---
title: "Column-parallel linear layer mathematical notation"
description: "Column-parallel linear layer is a recurring research-paper notation family. Partitions a linear layer's output dimension so each rank independently…"
canonical_url: "https://fanout.sh/labs/math-decoder/symbol/column-parallel-linear"
md_url: "https://fanout.sh/labs/math-decoder/symbol/column-parallel-linear.md"
last_updated: "2026-08-09"
access: "public"
---

# Column-parallel linear layer mathematical notation

Column-parallel linear layer is a recurring research-paper notation family. Partitions a linear layer's output dimension so each rank independently…

## Public overview

Column-parallel linear layer is a recurring research-paper notation family. Partitions a linear layer's output dimension so each rank independently produces a distinct output-feature shard.

Column-parallel linear layer: Partitions a linear layer's output dimension so each rank independently produces a distinct output-feature shard. Example: Each device computes different output features from the same input.

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