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FA-99091 / Learning rate schedules / Open access

Triangular schedule descends before reaching its peak · case 01

Triangular schedule descends before reaching its peak.

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

ROOT CAUSE

Distance from the peak is returned directly, inverting the intended triangle.

THE FAILURE

Distance from the peak is returned directly, inverting the intended triangle.

Unsuccessful approach: Adding one to the distance denominator lowers the peak below base.

Case contract

Repeat a triangular cycle with value base* (1-abs(phase-peak)/peak), phase=step%period, peak=period//2.

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, period):
    phase=step%period
    peak=period//2
    return base*abs(phase-peak)/peak
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('start',solve(0,10,6),0); check('ascending',solve(1,12,6),4); check('peak',solve(3,8,6),8); check('descending',solve(3,8,4),4); check('cycle reset',solve(6,9,6),0); check('second peak',solve(9,5,6),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 fixtureActualExpectedOutcome
start10.00Failed
ascending8.04Failed
peak0.08Failed
descending4.04Passed
cycle reset9.00Failed
second peak0.05Failed

SHA-256 / a202a51b15b2ff90330d96953dde449110a8a0964b737ff35a9d9a61956595a9

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(step, base, period):
    phase=step%period
    peak=period//2
    return base*(1-abs(phase-peak)/(peak+1))
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('start',solve(0,10,6),0); check('ascending',solve(1,12,6),4); check('peak',solve(3,8,6),8); check('descending',solve(3,8,4),4); check('cycle reset',solve(6,9,6),0); check('second peak',solve(9,5,6),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 fixtureActualExpectedOutcome
start2.50Failed
ascending6.04Failed
peak8.08Passed
descending5.3333333333333344Failed
cycle reset2.250Failed
second peak5.05Passed

SHA-256 / 5963dbe205d53a72cd1329fc675f65989b0afecbe0a9077f1fe7c9ec022f2e91

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 2026-09-30T16:48:20.351926+00:00.

Case digest / 2c0ce5af123237d0f13223944eb825f956ee259aa3709266e0b29fb777e8e2e8