Tensornätverk

Tensornätverk, also known as Tensor Networks, are a class of mathematical tools used in physics and machine learning to represent and manipulate high-dimensional data. They provide a way to decompose large tensors into smaller, interconnected tensors, making computations more efficient and revealing underlying structures. The core idea is to leverage the properties of tensors, which are multidimensional arrays, to capture complex correlations and relationships within data.

In quantum physics, tensor networks are particularly useful for simulating quantum many-body systems. These systems often involve a vast number of particles, leading to exponentially large state vectors that are intractable to store and compute directly. Tensor networks offer a compressed representation of these states, allowing physicists to study phenomena like quantum entanglement and phase transitions. Different types of tensor networks, such as Matrix Product States (MPS) and Projected Entangled-Pair States (PEPS), are tailored for specific types of quantum systems and their dimensionality.

In the realm of machine learning, tensor networks are emerging as a powerful tool for deep learning. They can be used to build more expressive and efficient neural network architectures. For instance, tensor network layers can capture higher-order interactions between features more effectively than traditional layers. This can lead to improved performance in tasks such as image recognition, natural language processing, and recommendation systems, while potentially requiring fewer parameters and less computational power. The ability to efficiently represent and process large, high-dimensional data makes tensor networks a promising avenue for future advancements in both scientific computation and artificial intelligence.