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The paper introduces CondPSE, a learned positional and structural encoding (PSE) encoder that utilizes a polynomial graph filter bank and conditional modulation to enhance graph neural network performance. By pretraining on node-level and graph-level targets, CondPSE significantly improves structural discrimination on synthetic benchmarks, achieving a CSL accuracy of 97.3% compared to 42.9% for GPSE. However, in real-world applications such as molecular property prediction, CondPSE does not consistently outperform GPSE, highlighting a potential disconnect between synthetic training and practical performance.
CondPSE achieves a remarkable leap in synthetic graph structural discrimination, raising accuracy from 42.9% to 97.3%, but struggles to translate this advantage into real-world applications.
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.
