slopesweep_v1

The sweep set out to ask whether the declining-α trajectory of child-directed speech helps the model once its magnitude is exaggerated.

Each arm's α schedule is plotted in images/schedules.png.

The collapse at a floor of 0 is worth stating precisely, because the model does not forget the language. On matching probes its accuracy stays at the ceiling, seen_match at 100 and unseen_match near 99, and what moves is the agreement rule itself. As the tail approaches uniform the model shifts from preferring the grammatical subject back toward agreeing with the nearest noun: on the 3-to-0 schedule, seen_mismatch falls to 15.2 while seen_match holds at 100. The dense waypoints, plotted per arm in images/curriculum_comparison.png, place this loss late in training. The 3-to-0 schedule climbs to a mean of 92.0 by step 750, then erodes to 47.4 by step 1050 and 19.0 by step 1200 as α descends through the low concentrations toward 0. These schedules reach their best score on the way down, as the descent passes through the low-α region a good floor would have held, and lose it only by continuing to uniform. This is the erosion seen in the earlier curriculum experiments, now located in time and identifiable as catastrophic interference: the rule was measurably present and then overwritten, rather than never formed.

The erosion does not fall the same way on every seed, which is why the three collapse claims separate. On the 3-to-0 schedule every replicate ends below the chance line of 50, so s3e0_collapses holds on all ten; on 4-to-0 nine of ten do, so s4e0_collapses holds; but on 5-to-0 three replicates hold above 50 while seven fall below, so s5e0_collapses is mixed, its mean of 32.1 sitting in the empty gap of a bimodal split whose per-seed finals run from 0.4 to 85.3. What decides whether a given seed keeps the rule or loses it under a uniform tail is not visible in the schedule alone.

Where the schedule begins decides how soon the rule appears, the speed axis the study tracks separately from height, and here the pre-registration was wrong. A high starting α was expected to bootstrap the rule early, and the steep 4-to-2 schedule was named as one that should peak early. The timing runs the other way.

The steep 4-to-2 schedule does stay high, keeping its accuracy above 70 on 8 of 10 seeds so that s4e2_stays_high holds, but it climbs slowly and reaches its maximum only at the final waypoint. It stays high without peaking early.

A start as low as 1 is too diffuse to build the rule reliably, which shows up as seed coverage rather than as timing. The fixed 1-to-1 schedule ends at the same good α = 1 floor yet reaches only 86.9, because it brings the rule to just 8 of its 10 seeds and leaves the other two at 62.4 and 19.2; the 1-to-0 schedule, a diffuse start with a deep tail on top, reaches a near-peak band of 80 and above on only 1 of 10 seeds. This seed coverage is a different quantity from the report's replicate-coverage check, which only confirms that every arm ran the same ten seeds.

Three questions stay open. The onset optimum sits at the low edge of the integer grid, so a finer sweep of starts between 1 and 3, and of floors between 0 and 1, would place both the speed optimum and the erosion edge more precisely. The stability of the start-2 schedule is established only to 1200 iterations, and the efficiency_v1 result is a reminder that erosion can appear later, so a longer horizon is worth running. And the floor-0 collapse divides seeds sharply, so what decides whether a given seed recovers or is lost remains unknown.