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Array programming provides a powerful, compact, expressive syntax for accessing, manipulating, and operating on data in vectors, matrices, and higher-dimensional arrays. NumPy is the primary array programming library for the Python language. It plays an essential role in research analysis pipelines in fields as diverse as physics, chemistry, astronomy, geoscience, biology, psychology, material science, engineering, finance, and economics. For example, in astronomy, NumPy was an important part of the software stack used in the discovery of gravitational waves and the first imaging of a black hole. Here we show how a few fundamental array concepts lead to a simple and powerful programming paradigm for organizing, exploring, and analyzing scientific data. NumPy is the foundation upon which the entire scientific Python universe is constructed. It is so pervasive that several projects, targeting audiences with specialized needs, have developed their own NumPy-like interfaces and array objects. Because of its central position in the ecosystem, NumPy increasingly plays the role of an interoperability layer between these new array computation libraries.
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Derivatives play a critical role in computational statistics, examples being Bayesian inference using Hamiltonian Monte Carlo sampling and the training of neural networks. Automatic differentiation is a powerful tool to automate the calculation of derivatives and is preferable to more traditional methods, especially when differentiating complex algorithms and mathematical functions. The implementation of automatic differentiation however requires some care to insure efficiency. Modern differentiation packages deploy a broad range of computational techniques to improve applicability, run time, and memory management. Among these techniques are operation overloading, region based memory, and expression templates. There also exist several mathematical techniques which can yield high performance gains when applied to complex algorithms. For example, semi-analytical derivatives can reduce by orders of magnitude the runtime required to numerically solve and differentiate an algebraic equation. Open problems include the extension of current packages to provide more specialized routines, and efficient methods to perform higher-order differentiation.
Automatic differentiation is a set of techniques to efficiently and accurately compute the derivative of a function represented by a computer program. Existing C++ libraries for automatic differentiation (e.g. Adept, Stan Math Library), however, exhibit large memory consumptions and runtime performance issues. This paper introduces FastAD, a new C++ template library for automatic differentiation, that overcomes all of these challenges in existing libraries by using vectorization, simpler memory management using a fully expression-template-based design, and other compile-time optimizations to remove some run-time overhead. Benchmarks show that FastAD performs 2-10 times faster than Adept and 2-19 times faster than Stan across various test cases including a few real-world examples.
In (Franceschi et al., 2018) we proposed a unified mathematical framework, grounded on bilevel programming, that encompasses gradient-based hyperparameter optimization and meta-learning. We formulated an approximate version of the problem where the inner objective is solved iteratively, and gave sufficient conditions ensuring convergence to the exact problem. In this work we show how to optimize learning rates, automatically weight the loss of single examples and learn hyper-representations with Far-HO, a software package based on the popular deep learning framework TensorFlow that allows to seamlessly tackle both HO and ML problems.
We introduce two new packages, Nemo and Hecke, written in the Julia programming language for computer algebra and number theory. We demonstrate that high performance generic algorithms can be implemented in Julia, without the need to resort to a low-level C implementation. For specialised algorithms, we use Julias efficient native C interface to wrap existing C/C++ libraries such as Flint, Arb, Antic and Singular. We give examples of how to use Hecke and Nemo and discuss some algorithms that we have implemented to provide high performance basic arithmetic.
EagerPy is a Python framework that lets you write code that automatically works natively with PyTorch, TensorFlow, JAX, and NumPy. Library developers no longer need to choose between supporting just one of these frameworks or reimplementing the library for each framework and dealing with code duplication. Users of such libraries can more easily switch frameworks without being locked in by a specific 3rd party library. Beyond multi-framework support, EagerPy also brings comprehensive type annotations and consistent support for method chaining to any framework. The latest documentation is available online at https://eagerpy.jonasrauber.de and the code can be found on GitHub at https://github.com/jonasrauber/eagerpy.
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