FA-14191 / Numerical aggregation / Open access
Group balanced squared loss: All observations receive equal weight instead of equal total group weight. · case 01
The reduction disagrees with its explicit aggregation oracle.
ROOT CAUSE
All observations receive equal weight instead of equal total group weight.
VERIFIED REPAIR
Preserve the group balanced squared loss contract at the identified reduction decision.
Unsuccessful approach: Dividing already normalized group means by row count double-normalizes large populations.
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: continue
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(Fraction(sum(e*e for values in groups.values() for e in values),sum(map(len,groups.values()))))
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 | 7 | 37/4 | Failed |
| regression 2 | 26/3 | 21/2 | Failed |
| regression 3 | None | None | Passed |
| regression 4 | None | None | Passed |
| regression 5 | 7/2 | 7/2 | Passed |
| regression 6 | 13/4 | 5/2 | Failed |
| regression 7 | 10 | 10 | Passed |
| regression 8 | 7 | 7 | Passed |
| variable group balance | 2 | 5/2 | Failed |
SHA-256 / 8cec481cbe8c8576cb215f601729ea287aa27bed903d87b1a406ffa48450df74
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: continue
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)/sum(map(len,groups.values())))
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 | 37/6 | 37/4 | Failed |
| regression 2 | 7 | 21/2 | Failed |
| regression 3 | None | None | Passed |
| regression 4 | None | None | Passed |
| regression 5 | 7/4 | 7/2 | Failed |
| regression 6 | 5/4 | 5/2 | Failed |
| regression 7 | 10 | 10 | Passed |
| regression 8 | 7 | 7 | Passed |
| variable group balance | 5/3 | 5/2 | Failed |
SHA-256 / 0daff24757fc23c6a7d67c3f4e7478367daab0a509d62d910841c1dd7a76c0ca
3 / The verified repair
Exit 0"""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: continue
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 | None | None | Passed |
| regression 5 | 7/2 | 7/2 | Passed |
| regression 6 | 5/2 | 5/2 | Passed |
| regression 7 | 10 | 10 | Passed |
| regression 8 | 7 | 7 | Passed |
| variable group balance | 5/2 | 5/2 | Passed |
SHA-256 / 37d21a2cc900138bb57366e9a3e5fcf9a8544a6c56d61385583ab74a4b2e6dd8
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 2026-09-29T14:39:14.435913+00:00.
Case digest / 2fd84d093b7e9042f08ac358b120b60b3cbb37f0031fbcecc2474ef3ddc50e06