Binary Classification as a Phase Separation Process

TL;DR

This paper introduces the Phase Separation Binary Classifier (PSBC), a novel binary classification model inspired by fluid phase separation, integrating physical principles with neural network architectures for improved interpretability and performance.

Contribution

The paper presents a new physics-inspired binary classifier based on reaction-diffusion equations, with trainable parameters and boundary conditions, and demonstrates its application on MNIST digit classification tasks.

Findings

PSBC effectively classifies MNIST digit pairs.

Model benefits from physical parameter interpretation.

Combining PSBC with ensemble and PCA improves accuracy.

Abstract

We propose a new binary classification model called Phase Separation Binary Classifier (PSBC). It consists of a discretization of a nonlinear reaction-diffusion equation coupled with an Ordinary Differential Equation, and is inspired by fluids behavior, namely, on how binary fluids phase separate. Thus, parameters and hyperparameters have physical meaning, whose effects are studied in several different scenarios. PSBC's equations can be seen as a dynamical system whose coefficients are trainable weights, with a similar architecture to that of a Recurrent Neural Network. As such, forward propagation amounts to an initial value problem. Boundary conditions are also present, bearing similarity with figure padding techniques in Computer Vision. Model compression is exploited in several ways, with weight sharing taking place both across and within layers. The model is tested on pairs of digits of the classical MNIST database. An associated multiclass classifier is also constructed using a combination of Ensemble Learning and one versus one techniques. It is also shown how the PSBC can be combined with other methods - like aggregation and PCA - in order to construct better binary classifiers. The role of boundary conditions and viscosity is thoroughly studied in the case of digits ``0'' and ``1''.