Double descent is the principle of least action

{'Problem': 'The paper addresses the double descent phenomenon in model test error as a function of the number of parameters, a gap in understanding that remains underexplored in the literature. The work is presented as a preprint and has not undergone peer review.', 'Method': "The author models the training trajectory of a neural network as a particle navigating an energy landscape defined by the training loss. The framework introduces a temperature parameter (T) that influences the training dynamics. The Boltzmann distribution is employed to describe the probability of the parameter vector's visits across the landscape. The concept of effective weight decay is introduced, arising from finite time diffusion during training, which impacts the exploration of the parameter space. Each parameter is treated as a quadratic degree of freedom, and the equipartition theorem is applied to distribute energy among these degrees of freedom, resulting in an average energy of T/2. The addition of parameters is shown to lower the L2 norm of the stationary path, suggesting a relationship between model complexity and training dynamics.", 'Results': 'The paper discusses the double descent phenomenon in relation to model test error versus the number of parameters, but the available text does not report quantitative results.', 'Limitations': "The authors note that finite time diffusion may restrict the exploration of the training trajectory, potentially limiting the model's ability to fully leverage the parameter space. Additionally, the lack of quantitative results may hinder the practical applicability of the findings.", 'Why it matters': 'This work provides a theoretical foundation for understanding the double descent phenomenon, which has significant implications for model design and training strategies in machine learning. By framing the training process in terms of physical principles, it opens avenues for further research into optimizing model performance and understanding the dynamics of overparameterization.'}