A central question in modern machine learning is how much a trained model can be compressed without changing its behavior, to reduce the memory, compute and energy required to deploy it. To study this, we quantify functional degeneracy through the behavioral recovery rank, defined as the number of leading behavioral-Hessian eigendirections required to recover a trained model's performance.

Using the behavioral recovery rank as a geometric benchmark for compression, we find that structural and magnitude pruning retain more degrees of freedom, even after the task is saturated. This gap suggests that functional redundancy is distributed across parameter directions and is not exposed by individual weights or neurons.