Distinguishing deterministic effects from true chaos in the chaos region

Determine whether the Topo$^2$ trajectory exhibits genuine chaotic dynamics in the identified chaos region, rather than a deterministic effect combined with the observed s42 anomaly, by using evidence beyond the current n=3 analysis.

Background

The determinism analysis shows that training trajectories depend on the RNG sequence and evaluation cadence, but the authors identify a remaining region in which the available evidence is insufficient to settle whether the observed behavior is genuinely chaotic. With only n=3 observations, the analysis cannot distinguish true chaos from a deterministic effect plus the s42-specific anomaly.

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