FA-98971 / Optimizer update state / Open access
Adam second moment keeps a signed gradient · case 01
Adam second moment keeps a signed gradient.
ROOT CAUSE
The squared-gradient accumulator uses g rather than g squared.
THE FAILURE
The squared-gradient accumulator uses g rather than g squared.
Unsuccessful approach: Taking the absolute gradient prevents negative state but still omits squaring.
Case contract
v_next=b2*v+(1-b2)*g*g.
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, v, b2):
return b2*v+(1-b2)*g
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('positive gradient',solve(4,0,0.5),8)
check('negative gradient',solve(-4,0,0.5),8)
check('prior state',solve(2,6,0.5),5)
check('beta zero',solve(3,7,0),9)
check('beta one',solve(-2,5,1),5)
check('zero gradient decays',solve(0,8,0.25),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 |
|---|---|---|---|
| positive gradient | 2.0 | 8 | Failed |
| negative gradient | -2.0 | 8 | Failed |
| prior state | 4.0 | 5 | Failed |
| beta zero | 3 | 9 | Failed |
| beta one | 5 | 5 | Passed |
| zero gradient decays | 2.0 | 2 | Passed |
SHA-256 / 3c3dca2a42a3575945d28da3e38304a19b4c5c94b160ac057754b07961760f3e
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(g, v, b2):
return b2*v+(1-b2)*abs(g)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('positive gradient',solve(4,0,0.5),8)
check('negative gradient',solve(-4,0,0.5),8)
check('prior state',solve(2,6,0.5),5)
check('beta zero',solve(3,7,0),9)
check('beta one',solve(-2,5,1),5)
check('zero gradient decays',solve(0,8,0.25),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 |
|---|---|---|---|
| positive gradient | 2.0 | 8 | Failed |
| negative gradient | 2.0 | 8 | Failed |
| prior state | 4.0 | 5 | Failed |
| beta zero | 3 | 9 | Failed |
| beta one | 5 | 5 | Passed |
| zero gradient decays | 2.0 | 2 | Passed |
SHA-256 / 9ae5e90531a6c2e01921d98e8c793c05ab18cf09808fef954101e436e1438699
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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Sign in to the archive ↗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 2026-09-30T16:48:19.000011+00:00.
Case digest / 2b82518cab127119fbca44000b98dcc403d7e01e2178f98147d88b38c551c314