FA-99076 / Learning rate schedules / Open access

Polynomial decay scales progress before subtracting from one · case 01

Polynomial decay scales progress before subtracting from one.

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

ROOT CAUSE

Power multiplies the progress fraction rather than shaping the remaining fraction.

THE FAILURE

Power multiplies the progress fraction rather than shaping the remaining fraction.

Unsuccessful approach: Reducing the exponent by one still gives incorrect curvature for non-linear powers.

Case contract

Return base*max(0,1-step/total)**power for nonnegative step.

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, power):
    return base*max(0,1-step/total*power)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('square midpoint',solve(2,16,4,2),4); check('start',solve(0,9,3,3),9); check('end',solve(3,9,3,2),0); check('after',solve(4,9,3,2),0); check('linear',solve(1,12,4,1),9); check('cube quarter',solve(1,8,4,3),3.375)
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
square midpoint	`0`	`4`	Failed
start	`9.0`	`9`	Passed
end	`0`	`0`	Passed
after	`0`	`0`	Passed
linear	`9.0`	`9`	Passed
cube quarter	`2.0`	`3.375`	Failed

SHA-256 / 16547ba5ca854ff5f053b1a50da87a778a37b0ff12514721807a7f8fc1fd06e7

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(step, base, total, power):
    return base*max(0,1-step/total)**(power-1)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('square midpoint',solve(2,16,4,2),4); check('start',solve(0,9,3,3),9); check('end',solve(3,9,3,2),0); check('after',solve(4,9,3,2),0); check('linear',solve(1,12,4,1),9); check('cube quarter',solve(1,8,4,3),3.375)
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
square midpoint	`8.0`	`4`	Failed
start	`9.0`	`9`	Passed
end	`0`	`0`	Passed
after	`0`	`0`	Passed
linear	`12.0`	`9`	Failed
cube quarter	`4.5`	`3.375`	Failed

SHA-256 / 05a7515304e33f5d72a87ca9c21c9348fe0aa02a37c35ff13cca755bdcbd2a79

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 2026-09-30T16:48:19.909870+00:00.

Case digest / fdd50e1519f3d6430dc4dee23f97690c35487eb35f62b77cc702b29455aacdd8