How far each run has moved
Relative displacement ‖Δ‖F / ‖θ0‖F per parameter family, log scale. Bars are the latest banked frame at or before the current step.
Norm preserved or not
‖θt‖ / ‖θ0‖ per family. HyperBall (MuonH) holds every matrix on its starting sphere, so v3e should sit on 1.000; AdamW has no such constraint.
Same direction, or not
Cosine between the two runs' displacement vectors per family, using the nearest banked frames (exactly aligned at step 18). Below zero would mean the runs pull the same weights opposite ways; near zero means unrelated directions.
How straight each trajectory is
Cosine between a run's displacement at consecutive banked frames, per family. 1.0 means later steps keep pushing along the same line; low values mean the direction keeps changing.
Depth profile
Relative displacement by layer index for one family. Reads which depths each optimizer moves.
What bf16 storage does to an update
Fraction of coordinates whose delta is exactly zero at the current frame, per family, next to the fraction of the SFT weights that a bf16 master copy cannot move at all with a step of size lr = 1e-5 (half-ulp larger than the step).
Expert by expert
Top: relative displacement of each of the 256 experts (log scale). Bottom: per-expert cosine between the two runs at the step-18 alignment (grey when a run has not reached that step). Adam-style normalization moves low-traffic experts as far as busy ones; look for the spread.
Update spectrum
Singular values of Δ divided by the largest, log scale, for one matrix. A flat spectrum is a full-rank, orthogonalized update (Muon's signature); a steep one is a few directions dominating (Adam's usual shape). Grey is θ0 itself for reference.
Size distribution of the deltas
Histogram of log10|Δ| over all coordinates in the family (share of coordinates, log-spaced bins). Grey is log10|θ0|. Exact zeros are shown as the leftmost bar.