Broader validation across architectures, datasets, and noise schedules

Expand the empirical validation of the Topo$^2$ framework across additional neural-network architectures, datasets, and noise schedules to establish the breadth of its reported laws and interventions.

Background

The reported evidence is concentrated in a limited set of architectures, datasets, and noise configurations, including ResNet and VGG experiments on CIFAR-10, CIFAR-100, and SVHN. The authors explicitly identify broader testing as an unresolved issue rather than claiming universal validity for the framework's laws.

References

What remains open: (i) the residual image term in $C$ ($\approx\pm0.02$ at the $\eta$50 / $K{=}12500$ caliber, beyond the feature-displacement route; Sec.~\ref{sec:C-mechanism}); (ii) determining factor of the co-evolution advantage (SVHN resnet); (iii) breadth --- more architectures/datasets/noise schedules; (iv) the dynamics of within --- why convergence reshapes the local-neighborhood graph (the reshuffle is quantified but not mechanistically explained); (v) the ``chaos region'' ($n{=}3$ cannot distinguish deterministic-effect-plus-s42-anomaly from true chaos).

— Measuring Memory and Generalization as Separable Geometric Channels: The Topo^2 Framework  (2608.30487 - Zhang et al., 31 Aug 2026) in Discussion and Outlook