Rust Tensor Einsum

A minimal, standalone Rust implementation of Einstein Summation (einsum) for tensor operations, designed for educational and experimental purposes.

This library provides a Tensor struct and a generalized einsum function that allows for concise expression of tensor contractions, mimicking the behavior of NumPy's einsum.

Features

• purely safe Rust (std only, no external dependencies).
• Support for arbitrary rank tensors.
• String-based einsum notation (e.g., "ij,jk->ik").
• Helper methods for tensor creation and CSV export.

Theoretical Motivation

This implementation explores the correspondence between Tensor Contraction and Cut Elimination in logic (specifically within the context of Categorical Semantics and Linear Logic).

• Transitivity as Contraction: The composition of relations $R(x, y)$ and $S(y, z)$ to form $T(x, z)$ via $\exists y . (R(x, y) \land S(y, z))$ is computationally equivalent to matrix multiplication (or tensor contraction along index $y$).
• Cut Elimination: In proof theory, eliminating a "Cut" (an intermediate lemma or concept) corresponds to contracting the shared index between two tensors representing the premises.

This library serves as a computational playground to verify these structural correspondences using simple tensor operations.

Usage

You can run the included demo to see the tensor operations in action, including examples of:

1. Transitivity: Matrix multiplication representing logical value propagation.
2. Syllogism: Modeling logical cuts as tensor contractions.
3. Contextual Inference: Handling multi-dimensional contexts in reasoning.

cargo run --example demo

Example Code

use rust_tensor_einsum::Tensor;

let a = Tensor::from_vec2(vec![vec![1.0, 2.0], vec![3.0, 4.0]]);
let b = Tensor::from_vec2(vec![vec![0.0, 1.0], vec![1.0, 0.0]]);

// Matrix multiplication: C_ik = sum_j A_ij * B_jk
let c = Tensor::einsum("ij,jk->ik", &[&a, &b]);
c.print_tensor();

License

MIT