FA-14201 / Numerical aggregation / Open access

Group balanced squared loss: Within-group loss totals are not normalized by group sizes. · case 01

The reduction disagrees with its explicit aggregation oracle.

Verified by executionVariant 1 · 9 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Within-group loss totals are not normalized by group sizes.

VERIFIED REPAIR

Preserve the group balanced squared loss contract at the identified reduction decision.

Unsuccessful approach: Dividing each total by number of groups uses the wrong inner population.

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)) 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	`21/2`	`37/4`	Failed
regression 2	`13`	`21/2`	Failed
regression 3	`None`	`None`	Passed
regression 4	`None`	`None`	Passed
regression 5	`7`	`7/2`	Failed
regression 6	`13/2`	`5/2`	Failed
regression 7	`10`	`10`	Passed
regression 8	`7`	`7`	Passed
variable group balance	`3`	`5/2`	Failed

SHA-256 / c6a0d048cd68b2c0dfcf66fb4b66057350348a2cec94d30c40115948e8f6e868

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(groups)) 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	`21/4`	`37/4`	Failed
regression 2	`13/2`	`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	`5`	`10`	Failed
regression 8	`7/3`	`7`	Failed
variable group balance	`3/2`	`5/2`	Failed

SHA-256 / 7bbae5097c065a599d018d4b40efe509c6f70cb8404a6a52930d97c4b6de8e47

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 2026-09-29T14:39:14.444413+00:00.

Case digest / d2d551174bef7a5888ab889dbb3010015994ee23b95f5d0b9a0ee453fc79fe90