Replace dense token-to-token attention by a learned binary relation generated from a small number of hierarchical predicates, while rejecting masks that contain a fixed K_{t,t} biclique. The paper's incidence bound predicts near-linear active edges for these structured relations, giving sparse attention with a measurable worst-case complexity target rather than relying only on average sparsity.
Represent a neural computation or verification pipeline as a directed acyclic graph whose nodes carry cached certificates for tensor shapes, numerical ranges, Lipschitz estimates, quantization error, or equivalence to a reference module. After locally replacing or optimizing one node, compare its old and new interface fingerprints and revoke certificates only along the dependency cone when the interface changed. This enables safe incremental verification during architecture search, compiler…
Replace a dense attention pattern by the exact intersection of a fixed or cheaply computed base graph H and a learned shared-label relation. Two tokens can exchange information only when they are adjacent in H and share at least one of d labels, producing a controllable structured sparsity pattern. The label count d becomes an explicit capacity and compute knob: increasing d enlarges the relation vocabulary without requiring a dense pairwise mask.