CondPSE: Polynomial-Filtered Structural Encoder for Graphs
CondPSE is an advanced encoder for graphs that utilizes a learnable polynomial graph filter bank alongside standard Gaussian node probes to achieve positional and structural encoding (PSE). It enhances structural-response branches via FiLM-style modulation, which is based on cross-filter, local message-passing, and graph-level signals. Initially, the encoder is pretrained to reconstruct both node-level positional/structural targets and graph-level invariants, after which it is fixed for subsequent applications. In tests using synthetic benchmarks, CondPSE successfully differentiates graph structures that the 1-WL test fails to identify, overcoming a significant drawback of message-passing graph neural networks. This research was published on arXiv under ID 2607.25169.
Key facts
- CondPSE uses a learnable polynomial graph filter bank on Gaussian node probes.
- It employs FiLM-style modulation for cross-filter, message-passing, and graph-level conditioning.
- Pretrained to reconstruct node-level and graph-level targets.
- Frozen encoder used as downstream input encoding.
- Outperforms 1-WL test on synthetic structural discrimination benchmarks.
- Addresses limitations of message-passing graph neural networks.
- Published on arXiv with ID 2607.25169.
Entities
Institutions
- arXiv