ChaCAL Resolvent

ChaCAL and Block-ChaCAL can solve shallow BOXES-style tasks because their inverse term aggregates longer paths directly. ChaCAL replaces one-hop attention with a resolvent-style operator applied to values. The ChaCAL resolvent aggregates multi-hop attention paths in one layer through the Neumann expansion. For causal attention matrices, the resolvent application can use forward substitution because the relevant matrix is triangular with positive diagonal entries.