Shunting Inhibition and Dendritic Branching Shape Local Credit Assignment

Biological neurons assign credit across branching dendrites, where synaptic drive, dendritic conductance, local voltage, and somatic teaching signals interact to shape synaptic plasticity. We study conductance-based dendritic networks with E/I synapse banks, shunting inhibition, and tree-structured branch-to-soma coupling, and examine when restricted somatic feedback can approximate compartment-specific backpropagated errors. Exact gradients factor into local eligibility x compartment error terms: the eligibility uses presynaptic activity, driving force, and input resistance, whereas the fast non-local term is a path-specific error obtained by transporting a soma error through dendritic gains. This factorization turns local learning into a credit-signal compression problem. We test the hypothesis that shunting inhibition benefits learning under these constraints when it reshapes the compartment-error field to better match global scalar, per-soma, low-rank, or path-structured feedback. Exact-gradient reconstruction verifies the factorization; path-gain, rank, broadcast-fidelity, inhibition-intervention, and transported-error-oracle diagnostics support the proposed mechanism. Under nonnegative conductances and per-soma 5-factor (5F) feedback, shunting LocalCA remains 5--6 percentage points below matched backpropagation on MNIST, Fashion-MNIST, and figure-ground MNIST, indicating that feedback-field fidelity remains a major bottleneck. These results show how E/I conductance, shunting inhibition, and dendritic branching can reshape credit-signal geometry in restricted local learning.