Auditing Plasticity Diagnostics with Function-Preserving Rescalings

Can several plasticity diagnostics, read together, distinguish networks that implement the same function but respond differently to adaptation? We audit specified activation-, gradient- and spectral-based diagnostic formulas under function-preserving rescalings of ReLU networks. Every audited formula that normalises a per-unit signal by its layer mean, or reads normalised singular values, is exactly invariant in its ideal form to a layer-uniform rescaling; the normalisation, not the signal family, decides it—the absolute-cutoff feature rank reads the same singular values but can change. We identify this shared invariance across the formulas and, for specified full score vectors, characterise its exact extent within positive diagonal rescalings. On 40 rescaled pairs of 10 trained checkpoints (MinAtar Breakout DQN agents, ReLU MLP) the implemented scores agree within numerical precision except for a stabiliser-induced residual, and all audited unit-level threshold masks remain identical; yet the finite-budget adaptation to an action permutation differs under a protocol with SGD and a fixed rate-selection rule. For the common rescaling, evaluation on adaptation seeds unused for grid placement or rate selection yields a mean difference of +0.317 return units (95% checkpoint-cluster bootstrap interval [0.228, 0.402]), positive on every checkpoint. A separate analysis also finds a response gap after selecting a scalar learning rate independently for each arm on the tested finite grids. Under SGD the rescaling induces the known change in per-block effective learning rates; a corresponding layer-uniform effect is not detected in the Adam experiment, and a fixed-data, fixed-target experiment shows the optimisation difference without environment interaction. These formulas measure relative activity and representation dimension as designed; the limitation concerns their use to infer adaptation response: equality of the audited invariant readouts does not imply equal performance under the specified protocol.