A.1 Proof of Theorem 1 In this proof, we adopt a simplified version of our message-passing function that ignores the skipconnection: The HGNN trained in the experimental results shown in Figure 2 also does not use skip-connections and hence represents a theoretically-exact KTN component. In the real experiments, we use (1) skip-connections, exploiting their usual benefits (12), and (2) the trainable version of KTN. Without loss of generality, we prove the result for the case where R = {(s,t): s,t T }, meaning the type of an edge is identified with the (ordered) types of the neighbor nodes. In other words, there is only one edge modality possible, such as a social networks with multiple node types (e.g. "friendship" and "message"), the result is extended trivially (through with more algebraically-dense forms of ats and qts). The output of Aggregate is a concatenation of edge-type-specific aggregations (see Equation 3).

With respect to experiments, our contributions are twofold.

The reason is that different types of agents have distinct behavior patterns or feasibility constraints. For example, the trajectories of on-road vehicles are restricted by roadways, traffic rules and physical constraints, while the restrictions on pedestrian behaviorsaremuchfewer. More specifically, in the first case of Figure 7, for the player of the green team in the middle, the historical steps move forward quickly, while our model can successfully predict that theplayer will suddenly stop, since heissurrounded bymanyopponents andheisnotcarrying theball. The movement ofthese particles contains twophases, corresponding totwo interaction graphs. Initially, particles are rigidly connected to each other and form a "star" shape.

Given a relational database (RDB), how can we predict missing column values in some target table of interest? Although RDBs store vast amounts of rich, informative data spread across interconnected tables, the progress of predictive machine learning models as applied to such tasks arguably falls well behind advances in other domains such as computer vision or natural language processing. This deficit stems, at least in part, from the lack of established/public RDB benchmarks as needed for training and evaluation purposes. As a result, related model development thus far often defaults to tabular approaches trained on ubiquitous single-table benchmarks, or on the relational side, graph-based alternatives such as GNNs applied to a completely different set of graph datasets devoid of tabular characteristics. To more precisely target RDBs lying at the nexus of these two complementary regimes, we explore a broad class of baseline models predicated on: (i) converting multi-table datasets into graphs using various strategies equipped with efficient subsampling, while preserving tabular characteristics; and (ii) trainable models with well-matched inductive biases that output predictions based on these input subgraphs. Then, to address the dearth of suitable public benchmarks and reduce siloed comparisons, we assemble a diverse collection of (i) large-scale RDB datasets and (ii) coincident predictive tasks.

Data continuously emitted from industrial ecosystems such as social or e-commerce platforms are commonly represented as heterogeneous graphs (HG) composed of multiple node/edge types. State-of-the-art graph learning methods for HGs known as heterogeneous graph neural networks (HGNNs) are applied to learn deep context-informed node representations. However, many HG datasets from industrial applications suffer from label imbalance between node types. As there is no direct way to learn using labels rooted at different node types, HGNNs have been applied to only a few node types with abundant labels. We propose a zero-shot transfer learning module for HGNNs called a Knowledge Transfer Network (KTN) that transfers knowledge from label-abundant node types to zero-labeled node types through rich relational information given in the HG. KTN is derived from the theoretical relationship, which we introduce in this work, between distinct feature extractors for each node type given in an HGNN model. KTN improves the performance of 6 different types of HGNN models by up to 960% for inference on zero-labeled node types and outperforms state-of-the-art transfer learning baselines by up to 73% across 18 different transfer learning tasks on HGs.

Relational multi-table data is common in domains such as e-commerce, healthcare, and scientific research, and can be naturally represented as heterogeneous temporal graphs with multi-modal node attributes. Existing graph neural networks (GNNs) rely on schema-specific feature encoders, requiring separate modules for each node type and feature column, which hinders scalability and parameter sharing. We introduce RELATE (Relational Encoder for Latent Aggregation of Typed Entities), a schema-agnostic, plug-and-play feature encoder that can be used with any general purpose GNN. RELATE employs shared modality-specific encoders for categorical, numerical, textual, and temporal attributes, followed by a Perceiver-style cross-attention module that aggregates features into a fixed-size, permutation-invariant node representation. We evaluate RELATE on ReLGNN and HGT in the RelBench benchmark, where it achieves performance within 3% of schema-specific encoders while reducing parameter counts by up to 5x. This design supports varying schemas and enables multi-dataset pretraining for general-purpose GNNs, paving the way toward foundation models for relational graph data.