FA-99006 / Optimizer update state / Open access

Decoupled decay contaminates gradient moments · case 01

Decoupled decay contaminates gradient moments.

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

ROOT CAUSE

Parameter decay is inserted into the gradient accumulator.

THE FAILURE

Parameter decay is inserted into the gradient accumulator.

Unsuccessful approach: Applying multiplicative decay and then subtracting a decay-augmented gradient double counts decay.

Case contract

For zero prior state return [p*(1-lr*wd)-lr*g,g,g*g].

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):
    q=g+wd*p
    return [p-lr*q,q,q*q]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('decay only',solve(4,0,0.5,0.25),[3.5,0,0])
check('gradient state untouched',solve(4,2,0.5,0.25),[2.5,2,4])
check('zero decay',solve(3,-2,1,0),[5,-2,4])
check('zero rate',solve(3,2,0,1),[3,2,4])
check('negative parameter',solve(-4,0,0.5,0.25),[-3.5,0,0])
check('combined sign',solve(2,-1,1,0.5),[2,-1,1])
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	`[3.5, 1.0, 1.0]`	`[3.5, 0, 0]`	Failed
gradient state untouched	`[2.5, 3.0, 9.0]`	`[2.5, 2, 4]`	Failed
zero decay	`[5, -2, 4]`	`[5, -2, 4]`	Passed
zero rate	`[3, 5, 25]`	`[3, 2, 4]`	Failed
negative parameter	`[-3.5, -1.0, 1.0]`	`[-3.5, 0, 0]`	Failed
combined sign	`[2.0, 0.0, 0.0]`	`[2, -1, 1]`	Failed

SHA-256 / 90481c345a705e047578045f8be2ab3565881fab37c4b64880fc4284b4a55138

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):
    q=g+wd*p
    return [p*(1-lr*wd)-lr*q,q,q*q]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('decay only',solve(4,0,0.5,0.25),[3.5,0,0])
check('gradient state untouched',solve(4,2,0.5,0.25),[2.5,2,4])
check('zero decay',solve(3,-2,1,0),[5,-2,4])
check('zero rate',solve(3,2,0,1),[3,2,4])
check('negative parameter',solve(-4,0,0.5,0.25),[-3.5,0,0])
check('combined sign',solve(2,-1,1,0.5),[2,-1,1])
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	`[3.0, 1.0, 1.0]`	`[3.5, 0, 0]`	Failed
gradient state untouched	`[2.0, 3.0, 9.0]`	`[2.5, 2, 4]`	Failed
zero decay	`[5, -2, 4]`	`[5, -2, 4]`	Passed
zero rate	`[3, 5, 25]`	`[3, 2, 4]`	Failed
negative parameter	`[-3.0, -1.0, 1.0]`	`[-3.5, 0, 0]`	Failed
combined sign	`[1.0, 0.0, 0.0]`	`[2, -1, 1]`	Failed

SHA-256 / 7d5697764d7664ddaa9942fac64a60438fbca75c252562dcecf102f341813f56

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 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 2026-09-30T16:48:19.455427+00:00.

Case digest / 9e8c554b15444b76138811c931a7469f7baf19a60b8ee4d0b6e06f5f89c5f6e7