Photonics-Enhanced Graph Convolutional Networks

TL;DR

This work proposes a physics-informed extension to graph neural networks by introducing photonic correlation-based embeddings (PhotPE) derived from light propagation on synthetic frequency lattices. PhotPE supplies global structural cues that complement local message passing in GCNs, and when tested on long-range molecular graphs from the LRGB peptides benchmarks, it yields measurable improvements over Laplacian-based positional embeddings, especially in shallower networks. The approach demonstrates a viable pathway toward optical acceleration of graph ML through fast, hardware-native feature generation and lays out concrete photonic implementation parameters and datasets. Overall, the study highlights the potential of photonic dynamics to enhance graph representations and points to future avenues in programmable photonic lattices and quantum-inspired photonic accelerators.

Abstract

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.

Figures (6)

• Figure 1: Workflow for photonics-enhanced machine learning of molecular graph structures using synthetic frequency lattices. (a) Chemical structure of a peptide molecule ($\mathrm{C_{148}H_{319}N_{41}O_{40}S_{6}}$) representing a sample from the Peptides-struct and Peptides-func datasets used for graph convolutional network analysis. (b) Graph representation $\Gamma$(Peptide) of the molecular structure shown in (a), where nodes represent heavy atoms and edges represent chemical bonds, providing the connectivity information for network analysis. (c) Schematic of the programmable photonic simulator employing synthetic frequency lattices (c.f. Ref. senanian2023programmable), where the intracavity field evolution enables mapping of arbitrary graph structures through phase modulation. (d) Normalized intensity-intensity correlations $\{G_{ij} \}$ for nodes $i$ and $j$, obtained from the photonic simulation setup in (c).
• Figure 2: Regression for different molecular properties. Mean absolute error (MAE) comparison across $11$ molecular properties in Peptides-struct dataset. Properties include physicochemical descriptors (GRAVY, isoelectric point, molecular weight, hydrophobicity, charge), structural features (secondary structure, solvent accessibility), and stability indices (instability, aromaticity, aliphatic, Boman). The GCN+PhotPE approach (green) consistently outperforms both the baseline GCN (blue) and GCN+LapPE (orange) methods, with horizontal lines indicating overall MAE for each model.
• Figure 3: Molecular property predictions for GCN model variants. Comparison of ground truth versus predicted values for (a) molecular weight, (b) secondary structure, (c) aromaticity, (d) solvent accessibility, (e) instability index, and (f) Boman index. Three models are shown: GCN (blue), GCN+LapPE (red), and GCN+PhotPE (green). Dashed lines indicate perfect prediction. MAE values are shown in each panel.
• Figure 4: Architecture of the graph convolutional network with Laplacian and photonic-enhanced positional embeddings (PEs). The model takes an input graph $X$ with nodes ($x_{1}, x_{2}, x_{3}, x_{4}$) and processes it through two parallel pathways to generate PEs. The photonic-enhanced PE (taking coupling matrix $J$ to the correlation matrix $G$) and graph Laplacian PE ($A$, $L_\mathrm{sym}$) are combined via a projection matrix $W_\mathrm{proj}$ to create PE. These PEs are concatenated with the node features and fed into a stack of $N$ GCN layers. Each GCN layer (detailed in the bottom inset) performs graph convolution by: concatenating the previous layer's hidden representation $H^{(\ell-1)}$ with PE, applying the normalized adjacency matrix aggregation $\widetilde{D}^{(-1/2)}\widetilde{A}\widetilde{D}^{(-1/2)}$, linear transformation with parameters $\Theta^{(\ell)}$, and ReLU activation $\sigma(\cdot)$. The final layer output $H^{(N)}$ is pooled to produce the prediction $y$. This architecture uses structural (Laplacian) and physical (photonic) properties of the graph to enhance node representation learning.
• Figure 5: Representations of peptide molecular graph structure. (a) Adjacency matrix $A$ showing the binary connectivity pattern between nodes (heavy atoms), where matrix elements are $1$ for connected nodes and $0$ otherwise. (b) Graph Laplacian $L_{\mathrm{sym}} = \mathbb{I} - D^{-1/2}AD^{-1/2}$, capturing the spectral properties of the graph structure. (c) Normalized correlation matrix $G$ computed from photonic dynamics. Matrix dimensions correspond to the number of nodes ($235$) in the peptide structure ($235\times235$). The insets (red box) in each panel highlight part of the diagonal region.