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FA-99056 / Learning rate schedules / Open access

Exponential decay raises the base rate to a power · case 01

Exponential decay raises the base rate to a power.

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

ROOT CAUSE

The base is multiplied by gamma before the whole product is exponentiated.

THE FAILURE

The base is multiplied by gamma before the whole product is exponentiated.

Unsuccessful approach: Replacing the exponent with a linear step multiplier creates a linear curve, not geometric decay.

Case contract

Return base*gamma**step for nonnegative step; negative steps clamp to 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, gamma):
    return (base*gamma)**max(0,step)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('two steps',solve(2,8,0.5),2); check('start',solve(0,7,0.4),7); check('one',solve(1,10,0.8),8); check('zero factor',solve(3,5,0),0); check('negative step',solve(-2,9,0.5),9); check('growth factor',solve(2,2,2),8)
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 fixtureActualExpectedOutcome
two steps16.02Failed
start1.07Failed
one8.08Passed
zero factor00Passed
negative step1.09Failed
growth factor168Failed

SHA-256 / 8847efec541f8641a4482ecc51c6fd384d91c21906bd52ce67014e3e8a58af47

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(step, base, gamma):
    return base*gamma*max(0,step)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('two steps',solve(2,8,0.5),2); check('start',solve(0,7,0.4),7); check('one',solve(1,10,0.8),8); check('zero factor',solve(3,5,0),0); check('negative step',solve(-2,9,0.5),9); check('growth factor',solve(2,2,2),8)
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 fixtureActualExpectedOutcome
two steps8.02Failed
start0.07Failed
one8.08Passed
zero factor00Passed
negative step0.09Failed
growth factor88Passed

SHA-256 / 160c76a7de7f938e8fad3975d8d173786dc08f0482150819607cb0caec3c9729

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 2026-09-30T16:48:19.909547+00:00.

Case digest / ecd40065094f6e7d00377863c4c5d7d414356e29732b95d899a451c7a4719fdd