Topological Dynamics Under Non-Stationary Supervision: Persistent Homology of Neural Network Weight Evolution

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

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