Eleven experiments converge on one account and then sharpen it.

The account was assembled in three steps. The first experiment found the asymmetry: a peaked start accelerates acquisition (curriculum_v1) but a uniform tail then undoes the rule it built (build, then erode), while the reverse direction holds what it learns (the anti-curriculum is durable). Burst mixing showed the same forces in miniature, brief deep-uniform bursts doing no harm (burst_v1) while the balance of build against erosion sets the endpoint (the balance). The efficiency comparison made the gain precise: the curriculum reaches a higher peak much sooner than fixed α = 1.4 (the fast peak), and the slide that follows is not specific to a uniform tail (erosion without one), so late decline is erosion at work rather than one bad schedule choice.

The shape of the optimal schedule turned out to be flatter than the search assumed. The starting height saturates (peaksweep_v1, anchor_v1), and the systematic φ-landscape walk found the landscape sloppy in most directions (the deformation map), with the real levers being where the schedule starts its descent (the start lever) and how much of the α range the bursts cover (coverage, not height). Speed and consistency move together rather than trading off (anchor_v1), and no smooth limit of the burst structure recovers its advantage (refine_v1).

Two boundaries close the account. Compressing the winning shape into a shorter horizon buys nothing: the model needs on the order of 196 steps to bootstrap the rule regardless of schedule (the hard floor), and what a short budget costs is seed coverage rather than peak height (the coverage cost). And the mirror test showed direction itself is not the operative variable (mirror_v1): descent wins retention when it lands at a safe floor (retention), but every pair ending at uniform reverses (final α dominates), and on interior pairs the ascending arm reaches the higher peak within the budget (ascent out-peaks), the signature of undertraining in the descending mirror rather than a directional law.

A sub-investigation took the speed half of that account and made it the objective, scoring a schedule by how soon nine seeds in ten reach a fixed generalization band rather than by where the accuracy curve ends (the schedule-opt campaign). Its answer is the account's shape with the descent compressed to a single switch: hold α at 4.76 for 160 steps, then drop once to 0.81 and stay (The fastest schedule the campaign has found). That schedule reaches the band at a held-out 90th percentile of 202.1 steps against 337.9 for the best constant α, which puts a number on the claim that a schedule buys speed and seed coverage rather than a higher ceiling: about 136 steps, more than a third of the horizon. Two searches over free-form curricula, one random and one surrogate-driven, have since found nothing faster, so on this objective the shape appears to be the finding rather than its tuning.

What would change this reading. The interior mirror pairs were read at a fixed horizon with the descending arms' peaks still rising, so a longer horizon could return the peak advantage to descent. And the account is built entirely on schedules that are piecewise-constant in α over a two-preposition grammar; a maintenance recipe that holds the rule indefinitely after the build phase has not been found, only diets that slow the slide.

alpha_grid

Configuration

Results

Downloads