Training instability in deep learning follows low-dimensional dynamical principles

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.

Learning to Trust Experience: A Monitor-Trust-Regulator Framework for Learning under Unobservable Feedback Reliability

Learning under unobservable feedback reliability poses a distinct challenge beyond optimization robustness: a system must decide whether to learn from an experience, not only how to learn stably. We study this setting as Epistemic Identifiability under Unobservable Reliability (EIUR), where each experience has a latent credibility, reliable and unreliable feedback can be locally indistinguishable, and data are generated in a closed loop by the learner's own evolving beliefs and actions. In EIUR, standard robust learning can converge stably yet form high-confidence, systematically wrong beliefs. We propose metacognitive regulation as a practical response: a second, introspective control loop that infers experience credibility from endogenous evidence in the learner's internal dynamics. We formalize this as a modular Monitor-Trust-Regulator (MTR) decomposition and instantiate it with self-diagnosis, which maintains a slowly varying experience-trust variable that softly modulates learning updates, without exogenous reliability labels or an explicit corruption model. Empirically, in the EIUR regimes studied here, self-diagnosis is associated with improved epistemic identifiability. In reinforcement learning, it enables calibrated skepticism and recovery under systematically corrupted rewards. In supervised learning, it exposes a critical dissociation: performance recovery does not imply epistemic recovery. Accuracy can rebound while internal belief dynamics remain locked-in by early misleading data, a failure detectable only through introspective diagnostics. Together, MTR and self-diagnosis provide an organizing abstraction and a concrete design template for intrinsic reliability assessment in autonomous learning under unobservable reliability.