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This framework aims to connect stochastic thermodynamics with phenomena observed in overparameterized linear regression and neural networks.

May 29, 2026Open Access

Slow Passage Through a Saddle-Node Bifurcation: A Unified Framework for Stochastic Thermodynamics and Learning Generalization Singularities

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Randomized trial analyzes phase transitions in overparameterized linear regression, suggesting deep learning insights.

This framework aims to connect stochastic thermodynamics with phenomena observed in overparameterized linear regression and neural networks.
Developed a canonical normal form via center-manifold reduction and adiabatic elimination.
Extended analysis from linear regression to deep neural networks across multiple regimes.
Applied categorical structure to delineate various features and behaviors within the studied systems.
Demonstrated a logarithmic crossover line in the kinetic Curie-Weiss model according to the cusp-catastrophe barrier exponent.
Validated dynamical critical exponents for linear regression consistent with the proposed theoretical models.
Predicted Airy-type delay statistics in neural networks, enhancing understanding of learning dynamics.

Alfredo Sepulveda-Jimenez (2026) studied this question.

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