FA-99106 / Learning rate schedules / Open access

Hold time consumes part of the decay ramp · case 01

Hold time consumes part of the decay ramp.

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

ROOT CAUSE

The decay fraction uses absolute step and therefore includes the preceding hold period.

THE FAILURE

The decay fraction uses absolute step and therefore includes the preceding hold period.

Unsuccessful approach: Adding one to decay duration prevents reaching zero at the scheduled endpoint.

Case contract

Hold base through hold_steps, then linearly decay to zero over decay_steps.

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, hold_steps, decay_steps):
    return base if step<hold_steps else base*max(0,1-step/decay_steps)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('hold',solve(1,10,2,4),10); check('boundary',solve(2,10,2,4),10); check('first decay',solve(3,10,2,4),7.5); check('middle',solve(4,10,2,4),5); check('end',solve(6,10,2,4),0); check('after',solve(7,10,2,4),0)
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
hold	`10`	`10`	Passed
boundary	`5.0`	`10`	Failed
first decay	`2.5`	`7.5`	Failed
middle	`0`	`5`	Failed
end	`0`	`0`	Passed
after	`0`	`0`	Passed

SHA-256 / e8bb9f205de9d5b4c264bcf0459eab165a5a00f029ab8ca9cb6b20c593d8458d

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(step, base, hold_steps, decay_steps):
    return base if step<=hold_steps else base*max(0,1-(step-hold_steps)/(decay_steps+1))
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('hold',solve(1,10,2,4),10); check('boundary',solve(2,10,2,4),10); check('first decay',solve(3,10,2,4),7.5); check('middle',solve(4,10,2,4),5); check('end',solve(6,10,2,4),0); check('after',solve(7,10,2,4),0)
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
hold	`10`	`10`	Passed
boundary	`10`	`10`	Passed
first decay	`8.0`	`7.5`	Failed
middle	`6.0`	`5`	Failed
end	`1.9999999999999996`	`0`	Failed
after	`0`	`0`	Passed

SHA-256 / 6d2b45531237f1ebd82a506cd6853ba627317d3f50470d33e7269f1b7f647a2e

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.

Member access is invitation-based. Sign in with your invited account to inspect the repair.

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 2026-09-30T16:48:20.352092+00:00.

Case digest / 4b35e906815360d2b10d37fafddf53a04ae16e90a0f800fca9c159af797c9c61