FA-99061 / Learning rate schedules / Open access
Staircase decay applies before the first interval boundary · case 01
Staircase decay applies before the first interval boundary.
ROOT CAUSE
The interval quotient is incremented before exponentiation, so every step is one decay level early.
THE FAILURE
The interval quotient is incremented before exponentiation, so every step is one decay level early.
Unsuccessful approach: Shifting the step before integer division still crosses some interval boundaries early, including unit intervals.
Case contract
Return base*gamma**(step//interval) for nonnegative 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, gamma, interval):
return base*gamma**(step//interval+1)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('before edge',solve(2,16,0.5,3),16); check('edge',solve(3,16,0.5,3),8); check('next interval',solve(6,16,0.5,3),4); check('zero',solve(0,7,0.2,4),7); check('negative clamp',solve(-1,9,0.5,3),9); check('unit interval',solve(2,8,0.5,1),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 |
|---|---|---|---|
| before edge | 8.0 | 16 | Failed |
| edge | 4.0 | 8 | Failed |
| next interval | 2.0 | 4 | Failed |
| zero | 1.4000000000000001 | 7 | Failed |
| negative clamp | 9.0 | 9 | Passed |
| unit interval | 1.0 | 2 | Failed |
SHA-256 / 8d390de9a5f8cb927bfd697a24c3e450235c387109f6ae3cf16bc0c427e52c41
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(step, base, gamma, interval):
return base*gamma**((step+1)//interval)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('before edge',solve(2,16,0.5,3),16); check('edge',solve(3,16,0.5,3),8); check('next interval',solve(6,16,0.5,3),4); check('zero',solve(0,7,0.2,4),7); check('negative clamp',solve(-1,9,0.5,3),9); check('unit interval',solve(2,8,0.5,1),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 |
|---|---|---|---|
| before edge | 8.0 | 16 | Failed |
| edge | 8.0 | 8 | Passed |
| next interval | 4.0 | 4 | Passed |
| zero | 7.0 | 7 | Passed |
| negative clamp | 9.0 | 9 | Passed |
| unit interval | 1.0 | 2 | Failed |
SHA-256 / 843ae8f272eeb312badcf9b9599f38ed7275285511e064f678c1b6ccb32c2803
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.
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Sign in to the archive ↗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 2026-09-30T16:48:19.909763+00:00.
Case digest / ab21ad33db4e3fce079d53364f8834097decb1407902747d53396adcd20dda83