NumPy is a library for the Python programming language, adding support for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays. The predecessor of NumPy, Numeric, was originally created by Jim Hugunin with contributions from several other developers. In 2005, Travis Oliphant created NumPy by incorporating features of the competing Numarray into Numeric, with extensive modifications. NumPy is open-source software and has many contributors. NumPy is a NumFOCUS fiscally sponsored project.
Compute Unified Device Architecture (CUDA) is a parallel computing platform and application programming interface (API) that allows software to use certain types of graphics processing units (GPUs) for accelerated general-purpose processing, an approach called general-purpose computing on GPUs (GPGPU). CUDA API and its runtime: The CUDA API is an extension of the C programming language that adds the ability to specify thread-level parallelism in C and also to specify GPU device specific operations (like moving data between the CPU and the GPU). CUDA is a software layer that gives direct access to the GPU's virtual instruction set and parallel computational elements for the execution of compute kernels. In addition to drivers and runtime kernels, the CUDA platform includes compilers, libraries and developer tools to help programmers accelerate their applications.
SymPy is an open-source Python library for symbolic computation. It provides computer algebra capabilities either as a standalone application, as a library to other applications, or live on the web as SymPy Live or SymPy Gamma. SymPy is simple to install and to inspect because it is written entirely in Python with few dependencies. This ease of access combined with a simple and extensible code base in a well known language make SymPy a computer algebra system with a relatively low barrier to entry.
Cython is a superset of the programming language Python, which allows developers to write Python code that yields performance comparable to that of C.
The following tables provide a comparison of linear algebra software libraries, either specialized or general purpose libraries with significant linear algebra coverage.
Julia is a high-level, general-purpose dynamic programming language, most commonly used for numerical analysis and computational science. Distinctive aspects of Julia's design include a type system with parametric polymorphism and the use of multiple dispatch as a core programming paradigm, efficient garbage collection, and a just-in-time (JIT) compiler.
Numba is an open-source JIT compiler that translates a subset of Python and NumPy into fast machine code using LLVM, via the llvmlite Python package. It offers a range of options for parallelising Python code for CPUs and GPUs, often with only minor code changes.
Eclipse Deeplearning4j is a programming library written in Java for the Java virtual machine (JVM). It is a framework with wide support for deep learning algorithms. Deeplearning4j includes implementations of the restricted Boltzmann machine, deep belief net, deep autoencoder, stacked denoising autoencoder and recursive neural tensor network, word2vec, doc2vec, and GloVe. These algorithms all include distributed parallel versions that integrate with Apache Hadoop and Spark.
TensorFlow is a free and open-source software library for machine learning and artificial intelligence. It can be used across a range of tasks but has a particular focus on training and inference of deep neural networks.
The following table compares notable software frameworks, libraries and computer programs for deep learning.
Keras is an open-source library that provides a Python interface for artificial neural networks. Keras acts as an interface for the TensorFlow library.
spaCy is an open-source software library for advanced natural language processing, written in the programming languages Python and Cython. The library is published under the MIT license and its main developers are Matthew Honnibal and Ines Montani, the founders of the software company Explosion.
PyMC is a probabilistic programming language written in Python. It can be used for Bayesian statistical modeling and probabilistic machine learning.
Caffe is a deep learning framework, originally developed at University of California, Berkeley. It is open source, under a BSD license. It is written in C++, with a Python interface.
PyTorch is a machine learning library based on the Torch library, used for applications such as computer vision and natural language processing, originally developed by Meta AI and now part of the Linux Foundation umbrella. It is recognized as one of the two most popular machine learning libraries alongside TensorFlow, offering free and open-source software released under the modified BSD license. Although the Python interface is more polished and the primary focus of development, PyTorch also has a C++ interface.
ROCm is an Advanced Micro Devices (AMD) software stack for graphics processing unit (GPU) programming. ROCm spans several domains: general-purpose computing on graphics processing units (GPGPU), high performance computing (HPC), heterogeneous computing. It offers several programming models: HIP, OpenMP/Message Passing Interface (MPI), and OpenCL.
Differentiable programming is a programming paradigm in which a numeric computer program can be differentiated throughout via automatic differentiation. This allows for gradient-based optimization of parameters in the program, often via gradient descent, as well as other learning approaches that are based on higher order derivative information. Differentiable programming has found use in a wide variety of areas, particularly scientific computing and machine learning. One of the early proposals to adopt such a framework in a systematic fashion to improve upon learning algorithms was made by the Advanced Concepts Team at the European Space Agency in early 2016.
Mila - Quebec AI Institute is a research institute in Montreal, Quebec, focusing mainly on machine learning research. Approximately 1000 students and researchers and 100 faculty members, were part of Mila in 2022. Along with Alberta's Amii and Toronto's Vector Institute, Mila is part of the Pan-Canadian Artificial Intelligence Strategy.
CuPy is an open source library for GPU-accelerated computing with Python programming language, providing support for multi-dimensional arrays, sparse matrices, and a variety of numerical algorithms implemented on top of them. CuPy shares the same API set as NumPy and SciPy, allowing it to be a drop-in replacement to run NumPy/SciPy code on GPU. CuPy supports Nvidia CUDA GPU platform, and AMD ROCm GPU platform starting in v9.0.
