Photonics-Enhanced Graph Convolutional Networks

Photonics can offer a hardware-native route for machine learning (ML). However, efficient deployment of photonics-enhanced ML requires hybrid workflows that integrate optical processing with conventional CPU/GPU based neural network architectures. Here, we propose such a workflow that combines photonic positional embeddings (PEs) with advanced graph ML models. We introduce a photonics-based method that augments graph convolutional networks (GCNs) with PEs derived from light propagation on synthetic frequency lattices whose couplings match the input graph. We simulate propagation and readout to obtain internode intensity correlation matrices, which are used as PEs in GCNs to provide global structural information. Evaluated on Long Range Graph Benchmark molecular datasets, the method outperforms baseline GCNs with Laplacian based PEs, achieving $6.3%$ lower mean absolute error for regression and $2.3%$ higher average precision for classification tasks using a two-layer GCN as a baseline. When implemented in high repetition rate photonic hardware, correlation measurements can enable fast feature generation by bypassing digital simulation of PEs. Our results show that photonic PEs improve GCN performance and support optical acceleration of graph ML.

💡 Research Summary

The paper introduces a hybrid workflow that enriches graph convolutional networks (GCNs) with photonic positional embeddings (PhotPE) derived from light propagation on synthetic frequency lattices whose coupling topology mirrors the input graph. Traditional GCNs aggregate information only from immediate neighbors, which limits their ability to capture long‑range dependencies crucial for tasks such as molecular property prediction. Existing remedies, notably Laplacian eigenvector‑based positional embeddings (LapPE), provide global context but require costly spectral decompositions and lack a direct physical interpretation.

To address these shortcomings, the authors model each graph as a network of coupled optical resonators. The coupling matrix J is set equal to the graph adjacency matrix, and the system dynamics follow the damped driven equation dψ/dt = –γψ – iJψ + P_m, where ψ(t) denotes complex field amplitudes, γ the loss rate, and P_m the pump applied to a source node. By numerically simulating the evolution and recording time‑averaged intensities I_i = ⟨|ψ_i|²⟩, they construct an intensity‑intensity correlation matrix G_ij = ⟨I_i I_j⟩. The leading eigenvectors of G form a low‑dimensional embedding U_C,k (the PhotPE), which is concatenated to the node features after each GCN layer: H’ =