FA-99086 / Learning rate schedules / Open access

Linear decay uses the full horizon after warmup · case 01

Linear decay uses the full horizon after warmup.

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

ROOT CAUSE

The decay numerator is divided by the full horizon despite starting after warmup.

THE FAILURE

The decay numerator is divided by the full horizon despite starting after warmup.

Unsuccessful approach: Correcting the denominator alone allows negative rates after the schedule end.

Case contract

Ramp to base through warmup, then linearly reach zero at total.

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, total):
    return base*step/warmup if step<warmup else base*(total-step)/total
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('warmup start',solve(0,8,2,6),0); check('warmup middle',solve(1,8,2,6),4); check('boundary',solve(2,8,2,6),8); check('decay middle',solve(4,8,2,6),4); check('end',solve(6,8,2,6),0); check('after',solve(7,8,2,6),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 start	`0.0`	`0`	Passed
warmup middle	`4.0`	`4`	Passed
boundary	`5.333333333333333`	`8`	Failed
decay middle	`2.6666666666666665`	`4`	Failed
end	`0.0`	`0`	Passed
after	`-1.3333333333333333`	`0`	Failed

SHA-256 / d5bdff508bb4ca062b64ede2b32f14562356ed8b707082bd9e886ae9b8ee448a

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(step, base, warmup, total):
    return base*step/warmup if step<warmup else base*(total-step)/(total-warmup)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('warmup start',solve(0,8,2,6),0); check('warmup middle',solve(1,8,2,6),4); check('boundary',solve(2,8,2,6),8); check('decay middle',solve(4,8,2,6),4); check('end',solve(6,8,2,6),0); check('after',solve(7,8,2,6),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 start	`0.0`	`0`	Passed
warmup middle	`4.0`	`4`	Passed
boundary	`8.0`	`8`	Passed
decay middle	`4.0`	`4`	Passed
end	`0.0`	`0`	Passed
after	`-2.0`	`0`	Failed

SHA-256 / fe232e0e386835ab623127843247b8d991e711423b6438d63907349c5da89021

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 2026-09-30T16:48:20.350711+00:00.

Case digest / d07e083da61282c239964d1cb93ff6d07c699403aa97a935f64bb7130c5b21aa