Extending machine learning classification capabilities with histogram reweighting
This enables precision measurements in physical systems lacking order parameters or where direct sampling is impossible, though it is incremental as it adapts existing histogram reweighting to ML.
The authors tackled the problem of extrapolating machine learning predictions over continuous parameter ranges by treating neural network outputs as observables in statistical systems, applying this to the 2D Ising model to yield accurate estimates for critical exponents and temperature.
We propose the use of Monte Carlo histogram reweighting to extrapolate predictions of machine learning methods. In our approach, we treat the output from a convolutional neural network as an observable in a statistical system, enabling its extrapolation over continuous ranges in parameter space. We demonstrate our proposal using the phase transition in the two-dimensional Ising model. By interpreting the output of the neural network as an order parameter, we explore connections with known observables in the system and investigate its scaling behaviour. A finite size scaling analysis is conducted based on quantities derived from the neural network that yields accurate estimates for the critical exponents and the critical temperature. The method improves the prospects of acquiring precision measurements from machine learning in physical systems without an order parameter and those where direct sampling in regions of parameter space might not be possible.