---
title: "All-reduce collective mathematical notation"
description: "All-reduce collective is a recurring research-paper notation family. Combines equal-shaped values from every rank with a reduction and returns the…"
canonical_url: "https://fanout.sh/labs/math-decoder/symbol/all-reduce"
md_url: "https://fanout.sh/labs/math-decoder/symbol/all-reduce.md"
last_updated: "2026-08-09"
access: "public"
---

# All-reduce collective mathematical notation

All-reduce collective is a recurring research-paper notation family. Combines equal-shaped values from every rank with a reduction and returns the…

## Public overview

All-reduce collective is a recurring research-paper notation family. Combines equal-shaped values from every rank with a reduction and returns the identical reduced result to every rank.

All-reduce collective: Combines equal-shaped values from every rank with a reduction and returns the identical reduced result to every rank. Example: Sum or average gradients across ranks and give the result back to each worker.

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