Progress Measures for Grokking in Minimal Recursive Transformers

We study grokking on modular addition (P=113) in the Tiny Recursive Model (TRM), a transformer equipped with an adaptive-computation (ACT) recurrence. When the recurrence is collapsed to a single effective step, the model learns a sparse Fourier multiplication circuit visible directly in its output logits, matching the one-layer transformer of Nanda et al. (5/5 seeds, adaptive trig-FVE 0.996 vs 0.989 for the one-layer calibration model). Restricted and excluded losses, Gini coefficients of the Fourier spectrum, and weight norms move before the test-accuracy jump, giving progress measures for the transition; key-frequency ablations confirm the circuit causally. With the full ACT recurrence, the model still groks, but the final-logit Fourier circuit no longer appears: the computation is carried by the latent recurrence (fixed-point violations, depth-sensitive accuracy). Extending the progress-measure framework to the per-step latent state shows the recurrence relocates the grokked computation from the logits into the latent loop. At the component level, individual neurons and attention heads do not admit clean trigonometric fits, so the match is claimed at the readout level rather than neuron-by-neuron. https://github.com/adityapandey9/Progress-Measures-for-Grokking-in-TRM