FA-99126 / Learning rate schedules / Open access

Warmup decay drops below the terminal floor · case 01

Warmup decay drops below the terminal floor.

Verified by executionVariant 1 · 6 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The post-warmup interpolation approaches zero and never uses the requested floor.

THE FAILURE

The post-warmup interpolation approaches zero and never uses the requested floor.

Unsuccessful approach: A lower bound alone bends the interpolation and fails to reach the floor at the endpoint.

Case contract

Warm linearly to base, then linearly decay to floor by total and hold floor.

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, floor, warmup, total):
    if step<warmup: return base*step/warmup
    return base*(total-step)/(total-warmup)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('warmup',solve(1,10,2,4,8),2.5); check('boundary',solve(4,10,2,4,8),10); check('decay',solve(6,10,2,4,8),6); check('end',solve(8,10,2,4,8),2); check('after',solve(9,10,2,4,8),2); check('start',solve(0,8,1,3,6),0)
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
warmup	`2.5`	`2.5`	Passed
boundary	`10.0`	`10`	Passed
decay	`5.0`	`6`	Failed
end	`0.0`	`2`	Failed
after	`-2.5`	`2`	Failed
start	`0.0`	`0`	Passed

SHA-256 / 2ef23fa635dc0b7f09d3c8d6cb72240cd57c2d793d96c60e45b7a333076a0c7a

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(step, base, floor, warmup, total):
    if step<warmup: return base*step/warmup
    return max(floor,base*(total-step)/(total-warmup+1))
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('warmup',solve(1,10,2,4,8),2.5); check('boundary',solve(4,10,2,4,8),10); check('decay',solve(6,10,2,4,8),6); check('end',solve(8,10,2,4,8),2); check('after',solve(9,10,2,4,8),2); check('start',solve(0,8,1,3,6),0)
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
warmup	`2.5`	`2.5`	Passed
boundary	`8.0`	`10`	Failed
decay	`4.0`	`6`	Failed
end	`2`	`2`	Passed
after	`2`	`2`	Passed
start	`0.0`	`0`	Passed

SHA-256 / 84fc2a086cdeff8edc00bb90c22733a8aacbf00ce83c3c8a6f4f2a70f1caff05

HELD IN THE MEMBER ARCHIVE

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

This mechanism has 6 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.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

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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 2026-09-30T16:48:20.799792+00:00.

Case digest / 72649431c748e84f25cc31f391f164d2dc002fa04aad6ab0638000f19558cf13