arXiv:2611.13701v1 Announce Type: new Abstract: We investigate how the persistent topology of neuron- weight point clouds evolves under stable and non-stationary supervision. An identical multilayer perceptron is trained on Fashion-MNIST with correct labels, a fixed random permutation of the training-label vector, or a fresh permutation every epoch. Five paired seeds share initialisation and minibatch order, yielding 15 models trained for 100 epochs. Raw and row-normalised incoming weight clouds are analysed with H0 and H1 Vietoris Rips persistence at 22 checkpoints. Correct-label models reach 89.39% mean true-label test accuracy; fixed-random models fit 67.94% of their assigned training targets without generalising to the original task. Correct-label models have descriptively greater time-averaged normalised fc3 H1 persistence than either random-label condition, but the configured exact comparisons do not reach conventional significance after Holm correction. Early condition classification achieves 60.0% mean balanced accuracy using topology, 66.7% using conventional diagnostics, and 60.0% using both. Thus, no incremental predictive improvement is demonstrated in this setting. The archive contains all 3,300 configured topology cases. Interpretation is limited by five seeds, a single architecture and dataset, 282 capped H1 distance comparisons, and deferred bottleneck analysis.