---
title: "einexpr"
description: "An experimental Python library for named tensor dimensions and Einstein-style array programming."
pubDate: 2022-06-08
updatedDate: 2026-08-11
visibility: "public"
category: "project"
tags: ["python", "machine-learning", "tensors", "numpy"]
homepage:
  featured: false
project:
  period: "2022–2024"
  status: "Experimental · archived"
  repository: "https://github.com/IsaacBreen/einexpr"
  package: "https://pypi.org/project/einexpr/"
---

`einexpr` is a Python framework I wrote for working with named tensor dimensions. You can write the dimension names directly on arrays and use them to align, contract, rename and group dimensions.

```python
import einexpr as ei

a = ei.array([1, 2])
b = ei.array([3, 4])
X = ei.array([[1, 2], [3, 4]])
Y = ei.array([[5, 6], [7, 8]])

dot = (a['i'] * b['i'])['']
outer = (a['i'] * b['j'])['i j']

product = (X['i j'] * Y['j k'])['i k']
```

The names determine how dimensions line up and which ones are contracted. In the matrix product, `j` appears in both inputs and disappears from the result. The expression does not depend on `j` occupying a particular axis.

## Multi-head attention

Here is multi-head attention written both ways. PyTorch uses reshapes, transposes and axis numbers. `einexpr` names the dimensions on each array instead. `t->s` renames the key/value position before the contraction, and the result names say which dimensions remain.

<div data-einexpr-comparison-lab-slot></div>

The package also supported grouped dimensions. For example, `context['b t (h d)']` joins the head and per-head feature dimensions while keeping the grouping explicit in the expression.