Fluctuation-dissipation relations for stochastic gradient descent
This work provides a theoretical framework for optimizing training in machine learning, though it appears incremental as it applies statistical mechanics concepts to a known algorithm.
The authors derived stationary fluctuation-dissipation relations for stochastic gradient descent, linking measurable quantities and hyperparameters to adaptively set training schedules and extract information about loss-function landscapes like Hessian magnitudes, with empirical verification.
The notion of the stationary equilibrium ensemble has played a central role in statistical mechanics. In machine learning as well, training serves as generalized equilibration that drives the probability distribution of model parameters toward stationarity. Here, we derive stationary fluctuation-dissipation relations that link measurable quantities and hyperparameters in the stochastic gradient descent algorithm. These relations hold exactly for any stationary state and can in particular be used to adaptively set training schedule. We can further use the relations to efficiently extract information pertaining to a loss-function landscape such as the magnitudes of its Hessian and anharmonicity. Our claims are empirically verified.