Explaining the Machine Learning Solution of the Ising Model
As powerful as machine learning (ML) techniques are in solving problems involving data with large dimensionality, explaining the results from the fitted parameters remains a challenging task of utmost importance, especially in physics applications. This work shows how this can be accomplished for the ferromagnetic Ising model, the main target of several ML studies in statistical physics. Here it is demonstrated that the successful unsupervised identification of the phases and order parameter by principal component analysis, a common method in those studies, detects that the magnetization per spin has its greatest variation with the temperature, the actual control parameter of the phase transition. Then, by using a neural network (NN) without hidden layers (the simplest possible) and informed by the symmetry of the Hamiltonian, an explanation is provided for the strategy used in finding the supervised learning solution for the critical temperature of the model's continuous phase transition. This allows the prediction of the minimal extension of the NN to solve the problem when the symmetry is not known, which becomes also explainable. These results pave the way to a physics-informed explainable generalized framework, enabling the extraction of physical laws and principles from the parameters of the models.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Explainable Data-Driven Optimization: From Context to Decision and Back Again
Data-driven optimization uses contextual information and machine learning algorithms to find solutions to decision problems with uncertain parameters. While a vast body of work is dedicated to interpreting machine learni…
counterfactualCounterfactual ExplanationManagementUnderstanding food inflation in India: A Machine Learning approach
Over the past decade, the stellar growth of Indian economy has been challenged by persistently high levels of inflation, particularly in food prices. The primary reason behind this stubborn food inflation is mismatch in …
BIG-bench Machine LearningExplaining Reject Options of Learning Vector Quantization Classifiers
While machine learning models are usually assumed to always output a prediction, there also exist extensions in the form of reject options which allow the model to reject inputs where only a prediction with an unacceptab…
counterfactualQuantizationAutomatically Explaining Machine Learning Prediction Results: A Demonstration on Type 2 Diabetes Risk Prediction
Background: Predictive modeling is a key component of solutions to many healthcare problems. Among all predictive modeling approaches, machine learning methods often achieve the highest prediction accuracy, but suffer fr…
BIG-bench Machine LearningPredictionTowards Robust Interpretability with Self-Explaining Neural Networks
Most recent work on interpretability of complex machine learning models has focused on estimating a-posteriori explanations for previously trained models around specific predictions. Self-explaining models where interpre…