Introduction

omeinsum-rs is a Rust library for efficient tensor network contractions supporting both standard and tropical (semiring) algebras. It provides a unified interface for einsum operations with automatic contraction order optimization.

What is Einsum?

Einstein summation (einsum) is a compact notation for expressing tensor operations. Instead of writing explicit loops, you specify index labels:

C[i,k] = Σ_j A[i,j] × B[j,k]    # Matrix multiplication

In einsum notation: ij,jk->ik

What are Tropical Algebras?

Tropical algebras replace standard arithmetic with alternative operations:

Key Features

• Multiple Algebras: Standard arithmetic, MaxPlus, MinPlus, MaxMul
• Contraction Optimization: Uses omeco for optimal contraction order
• Backpropagation Support: Argmax tracking for tropical gradient computation
• Flexible Tensors: Stride-based views with zero-copy permute/reshape
• Backend Abstraction: CPU now, GPU planned

Example

#![allow(unused)]
fn main() {
use omeinsum::{einsum, Tensor, Cpu};
use omeinsum::algebra::MaxPlus;

// Create tensors
let a = Tensor::<f32, Cpu>::from_data(&[1.0, 2.0, 3.0, 4.0], &[2, 2]);
let b = Tensor::<f32, Cpu>::from_data(&[1.0, 2.0, 3.0, 4.0], &[2, 2]);

// Tropical matrix multiplication: C[i,k] = max_j (A[i,j] + B[j,k])
let c = einsum::<MaxPlus<f32>, _, _>(&[&a, &b], &[&[0, 1], &[1, 2]], &[0, 2]);
}

Relationship to OMEinsum.jl

This library is inspired by OMEinsum.jl, bringing its powerful tensor contraction capabilities to Rust with support for tropical algebras from tropical-gemm.