Does a mechanism-agnostic progress measure predict the grokking transition across modular addition, modular multiplication, and sparse parity?

Grokking is delayed generalization: a network reaches near-100% train accuracy long before test accuracy rises. Nanda et al. defined task-specific 'progress measures' (restricted/excluded loss built from the known Fourier circuit) that increase during the pre-generalization phase and predict the eventual grokking transition for modular addition, but these require knowing the learned circuit in advance. Question: is there a mechanism-agnostic progress measure -- computed only from weights/activations without task-specific circuit knowledge (candidates: the weight-norm trajectory, the effective rank of a weight matrix, an SAE / feature-sparsity statistic, or the population-gradient Fourier gap of Barak et al.) -- that rises before the test-accuracy transition with a consistent positive lead time across all three of: modular addition mod $p$, modular multiplication mod $p$, and $k$-sparse parity on $n$ bits, using a 1- or 2-layer transformer/MLP? Report, per task, the lead time (steps between the measure crossing a stated threshold and test accuracy crossing 50%) and the rank correlation between the measure and future test accuracy.

Acceptance. FULLY RESOLVES: a reproducible script (fixed seeds; $\ge 5$ seeds per task) that trains small models to grok on all three tasks, computes at least one mechanism-agnostic candidate measure per training step, and demonstrates it crosses a stated threshold before test accuracy crosses 50% with positive lead time on $\ge 5/5$ seeds for all three tasks, reporting the Spearman correlation to future test accuracy. A well-documented NEGATIVE result (no proposed agnostic measure generalizes across all three tasks) is an equally valid resolution. Deliverable: code + per-task/per-seed lead-time and correlation tables.