FA-13826 / Numerical aggregation / Open access
Huber residual total: Negative tail residuals contribute negative loss. · case 01
The reduction disagrees with its explicit aggregation oracle.
ROOT CAUSE
Negative tail residuals contribute negative loss.
VERIFIED REPAIR
Preserve the huber residual total contract at the identified reduction decision.
Unsuccessful approach: Taking absolute value after subtracting the offset produces asymmetric losses.
Case contract
For integer residuals and nonnegative integer threshold delta, sum the convex Huber loss: e**2/2 inside threshold and delta*(abs(e)-delta/2) outside. Return exact Fraction string; this is a bounded loss reduction, not an optimizer.
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(errors, delta):
if not errors: return "0"
d=Fraction(delta)
total=Fraction(0)
for e in errors:
a=abs(e)
total+=Fraction(e*e,2) if a<=d else d*(e-d/2)
return str(total)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([2, 2, 4], 2)), '10')
check('regression 2', solve(*([0, 1, -1, 4, -4], 2)), '13')
check('regression 3', solve(*([], 2)), '0')
check('regression 4', solve(*([2, -2], 2)), '4')
check('regression 5', solve(*([1, -1, 3], 1)), '7/2')
check('regression 6', solve(*([-5, 0, 2], 3)), '25/2')
check('regression 7', solve(*([7, -2, 1], 0)), '0')
check('regression 8', solve(*([1, 2, 3], 4)), '7')
check("variable Huber tail",solve([N+2,-N-2],2),str(4*N+4))
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 | 10 | 10 | Passed |
| regression 2 | -3 | 13 | Failed |
| regression 3 | 0 | 0 | Passed |
| regression 4 | 4 | 4 | Passed |
| regression 5 | 7/2 | 7/2 | Passed |
| regression 6 | -35/2 | 25/2 | Failed |
| regression 7 | 0 | 0 | Passed |
| regression 8 | 7 | 7 | Passed |
| variable Huber tail | -4 | 8 | Failed |
SHA-256 / 2c7b64c4d68a4ccb43bdd793d96ffcc28ad9e46934737e82cbadcc02cac7df7f
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(errors, delta):
if not errors: return "0"
d=Fraction(delta)
total=Fraction(0)
for e in errors:
a=abs(e)
total+=Fraction(e*e,2) if a<=d else abs(d*(e-d/2))
return str(total)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([2, 2, 4], 2)), '10')
check('regression 2', solve(*([0, 1, -1, 4, -4], 2)), '13')
check('regression 3', solve(*([], 2)), '0')
check('regression 4', solve(*([2, -2], 2)), '4')
check('regression 5', solve(*([1, -1, 3], 1)), '7/2')
check('regression 6', solve(*([-5, 0, 2], 3)), '25/2')
check('regression 7', solve(*([7, -2, 1], 0)), '0')
check('regression 8', solve(*([1, 2, 3], 4)), '7')
check("variable Huber tail",solve([N+2,-N-2],2),str(4*N+4))
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 | 10 | 10 | Passed |
| regression 2 | 17 | 13 | Failed |
| regression 3 | 0 | 0 | Passed |
| regression 4 | 4 | 4 | Passed |
| regression 5 | 7/2 | 7/2 | Passed |
| regression 6 | 43/2 | 25/2 | Failed |
| regression 7 | 0 | 0 | Passed |
| regression 8 | 7 | 7 | Passed |
| variable Huber tail | 12 | 8 | Failed |
SHA-256 / d4ac3db8a98b4ca589eceb73550cfb7c9d7cca8caa64011d70eb8dabf83e0db8
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(errors, delta):
if not errors: return "0"
d=Fraction(delta)
total=Fraction(0)
for e in errors:
a=abs(e)
total+=Fraction(e*e,2) if a<=d else d*(a-d/2)
return str(total)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([2, 2, 4], 2)), '10')
check('regression 2', solve(*([0, 1, -1, 4, -4], 2)), '13')
check('regression 3', solve(*([], 2)), '0')
check('regression 4', solve(*([2, -2], 2)), '4')
check('regression 5', solve(*([1, -1, 3], 1)), '7/2')
check('regression 6', solve(*([-5, 0, 2], 3)), '25/2')
check('regression 7', solve(*([7, -2, 1], 0)), '0')
check('regression 8', solve(*([1, 2, 3], 4)), '7')
check("variable Huber tail",solve([N+2,-N-2],2),str(4*N+4))
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 | 10 | 10 | Passed |
| regression 2 | 13 | 13 | Passed |
| regression 3 | 0 | 0 | Passed |
| regression 4 | 4 | 4 | Passed |
| regression 5 | 7/2 | 7/2 | Passed |
| regression 6 | 25/2 | 25/2 | Passed |
| regression 7 | 0 | 0 | Passed |
| regression 8 | 7 | 7 | Passed |
| variable Huber tail | 8 | 8 | Passed |
SHA-256 / 78a8c2ac27d7f0b31f615e117198e611fa6bf184213587c0dee4eeb9201c804f
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 2026-09-29T14:39:10.968612+00:00.
Case digest / 0d512acfce488fdf1b90a8a975d0c7109fcdbbf66d30be23eff388634db68800