FA-99121 / Learning rate schedules / Open access

Linear schedule exceeds its configured rate ceiling · case 01

Linear schedule exceeds its configured rate ceiling.

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

ROOT CAUSE

The increasing ramp returns its raw value without enforcing the ceiling.

THE FAILURE

The increasing ramp returns its raw value without enforcing the ceiling.

Unsuccessful approach: Applying the ceiling without clamping negative steps can return a rate below the initial value.

Case contract

Return min(ceiling, base+slope*step) with step clamped at zero.

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, slope, ceiling):
    return base+slope*max(0,step)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('initial',solve(0,2,1,6),2); check('rising',solve(2,2,1,6),4); check('at ceiling',solve(4,2,1,6),6); check('above ceiling',solve(8,2,1,6),6); check('negative step',solve(-2,2,1,6),2); check('flat',solve(9,5,0,5),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
initial	`2`	`2`	Passed
rising	`4`	`4`	Passed
at ceiling	`6`	`6`	Passed
above ceiling	`10`	`6`	Failed
negative step	`2`	`2`	Passed
flat	`5`	`5`	Passed

SHA-256 / 8a75a343009369e1f8946c62bc36c7e758e394fa40889d347a9d6712741bdf00

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(step, base, slope, ceiling):
    return min(ceiling,base+slope*step)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('initial',solve(0,2,1,6),2); check('rising',solve(2,2,1,6),4); check('at ceiling',solve(4,2,1,6),6); check('above ceiling',solve(8,2,1,6),6); check('negative step',solve(-2,2,1,6),2); check('flat',solve(9,5,0,5),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
initial	`2`	`2`	Passed
rising	`4`	`4`	Passed
at ceiling	`6`	`6`	Passed
above ceiling	`6`	`6`	Passed
negative step	`0`	`2`	Failed
flat	`5`	`5`	Passed

SHA-256 / 358eb8dc2a9091f6ac41845735de9dabbd4668101f5abd6236ede1c26715c7fe

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 2026-09-30T16:48:20.799393+00:00.

Case digest / 57e905f298e755eba1c4b848c40613b3f73d8938481c53f1cbba44372b277486