A Topological Signature of Learning under Noisy Labels

Zhongtian Sun, Fan Mo, Prayag Tiwari, Kelin Xia

How does noisy supervision change the representations learned by a neural network? Training accuracy measures agreement with training labels but provides little information about representation geometry. We use persistent homology to track loop structure across distance thresholds in neural activations. Experiments span image classification, text classification, and modular arithmetic. On a fixed CIFAR-10/ResNet-18 training probe, equally sized clean-label and corrupted-label subsets show no detectable persistence difference at epoch 10, whereas corrupted-label subsets have higher persistence at epoch 50. The contrast survives uniform-scale controls, even though predictions match the assigned noisy labels for only 7-11% of corrupted probe examples at that checkpoint. Normalisation preserves the crossover between clean and noisy training trajectories on CIFAR-10/ResNet-18, whereas CIFAR-100/ResNet-18 shows no crossover under any of the five evaluated constructions. In a separate noise-rate calibration comparison across five pipelines, mean activation norm achieves a higher mean in-sample R2 than raw persistence (0.936 versus 0.908). These findings show that noisy supervision…