Polaritonic machine learning for graph-based data analysis.

Photonic and polaritonic systems offer a fast and efficient platform for accelerating machine learning (ML) through physics-based computing. To gain a computational advantage, however, polaritonic systems must meet the following: (1) exploit features that specifically favor nonlinear optical processing; (2) address problems that are computationally hard and depend on these features; and (3) integrate photonic processing within broader ML pipelines. In this work, we propose a polaritonic machine learning approach for solving graph-based data problems. We demonstrate how lattices of condensates can efficiently embed relational and topological information from point cloud datasets. This information is then incorporated into a pattern recognition workflow based on convolutional neural networks (CNNs), leading to significantly improved learning performance compared to physics-agnostic methods. Our extensive benchmarking shows that photonic machine learning achieves over 90% accuracy for Betti number classification and clique detection tasks, a substantial improvement over the 35% accuracy of bare CNNs. Our study introduces a distinct way of using photonic systems as fast tools for feature engineering, while building on top of high-performing digital machine learning.