arXiv:2607.07458 2026 Architecture 1 ideas extracted · analyzed Aug 30, 2026
The paper represents graph-pair determinantal generators by an explicit matrix whose linear-matroid rank measures how many candidate generators are algebraically independent. Its transferable asset is a principled rank-based notion of nonredundant interactions, supported by connectivity bounds and explicit nullspace certificates. A neural adaptation can use rank-revealing selection on interaction or Jacobian features to construct a compact interaction bottleneck, replacing heuristic magnitude pruning with diversity and independence selection. The main risk is that numerical Jacobian rank may be expensive and task-dependent, so the method should first be tested on small structured interaction layers.
Construct a candidate feature for every edge pair or structured token pair, then retain a numerically independent subset under a feature-Jacobian matroid. The neural layer computes only the selected interactions, preserving directions that add new information rather than pruning solely by magnitude or attention score.