FA-99251 / Distributed training aggregation / Open access

Replica mean omits one received contribution from its denominator · case 01

Replica mean omits one received contribution from its denominator.

Verified by executionVariant 1 · 6 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The denominator is computed as one fewer than the number of received replicas.

THE FAILURE

The denominator is computed as one fewer than the number of received replicas.

Unsuccessful approach: Filtering zero-valued replicas removes valid contributions and biases the mean.

Case contract

Given a list of scalar replica gradients, return their arithmetic mean; empty input returns None.

Why this case matters

A toy distributed-training contract makes replica and shard contribution rules explicit without claiming framework compatibility or performance.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(values):
    return sum(values)/max(1,len(values)-1) if values else None
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('two replicas',solve([N,3*N]),2*N)
check('zero is a participant',solve([0,N]),N/2)
check('empty round',solve([]),None)
check('one replica',solve([N]),N)
check('three uneven values',solve([N,2*N,6*N]),3*N)
check('negative mean',solve([-N,N,2*N]),2*N/3)
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
two replicas	`4.0`	`2`	Failed
zero is a participant	`1.0`	`0.5`	Failed
empty round	`None`	`None`	Passed
one replica	`1.0`	`1`	Passed
three uneven values	`4.5`	`3`	Failed
negative mean	`1.0`	`0.6666666666666666`	Failed

SHA-256 / 41cfbf575fe876e97ac98273f50864ef22d3b8b9752cc1ca85587d6639d989a6

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(values):
    v=[x for x in values if x]; return sum(v)/len(v) if v else None
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('two replicas',solve([N,3*N]),2*N)
check('zero is a participant',solve([0,N]),N/2)
check('empty round',solve([]),None)
check('one replica',solve([N]),N)
check('three uneven values',solve([N,2*N,6*N]),3*N)
check('negative mean',solve([-N,N,2*N]),2*N/3)
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
two replicas	`2.0`	`2`	Passed
zero is a participant	`1.0`	`0.5`	Failed
empty round	`None`	`None`	Passed
one replica	`1.0`	`1`	Passed
three uneven values	`3.0`	`3`	Passed
negative mean	`0.6666666666666666`	`0.6666666666666666`	Passed

SHA-256 / 6aa293dbfa8d22c1b6c4b9b63e191c76d9e6db82141bde2122cab7de01f5a2b5

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 6 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.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

Member access is invitation-based. Sign in with your invited account to inspect the repair.

Verification & scope

Inputs are already materialized Python values from a fixed toy collective; no transport, failure recovery, optimizer state, or real model behavior is represented. 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 2026-09-30T16:48:22.178504+00:00.

Case digest / 3af444c1a9ae9daf17b7295d029bf60f0f540f285e158d6bd708857732f44dc7