TensorLy: Tensor Learning in Python

Abstract: Tensors are higher-order extensions of matrices. While matrix methods form the cornerstone of machine learning and data analysis, tensor methods have been gaining increasing traction. However, software support for tensor operations is not on the same footing. In order to bridge this gap, we have developed \emph{TensorLy}, a high-level API for tensor methods and deep tensorized neural networks in Python. TensorLy aims to follow the same standards adopted by the main projects of the Python scientific community, and seamlessly integrates with them. Its BSD license makes it suitable for both academic and commercial applications. TensorLy's backend system allows users to perform computations with NumPy, MXNet, PyTorch, TensorFlow and CuPy. They can be scaled on multiple CPU or GPU machines. In addition, using the deep-learning frameworks as backend allows users to easily design and train deep tensorized neural networks. TensorLy is available at https://github.com/tensorly/tensorly

• The paper introduces TensorLy, a Python library that simplifies advanced tensor operations through state-of-the-art decompositions and regression methods.
• It supports multiple backends including NumPy, MXNet, PyTorch, TensorFlow, and CuPy, ensuring efficient computation on both CPU and GPU platforms.
• Comprehensive documentation with 97% test coverage and robust performance on large tensor datasets underscores its reliability and broad applicability.

Overview of "TensorLy: Tensor Learning in Python"

The paper "TensorLy: Tensor Learning in Python" presents an in-depth discussion on TensorLy, a comprehensive library developed to support tensor manipulations and computations within the Python programming ecosystem. Authored by Jean Kossaifi, Yannis Panagakis, Anima Anandkumar, and Maja Pantic, the paper addresses the increasing prominence of tensor methods in machine learning and data analysis, alongside the existing gap in software support for tensor operations, especially in comparison to matrix methods.

TensorLy is designed to simplify the application of tensor methodologies by offering a high-level API facilitating various tensor operations, including core tensor algebra, decomposition, and regression methods. Its capability extends to the training and designing of deep tensorized neural networks. This is particularly valuable given the richness of tensor applications in areas such as psychometrics, quantum mechanics, signal processing, and more recently, machine learning, driven by the advent of large-scale, multi-dimensional datasets that naturally fit into the tensor framework.

Core Contributions of TensorLy

The paper delineates several key contributions provided by TensorLy:

1. State-of-the-Art Tensor Methods: TensorLy incorporates advanced tensor tasks such as CP and Tucker decompositions, non-negative decompositions, robust tensor PCA, and low-rank tensor regression, which are pivotal for extensive tensor applications across various domains.
2. Flexible Backend System: An innovative feature of TensorLy is its support for multiple backend systems including NumPy, MXNet, PyTorch, TensorFlow, and CuPy, which allows the ease of tensor computations across different hardware configurations, leveraging CPU and GPU capabilities. This flexibility also integrates tensor methods seamlessly with popular deep-learning frameworks.
3. Open Source and Licensing: TensorLy is released under the BSD license, ensuring its applicability to both academic and commercial settings, encouraging widespread adoption and contribution from the community. The library's reliance primarily on NumPy and SciPy ensures a stable base of fundamental operations with a high degree of compatibility.
4. Comprehensive Documentation and Testing: Emphasizing reliability and user-friendliness, the TensorLy library is well-documented and extensively tested, with a coverage of 97%, which facilitates a smooth experience for researchers and developers.

Performance Evaluation

Performance tests indicate that TensorLy is competitive with other existing tensor libraries, owing to its optimized method formulations and efficient implementation strategies. The experimental validations, performed on substantial tensor datasets (500x500x500), demonstrate TensorLy's capability to execute tensor decompositions swiftly and effectively on high-performance computational resources. Moreover, it reveals the advantageous performance enhancements offered by GPU-backed backends, crucial for tensor operations at scale.

Significance and Future Directions

The availability of TensorLy marks a significant advancement in making tensor methodologies more accessible and integrated into the Python scientific computing landscape. Its role is particularly consequential in machine learning contexts, where expanding the utilization of tensor methods could lead to improved modeling capacities and enhanced understanding of complex data structures.

Looking ahead, TensorLy’s development roadmap includes extending its method library to cover additional sophisticated techniques such as PARAFAC2 and DEDICOM. Other potential research directions involve refining performance through developments in BLAS primitives, offering more computationally efficient operations.

In summary, the introduction of TensorLy provides a robust and versatile toolset for researchers focused on multi-dimensional data analysis and serves as a substantial contribution to computational frameworks elevating tensor-based machine learning strategies.