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· Gain axis · Held

The harder the task, the more the acceptance gate is worth

The early-stop gate delivers 7.8 percentage points more on MBPP+, and 20.9 percentage points more on hard LiveCodeBench problems. And the "leak rate" drops from 44 to 11 — refusing delivery is worth the most on hard tasks.

LiveCodeBenchgatedifficultygain

#A comparison along three dimensions

MBPP+LCB v1 (hard tasks)
Tasks17991
OFF (single draw) failure rate31.8%48.4%
Gate vs single draw+7.82 pp+20.88 pp
b / c (rescued by early stop / right on the single draw)14 / 019 / 0
Candidate-pool ceiling82.68%75.82%
Single-draw success rate78.2%45.05%

#Leak rate: refusing delivery is worth the most on hard tasks

ArmMBPP+ leaksLCB hard-task leaks
OFF (single draw)—44 / 91
OFF5 (five-way vote)—35
CONFORM (gate)—11
MBPP+LCB hard tasks
Gate vs five-way vote+4.47 pp+4.40 pp
p0.09630.424
Gate vs single draw+7.82 pp+20.88 pp
p0.0001< 0.0001

This is because on hard tasks the model is more likely to confidently hand over something bad. The gate's mechanism is "run your tests, deliver only on a pass" — on hard tasks it can still judge "this doesn't pass," while a voting mechanism can only be wrong when all five are wrong.

#The 41 tasks where delivery was refused

A post-hoc audit of every task where the gate refused delivery, checking whether all five drafts really were wrong:

BatchRefusedAll five wrong
r44777 / 7
r449b88 / 8
r449c1010 / 10
r4611515 / 15

#Convergence across three task banks

R445 converged across three task-bank sets (gate vs single draw):

Task banknΔStatisticsCalls per task
MBPP+ (pooled, 371)371+4.58 pp95% CI [+0.57, +8.04]1.51
LCB v2 (hard tasks)120+19.17 ppb=31 c=8, p = 0.00031.71
LCB v3189+7.94 ppb=25 c=10, p = 0.01671.55

R445's 8 predictions made in advance: 7 hit, 1 missed (the miss was that the interval half-width was larger than predicted).

#The mechanism behind this finding

② The information value of refusal. On hard tasks the model's false delivery rate is higher (44 / 91 = 48.3%), so being "able to judge that it doesn't pass" is worth more.

#What this means for the claim "our mechanism works"

There is a tension here

The H-B hypothesis was "MBPP+ is too easy for modern models; switch to a hard task bank and the gain will show." The object of that hypothesis was the committee design.

Result: after switching to the hard task bank, the committee's gain still did not appear (ON vs OFF5 on hard LCB tasks, p = 0.4244).

#Honest boundaries

#Next

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