Residual image contribution to the memorization-cost coefficient

Determine the residual image term contributing approximately ±0.02 to the memorization-cost coefficient C at noise rate η=50 and overlay size K=12,500, beyond the feature-displacement mechanism already identified.

Background

The paper models validation accuracy under memorization using a cost law with an effective coefficient C. The authors trace most of C to normalized clean-sample feature displacement during memory overlay, but report a residual image-dependent contribution of approximately ±0.02 at the η=50 and K=12,500 calibration. They explicitly leave this component unresolved because it is not explained by the feature-displacement route.

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 What the Framework Does NOT Claim, Section C-mechanism; Discussion and Outlook