FA-99131 / Learning rate schedules / Open access

One-cycle schedule extrapolates beyond its endpoints · case 01

One-cycle schedule extrapolates beyond its endpoints.

Verified by executionVariant 1 · 7 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The piecewise ramp uses raw step values with no bounds at either end of the cycle.

THE FAILURE

The piecewise ramp uses raw step values with no bounds at either end of the cycle.

Unsuccessful approach: Clamping only the upper endpoint leaves negative steps below the configured low rate.

Case contract

Rise linearly from low to peak over rise_steps, then fall linearly to low by 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, low, peak, rise_steps, total):
    if step<=rise_steps: return low+(peak-low)*step/rise_steps
    return peak-(peak-low)*(step-rise_steps)/(total-rise_steps)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('start',solve(0,2,10,2,6),2); check('rise',solve(1,2,10,2,6),6); check('peak',solve(2,2,10,2,6),10); check('fall',solve(4,2,10,2,6),6); check('end',solve(6,2,10,2,6),2); check('after',solve(8,2,10,2,6),2); check('before',solve(-1,2,10,2,6),2)
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
start	`2.0`	`2`	Passed
rise	`6.0`	`6`	Passed
peak	`10.0`	`10`	Passed
fall	`6.0`	`6`	Passed
end	`2.0`	`2`	Passed
after	`-2.0`	`2`	Failed
before	`-2.0`	`2`	Failed

SHA-256 / 8a597af6b1659139f88305ab9fab1921f9f2c10c2eea3ad39dea76c10cf8797f

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(step, low, peak, rise_steps, total):
    step=min(total,step)
    if step<=rise_steps: return low+(peak-low)*step/rise_steps
    return peak-(peak-low)*(step-rise_steps)/(total-rise_steps)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('start',solve(0,2,10,2,6),2); check('rise',solve(1,2,10,2,6),6); check('peak',solve(2,2,10,2,6),10); check('fall',solve(4,2,10,2,6),6); check('end',solve(6,2,10,2,6),2); check('after',solve(8,2,10,2,6),2); check('before',solve(-1,2,10,2,6),2)
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
start	`2.0`	`2`	Passed
rise	`6.0`	`6`	Passed
peak	`10.0`	`10`	Passed
fall	`6.0`	`6`	Passed
end	`2.0`	`2`	Passed
after	`2.0`	`2`	Passed
before	`-2.0`	`2`	Failed

SHA-256 / 0ce63601487ae5888537ac102ce95f929a51af43e87dc142eb5833c8a7bac2cc

HELD IN THE MEMBER ARCHIVE

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This mechanism has 7 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.

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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 2026-09-30T16:48:20.798992+00:00.

Case digest / 5f9ab18a7a4b0bf3a895047356690702ef2b4b623656e03f5e3443874ef15765