FA-98961 / Optimizer update state / Open access

Momentum state stores the descent direction rather than gradient history · case 01

Momentum state stores the descent direction rather than gradient history.

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

ROOT CAUSE

The velocity sign convention is inconsistent with the parameter subtraction.

THE FAILURE

The velocity sign convention is inconsistent with the parameter subtraction.

Unsuccessful approach: Adding the signed velocity to the parameter repairs a fresh-buffer step but still stores gradient history under the opposite sign convention.

Case contract

State stores gradient-direction velocity; update p-lr*v_next.

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, v, lr, mu):
    nv=mu*v-g
    return [p-lr*nv,nv]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('positive input',solve(5,2,0,1,0.5),[3,2])
check('negative input',solve(5,-2,0,1,0.5),[7,-2])
check('old positive state',solve(10,1,4,1,0.5),[7,3])
check('old negative state',solve(10,1,-4,1,0.5),[11,-1])
check('zero gradient',solve(3,0,8,1,0.5),[-1,4])
check('zero rate still evolves state',solve(2,-3,6,0,0.5),[2,0])
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
positive input	`[7.0, -2.0]`	`[3, 2]`	Failed
negative input	`[3.0, 2.0]`	`[7, -2]`	Failed
old positive state	`[9.0, 1.0]`	`[7, 3]`	Failed
old negative state	`[13.0, -3.0]`	`[11, -1]`	Failed
zero gradient	`[-1.0, 4.0]`	`[-1, 4]`	Passed
zero rate still evolves state	`[2.0, 6.0]`	`[2, 0]`	Failed

SHA-256 / d2df2770bc5c6acd98cbf483542579d34a73eaf13226618e00112c25cf04f6f9

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(p, g, v, lr, mu):
    nv=mu*v-g
    return [p+lr*nv,nv]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('positive input',solve(5,2,0,1,0.5),[3,2])
check('negative input',solve(5,-2,0,1,0.5),[7,-2])
check('old positive state',solve(10,1,4,1,0.5),[7,3])
check('old negative state',solve(10,1,-4,1,0.5),[11,-1])
check('zero gradient',solve(3,0,8,1,0.5),[-1,4])
check('zero rate still evolves state',solve(2,-3,6,0,0.5),[2,0])
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
positive input	`[3.0, -2.0]`	`[3, 2]`	Failed
negative input	`[7.0, 2.0]`	`[7, -2]`	Failed
old positive state	`[11.0, 1.0]`	`[7, 3]`	Failed
old negative state	`[7.0, -3.0]`	`[11, -1]`	Failed
zero gradient	`[7.0, 4.0]`	`[-1, 4]`	Failed
zero rate still evolves state	`[2.0, 6.0]`	`[2, 0]`	Failed

SHA-256 / e8b163e63cbdbc11a0a13643d33c735f462aaa1d8f32bfcf669d8c8161e71b6b

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 2026-09-30T16:48:19.000023+00:00.

Case digest / 71ce066a05189eaf19705d2d18bb82dcb382cc39efe6b829b6c9074f68ff6800