arXiv:2512.21208v3 Announce Type: replace Abstract: We develop a finite-dimensional sensitivity framework for studying stability in learning systems whose states include representations, parameters, and update variables. The central object is the \emph{Learning Stability Profile}, a collection of directional sensitivity operators that records how perturbations in inputs, parameter initialization, and update mechanisms propagate along a specified learning trajectory. The main result is a Lyapunov criterion for controlling this profile. Under explicit regularity, coercivity, and dissipation assu
The rapid development and deployment of complex AI models necessitates more robust methods for understanding and ensuring their stability as they become integrated into critical systems.
This research provides a foundational framework to mathematically analyze and control stability in learning systems, which is crucial for the reliability, safety, and trustworthiness of advanced AI.
We now have a theoretical tool, the Learning Stability Profile, to systematically quantify and manage how perturbations affect AI system behavior, moving beyond ad-hoc stability assessments.
- · AI developers
- · High-stakes AI applications (e.g., autonomous systems, finance)
- · Regulatory bodies
- · Academic researchers in AI safety
- · AI systems with opaque or unmanaged stability issues
- · Developers neglecting stability considerations
Improved methods for training and deploying more robust and predictable AI models.
Increased trust and adoption of AI in critical infrastructure and decision-making processes.
Potential for new quality standards and regulatory guidelines for AI model stability across various industries.
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Read at arXiv cs.LG