Charting the Design Space of Neural Graph Representations for Subgraph Matching

TL;DR

This work tackles subgraph matching by reframing contemporary neural methods as a design space with five axes: relevance distance (set alignment vs aggregated embeddings), interaction stage (early vs late), interaction structure (injective vs non-injective), interaction non-linearity (neural vs. hinge vs. dot product), and interaction granularity (node vs edge). Through extensive experiments across ten real-world datasets, the authors show that certain unexploited combinations—particularly set alignment, early interaction, injective mapping, hinge non-linearity, and edge-level interaction—consistently yield the best accuracy, while also discussing time-accuracy trade-offs. They provide practical design tips and demonstrate that many existing models occupy only a small region of the broader space, with their best configuration outperforming state-of-the-art baselines on most datasets. The results establish general design principles for neural graph representations in subgraph matching and offer a framework for future work to optimize performance under computational constraints.

Abstract

Subgraph matching is vital in knowledge graph (KG) question answering, molecule design, scene graph, code and circuit search, etc. Neural methods have shown promising results for subgraph matching. Our study of recent systems suggests refactoring them into a unified design space for graph matching networks. Existing methods occupy only a few isolated patches in this space, which remains largely uncharted. We undertake the first comprehensive exploration of this space, featuring such axes as attention-based vs. soft permutation-based interaction between query and corpus graphs, aligning nodes vs. edges, and the form of the final scoring network that integrates neural representations of the graphs. Our extensive experiments reveal that judicious and hitherto-unexplored combinations of choices in this space lead to large performance benefits. Beyond better performance, our study uncovers valuable insights and establishes general design principles for neural graph representation and interaction, which may be of wider interest.

Figures (6)

• Figure 1: Early interaction: Cross graph interactions occur during embedding computation layers, with both Green signals from $G_c$ and blue signals from $G_q$ feeding into both graphs. Late interaction: No cross-graph signal transfer occurs. Green signals from $G_c$ and blue signals from $G_q$ are restricted to their respective graphs. Final layer embeddings, $\bm{H} ^{(q)}_K$, $\bm{H} ^{(c)}_K$ (node) or $\bm{M} ^{(q)}_K$, $\bm{M} ^{(c)}_K$ (edge), are used to compute relevance distance. Axes of the design space: Subgraph matching models work in two stages: message passing and relevance distance. Relevance distance $\mathrm{dist}(\cdot,\cdot)$ can be set alignment, aggregated-hinge, aggregated-MLP or aggregated-NTN. $\omega$ represents the interaction structure (injective vs. non-injective), and $\eta$ defines the interaction non-linearity (Neural, dot product, or hinge). For early interaction (bottom left panel), message passing involves obtaining embeddings via cross-graph alignment, which is used for $\mathrm{dist}(\cdot,\cdot)$ if set alignment is used for relevance distance (shown by thick arrow). In late interaction (bottom right panel), $\eta$ and $\omega$ are absent during message passing, but become active if we use set alignment to approximate $\mathrm{dist}(G_q,G_c)$.
• Figure 2: MAP for various choices of design axes. Each column corresponds to a data set. Each chart has four bar groups, corresponding to interaction stage (late, early) $\times$ granularity (node, edge). In the top row, each color represents a relevance distance (set alignment vs. aggregated hinge, MLP, and NTN). In the middle row, colors correspond to non-injective and injective interactions. In the bottom row, each color represents a different form of interaction non-linearity (neural, dot product, and hinge). Each bar shows the test MAP after choosing all other axes, policies or hyperparameters to maximize validation MAP. Individually, set alignment (first row), early interaction (third and fourth groups of bars in each row), injective mapping (second row), hinge nonlinearity (third row) and edge based interaction (second and fourth groups of bars) are the best choices in their corresponding axes.
• Figure 3: Scatter plot of MAP versus inference time for different design choices on the AIDS dataset. Each point represents a unique combination of design axes, with colors indicating variations in relevance distance, interaction structure, stage, non-linearity, and granularity.
• Figure 4: Each column corresponds to a dataset. Each chart has four bar groups, corresponding to interaction stage (late, early) $\times$ granularity (node, edge). In the top row, each color represents a relevance distance (set alignment vs. aggregated hinge, MLP, and NTN). In the middle row, colors correspond to non-injective and injective interactions. In the bottom row, each color represents a different form of interaction non-linearity (neural, dot product, and hinge). Each bar shows the test MAP after choosing all other axes, policies or hyperparameters to maximize validation MAP. Individually, set alignment (first row), early interaction (third and fourth groups of bars in each row), injective mapping (second row), hinge nonlinearity (third row) and edge based interaction (second and fourth groups of bars) are the best choices in their corresponding design axes.
• Figure 5: Scatter plot of MAP versus inference time for different design choices. Each point represents a unique combination of design axes, with colors indicating variations in relevance distance, interaction structure, stage, non-linearity, and granularity.