FA-99081 / Learning rate schedules / Open access

Cosine decay starts partway through its phase after warmup · case 01

Cosine decay starts partway through its phase after warmup.

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

ROOT CAUSE

The cosine phase uses the global step instead of elapsed post-warmup steps.

THE FAILURE

The cosine phase uses the global step instead of elapsed post-warmup steps.

Unsuccessful approach: Using the full horizon as the denominator leaves a positive rate at the requested end step.

Case contract

Linearly warm up through warmup; then cosine-decay to 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):
    import math
    return base*step/warmup if step<warmup else base*(1+math.cos(math.pi*step/total))/2
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('warmup middle',solve(2,12,4,8),6); check('warmup end',solve(4,12,4,8),12); check('decay midpoint',solve(6,12,4,8),6); check('end',solve(8,12,4,8),0); check('after',solve(9,12,4,8),0); check('start',solve(0,8,4,8),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 middle	`6.0`	`6`	Passed
warmup end	`6.0`	`12`	Failed
decay midpoint	`1.7573593128807152`	`6`	Failed
end	`0.0`	`0`	Passed
after	`0.4567228049322789`	`0`	Failed
start	`0.0`	`0`	Passed

SHA-256 / 0467a26b6cd05139ad8dde1b43e71889830618df8309c632ede5a6fa648044ac

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):
    import math
    return base*step/warmup if step<warmup else base*(1+math.cos(math.pi*(step-warmup)/total))/2 if step<=total else 0
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('warmup middle',solve(2,12,4,8),6); check('warmup end',solve(4,12,4,8),12); check('decay midpoint',solve(6,12,4,8),6); check('end',solve(8,12,4,8),0); check('after',solve(9,12,4,8),0); check('start',solve(0,8,4,8),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 middle	`6.0`	`6`	Passed
warmup end	`12.0`	`12`	Passed
decay midpoint	`10.242640687119284`	`6`	Failed
end	`6.0`	`0`	Failed
after	`0`	`0`	Passed
start	`0.0`	`0`	Passed

SHA-256 / 8c538316c78dc241978d4c65588b1593e2f5ad6397b816ed3d70ad64bde810fe

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 2026-09-30T16:48:20.352005+00:00.

Case digest / d3a5dfbc8c81e6570cce14b694a44a24d693e52b1e1c59ce322dc0ad53909fad