Stability Annealing Selects the Implicit Bias of Smoothed Sign Descent: A Rate-Indexed Barrier Path on Separable Data
arXiv:2607.06013v1 Announce Type: new Abstract: Adaptive gradient methods can favor max-margin separators that differ from gradient descent, yet a fixed positive numerical stability constant eventually changes the update geometry again. This paper studies the rate-controlled middle case for full-batch linear classification on separable data. For memoryless stability-annealed smoothed-sign descent with weighted exponential loss, we prove that the normalized iterates converge to the minimizer of a convex Burg-type barrier over a margin slice. The proof rewrites the dynamics exactly as entropic m
This research is part of an ongoing effort to better understand and control the implicit biases of adaptive gradient methods, which are crucial for the development of more robust and predictable AI systems.
Understanding how different optimization algorithms converge to specific solutions (their 'implicit bias') is fundamental for developing more reliable, safe, and interpretable AI, particularly in sensitive applications.
This paper provides a new theoretical understanding of how 'stability annealing' can guide smoothed sign descent towards specific types of max-margin separators, refining our knowledge of AI optimization dynamics.
- · AI researchers
- · Machine learning framework developers
- · AI safety practitioners
- · Developers relying on black-box optimization
It provides a more granular theoretical framework for understanding the behavior of specific adaptive gradient methods.
This improved understanding could lead to the design of new, more controllable optimization algorithms for deep learning.
More controllable optimization might enable AI systems with more predictable and interpretable outputs, increasing trust and broader adoption in critical domains.
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Read at arXiv cs.LG