FA-99001 / Optimizer update state / Open access

Coupled decay is omitted from the gradient moments · case 01

Coupled decay is omitted from the gradient moments.

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

ROOT CAUSE

The gradient and its squared-state summary omit the regularization contribution entirely.

THE FAILURE

The gradient and its squared-state summary omit the regularization contribution entirely.

Unsuccessful approach: Adding decay to the update direction skips its contribution to squared-gradient state.

Case contract

This unit-coefficient toy step forms q=g+wd*p, then returns [p-lr*q,q,q*q]; it does not perform adaptive normalization.

Why this case matters

Optimizer implementations must associate each parameter with its own mathematically specified update state.

1 / The failure

Exit 1

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

N = 1
observations = []
def solve(p, g, lr, wd):
    return [p-lr*g,g,g*g]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('decay-only',solve(2,0,1,0.5),[1,1,1])
check('gradient plus decay',solve(2,1,0.5,0.5),[1,2,4])
check('negative parameter',solve(-2,0,1,0.25),[-1.5,-0.5,0.25])
check('zero decay',solve(3,-2,1,0),[5,-2,4])
check('zero rate still moments',solve(2,1,0,0.5),[2,2,4])
check('zero parameter',solve(0,3,1,2),[-3,3,9])
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
decay-only	`[2, 0, 0]`	`[1, 1, 1]`	Failed
gradient plus decay	`[1.5, 1, 1]`	`[1, 2, 4]`	Failed
negative parameter	`[-2, 0, 0]`	`[-1.5, -0.5, 0.25]`	Failed
zero decay	`[5, -2, 4]`	`[5, -2, 4]`	Passed
zero rate still moments	`[2, 1, 1]`	`[2, 2, 4]`	Failed
zero parameter	`[-3, 3, 9]`	`[-3, 3, 9]`	Passed

SHA-256 / 30f15b3d7441ce0fd150be257e76f3a7a3b958702a0df24abdc6b422b079438c

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(p, g, lr, wd):
    return [p-lr*(g+wd*p),g,g*g]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('decay-only',solve(2,0,1,0.5),[1,1,1])
check('gradient plus decay',solve(2,1,0.5,0.5),[1,2,4])
check('negative parameter',solve(-2,0,1,0.25),[-1.5,-0.5,0.25])
check('zero decay',solve(3,-2,1,0),[5,-2,4])
check('zero rate still moments',solve(2,1,0,0.5),[2,2,4])
check('zero parameter',solve(0,3,1,2),[-3,3,9])
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
decay-only	`[1.0, 0, 0]`	`[1, 1, 1]`	Failed
gradient plus decay	`[1.0, 1, 1]`	`[1, 2, 4]`	Failed
negative parameter	`[-1.5, 0, 0]`	`[-1.5, -0.5, 0.25]`	Failed
zero decay	`[5, -2, 4]`	`[5, -2, 4]`	Passed
zero rate still moments	`[2.0, 1, 1]`	`[2, 2, 4]`	Failed
zero parameter	`[-3, 3, 9]`	`[-3, 3, 9]`	Passed

SHA-256 / 15b8b0f97813ee7bb83dc4df6caba3458e77d8769800b5a1f9096cd111af1ff6

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 deterministic scalar or short-vector toy contracts, not claims about production optimizer APIs or training quality. 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 2026-09-30T16:48:19.455849+00:00.

Case digest / dd43898d6e8104b26977432f1461783b3fa5727067b260cf59a0d3df6df6e425