Spectral Flow Certificates Enable Pre-Training Graph Analysis
Researchers propose Spectral Flow Certificates (SFCs), single scalars computed from a graph's normalized Laplacian in seconds, to predict whether Graph Neural Networks (GNNs) can solve long-range tasks before training begins. SFCs fuse algebraic connectivity with message-passing depth, offering a depth-aware diagnostic superior to static spectral gaps. The method requires no model training or labeled data, addressing the problem of graph topologies that silently prevent information propagation. This work appears on arXiv as preprint 2607.21607.
Key facts
- Spectral Flow Certificates (SFCs) are single scalars computed from normalized Laplacians.
- SFCs require no model training and no labeled data.
- SFCs fuse algebraic connectivity with message-passing depth.
- SFCs measure how much of the spectral bottleneck can be traversed within the depth budget.
- SFCs are depth-adaptive, unlike static spectral gaps.
- The method addresses long-range information propagation in GNNs.
- The work is published on arXiv with ID 2607.21607.
- Computation takes seconds.
Entities
Institutions
- arXiv