arXiv:2605.23476v1 Announce Type: new Abstract: Training instabilities in deep networks - loss spikes, oscillatory convergence, and gradient pathologies - are empirically prevalent but lack a rigorous operator-theoretic explanation. We show that the linearized update operators for practically used optimizers are generically non-normal: for Adam, non-normality is controlled by the commutator [H, M] between the Hessian and the diagonal adaptive preconditioner, while for SGD with momentum it arises from the augmented state-space structure of the update map. Applying non-normal stability theory to
This paper presents a new theoretical framework for understanding and mitigating a common practical issue in deep learning, indicating a maturation of AI research into foundational principles.
Understanding the fundamental causes of neural network instability can lead to more robust, efficient, and reliable AI systems, accelerating development and deployment across various applications.
The theoretical understanding of neural network training dynamics deepens, potentially leading to new optimizer designs and training methodologies that are less prone to instability.
- · AI researchers
- · Deep learning practitioners
- · Developers of AI optimizers
- · AI infrastructure providers
- · Trial-and-error AI development approaches
Improved stability and efficiency in training large-scale neural networks.
Faster development cycles for new AI models and potentially more performant AI systems.
Enhanced reliability of AI applications in critical domains due to more stable underlying models.
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