Disentangling Computation in Multi-Task Neural Networks with the Green's Operator

תקציר מקורי באנגליתarXiv:2609.40292v1 Announce Type: new Abstract: How is computation organized and reused across tasks and time in a trained recurrent network? Most analyses emphasize the geometry of neural activity, dynamical motifs, or local perturbation growth. We instead study the network's global first-order perturbation response. The finite-horizon Green's operator maps perturbations at each source along a trajectory to their downstream state-space responses and therefore directly represents perturbation routing. Simple reductions of this operator provide task-to-task and time-to-time views of the same computation, while matrix-free products make these views accessible without constructing the full operator. In a flexible multitask recurrent network, task reductions reveal structured reuse of known co