FA-99046 / Learning rate schedules / Open access

Linear decay reaches zero one step too early · case 01

Linear decay reaches zero one step too early.

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

ROOT CAUSE

Subtracting one from remaining steps advances the decay by one unit at every point.

THE FAILURE

Subtracting one from remaining steps advances the decay by one unit at every point.

Unsuccessful approach: Using a shorter denominator makes the rate fall too quickly throughout the schedule.

Case contract

Return base*(total-step)/total clipped to [0,total], with zero after 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, total):
    return base*max(0,total-step-1)/total
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('interior',solve(N,12,6),12*(6-N)/6); check('start',solve(0,8,4),8); check('last',solve(3,8,4),2); check('end',solve(4,8,4),0); check('after',solve(5,8,4),0); check('fraction',solve(1,10,4),7.5)
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
interior	`8.0`	`10.0`	Failed
start	`6.0`	`8`	Failed
last	`0.0`	`2`	Failed
end	`0.0`	`0`	Passed
after	`0.0`	`0`	Passed
fraction	`5.0`	`7.5`	Failed

SHA-256 / 97e4b50c682dc7656ba908cae1bc8b18735a04a6ba22499ed268bc949774241a

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(step, base, total):
    return base*(total-step)/(total-1) if step<total else 0
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('interior',solve(N,12,6),12*(6-N)/6); check('start',solve(0,8,4),8); check('last',solve(3,8,4),2); check('end',solve(4,8,4),0); check('after',solve(5,8,4),0); check('fraction',solve(1,10,4),7.5)
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
interior	`12.0`	`10.0`	Failed
start	`10.666666666666666`	`8`	Failed
last	`2.6666666666666665`	`2`	Failed
end	`0`	`0`	Passed
after	`0`	`0`	Passed
fraction	`10.0`	`7.5`	Failed

SHA-256 / 0b2567f4c1d941fc4edc1f7d3771a5eb945b38785e1ba42f2bd983cedfe2aa8c

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 2026-09-30T16:48:19.909485+00:00.

Case digest / 2dd6e81ab3eb9e39b0b6d683b60a2fd1c3c226f52b0bab6ecdfe7d71cd8a6a7c