Layer-Selective Utility Gating for Continual Learning

Neural networks in continual learning suffer from plasticity loss. Utility-based perturbed gradient descent (UPGD-W) mitigates this problem through utility-dependent modulation of parameter updates. We investigate how this modulation should be allocated across network layers. We first analyze an idealized continuous-time model and show that, under regularity and stationarity assumptions, its expected displacement-based utility rate relates to gated local curvature with an explicit correction for non-equilibrium probability currents. We then derive a distributional tracking bound that separates the contributions of representation and head drift. These results provide a theoretical motivation for comparing output-only, hidden-only, and full gating across different adaptation settings. On three supervised label-permutation benchmarks, output-only gating applies utility modulation to only 0.16%–2.5% of parameters while achieving 114%–285% higher mean accuracy than Shrink and Perturb and up to 13% higher than full gating. All layers continue to update. The gating variants perform similarly on Input-Permuted MNIST. In Gridworld with controlled dynamics shifts, hidden-only gating achieves higher mean return than output-only gating. Together, these findings show that the benefits of utility gating depend on its placement and the adaptation demands of the learning setting.