Compare transition count with activation- and gradient-level predictors

Determine whether phase-transition count in ResNet fine-tuning carries information about final test accuracy beyond effective rank, Fisher information, Hessian sharpness, margin, and neural-collapse metrics derived from activation or gradient tensors, or whether it is merely a cheaper proxy for one of these competitors.

Background

The study compares phase-transition count only with seven signals that could be extracted from existing experiment records, including architecture depth, training-curve gaps, convergence stability, test-curve peaks, and convergence speed. The paper does not evaluate several stronger competitors from the literature because doing so would require collecting per-epoch activation and gradient tensors across the experimental configurations.

The unresolved issue is whether transition count provides genuinely additional predictive information about test accuracy or instead summarizes information already captured by activation- or gradient-level measures such as effective rank, Fisher information, Hessian sharpness, margin, or neural-collapse metrics.

References

Comparisons against those would require re-collecting per-epoch activation and gradient tensors and are noted as future work in Section 7. On the strength of the evidence available here, therefore, the claim is that transition count achieved the strongest correlation among the evaluated signals on CIFAR-100 and one of the strongest on CIFAR-10, and that the question of whether it carries information beyond activation- or gradient-level competitors is open.

— Phase Transition Frequency as a Training Time Predictor of Test Accuracy in ResNets  (2609.05194 - J, 4 Sep 2026) in Section 4.4; Section 6

Conjecture 2 (Phase Transition Characterisation) A phase transition occurs at epoch t when the spectral structure at some layer reorganises discretely and irreversibly, with transition timing approximately consistent across random seeds.

— Phase Transition Frequency as a Training Time Predictor of Test Accuracy in ResNets  (2609.05194 - J, 4 Sep 2026) in Appendix A.2, Conjecture 2