Concepts

Understanding these core concepts will help you use omeco effectively.

Overview

Tensor network contraction is a fundamental operation in many scientific and machine learning applications. This section explains:

• What tensor networks are and why they matter
• Why contraction order makes an exponential difference
• How to interpret complexity metrics

Topics

• Tensor Networks - Einstein summation and tensor operations
• Contraction Order Problem - Why order matters
• Complexity Metrics - Understanding tc, sc, and rwc

Quick Summary

The Problem: Contracting N tensors can be done in many orders, with costs differing exponentially.

The Solution: Heuristic algorithms find near-optimal orders in polynomial time.

The Trade-off: Time vs quality - greedy is fast, simulated annealing is better.