Module tensor_networks 

Tensor Networks

Efficient representations of high-dimensional tensors using network decompositions.

Background

High-dimensional tensors suffer from the “curse of dimensionality” - a tensor of order d with mode sizes n has O(n^d) elements. Tensor networks provide compressed representations with controllable approximation error.

Decompositions

• Tensor Train (TT): A[i1,…,id] = G1[i1] × G2[i2] × … × Gd[id]
• Tucker: Core tensor with factor matrices
• CP (CANDECOMP/PARAFAC): Sum of rank-1 tensors

Applications

• Quantum-inspired algorithms
• High-dimensional integration
• Attention mechanism compression
• Scientific computing

Structs

CPConfig

CP decomposition configuration

CPDecomposition

CP decomposition result

DenseTensor

Dense tensor for input/output

NetworkContraction

Optimal contraction order finder

TTCore

A single TT-core: 3D tensor of shape (rank_left, mode_size, rank_right)

TensorNetwork

Tensor network for contraction operations

TensorNode

A node in a tensor network

TensorTrain

Tensor Train representation

TensorTrainConfig

Tensor Train configuration

TuckerConfig

Tucker decomposition configuration

TuckerDecomposition

Tucker decomposition of a tensor