FA-98876 / Gradient accumulation weighting / Open access
Sequence means are averaged for a token-mean objective · case 01
Sequence means are averaged for a token-mean objective.
ROOT CAUSE
The broken path averages per-sequence means, giving short and long sequences equal weight.
THE FAILURE
The broken path averages per-sequence means, giving short and long sequences equal weight.
Unsuccessful approach: Averaging means still overweights short sequences.
Case contract
Aggregate sequence loss sums and token counts, then divide once by total tokens. No tokens 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(sequence_sums, token_counts):
return sum(s / c for s,c in zip(sequence_sums,token_counts) if c) / max(1,sum(c > 0 for c in token_counts))
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('different lengths',solve([2*N,12*N],[N,3*N]),3.5)
check('equal lengths',solve([2*N,4*N],[N,N]),3)
check('one sequence',solve([6*N],[2*N]),3)
check('empty',solve([],[]),0)
check('empty sequence ignored',solve([0,8*N],[0,2*N]),4)
check('zero objective',solve([0,9*N],[N,3*N]),2.25)
check('three sequences',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 |
|---|---|---|---|
| different lengths | 3.0 | 3.5 | Failed |
| equal lengths | 3.0 | 3 | Passed |
| one sequence | 3.0 | 3 | Passed |
| empty | 0.0 | 0 | Passed |
| empty sequence ignored | 4.0 | 4 | Passed |
| zero objective | 1.5 | 2.25 | Failed |
| three sequences | 2.0 | 2.142857142857143 | Failed |
SHA-256 / bfb702839dd418b91654e97209ba3741da5369c5d84a276d70a2865e0182d45e
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(sequence_sums, token_counts):
return sum(s / c for s,c in zip(sequence_sums,token_counts) if c) / max(1,len(sequence_sums))
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('different lengths',solve([2*N,12*N],[N,3*N]),3.5)
check('equal lengths',solve([2*N,4*N],[N,N]),3)
check('one sequence',solve([6*N],[2*N]),3)
check('empty',solve([],[]),0)
check('empty sequence ignored',solve([0,8*N],[0,2*N]),4)
check('zero objective',solve([0,9*N],[N,3*N]),2.25)
check('three sequences',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 |
|---|---|---|---|
| different lengths | 3.0 | 3.5 | Failed |
| equal lengths | 3.0 | 3 | Passed |
| one sequence | 3.0 | 3 | Passed |
| empty | 0.0 | 0 | Passed |
| empty sequence ignored | 2.0 | 4 | Failed |
| zero objective | 1.5 | 2.25 | Failed |
| three sequences | 2.0 | 2.142857142857143 | Failed |
SHA-256 / 4f4f75b8f347e62aacc3565e92d9712082237e7730baba07e3cae8f616a2c3c4
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 2026-09-30T16:48:17.605611+00:00.
Case digest / a82b566e0a9de5883bc2eb474446db27257e9f97d27d5323fa4ce5d5abff039e