FA-98991 / Optimizer update state / Open access

Optimizer state follows list position instead of parameter identity · case 01

Optimizer state follows list position instead of parameter identity.

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

ROOT CAUSE

Moments are sorted by parameter ID and then paired positionally with parameters that retain their input order.

THE FAILURE

Moments are sorted by parameter ID and then paired positionally with parameters that retain their input order.

Unsuccessful approach: Replacing the mismatched prior moment with the current gradient removes cross-parameter borrowing but discards all stored history.

Case contract

For records [id,p,g,m], update each record independently using m_next=.5*m+.5*g and p_next=p-m_next; preserve record order.

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(records):
    states=[r[3] for r in sorted(records,key=lambda r:r[0])]
    return [[r[0],r[1]-(0.5*r[2]+0.5*m),0.5*r[2]+0.5*m] for r,m in zip(records,states)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('two parameter state',solve([['a',10,2,4],['b',20,-2,0]]),[['a',7,3],['b',21,-1]])
check('reordered records',solve([['b',20,-2,0],['a',10,2,4]]),[['b',21,-1],['a',7,3]])
check('singleton',solve([['x',N,2,0]]),[['x',N-1,1]])
check('empty records',solve([]),[])
check('zero gradient preserves history',solve([['p',5,0,6]]),[['p',2,3]])
check('distinct state values',solve([['u',0,4,2],['v',0,4,8]]),[['u',-3,3],['v',-6,6]])
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
two parameter state	`[['a', 7.0, 3.0], ['b', 21.0, -1.0]]`	`[['a', 7, 3], ['b', 21, -1]]`	Passed
reordered records	`[['b', 19.0, 1.0], ['a', 9.0, 1.0]]`	`[['b', 21, -1], ['a', 7, 3]]`	Failed
singleton	`[['x', 0.0, 1.0]]`	`[['x', 0, 1]]`	Passed
empty records	`[]`	`[]`	Passed
zero gradient preserves history	`[['p', 2.0, 3.0]]`	`[['p', 2, 3]]`	Passed
distinct state values	`[['u', -3.0, 3.0], ['v', -6.0, 6.0]]`	`[['u', -3, 3], ['v', -6, 6]]`	Passed

SHA-256 / 852290b9085d08dfd5c376a0e53010779250f9fc01ea880f759080497b5f67ca

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(records):
    return [[r[0],r[1]-(0.5*r[2]+0.5*r[2]),0.5*r[2]+0.5*r[2]] for r in records]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('two parameter state',solve([['a',10,2,4],['b',20,-2,0]]),[['a',7,3],['b',21,-1]])
check('reordered records',solve([['b',20,-2,0],['a',10,2,4]]),[['b',21,-1],['a',7,3]])
check('singleton',solve([['x',N,2,0]]),[['x',N-1,1]])
check('empty records',solve([]),[])
check('zero gradient preserves history',solve([['p',5,0,6]]),[['p',2,3]])
check('distinct state values',solve([['u',0,4,2],['v',0,4,8]]),[['u',-3,3],['v',-6,6]])
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
two parameter state	`[['a', 8.0, 2.0], ['b', 22.0, -2.0]]`	`[['a', 7, 3], ['b', 21, -1]]`	Failed
reordered records	`[['b', 22.0, -2.0], ['a', 8.0, 2.0]]`	`[['b', 21, -1], ['a', 7, 3]]`	Failed
singleton	`[['x', -1.0, 2.0]]`	`[['x', 0, 1]]`	Failed
empty records	`[]`	`[]`	Passed
zero gradient preserves history	`[['p', 5.0, 0.0]]`	`[['p', 2, 3]]`	Failed
distinct state values	`[['u', -4.0, 4.0], ['v', -4.0, 4.0]]`	`[['u', -3, 3], ['v', -6, 6]]`	Failed

SHA-256 / 0b5cc35d3ae13864311e55b71a0ee4008bbd563fb9197373382187620c368796

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 2026-09-30T16:48:18.999897+00:00.

Case digest / e44a6a280885b50b8971ec1ca320346c40b58ad46e1c4131f5357bb6f315b7c6