Training instability in deep learning follows low-dimensional dynamical principles

2026-01-19

AI Summary

Deep learning training often suffers sudden collapses due to minute perturbations, undermining reproducibility and scalability. This work reframes training stability as an intrinsic property of the learning system through the lens of dynamical systems theory, proposing a unified analytical framework that integrates optimization dynamics, data structure, parameter evolution, and learning signals. The authors introduce a controlled perturbation auditing method to quantify how training trajectories respond to structured disturbances. Their analysis reveals three key principles: high performance and stability are frequently decoupled; controlled randomness generally enhances robustness; and low-dimensional latent meta-state deviations consistently precede performance collapse. These findings are validated across both reinforcement learning and large language models, offering a measurable, comparable, and actionable theoretical foundation for understanding learning dynamics beyond final performance metrics.

Technology Category

• Machine Learning: Learning Theory
• Search and Optimization: Learning to Search
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Deep learning systems achieve remarkable empirical performance, yet the stability of the training process itself remains poorly understood. Training unfolds as a high-dimensional dynamical system in which small perturbations to optimization, data, parameters, or learning signals can induce abrupt and irreversible collapse, undermining reproducibility and scalability. We propose a unified dynamical perspective that characterizes training stability as an intrinsic property of learning systems, organized along four interacting dimensions: optimization, environmental/data, parametric, and learning-signal stability. We operationalize this perspective through controlled perturbation auditing of training trajectories, probing how learning dynamics respond to structured disturbances without modifying learning algorithms. Across reinforcement learning and large language model training, we identify three recurring regularities: high final performance is frequently decoupled from training stability; controlled stochasticity consistently buffers learning dynamics across paradigms; and deviations in low-dimensional latent meta-states systematically precede observable performance collapse. Together, these findings establish training stability as a measurable and comparable dynamical property of learning systems, providing a descriptive foundation for studying learning dynamics beyond final performance outcomes.

Problem

• training instability
• deep learning
• dynamical systems
• learning dynamics
• reproducibility

Innovation

• training stability
• dynamical systems
• perturbation auditing
• low-dimensional latent states
• controlled stochasticity