CondPSE: A Polynomial-Filtered Structural Encoder with Conditional Modulation for Graphs

2026-07-27

AI Summary

This work addresses the limited expressive power of conventional message-passing graph neural networks, which are constrained by the 1-Weisfeiler-Lehman (1-WL) test and thus struggle to distinguish non-isomorphic graph structures. To overcome this limitation, the authors propose CondPSE, a novel encoder that integrates learnable polynomial graph filter banks with multi-level FiLM-based conditional modulation. By leveraging Gaussian node probes to capture both local and global structural signals, and employing a pretrain-and-freeze paradigm optimized via a graph-level invariant reconstruction objective, CondPSE significantly enhances graph isomorphism discrimination. The method achieves state-of-the-art performance on the CSL and EXP benchmarks with accuracies of 97.3% and 99.9%, respectively, substantially outperforming GPSE. However, it does not consistently surpass existing approaches across all molecular property prediction tasks.

Abstract

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.

Problem

• graph neural networks
• 1-WL test
• structural encoding
• graph isomorphism
• topological structure

Innovation

• polynomial graph filter
• conditional modulation
• positional and structural encoding
• graph neural networks
• 1-WL expressivity