FA-99041 / Learning rate schedules / Open access

Warmup reaches its base rate before the final warmup step · case 01

Warmup reaches its base rate before the final warmup step.

Verified by executionVariant 1 · 7 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The denominator is one less than the number of warmup intervals, so the ramp reaches base early.

THE FAILURE

The denominator is one less than the number of warmup intervals, so the ramp reaches base early.

Unsuccessful approach: Adding one to every warmup index fixes the endpoint direction but makes the initial rate nonzero.

Case contract

Return base * step / warmup_steps for steps in [0,warmup_steps], then base.

Why this case matters

A deterministic scalar schedule makes step-to-rate mapping explicit for a small training loop.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(step, base, warmup_steps):
    return base if step>=warmup_steps else base*step/(warmup_steps-1)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('midpoint',solve(N,12,4),12*min(N,4)/4); check('start',solve(0,12,4),0); check('end',solve(4,12,4),12); check('after',solve(5,12,4),12); check('single interval',solve(1,6,1),6); check('fraction',solve(1,10,4),2.5); check('distinct warmup point',solve(2,12,4),6)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
midpoint	`4.0`	`3.0`	Failed
start	`0.0`	`0`	Passed
end	`12`	`12`	Passed
after	`12`	`12`	Passed
single interval	`6`	`6`	Passed
fraction	`3.3333333333333335`	`2.5`	Failed
distinct warmup point	`8.0`	`6`	Failed

SHA-256 / 4fadcebdb0db0514d5d1fc0f7a8e696721a103df40c16851d88a3a439ea0d1f4

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(step, base, warmup_steps):
    return base if step>=warmup_steps else base*(step+1)/warmup_steps
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('midpoint',solve(N,12,4),12*min(N,4)/4); check('start',solve(0,12,4),0); check('end',solve(4,12,4),12); check('after',solve(5,12,4),12); check('single interval',solve(1,6,1),6); check('fraction',solve(1,10,4),2.5); check('distinct warmup point',solve(2,12,4),6)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
midpoint	`6.0`	`3.0`	Failed
start	`3.0`	`0`	Failed
end	`12`	`12`	Passed
after	`12`	`12`	Passed
single interval	`6`	`6`	Passed
fraction	`5.0`	`2.5`	Failed
distinct warmup point	`9.0`	`6`	Failed

SHA-256 / 542afbd8a895f492344191dc3d281d0e8d94415aeb670799308eb921a3f9d1f7

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 7 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

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Verification & scope

These are toy scalar contracts with integer steps and finite parameters; they do not model framework defaults or optimizer state. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.

Observations recorded using Python 3.12.14 at 2026-09-30T16:48:19.909891+00:00.

Case digest / 8de772f00f5d13156dc1e3ee32b7a0d8ca2c59005a0355bfbe3ae00b7fa75f8b