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FA-98966 / Optimizer update state / Open access

Adam first moment drops its exponential history · case 01

Adam first moment drops its exponential history.

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

ROOT CAUSE

The first moment is set to the current gradient each step.

THE FAILURE

The first moment is set to the current gradient each step.

Unsuccessful approach: Blending the absolute gradient retains history but reverses the contribution of negative gradients.

Case contract

m_next=b1*m+(1-b1)*g; return the updated first moment.

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(g, m, b1):
    return g
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('first observation',solve(4,0,0.5),2)
check('retained history',solve(4,6,0.5),5)
check('negative gradient',solve(-4,2,0.5),-1)
check('coefficient zero',solve(3,9,0),3)
check('coefficient one',solve(3,9,1),9)
check('zero gradient decay',solve(0,8,0.5),4)
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 fixtureActualExpectedOutcome
first observation42Failed
retained history45Failed
negative gradient-4-1Failed
coefficient zero33Passed
coefficient one39Failed
zero gradient decay04Failed

SHA-256 / 1a768d929c7266524f62fd7242e24bfbde957523c260110bbd6335721a4deb25

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(g, m, b1):
    return b1*m+(1-b1)*abs(g)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('first observation',solve(4,0,0.5),2)
check('retained history',solve(4,6,0.5),5)
check('negative gradient',solve(-4,2,0.5),-1)
check('coefficient zero',solve(3,9,0),3)
check('coefficient one',solve(3,9,1),9)
check('zero gradient decay',solve(0,8,0.5),4)
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 fixtureActualExpectedOutcome
first observation2.02Passed
retained history5.05Passed
negative gradient3.0-1Failed
coefficient zero33Passed
coefficient one99Passed
zero gradient decay4.04Passed

SHA-256 / b2bb0a1959d084c56b5681a1d7445c7e9a28a2abba4c8d2d1c44a35687abc12c

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 2026-09-30T16:48:18.999693+00:00.

Case digest / 73e7dd20068671e3276105a362043f4534d79110a0d1c74e6269f1502fd62538