Detecting Unique Neural Network "Fingerprints" After Collapse

Independently trained neural networks typically lack a common reference frame for their neurons, making direct comparisons challenging due to "coordinate freedom." This problem is exacerbated by Neural Collapse, a phenomenon where networks converge to a shared, low-dimensional geometric structure. A key question arises: can unique, trajectory-specific functional variations still be distinguished once this convergence has occurred? This research addresses the detectability aspect of this question, distinguishing it from transplantability or causal persistence. Using five independently trained networks that exhibited Neural Collapse on the MNIST dataset, the team applied a verified affine-correct alignment mapping to translate "donor" network heads into "recipient" coordinates. The findings demonstrated that donor-specific functional fingerprints remained distinguishable even after recipient-level baseline correction. All twenty ordered donor-recipient pairs were correctly identified, achieving a statistically significant exact permutation p-value of 0.0083. This result was robustly confirmed through a leakage audit. The study successfully establishes detectability under the specific testing conditions, providing a methodology for testing cross-network variation in a controlled environment, though its generalizability beyond this setting remains an open question.