Deep learning frameworks have often focused on either usability or speed, but not both. PyTorch is a machine learning library that shows that these two goals are in fact compatible: it provides an imperative and Pythonic programming style that supports code as a model, makes debugging easy and is consistent with other popular scientific computing libraries, while remaining efficient and supporting hardware accelerators such as GPUs. 
In this paper, we detail the principles that drove the implementation of PyTorch and how they are reflected in its architecture. We emphasize that every aspect of PyTorch is a regular Python program under the full control of its user. We also explain how the careful and pragmatic implementation of the key components of its runtime enables them to work together to achieve compelling performance. 
We demonstrate the efficiency of individual subsystems, as well as the overall speed of PyTorch on several common benchmarks.

PyTorch: An Imperative Style, High-Performance Deep Learning Library

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

From the Publisher: 
The accessible presentation of this book gives both a general view of the entire computer vision enterprise and also offers sufficient detail to be able to build useful applications. Users learn techniques that have proven to be useful by first-hand experience and a wide range of mathematical methods. A CD-ROM with every copy of the text contains source code for programming practice, color images, and illustrative movies. Comprehensive and up-to-date, this book includes essential topics that either reflect practical significance or are of theoretical importance. Topics are discussed in substantial and increasing depth. Application surveys describe numerous important application areas such as image based rendering and digital libraries. Many important algorithms broken down and illustrated in pseudo code. Appropriate for use by engineers as a comprehensive reference to the computer vision enterprise.

Computer vision : a modern approach = 计算机视觉 : 一种现代的方法

We introduce a new family of deep neural network models. Instead of specifying a discrete sequence of hidden layers, we parameterize the derivative of the hidden state using a neural network. The output of the network is computed using a black-box differential equation solver. These continuous-depth models have constant memory cost, adapt their evaluation strategy to each input, and can explicitly trade numerical precision for speed. We demonstrate these properties in continuous-depth residual networks and continuous-time latent variable models. We also construct continuous normalizing flows, a generative model that can train by maximum likelihood, without partitioning or ordering the data dimensions. For training, we show how to scalably backpropagate through any ODE solver, without access to its internal operations. This allows end-to-end training of ODEs within larger models.

/pdf/neural-ordinary-differential-equations-14lrofzsgs.pdf

Neural ordinary differential equations

Neural Ordinary Differential Equations

Derivatives, mostly in the form of gradients and Hessians, are ubiquitous in machine learning. Automatic differentiation (AD), also called algorithmic differentiation or simply "autodiff", is a family of techniques similar to but more general than backpropagation for efficiently and accurately evaluating derivatives of numeric functions expressed as computer programs. AD is a small but established field with applications in areas including computational fluid dynamics, atmospheric sciences, and engineering design optimization. Until very recently, the fields of machine learning and AD have largely been unaware of each other and, in some cases, have independently discovered each other's results. Despite its relevance, general-purpose AD has been missing from the machine learning toolbox, a situation slowly changing with its ongoing adoption under the names "dynamic computational graphs" and "differentiable programming". We survey the intersection of AD and machine learning, cover applications where AD has direct relevance, and address the main implementation techniques. By precisely defining the main differentiation techniques and their interrelationships, we aim to bring clarity to the usage of the terms "autodiff", "automatic differentiation", and "symbolic differentiation" as these are encountered more and more in machine learning settings.

Automatic differentiation in machine learning: a survey

Derivatives, mostly in the form of gradients and Hessians, are ubiquitous in machine learning. Automatic differentiation (AD), also called algorithmic differentiation or simply "auto-diff", is a family of techniques similar to but more general than backpropagation for efficiently and accurately evaluating derivatives of numeric functions expressed as computer programs. AD is a small but established field with applications in areas including computational uid dynamics, atmospheric sciences, and engineering design optimization. Until very recently, the fields of machine learning and AD have largely been unaware of each other and, in some cases, have independently discovered each other's results. Despite its relevance, general-purpose AD has been missing from the machine learning toolbox, a situation slowly changing with its ongoing adoption under the names "dynamic computational graphs" and "differentiable programming". We survey the intersection of AD and machine learning, cover applications where AD has direct relevance, and address the main implementation techniques. By precisely defining the main differentiation techniques and their interrelationships, we aim to bring clarity to the usage of the terms "autodiff", "automatic differentiation", and "symbolic differentiation" as these are encountered more and more in machine learning settings.

/pdf/automatic-differentiation-in-machine-learning-a-survey-4s77ht2sqh.pdf

We describe a simple, low-level approach for embedding probabilistic programming in a deep learning ecosystem. In particular, we distill probabilistic programming down to a single abstraction—the random variable. Our lightweight implementation in TensorFlow enables numerous applications: a model-parallel variational auto-encoder (VAE) with 2nd-generation tensor processing units (TPUv2s); a data-parallel autoregressive model (Image Transformer) with TPUv2s; and multi-GPU No-U-Turn Sampler (NUTS). For both a state-of-the-art VAE on 64x64 ImageNet and Image Transformer on 256x256 CelebA-HQ, our approach achieves an optimal linear speedup from 1 to 256 TPUv2 chips. With NUTS, we see a 100x speedup on GPUs over Stan and 37x over PyMC3.

/pdf/simple-distributed-and-accelerated-probabilistic-programming-2a892k4mb9.pdf

Simple, Distributed, and Accelerated Probabilistic Programming

We introduce inference metaprogramming for probabilistic programming languages, including new language constructs, a formalism, and the rst demonstration of e ectiveness in practice. Instead of relying on rigid black-box inference algorithms hard-coded into the language implementation as in previous probabilistic programming languages, infer- ence metaprogramming enables developers to 1) dynamically decompose inference problems into subproblems, 2) apply in- ference tactics to subproblems, 3) alternate between incorpo- rating new data and performing inference over existing data, and 4) explore multiple execution traces of the probabilis- tic program at once. Implemented tactics include gradient- based optimization, Markov chain Monte Carlo, variational inference, and sequental Monte Carlo techniques. Inference metaprogramming enables the concise expression of proba- bilistic models and inference algorithms across diverse elds, such as computer vision, data science, and robotics, within a single probabilistic programming language.

Probabilistic programming with programmable inference

We develop a programming model built on the idea that the basic computational elements are autonomous machines interconnected by shared cells through which they communicate. Each machine continuously examines the cells it is interested in, and adds information to some based on deductions it can make from information from the others. This model makes it easy to smoothly combine expressionoriented and constraint-based programming; it also easily accommodates implicit incremental distributed search in ordinary programs. This work builds on the original research of Guy Lewis Steele Jr. [19] and was developed more recently with the help of Chris Hanson. This document, together with complete supporting code, is available as an MIT CSAIL Technical Report via http://dspace.mit.edu.

/pdf/the-art-of-the-propagator-58v00eg0he.pdf

Alexey Radul

Papers

Automatic differentiation in machine learning: a survey

Automatic differentiation in machine learning: a survey

Simple, Distributed, and Accelerated Probabilistic Programming

Probabilistic programming with programmable inference

The Art of the Propagator