Message-passing graph neural networks are bounded by the 1-WL test and can miss topological structure that distinguishes non-isomorphic graphs. Positional and structural encodings (PSE) inject such topology-derived signals, and learned PSE encoders such as GPSE pretrain a single encoder to produce these signals from random node probes, which can then be frozen and reused as inputs across downstream graph models. We present CondPSE, a learned PSE encoder that applies a learnable polynomial graph filter bank to standard Gaussian node probes and refines the resulting structural-response branches through FiLM-style modulation conditioned on cross-filter, local message-passing, and graph-level signals. CondPSE is pretrained to reconstruct node-level positional/structural targets and graph-level invariants, and is then frozen for use as a downstream input encoding. On synthetic structural-discrimination benchmarks, CondPSE separates graph structures that 1-WL-bounded message passing cannot: it raises CSL accuracy from 42.9% to 97.3% and EXP accuracy from 68.3% to 99.9% relative to GPSE, and ablations show that the polynomial filter bank accounts for most of this gain. On real molecular property prediction, the picture is more limited. With a hybrid local-message-passing/global-attention backbone, CondPSE performs comparably to GPSE without surpassing it, and a ZINC backbone sweep shows no consistent ordering between the two encoders. We report these results and discuss why strong synthetic structural discrimination does not, on its own, yield a downstream advantage for frozen learned PSE encoders, including the role of downstream integration and possible mismatch between structural pretraining targets and molecular property labels.
Temporal Knowledge Graph (TKG) reasoning under the extrapolation setting focuses on forecasting future time-stamped events (facts) from historical data in a temporal knowledge graph. Existing approaches, reinforcement learning (RL)-based multi-hop reasoning methods are prominent for TKG reasoning because they produce human-interpretable predictions via explicit multi-hop path tracing. However, during RL training, rewards are typically sparse, and exploration is highly inefficient due to the vast, time-evolving action space. These issues hinder efficient training and often limit overall performance. To address these challenges, we propose RAPTOR (Reachability-Aware Pretraining for Efficient Target-Oriented Path Exploration), a self-supervised pretraining method that injects a reachability-aware inductive bias to the agent. By learning to estimate the reachability of candidate actions to the target entity, RAPTOR reduces exploration over unpromising paths and provides a strong initialization for downstream RL fine-tuning. Experimental results on the ICEWS14, ICEWS05-15, and ICEWS18 datasets demonstrate that RAPTOR pretraining markedly improves the training efficiency and consistently outperforms conventional baselines, establishing it as an effective approach for enhancing RL-based multi-hop reasoning methods for TKG reasoning.
Relational Deep Learning (RDL) models multi-tabular databases as temporal heterogeneous graphs for end-to-end representation learning. While RDL is evolving rapidly, existing approaches face significant generalization obstacles. They are either schema-specific, requiring training from scratch for every new database, or they rely on monolithic architectures that entangle feature encoding with graph message-passing. Analyzing these limitations, we establish four core pillars for building foundational relational models: semantic granularity, structural topology, temporal causality, and unified optimization. Addressing these pillars, we propose a modular approach that decouples row encoding from graph message-passing. We introduce the Universal Row Encoder, a transformer-based module that integrates raw cell data with schema metadata$-$including column semantics, table names, and global distribution statistics$-$to produce table-width invariant row embeddings. By explicitly feeding global statistics to an intra-row self-attention mechanism, the encoder natively contextualizes unseen features and handles sparse data. Serving as a flexible "backend" for any downstream graph architecture, our pretrained encoder enhances cross-database knowledge transfer on the established RelBench benchmarks while improving learning convergence and memory footprint.