FA-99016 / Optimizer update state / Open access

Frozen parameters accumulate optimizer state · case 01

Frozen parameters accumulate optimizer state.

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

ROOT CAUSE

Gradient moments are updated without consulting the active flag, including when a parameter is explicitly frozen.

THE FAILURE

Gradient moments are updated without consulting the active flag, including when a parameter is explicitly frozen.

Unsuccessful approach: Skipping inactive moments repairs freezing but leaves active parameter values unchanged despite their new moments.

Case contract

If inactive return [p,m,v]. Otherwise set nm=.5*m+.5*g, nv=.5*v+.5*g*g, and return [p-nm/(sqrt(nv)+1),nm,nv]; v is nonnegative.

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, m, v, active):
    nm=0.5*m+0.5*g; nv=0.5*v+0.5*g*g
    return [p,nm,nv]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('frozen nonzero gradient',solve(3,4,2,6,False),[3,2,6])
check('active update',solve(3,4,2,6,True),[3-3/(11**0.5+1),3,11])
check('frozen negative gradient',solve(-2,-4,5,8,False),[-2,5,8])
check('frozen zero state',solve(0,0,0,0,False),[0,0,0])
check('active zero gradient',solve(5,0,4,8,True),[5-2/(4**0.5+1),2,4])
check('active singleton',solve(N,2,0,0,True),[N-1/(2**0.5+1),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
frozen nonzero gradient	`[3, 3.0, 11.0]`	`[3, 2, 6]`	Failed
active update	`[3, 3.0, 11.0]`	`[2.30501256289338, 3, 11]`	Failed
frozen negative gradient	`[-2, 0.5, 12.0]`	`[-2, 5, 8]`	Failed
frozen zero state	`[0, 0.0, 0.0]`	`[0, 0, 0]`	Passed
active zero gradient	`[5, 2.0, 4.0]`	`[4.333333333333333, 2, 4]`	Failed
active singleton	`[1, 1.0, 2.0]`	`[0.5857864376269049, 1, 2]`	Failed

SHA-256 / 89c29fee0b6004462e0683b21b648b3b0fd1f88582fe784f2773b588adb85079

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(p, g, m, v, active):
    nm=m if not active else 0.5*m+0.5*g; nv=v if not active else 0.5*v+0.5*g*g
    return [p,nm,nv]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('frozen nonzero gradient',solve(3,4,2,6,False),[3,2,6])
check('active update',solve(3,4,2,6,True),[3-3/(11**0.5+1),3,11])
check('frozen negative gradient',solve(-2,-4,5,8,False),[-2,5,8])
check('frozen zero state',solve(0,0,0,0,False),[0,0,0])
check('active zero gradient',solve(5,0,4,8,True),[5-2/(4**0.5+1),2,4])
check('active singleton',solve(N,2,0,0,True),[N-1/(2**0.5+1),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
frozen nonzero gradient	`[3, 2, 6]`	`[3, 2, 6]`	Passed
active update	`[3, 3.0, 11.0]`	`[2.30501256289338, 3, 11]`	Failed
frozen negative gradient	`[-2, 5, 8]`	`[-2, 5, 8]`	Passed
frozen zero state	`[0, 0, 0]`	`[0, 0, 0]`	Passed
active zero gradient	`[5, 2.0, 4.0]`	`[4.333333333333333, 2, 4]`	Failed
active singleton	`[1, 1.0, 2.0]`	`[0.5857864376269049, 1, 2]`	Failed

SHA-256 / c31419ec432bd5206ac380d25f7fb7d4b52006d7d79def7a6aa39e4f76cde0c4

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 2026-09-30T16:48:19.456305+00:00.

Case digest / 8554241a0ba0746611a5e8d924f18e79f4b22976ff249324af3828246c6f9958