schedopt_v4

The search began with 400 curricula, not with the arms listed on this page. Every one was drawn at random before anything was measured. A candidate is a piecewise-constant schedule over a 400-step cap, with its stages drawn as K blocks of level and duration across the first 300 steps and the last level held to the cap. K was drawn uniformly between 2 and 14, block boundaries were free integers of at least 10 steps, and levels were free in the interval 0 to 5. The realized sample spans total variation of α from 0.1 to 55 with a median of 13.9. Half the draws alternated between a high and a low band and half were unconstrained, so that a preference for oscillation could not quietly become another cage. No shape was proposed by a model anywhere in this round.

All 400 were then measured on a successive-halving ladder over the seed budget. Every candidate ran at 6 seeds; the fastest third of those advanced to 20, and the fastest third again to 60, with the cohorts nested so that a promotion trains only the seeds the candidate does not already have. That funnel is why the arms here number 32 rather than 400: the other 368 were measured and dropped, at 5,024 seed-runs in total against 24,000 for running every candidate at the full budget. The dropped candidates are not absent from the evidence. Every one of the 400 appears in the scatter and profile figures and in data/search_candidates.csv, which carries each candidate's specification alongside the rung it reached and what it scored; data/sampled_schedules.json carries the draw itself. The sampler and its seed are committed at scripts/schedopt_v4/sample_free.py, so the exact 400 regenerate from the manifest and that script alone.

Twenty-six reference arms were measured alongside them under the same instrument: every constant α from 0.8 to 3.0 in steps of 0.1, and the three schedules that won the earlier rounds, realized at this cap. These ran at 20 seeds and were never promoted, since they are the bar rather than candidates. All arms share one seed base, so any two can be compared per-seed rather than through their separate distributions, and all use with replacement sampling.

Because the surviving population is small enough to look at directly, it is drawn rather than summarized. All 96 schedules the ladder promoted past the first screen appear individually, ordered by result, and so do all 32 that reached 60 seeds. Reading down the ordering, the fast end is dominated by schedules that hold one high level for a long opening and then fall, and the arms whose quantile never became identifiable are concentrated at the busy end, oscillating between bands throughout. The schedules of the 96 are also the closest thing this round has to a quartile cut: 96 of 400 survived, where a literal top quarter would have been 100.

The seven fastest finalists are written out below as the levels they hold and the number of steps they hold them for. The top four are variations on one shape. Each opens between α 3.6 and 4.8 and holds there for 160 to 175 steps, then falls to somewhere below 0.9 and stays, and the median crossing follows the fall by about 20 steps. Two of them interrupt the opening with a brief excursion to the floor and climb back, which costs them nothing and gains them nothing. The three below that are busier, and slower.

The reference arms and every one of the 400 draws are written out the same way in data/search_candidates.csv.

Two of the generated checks fail, and both are consequences of the design rather than faults in the data. Replicate counts are uneven because the ladder is the point: an arm promoted twice carries 60 seeds and one that was screened and dropped carries 6, and the rungs are nested, so the smaller cohort is a prefix of the larger rather than a different sample. Schedule totals also disagree with the final waypoint on most arms, because a run stops as soon as its crossing is confirmed and writes no waypoint past that step. Both checks assume every arm trains to the same cap, which is exactly the assumption this design drops.