FA-99301 / Distributed training aggregation / Open access

Reduce-scatter gives every rank the first slice · case 01

Reduce-scatter gives every rank the first slice.

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

ROOT CAUSE

After summing gradients, each rank should own its indexed equal-width segment.

THE FAILURE

After summing gradients, each rank should own its indexed equal-width segment.

Unsuccessful approach: Offsetting by rank while returning too short a slice truncates later ownership blocks.

Case contract

Sum equal-length worker vectors, then return width values beginning at rank*width; invalid/empty slices return [].

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, rank, width):
    s=[sum(v[j] for v in parts) for j in range(len(parts[0]))] if parts else []; return s[:width]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
p=[[N,2,3,4],[10,20,30,40]]
check('rank one',solve(p,1,2),[33,44])
check('rank zero',solve(p,0,2),[N+10,22])
check('last short',solve(p,1,3),[44])
check('empty input',solve([],0,2),[])
check('zero width',solve(p,1,0),[])
check('singleton block',solve([[N,2]],0,1),[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
rank one	`[11, 22]`	`[33, 44]`	Failed
rank zero	`[11, 22]`	`[11, 22]`	Passed
last short	`[11, 22, 33]`	`[44]`	Failed
empty input	`[]`	`[]`	Passed
zero width	`[]`	`[]`	Passed
singleton block	`[1]`	`[1]`	Passed

SHA-256 / 22cf32792ed557715f2ff70b468ea503bc3ddae4c073827786a32a8d7adf79c3

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(parts, rank, width):
    s=[sum(v[j] for v in parts) for j in range(len(parts[0]))] if parts else []; return s[rank:rank+width]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
p=[[N,2,3,4],[10,20,30,40]]
check('rank one',solve(p,1,2),[33,44])
check('rank zero',solve(p,0,2),[N+10,22])
check('last short',solve(p,1,3),[44])
check('empty input',solve([],0,2),[])
check('zero width',solve(p,1,0),[])
check('singleton block',solve([[N,2]],0,1),[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
rank one	`[22, 33]`	`[33, 44]`	Failed
rank zero	`[11, 22]`	`[11, 22]`	Passed
last short	`[22, 33, 44]`	`[44]`	Failed
empty input	`[]`	`[]`	Passed
zero width	`[]`	`[]`	Passed
singleton block	`[1]`	`[1]`	Passed

SHA-256 / 727af68e7734a81880eb734f371f3e4c7252f76611564c07d8230c768a34d11d

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 2026-09-30T16:48:22.633689+00:00.

Case digest / ae49bfba080a0af8c8413ac1f7e62a9c26bf8161ad49a783c5647ad2d4643e1d