practitioners relying on simplified SGD assumptions
Refined theoretical understanding of stochastic gradient descent in deep learning.
Development of new or improved optimization algorithms for training neural networks based on this understanding.
More efficient and resource-optimized training of sophisticated AI agents and models due to enhanced optimization techniques.
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