13 records · the arc from 037 (10 records, depth 3) ∪ records tagged training-dynamics (10) · read at a354234
A second project in the same record format: the Grokking chip in Lab’s row opens its records, and its arcs, waiting and frontier pages scope the whole-site templates to them. Its spine is its arc; its tag is a convenience.
037, N-039, P-019 are in the arc and carry no training-dynamics tag, so they are missing from the tag page. The arc has them; the tag is a convenience and is not filled in here.
P-030, P-032, P-033 carry the tag and no builds_on: edge into the arc — in the project by tag, not by chain.
037Trained to grokking on multiplication mod p, which characters does a small network learn — the additive characters of Z/p, or the multiplicative (Dirichlet) characters, i.e. Fourier modes in discrete-log coordinates on (Z/p)^x?run
probes10
P-019Does every computable magnitude come through a convex dual?probe
P-027Can the staircase of a deep linear network's loss be read backwards, as a measurement of a chosen spectrum?probe
P-028Is the period-doubling past the edge of stability Feigenbaum's cascade, and in what dimension does that stop holding?probe
P-029Is the double-descent spike at p = n quantitatively the Marchenko–Pastur edge?probe
P-030Do a primality classifier's residual errors fingerprint its algorithm — Fermat pseudoprimes for a Fermat-like test, no-small-factor composites for a sieve?probe
P-031Grokking multiplication on the units of Z/561 — which characters appear when the group is not cyclic and no discrete log exists?probe
P-032Do a learned Franklin involution's errors concentrate exactly on the pentagonal-number shapes where the map is undefined?probe
P-033Under weight decay, does a partition-recurrence readout become sparse exactly on the generalized pentagonal lags, with alternating-pair signs?probe
P-034Eta's coefficients indexed by n versus by m — is one coordinate trivial and the other near-impossible?probe
P-035Are learning-curve shapes exactly two kinds — spectral readouts and competitions between coexisting solutions?probe
notes2
N-031MPS and CPU training diverge for the same seed in R26_training_dynamics — so a retrain meant to reproduce 037's W_E must run on the same device, and be checkednote
N-039Loop-in from the grokking chat, 2026-10-03 — "define the geometry by what the shapes optimise" is a duality bridge run backwards plus the rigidity question, not a new term; candidate §67 entries; two candidate probes on merging grokked seeds; a speculative physics chain with every attribution unverifiednote
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