FA-99246 / Distributed training aggregation / Open access

Disjoint gradient contributions are averaged instead of summed · case 01

Disjoint gradient contributions are averaged instead of summed.

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

ROOT CAUSE

Each worker owns a disjoint parameter slice, so their partial gradients are additive contributions.

THE FAILURE

Each worker owns a disjoint parameter slice, so their partial gradients are additive contributions.

Unsuccessful approach: Taking only the first contribution loses later shard contributions.

Case contract

Given equal-length partial gradient vectors for one parameter block, return their elementwise sum; empty input returns [].

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(parts):
    return [sum(v[j] for v in parts)/len(parts) for j in range(len(parts[0]))] if parts else []
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('two workers',solve([[N,2],[3*N,4]]),[4*N,6])
check('negative cancellation',solve([[N],[-N],[2*N]]),[2*N])
check('empty block',solve([]),[])
check('single worker',solve([[N,0]]),[N,0])
check('three partials',solve([[1],[2],[N]]),[N+3])
check('signed coordinates',solve([[-N,2*N],[N,-N]]),[0,N])
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 workers	`[2.0, 3.0]`	`[4, 6]`	Failed
negative cancellation	`[0.6666666666666666]`	`[2]`	Failed
empty block	`[]`	`[]`	Passed
single worker	`[1.0, 0.0]`	`[1, 0]`	Passed
three partials	`[1.3333333333333333]`	`[4]`	Failed
signed coordinates	`[0.0, 0.5]`	`[0, 1]`	Failed

SHA-256 / 647e6cefd913be653eddd40fe879325c2b5bdd8f0dea094588c2e82471b2bfbc

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(parts):
    return list(parts[0]) if parts else []
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('two workers',solve([[N,2],[3*N,4]]),[4*N,6])
check('negative cancellation',solve([[N],[-N],[2*N]]),[2*N])
check('empty block',solve([]),[])
check('single worker',solve([[N,0]]),[N,0])
check('three partials',solve([[1],[2],[N]]),[N+3])
check('signed coordinates',solve([[-N,2*N],[N,-N]]),[0,N])
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 workers	`[1, 2]`	`[4, 6]`	Failed
negative cancellation	`[1]`	`[2]`	Failed
empty block	`[]`	`[]`	Passed
single worker	`[1, 0]`	`[1, 0]`	Passed
three partials	`[1]`	`[4]`	Failed
signed coordinates	`[-1, 2]`	`[0, 1]`	Failed

SHA-256 / a0c5414c70ec0582d3a4d1f5c1c3fe82e3c0bf5aa199aef3f1f866939501f3c9

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.

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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 2026-09-30T16:48:22.178335+00:00.

Case digest / 5d017652ac7898b1a2b0e3ce79f6cde4d2ea720a841c6b9acecdb5188f08ac4e