A Learning Stability Profile for Finite-Dimensional Learning Dynamics
Read the original on arXiv Machine Learning →The paper introduces a finite‑dimensional sensitivity framework called the Learning Stability Profile, which captures how perturbations in inputs, parameter initialization, and update mechanisms propagate along a learning trajectory. It presents a Lyapunov criterion that, under regularity, coercivity, and dissipation assumptions, yields uniform or exponentially decaying bounds on linearized transition operators, distinguishing between terminal decay, boundedness, and subexponential growth. The framework is applied to various learning mechanisms—including feedforward networks, residual architectures, stochastic gradient methods, and locally Lipschitz systems—providing spectral, dissipativity, and contraction‑based stability bounds.
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