Online learning stability shown for deep neural networks in real time
End-to-End Stability of Online Active Learning in Large-Scale Neural Systems
Machine LearningComputer Vision and Pattern Recognition
Summary
Adapting deep learning models while they run, instead of only training them beforehand, is important for safety-critical tasks but hard to guarantee stable updates. The authors study why simply reducing prediction errors isn’t enough for smooth learning in deep networks. They develop a new framework using energy principles and stability theory to ensure the whole system remains steady as it learns continuously. This work lays a mathematical foundation for safely updating large neural networks in changing environments.
What this means in practice
- •For autonomous vehicle engineers: Use the proven stable online learning method to continuously adapt vehicle perception models safely in changing environments.
- •For industrial robotics teams: Implement the stability-guaranteed learning framework to maintain reliable robot control during real-time adaptation on production floors.
A theory result. No direct application yet.
Authors
Shuiwen Shen, Jinhua Zhang, Chenlei Hou, Peng Shi, Yong Han, Bo Gao, Xiaoxiao Na, Zhihui Lin, Pengtao Du
Abstract
Online Active Learning (OAL) aims to extend deep learning from static inference after offline training to continuous adaptation during real-time interaction with a changing physical environment. This transition is essential for safety-critical applications, but it raises a central theoretical question: whether the online parameter update process remains stable when scaled to multilayer neural architectures. This paper develops a stability-focused OAL framework. The framework uses prediction error as a feedback signal to update a structured deep model, thereby linking online learning with Lyapunov-based energy minimization. We show that prediction error convergence alone is insufficient for global parameter convergence because multilayer networks may admit high-dimensional manifolds of equivalent output solutions. The analysis therefore separates output error regulation, internal zero dynamics, interlayer coupling, and parameter convergence. Persistency of excitation and active damping are then used to remove the residual null-space modes that remain after output error convergence. A cascaded Lyapunov analysis establishes asymptotic stability of the overall OAL learning process, while monotonic activation functions and diffeomorphic layer mappings provide the uniqueness condition for the target parameter trajectory. The resulting proof provides a theoretical basis for applying online adaptive learning to large-scale neural systems in nonstationary and safety-critical settings.