The tail that isn't in the public 50
whest-fusion · deployed_estimator · submission 325219

The tail that isn't in the public 50

The same estimator scores 1.587e-7 on AIcrowd's 50 leaderboard MLPs and 2.235e-7 on 512 MLPs of the public full split. The typical MLP is equally hard in both — the medians differ by 17%. What the public 50 don't have is the upper tail: 11.3% of full MLPs sit beyond the leaderboard set's entire range, and they carry 35.7% of its total error.

Grader: sub 325219, GRADED, 50/50 Local: HF v1-phase1, flopscope 0.10.0 Same code: F/B 0.2669 vs 0.2665 Measured: 2026-08-10
Adjusted score, AIcrowd grader
1.587e−7
50 leaderboard MLPs · submission 325219
Adjusted score, full split
2.235e−7
512 MLPs · analytic FLOPs only
Median per-MLP MSE
17%
apart: 4.93e−7 vs 5.77e−7 — the typical MLP is the same
Full-split MLPs beyond the public 50's entire range
11.3%
58 of 512, carrying 35.7% of total MSE
Figure 1 · per-MLP final-layer MSE

Three samples of the same estimator, one shared log axis

Each panel is one MLP sample, binned at ⅛-decade resolution and drawn as a share of that sample's own MLPs so the three are comparable despite differing n. The rug beneath each panel is one tick per MLP. The shaded band marks everything beyond the largest MSE the leaderboard set contains (1.534e-6) — empty in the top panel by construction, populated in both local samples.

Public 504.22e−6 – 5.62e−6
0 MLPs · 0.0% of 50
0%12.5%25%Public 50n = 500 of 50 MLPs beyond0%12.5%25%Full splitn = 51258 of 512 beyond — 35.7% of total MSE0%12.5%25%Mini splitn = 1009 of 100 beyond — 38.4% of total MSEpublic-50 maximum · 1.534e−6 →10⁻⁷10⁻⁶10⁻⁵Final-layer MSE per MLP — log scaleBar height = share of that sample's MLPs
Bin width ⅛ decade. Vertical rules mark each sample's median (solid) and mean (dotted) — the distance between them is the skew; exact values are in the table below. Hover any bin for its range and count.
Figure 2 · could the public 50 be an ordinary draw?

Resampling 50 MLPs from the full split, 20,000 times

If the leaderboard's 50 MLPs were a plain random sample of the same population, their mean MSE would land inside this distribution. It doesn't: 0.19% of draws come in at or below the observed 5.757e-7. That is the same conclusion Line P reached by a different route, and it holds for the current estimator.

1.131e−6 – 1.150e−6119 of 20,000 draws
observed public-50 mean · 5.757e−7only 0.19% of draws land here or lowermedian 50-draw · 8.330e−795% of draws6.0e−78.0e−71.0e−61.2e−61.4e−61.6e−6Mean MSE of a 50-MLP resample from the full split
20,000 bootstrap resamples (with replacement) of 50 MLPs drawn from the 512-MLP full-split run. Seed 0.
Table · every number in the figures

Distribution statistics

SamplenAdjusted scoreMean MSEMedian p90p99MaxMax ÷ medianSkew Top 10% shareBeyond 1.534e-6
Public 50 501.587e−75.757e−74.925e−7 1.006e−61.524e−61.534e−6 3.1×1.08 23.1% 0 (0.0%)
Full split 5122.235e−78.459e−75.767e−7 1.653e−64.120e−69.606e−6 16.7×4.30 33.2% 58 (11.3%)
Mini split 1002.338e−78.944e−75.409e−7 1.399e−64.044e−61.533e−5 28.3×7.74 40.0% 9 (9.0%)

Adjusted score is mean(mse × max(0.1, C/B)). The grader row uses its own C including residual wall time; the local rows use analytic FLOPs only (F/B), since residual time on a shared 192-core node is a property of the node, not the estimator.

Reading it

What follows, and what doesn't

Caveats worth holding: the two sources use different ground truth (the grader's own Monte Carlo versus the HF-baked final_means) on disjoint MLP seeds, so they are not paired; and 512 of the 1000 full-split MLPs were run, not all 1000. Neither affects the shape comparison, which is what the figures are about.