FA-98856 / Gradient accumulation weighting / Open access
An empty microbatch dilutes the equal-microbatch mean · case 01
An empty microbatch dilutes the equal-microbatch mean.
ROOT CAUSE
Empty segments are included in the divisor, although only participating segment means belong in this contract.
THE FAILURE
Empty segments are included in the divisor, although only participating segment means belong in this contract.
Unsuccessful approach: Using participation counts as weights turns equal segment influence into count weighting.
Case contract
Inputs are already per-microbatch means and a positive participation count. Average nonempty microbatch means equally; empty batches are ignored.
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(means, nonempty):
return sum(means) / max(1,len(means))
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('different batch sizes',solve([2*N,4*N],[N,3*N]),3*N)
check('empty batch skipped',solve([0,7*N],[0,1]),7*N)
check('all empty',solve([0,0],[0,0]),0)
check('single batch',solve([5*N],[1]),5*N)
check('three batch means',solve([N,3*N,8*N],[1,1,1]),4*N)
check('empty input',solve([],[]),0)
check('one of two',solve([9*N,0],[1,0]),9*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 |
|---|---|---|---|
| different batch sizes | 3.0 | 3 | Passed |
| empty batch skipped | 3.5 | 7 | Failed |
| all empty | 0.0 | 0 | Passed |
| single batch | 5.0 | 5 | Passed |
| three batch means | 4.0 | 4 | Passed |
| empty input | 0.0 | 0 | Passed |
| one of two | 4.5 | 9 | Failed |
SHA-256 / 1d6c1e0cc372d90da0e46f85c5072ad1e9d60bbc47e6c13e75be98c85d8123c0
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(means, nonempty):
return sum(m for m,c in zip(means,nonempty) if c) / max(1,sum(nonempty))
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('different batch sizes',solve([2*N,4*N],[N,3*N]),3*N)
check('empty batch skipped',solve([0,7*N],[0,1]),7*N)
check('all empty',solve([0,0],[0,0]),0)
check('single batch',solve([5*N],[1]),5*N)
check('three batch means',solve([N,3*N,8*N],[1,1,1]),4*N)
check('empty input',solve([],[]),0)
check('one of two',solve([9*N,0],[1,0]),9*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 |
|---|---|---|---|
| different batch sizes | 1.5 | 3 | Failed |
| empty batch skipped | 7.0 | 7 | Passed |
| all empty | 0.0 | 0 | Passed |
| single batch | 5.0 | 5 | Passed |
| three batch means | 4.0 | 4 | Passed |
| empty input | 0.0 | 0 | Passed |
| one of two | 9.0 | 9 | Passed |
SHA-256 / 50c7a6d4db0413ca25302dc8610618b5d7d105bdfeb21ac4fc4e8cba0e1237b6
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.
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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 2026-09-30T16:48:17.605732+00:00.
Case digest / b7dd0e370bf5a4744302b1a9b702ae4e72e2dfb2a43bfb18efed7636e2c6c777