Measuring Memory and Generalization as Separable Geometric Channels: The Topo^2 Framework
Deep networks trained on noisy labels simultaneously generalize on clean data and memorize flipped labels. These are usually conflated as pressures on one capacity. We present Topo^2, a measurement framework that makes them causally separable, measurable, and law-governed. Persistent-homology H1 structure of the representation space separates into a within-class manifold channel (a function of the training stopping point) and a cross-class channel (a monotone readout of memorized flipped samples). An intervention, the FM0 prescription (zero loss on flipped samples from epoch 0), reaches each setting's generalization ceiling while memorizing essentially nothing. Within the framework we est...
| Authors | Zhanbo Zhang, Ming Liu, Qing Wang |
|---|---|
| Primary category | cs.LG |
| Published | 31 August 2026 |
| Last updated at source | 31 August 2026 |
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