FA-98841 / Gradient accumulation weighting / Open access
Unequal example batches receive equal mean-gradient weight · case 01
Unequal example batches receive equal mean-gradient weight.
ROOT CAUSE
Each microbatch is represented by a summed gradient and its example count; the implementation averages microbatch means instead of weighting by examples.
THE FAILURE
Each microbatch is represented by a summed gradient and its example count; the implementation averages microbatch means instead of weighting by examples.
Unsuccessful approach: Weighting each batch mean equally only matches the contract when batch sizes are equal.
Case contract
Gradient sums and example counts describe microbatches. Return their global example-weighted mean; zero total examples returns 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(sums, counts):
return sum(s / max(1, c) for s, c in zip(sums, counts))
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('unequal batches',solve([2*N,12*N],[N,3*N]),3.5)
check('equal batches',solve([2*N,4*N],[N,N]),3)
check('single batch',solve([7*N],[N]),7)
check('empty window',solve([],[]),0)
check('zero numerator',solve([0,9*N],[N,3*N]),2.25)
check('one large batch',solve([12*N],[4*N]),3)
check('three batches',solve([N,6*N,8*N],[1,2,4]),15*N/7)
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 |
|---|---|---|---|
| unequal batches | 6.0 | 3.5 | Failed |
| equal batches | 6.0 | 3 | Failed |
| single batch | 7.0 | 7 | Passed |
| empty window | 0 | 0 | Passed |
| zero numerator | 3.0 | 2.25 | Failed |
| one large batch | 3.0 | 3 | Passed |
| three batches | 6.0 | 2.142857142857143 | Failed |
SHA-256 / 3e6d17b77c9a172ed11f6907e093bb9b84b5685d3eaca38a3ee1437a914b20fa
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(sums, counts):
return sum(s / c for s, c in zip(sums, counts) if c) / max(1, len(sums))
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('unequal batches',solve([2*N,12*N],[N,3*N]),3.5)
check('equal batches',solve([2*N,4*N],[N,N]),3)
check('single batch',solve([7*N],[N]),7)
check('empty window',solve([],[]),0)
check('zero numerator',solve([0,9*N],[N,3*N]),2.25)
check('one large batch',solve([12*N],[4*N]),3)
check('three batches',solve([N,6*N,8*N],[1,2,4]),15*N/7)
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 |
|---|---|---|---|
| unequal batches | 3.0 | 3.5 | Failed |
| equal batches | 3.0 | 3 | Passed |
| single batch | 7.0 | 7 | Passed |
| empty window | 0.0 | 0 | Passed |
| zero numerator | 1.5 | 2.25 | Failed |
| one large batch | 3.0 | 3 | Passed |
| three batches | 2.0 | 2.142857142857143 | Failed |
SHA-256 / 647fe9a2a2d27e8bf125a4ecb8bf419c20a2f99215990c25dc189448f198937d
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 2026-09-30T16:48:17.605217+00:00.
Case digest / 495faca851ccd317ff9373e1212e905e6f24e08c6bc5ccd686ebfd4618c24543