FA-98946 / Optimizer update state / Open access

Momentum ignores the prior velocity · case 01

Momentum ignores the prior velocity.

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

ROOT CAUSE

Only the current gradient contributes to the update.

THE FAILURE

Only the current gradient contributes to the update.

Unsuccessful approach: Adding the previous velocity without its mu coefficient omits the specified decay of carried state.

Case contract

Return [new_parameter,new_velocity] for v_next=mu*v+g and p_next=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):
    return [p-lr*g,g]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('first step',solve(10,2,0,N,0.5),[10-2*N,2])
check('carried velocity',solve(10,2,4,N,0.5),[10-N*4,4])
check('negative gradient',solve(0,-2,4,1,0.5),[0,0])
check('zero rate keeps state',solve(3,2,1,0,0.9),[3,2.9])
check('zero momentum',solve(7,3,8,N,0),[7-3*N,3])
check('zero gradient decays buffer',solve(5,0,4,1,0.5),[3,2])
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
first step	`[8, 2]`	`[8, 2]`	Passed
carried velocity	`[8, 2]`	`[6, 4]`	Failed
negative gradient	`[2, -2]`	`[0, 0]`	Failed
zero rate keeps state	`[3, 2]`	`[3, 2.9]`	Failed
zero momentum	`[4, 3]`	`[4, 3]`	Passed
zero gradient decays buffer	`[5, 0]`	`[3, 2]`	Failed

SHA-256 / e167175a7205b0d8147e8ebd2ce7b5a3703ee32f7135d23b852fe5fa7fda477b

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):
    return [p-lr*(g+v),g+v]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('first step',solve(10,2,0,N,0.5),[10-2*N,2])
check('carried velocity',solve(10,2,4,N,0.5),[10-N*4,4])
check('negative gradient',solve(0,-2,4,1,0.5),[0,0])
check('zero rate keeps state',solve(3,2,1,0,0.9),[3,2.9])
check('zero momentum',solve(7,3,8,N,0),[7-3*N,3])
check('zero gradient decays buffer',solve(5,0,4,1,0.5),[3,2])
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
first step	`[8, 2]`	`[8, 2]`	Passed
carried velocity	`[4, 6]`	`[6, 4]`	Failed
negative gradient	`[-2, 2]`	`[0, 0]`	Failed
zero rate keeps state	`[3, 3]`	`[3, 2.9]`	Failed
zero momentum	`[-4, 11]`	`[4, 3]`	Failed
zero gradient decays buffer	`[1, 4]`	`[3, 2]`	Failed

SHA-256 / 1e3458decf318018061b7d37de28387d1373dda92fc51a1ba233a5e041700cbc

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 2026-09-30T16:48:18.534850+00:00.

Case digest / 5e55c67a45554ba80cc7a3e9eefb5423a040ae98e06699c71297912229045457