FA-14226 / Numerical aggregation / Open access
Group balanced squared loss: Worst-group loss replaces the group average. · case 01
The reduction disagrees with its explicit aggregation oracle.
ROOT CAUSE
Worst-group loss replaces the group average.
THE FAILURE
Worst-group loss replaces the group average.
Unsuccessful approach: Best-group loss also does not average across observed groups.
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(max(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 | 16 | 37/4 | Failed |
| regression 2 | 16 | 21/2 | Failed |
| regression 3 | None | None | Passed |
| regression 4 | None | None | Passed |
| regression 5 | 5 | 7/2 | Failed |
| regression 6 | 4 | 5/2 | Failed |
| regression 7 | 16 | 10 | Failed |
| regression 8 | 16 | 7 | Failed |
| variable group balance | 4 | 5/2 | Failed |
SHA-256 / af90ae548c4d3e1ecf37733db2eba77c63ecbf8ccb5157d0c672d4aab4f18418
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(min(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 | 5/2 | 37/4 | Failed |
| regression 2 | 5 | 21/2 | Failed |
| regression 3 | None | None | Passed |
| regression 4 | None | None | Passed |
| regression 5 | 2 | 7/2 | Failed |
| regression 6 | 1 | 5/2 | Failed |
| regression 7 | 4 | 10 | Failed |
| regression 8 | 1 | 7 | Failed |
| variable group balance | 1 | 5/2 | Failed |
SHA-256 / 87641a2de577ce0da5d477c57919f84cadccd374b95c0fd81a0454117f9f76e4
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 / b6a9b6dc07ffcd112174de0e6da3e371e7ced8e52c01752eba317fc92fabda75