FA-98936 / Gradient accumulation weighting / Open access
Microbatch gradients are summed when the objective expects their mean · case 01
Microbatch gradients are summed when the objective expects their mean.
ROOT CAUSE
The broken path returns the raw sum of already normalized microbatch gradients.
THE FAILURE
The broken path returns the raw sum of already normalized microbatch gradients.
Unsuccessful approach: Dividing by update count plus one assumes an extra empty contribution that is not in the window.
Case contract
Each input is one already-normalized microbatch gradient. Return the arithmetic mean over updates; no updates yields zero.
Why this case matters
A deterministic toy model isolates one local accumulation contract.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(gradient_sums):
return sum(gradient_sums)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('two sums',solve([2*N,4*N]),3*N)
check('uneven sums',solve([N,9*N,2*N]),4*N)
check('singleton',solve([8*N]),8*N)
check('empty',solve([]),0)
check('zero term',solve([0,6*N]),3*N)
check('cancellation',solve([4*N,-2*N]),N)
check('four sums',solve([N,2*N,3*N,10*N]),4*N)
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 |
|---|---|---|---|
| two sums | 6 | 3 | Failed |
| uneven sums | 12 | 4 | Failed |
| singleton | 8 | 8 | Passed |
| empty | 0 | 0 | Passed |
| zero term | 6 | 3 | Failed |
| cancellation | 2 | 1 | Failed |
| four sums | 16 | 4 | Failed |
SHA-256 / b1c1c9071d05aa5293c01f3b9d13ff597e163eb66a69c4e2f48c79e1ed6e9af2
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(gradient_sums):
return sum(gradient_sums) / (len(gradient_sums)+1) if gradient_sums else 0
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('two sums',solve([2*N,4*N]),3*N)
check('uneven sums',solve([N,9*N,2*N]),4*N)
check('singleton',solve([8*N]),8*N)
check('empty',solve([]),0)
check('zero term',solve([0,6*N]),3*N)
check('cancellation',solve([4*N,-2*N]),N)
check('four sums',solve([N,2*N,3*N,10*N]),4*N)
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 |
|---|---|---|---|
| two sums | 2.0 | 3 | Failed |
| uneven sums | 3.0 | 4 | Failed |
| singleton | 4.0 | 8 | Failed |
| empty | 0 | 0 | Passed |
| zero term | 2.0 | 3 | Failed |
| cancellation | 0.6666666666666666 | 1 | Failed |
| four sums | 3.2 | 4 | Failed |
SHA-256 / d351604d6b22ab93e89734cb226bd27e0376466a737606a4d9014ceba7f73cf2
HELD IN THE MEMBER ARCHIVE
The verified repair and its recorded checks are member-only.
This mechanism has 7 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
Inputs are scalar or short-list summaries and do not model autodiff, devices, or an optimizer. 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 2026-09-30T16:48:18.534684+00:00.
Case digest / cb9b9290e676f8d06d632868f7e8d6aa00e358e3bc8c86a6f4d5e4d773409832