Relational databases underpin critical infrastructure across a wide range of domains, yet the design of generalizable pre-training strategies for learning from relational databases remains an open challenge due to task heterogeneity. Specifically, there exist many possible downstream tasks, as tasks are defined based on relational schema graphs, temporal dependencies, and SQL-defined label logics. An effective pre-training framework is desired to take these factors into account in order to obtain task-aware representations. By incorporating knowledge of the underlying distribution that drives label generation, downstream tasks can benefit from relevant side-channel information. To bridge this gap, we introduce Task Vector Estimation (TVE), a novel pre-training framework that constructs predictive supervisory signals via set-based aggregation over schema traversal graphs, explicitly modeling next-window relational dynamics. We formalize our approach through an information-theoretic lens, demonstrating that task-informed representations retain more relevant signals than those obtained without task priors. Extensive experiments on the RelBench benchmark show that TVE consistently outperforms traditional pre-training baselines. Our findings advocate for pre-training objectives that encode task heterogeneity and temporal structure as design principles for predictive modeling on relational databases. Our code is publicly available at https://github.com/quang-truong/task-vector-estimation.

Graph Neural Networks (GNNs), despite achieving remarkable performance across different tasks, are theoretically bounded by the 1-Weisfeiler-Lehman test, resulting in limitations in terms of graph expressivity. Even though prior works on topological higher-order GNNs overcome that boundary, these models often depend on assumptions about sub-structures of graphs. Specifically, topological GNNs leverage the prevalence of cliques, cycles, and rings to enhance the message-passing procedure. Our study presents a novel perspective by focusing on simple paths within graphs during the topological message-passing process, thus liberating the model from restrictive inductive biases. We prove that by lifting graphs to path complexes, our model can generalize the existing works on topology while inheriting several theoretical results on simplicial complexes and regular cell complexes. Without making prior assumptions about graph sub-structures, our method outperforms earlier works in other topological domains and achieves state-of-the-art results on various benchmarks.

We introduce TopoX, a Python software suite that provides reliable and user-friendly building blocks for computing and machine learning on topological domains that extend graphs: hypergraphs, simplicial, cellular, path and combinatorial complexes. TopoX consists of three packages: TopoNetX facilitates constructing and computing on these domains, including working with nodes, edges and higher-order cells; TopoEmbedX provides methods to embed topological domains into vector spaces, akin to popular graph-based embedding algorithms such as node2vec; TopoModelX is built on top of PyTorch and offers a comprehensive toolbox of higher-order message passing functions for neural networks on topological domains. The extensively documented and unit-tested source code of TopoX is available under MIT license at https://pyt-team.github.io.