tensorized

Tensorized refers to the process or approach of representing complex data structures, models, or computations using tensor formats. Tensors are multi-dimensional arrays that generalize scalars (zero-dimensional), vectors (one-dimensional), and matrices (two-dimensional) to higher dimensions. The tensorized approach aims to exploit the inherent structure and redundancies within data to achieve more efficient storage, computation, and analysis.

In various fields such as machine learning, signal processing, and scientific computing, tensorization involves transforming data or models into tensor representations. This often enables the application of tensor decomposition techniques, such as CANDECOMP/PARAFAC, Tucker, or Tensor Train decompositions, which break down high-dimensional tensors into smaller, more manageable components. These decompositions can reduce computational costs, improve interpretability, and enable the handling of larger datasets.

Tensorized models are widely used in neural network architectures to compress large models, enhance training efficiency, and facilitate scalable learning. For example, tensorized neural networks incorporate tensor algebra to replace traditional weight matrices with tensor formats, leading to parameters compression without significant loss of accuracy.

Overall, the concept of tensorized encapsulates the idea of leveraging multi-dimensional algebra to optimize data representation and processing, making it a vital component of modern computational techniques in data science and engineering.