Intrinsic-Extrinsic Coupling in Learning Dynamics

Abstract: A learner's current observations need not determine its response to further training. We formulate intrinsic-extrinsic coupling through the continuation-conditioned value of a constrained learning-state intervention, with observation-relative fibers describing present agreement. An executable finite-frame classifier-head write protects current logits while repairing specified historical margins under finite-precision acceptance checks. We distinguish local admissibility, continuation-conditioned intervention value, and complete-policy performance. A matched four-cell contrast identifies readout-specific non-additivity between the same intrinsic intervention and alternative external continuations. In a CLINC-derived class-incremental setting, replay changes the write's 32-update contribution from five correct predictions to zero. Nonzero interactions also occur under output distillation, with a RoBERTa backbone, and under optimizer-native SGDW dynamics. Under SGDW, correct-count interactions are negative in all three activated roots at 128 updates, showing that coupling need not imply positive synergy. The mathematical analysis distinguishes feasible local repairs and favorable terminal outputs from training-reachable repair regions. Separate coordination tests show that content controls match or exceed the development gain, while a five-root fresh-test comparison with Fiber present in every arm shows root-dependent rather than uniformly beneficial correct-count effects. On the secondary cross-entropy readout, guided allocation yields lower mean loss than standard replay in all five pairs. Together, these results make intrinsic-extrinsic coupling operational by connecting executable state geometry to continuation-conditioned value, matched interaction identification, and closed-loop coordination, while separating identified coupling from complete-policy performance.