FA-14206 / Numerical aggregation / Open access
Group balanced squared loss: Missing residuals are imputed as zero and counted. · case 01
The reduction disagrees with its explicit aggregation oracle.
ROOT CAUSE
Missing residuals are imputed as zero and counted.
THE FAILURE
Missing residuals are imputed as zero and counted.
Unsuccessful approach: A nonzero default also invents residual evidence and group presence.
Case contract
Rows [group label, integer residual or None] are reduced into mean squared residual per group, then arithmetic mean across observed groups. Missing residuals contribute neither count nor group presence; group labels are case-sensitive. Empty observed population returns None. Exact Fraction string.
Why this case matters
Exact bounded examples isolate a reduction defect without floating-point or external-service effects.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
from collections import Counter, defaultdict
import math
import itertools
N = 1
observations = []
def solve(rows):
groups={}
for label,error in rows:
if error is None: error=0
groups.setdefault(label,[]).append(error)
if not groups: return None
means=[Fraction(sum(e*e for e in values),len(values)) for values in groups.values()]
return str(sum(means)/len(means))
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([('a', 1), ('a', 2), ('b', 4)],)), '37/4')
check('regression 2', solve(*([('a', 1), ('a', 3), ('b', 4)],)), '21/2')
check('regression 3', solve(*([],)), None)
check('regression 4', solve(*([('a', None), ('b', None)],)), None)
check('regression 5', solve(*([('a', 0), ('a', 2), ('b', -3), ('b', 1)],)), '7/2')
check('regression 6', solve(*([('a', 1), ('b', 2), ('b', 2), ('b', 2)],)), '5/2')
check('regression 7', solve(*([('a', None), ('a', 2), ('b', 4)],)), '10')
check('regression 8', solve(*([('A', 1), ('a', 4), ('B', 2)],)), '7')
check("variable group balance",solve([("a",N),("a",-N),("b",2*N)]),str(Fraction(5*N*N,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 |
|---|---|---|---|
| regression 1 | 37/4 | 37/4 | Passed |
| regression 2 | 21/2 | 21/2 | Passed |
| regression 3 | None | None | Passed |
| regression 4 | 0 | None | Failed |
| regression 5 | 7/2 | 7/2 | Passed |
| regression 6 | 5/2 | 5/2 | Passed |
| regression 7 | 9 | 10 | Failed |
| regression 8 | 7 | 7 | Passed |
| variable group balance | 5/2 | 5/2 | Passed |
SHA-256 / 37d64c35d3f30027991be967403e2250db343085cc2e25872df77467dc8aaf30
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
from collections import Counter, defaultdict
import math
import itertools
N = 1
observations = []
def solve(rows):
groups={}
for label,error in rows:
if error is None: error=1
groups.setdefault(label,[]).append(error)
if not groups: return None
means=[Fraction(sum(e*e for e in values),len(values)) for values in groups.values()]
return str(sum(means)/len(means))
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([('a', 1), ('a', 2), ('b', 4)],)), '37/4')
check('regression 2', solve(*([('a', 1), ('a', 3), ('b', 4)],)), '21/2')
check('regression 3', solve(*([],)), None)
check('regression 4', solve(*([('a', None), ('b', None)],)), None)
check('regression 5', solve(*([('a', 0), ('a', 2), ('b', -3), ('b', 1)],)), '7/2')
check('regression 6', solve(*([('a', 1), ('b', 2), ('b', 2), ('b', 2)],)), '5/2')
check('regression 7', solve(*([('a', None), ('a', 2), ('b', 4)],)), '10')
check('regression 8', solve(*([('A', 1), ('a', 4), ('B', 2)],)), '7')
check("variable group balance",solve([("a",N),("a",-N),("b",2*N)]),str(Fraction(5*N*N,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 |
|---|---|---|---|
| regression 1 | 37/4 | 37/4 | Passed |
| regression 2 | 21/2 | 21/2 | Passed |
| regression 3 | None | None | Passed |
| regression 4 | 1 | None | Failed |
| regression 5 | 7/2 | 7/2 | Passed |
| regression 6 | 5/2 | 5/2 | Passed |
| regression 7 | 37/4 | 10 | Failed |
| regression 8 | 7 | 7 | Passed |
| variable group balance | 5/2 | 5/2 | Passed |
SHA-256 / a187b3bb8f7f19c45ccab91b1b1f4da63c6b15b3185143d3e9c63d3c77d70cc0
HELD IN THE MEMBER ARCHIVE
The verified repair and its recorded checks are member-only.
This mechanism has 9 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
Small offline integer/rational inputs only; no performance, statistical inference, or production-library conformance claim. 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 2026-09-29T14:39:14.981710+00:00.
Case digest / bdcfa8e3d5672dfef454abb2abb4c6e2167ecb854673a81b8159cb2e9aa1a899