🤖 AI Summary
This work addresses the inconsistency and instability in learning caused by missing training data by formulating the problem from a dynamical systems perspective, where missingness is modeled as a structured control-constrained perturbation in parameter error dynamics. The authors propose a directional observability-aware adaptive learning method that, for the first time, integrates closed-loop control principles into learning with missing data. By synergistically combining Lyapunov stability analysis, input-to-state stability (ISS) bound estimation, and geometrically designed preconditioned updates, the approach establishes a theoretically grounded stable update mechanism. Experimental results across multimodal tasks demonstrate that the method significantly enhances learning consistency and convergence performance, particularly under extreme data sparsity.
📝 Abstract
What should a machine learning model learn when data is missing during training? We look at the learning process from a dynamical systems perspective, cast data missingness as a structured loss of actuation that limits controllability of the parameter error dynamics, and ultimately derive adaptation mechanisms with Lyapunov stability characteristics that throttle model updates in ways that preserve learning coherence under partial, intermittent observability. Under recurrent excitation, our analysis provides ISS-type residual-to-state bounds with respect to a bounded closed-loop mismatch between the loss residual and the preconditioned update geometry. We evaluate the efficacy of our directional observability-aware adaptive learning approach on multimodal contexts, reinforcing its premise in promoting learning coherence and stability even in pathologically sparse domains and problems.