FA-98956 / Optimizer update state / Open access

Nesterov update uses the ordinary momentum direction · case 01

Nesterov update uses the ordinary momentum direction.

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

ROOT CAUSE

The lookahead gradient is replaced by the accumulated buffer alone.

THE FAILURE

The lookahead gradient is replaced by the accumulated buffer alone.

Unsuccessful approach: Using g+mu*v uses the previous buffer rather than the newly updated one.

Case contract

v_next=mu*v+g; p_next=p-lr*(g+mu*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('initial lookahead',solve(10,2,0,1,0.5),[7,2])
check('existing velocity',solve(10,2,4,1,0.5),[6,4])
check('negative gradient',solve(0,-2,4,0.5,0.5),[1,0])
check('zero momentum',solve(5,3,7,2,0),[-1,3])
check('zero rate',solve(3,4,2,0,0.9),[3,5.8])
check('zero gradient with velocity',solve(6,0,4,1,0.5),[5,2])
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
initial lookahead	`[8.0, 2.0]`	`[7, 2]`	Failed
existing velocity	`[6.0, 4.0]`	`[6, 4]`	Passed
negative gradient	`[0.0, 0.0]`	`[1, 0]`	Failed
zero momentum	`[-1, 3]`	`[-1, 3]`	Passed
zero rate	`[3.0, 5.8]`	`[3, 5.8]`	Passed
zero gradient with velocity	`[4.0, 2.0]`	`[5, 2]`	Failed

SHA-256 / dc8e628f1ce57ae54d539544f3e27af8869876968b817e2260dc4dfcfd06da45

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*(g+mu*v),nv]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('initial lookahead',solve(10,2,0,1,0.5),[7,2])
check('existing velocity',solve(10,2,4,1,0.5),[6,4])
check('negative gradient',solve(0,-2,4,0.5,0.5),[1,0])
check('zero momentum',solve(5,3,7,2,0),[-1,3])
check('zero rate',solve(3,4,2,0,0.9),[3,5.8])
check('zero gradient with velocity',solve(6,0,4,1,0.5),[5,2])
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
initial lookahead	`[8.0, 2.0]`	`[7, 2]`	Failed
existing velocity	`[6.0, 4.0]`	`[6, 4]`	Passed
negative gradient	`[0.0, 0.0]`	`[1, 0]`	Failed
zero momentum	`[-1, 3]`	`[-1, 3]`	Passed
zero rate	`[3.0, 5.8]`	`[3, 5.8]`	Passed
zero gradient with velocity	`[4.0, 2.0]`	`[5, 2]`	Failed

SHA-256 / c6a6f79d34ca7e7804ba456b2df775c83be8c874eb9e3441cc9f9a89781fae0a

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 2026-09-30T16:48:18.534905+00:00.

Case digest / 5bfd2d3fd5bfdd53d7e2ed4445b83d5c8910c3fbef7c3c3e7e0fa7dffd3aad7e