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This literate programming exercise will construct a simple 2-layer feed-forward neural network to compute the exclusive or, using symbolic differentiation to compute the gradients automatically. In total, about 500 lines of code, including comments. The only functional dependency is numpy. I highly recommend reading Chris Olah's Calculus on Computational Graphs: Backpropagation for more background on what this code is doing.

http://jimfleming.me/differentiation/main.htmlhttps://github.com/jimfleming/differentiation

Tags | differentiation tensorflow numpy |

Implementation | Python |

License | Public |

Platform | Windows Linux |

We aim to gradually expand this series by adding new articles and keep the content up to date with the latest releases of TensorFlow API. If you have suggestions on how to improve this series or find the explanations ambiguous, feel free to create an issue, send patches, or reach out by email. The most striking difference between TensorFlow and other numerical computation libraries such as NumPy is that operations in TensorFlow are symbolic. This is a powerful concept that allows TensorFlow to do all sort of things (e.g. automatic differentiation) that are not possible with imperative libraries such as NumPy. But it also comes at the cost of making it harder to grasp. Our attempt here is to demystify TensorFlow and provide some guidelines and best practices for more effective use of TensorFlow.

tensorflow neural-network deep-learning machine-learning ebookGorgonia is a library that helps facilitate machine learning in Go. Write and evaluate mathematical equations involving multidimensional arrays easily. If this sounds like Theano or TensorFlow, it's because the idea is quite similar. Specifically, the library is pretty low-level, like Theano, but has higher goals like Tensorflow. The main reason to use Gorgonia is developer comfort. If you're using a Go stack extensively, now you have access to the ability to create production-ready machine learning systems in an environment that you are already familiar and comfortable with.

machine-learning artificial-intelligence neural-network computation-graph differentiation gradient-descent gorgonia deep-learning deeplearning deep-neural-networks automatic-differentiation symbolic-differentiationSwift for TensorFlow is a new way to develop machine learning models. It gives you the power of TensorFlow directly integrated into the Swift programming language. With Swift, you can write the following imperative code, and Swift automatically turns it into a single TensorFlow Graph and runs it with the full performance of TensorFlow Sessions on CPU, GPU and TPU. Swift combines the flexibility of Eager Execution with the high performance of Graphs and Sessions. Behind the scenes, Swift analyzes your Tensor code and automatically builds graphs for you. Swift also catches type errors and shape mismatches before running your code, and has Automatic Differentiation built right in. We believe that machine learning tools are so important that they deserve a first-class language and a compiler.

machine-learning automatic-differentiation compilerNOTE: Building on the momentum of deeplearn.js, we have joined the TensorFlow family and we are starting a new ecosystem of libraries and tools for Machine Learning in Javascript, called TensorFlow.js. This repo moved from PAIR-code/deeplearnjs to tensorflow/tfjs-core. A part of the TensorFlow.js ecosystem, this repo hosts @tensorflow/tfjs-core, the TensorFlow.js Core API, which provides low-level, hardware-accelerated linear algebra operations and an eager API for automatic differentiation.

deep-learning typescript webgl machine-learning neural-network deep-neural-networks gpu-accelerationGorgonia is a library that helps facilitate machine learning in Go. Write and evaluate mathematical equations involving multidimensional arrays easily. If this sounds like Theano or TensorFlow, it's because the idea is quite similar. Specifically, the library is pretty low-level, like Theano, but has higher goals like Tensorflow.The main reason to use Gorgonia is developer comfort. If you're using a Go stack extensively, now you have access to the ability to create production-ready machine learning systems in an environment that you are already familiar and comfortable with.

machine-learning artificial-intelligence neural-network computation-graph differentiation gradient-descent gorgonia deep-learning deeplearning deep-neural-networks automatic-differentiation symbolic-differentiation go-libraryAutograd can automatically differentiate native Python and Numpy code. It can handle a large subset of Python's features, including loops, ifs, recursion and closures, and it can even take derivatives of derivatives of derivatives. It supports reverse-mode differentiation (a.k.a. backpropagation), which means it can efficiently take gradients of scalar-valued functions with respect to array-valued arguments, as well as forward-mode differentiation, and the two can be composed arbitrarily. The main intended application of Autograd is gradient-based optimization. For more information, check out the tutorial and the examples directory. See the tanh example file for the code.

Tangent is a new, free, and open-source Python library for automatic differentiation.Existing libraries implement automatic differentiation by tracing a program's execution (at runtime, like PyTorch) or by staging out a dynamic data-flow graph and then differentiating the graph (ahead-of-time, like TensorFlow). In contrast, Tangent performs ahead-of-time autodiff on the Python source code itself, and produces Python source code as its output. Tangent fills a unique location in the space of machine learning tools.

autodiff automatic-differentiation machine-learning deep-learningTensorFlow Probability is a library for probabilistic reasoning and statistical analysis in TensorFlow. As part of the TensorFlow ecosystem, TensorFlow Probability provides integration of probabilistic methods with deep networks, gradient-based inference via automatic differentiation, and scalability to large datasets and models via hardware acceleration (e.g., GPUs) and distributed computation. Our probabilistic machine learning tools are structured as follows.

tensorflow bayesian-methods deep-learning machine-learning data-science neural-networks statistics probabilistic-programmingThis library provides high-performance components leveraging the hardware acceleration support and automatic differentiation of TensorFlow. The library will provide TensorFlow support for foundational mathematical methods, mid-level methods, and specific pricing models. The coverage is being rapidly expanded over the next few months. Foundational methods. Core mathematical methods - optimisation, interpolation, root finders, linear algebra, random and quasi-random number generation, etc.

tensorflow quantitative-finance finance numerical-methods numerical-optimization numerical-integration high-performance high-performance-computing gpu gpu-computing quantlibTheano is a Python library that allows you to define, optimize, and efficiently evaluate mathematical expressions involving multi-dimensional arrays. It is built on top of NumPy. Its features include tight integration with NumPy, transparent use of a GPU, dynamic C code generation and lot more.

deep-learning neural-network math numerical symbolic blas numpy gpu autodiff differentiationEdward is a Python library for probabilistic modeling, inference, and criticism. It is a testbed for fast experimentation and research with probabilistic models, ranging from classical hierarchical models on small data sets to complex deep probabilistic models on large data sets. Edward fuses three fields: Bayesian statistics and machine learning, deep learning, and probabilistic programming. Edward is built on top of TensorFlow. It enables features such as computational graphs, distributed training, CPU/GPU integration, automatic differentiation, and visualization with TensorBoard.

bayesian-methods deep-learning machine-learning data-science tensorflow neural-networks statistics probabilistic-programmingADMC++ -- An Automatic Differentiation Package for MATLAB and C++ ADMC++ is an automatic differentiation package designed for MATLAB and C++. Automatic differentiation is a technique for computing derivatives of functions.

C# automatic differentiation and numerical optimization library, transparent use with operator overloading, unlimited order of differentiation and unlimited number of variables, very flexible support for matrix algebra, on-the-fly function compilation to IL code for very fast ...

differentiation mathematics matrix optimizationArraymancer is a tensor (N-dimensional array) project in Nim. The main focus is providing a fast and ergonomic CPU, Cuda and OpenCL ndarray library on which to build a scientific computing and in particular a deep learning ecosystem. The library is inspired by Numpy and PyTorch. The library provides ergonomics very similar to Numpy, Julia and Matlab but is fully parallel and significantly faster than those libraries. It is also faster than C-based Torch.

tensor nim multidimensional-arrays cuda deep-learning machine-learning cudnn high-performance-computing gpu-computing matrix-library neural-networks parallel-computing openmp linear-algebra ndarray opencl gpgpu iot automatic-differentiation autogradChainer is a Python-based deep learning framework aiming at flexibility. It provides automatic differentiation APIs based on the define-by-run approach (a.k.a. dynamic computational graphs) as well as object-oriented high-level APIs to build and train neural networks. It also supports CUDA/cuDNN using CuPy for high performance training and inference. For more details of Chainer, see the documents and resources listed above and join the community in Forum, Slack, and Twitter. The stable version of current Chainer is separated in here: v3.

deep-learning neural-networks machine-learning gpu cuda cudnn numpy cupy chainer neural-networkTensorFlow is arugably the most popular deep learning library as of 2017. This is designed to help those who want to familiarize themselves with TensorFlow functions. Particulary, I focus on comparing TensorFlow functions with the equivalent functions in NumPy, the de facto standard numerical computation library. I hope this will help you get comfortable with TensorFlow quickly.

tensorflow tensorflow-exercises numpyAn implementation of neural style in TensorFlow.This implementation is a lot simpler than a lot of the other ones out there, thanks to TensorFlow's really nice API and automatic differentiation.

Knet uses dynamic computational graphs generated at runtime for automatic differentiation of (almost) any Julia code. This allows machine learning models to be implemented by defining just the forward calculation (i.e. the computation from parameters and data to loss) using the full power and expressivity of Julia. The implementation can use helper functions, loops, conditionals, recursion, closures, tuples and dictionaries, array indexing, concatenation and other high level language features, some of which are often missing in the restricted modeling languages of static computational graph systems like Theano, Torch, Caffe and Tensorflow. GPU operation is supported by simply using the KnetArray type instead of regular Array for parameters and data. Knet builds a dynamic computational graph by recording primitive operations during forward calculation. Only pointers to inputs and outputs are recorded for efficiency. Therefore array overwriting is not supported during forward and backward passes. This encourages a clean functional programming style. High performance is achieved using custom memory management and efficient GPU kernels. See Under the hood for more details.

Tuning hyperparameters of learning algorithms is hard because gradients are usually unavailable. We compute exact gradients of cross-validation performance with respect to all hyperparameters by chaining derivatives backwards through the entire training procedure. These gradients allow us to optimize thousands of hyperparameters, including step-size and momentum schedules, weight initialization distributions, richly parameterized regularization schemes, and neural network architectures. We compute hyperparameter gradients by exactly reversing the dynamics of stochastic gradient descent with momentum. You'll need to install autograd, our automatic differentiation package. However, autograd (aka funkyYak) has changed a lot since we wrote the hypergrad code, and it would take a little bit of work to make them compatible again.

The Stan Math Library is a C++, reverse-mode automatic differentiation library designed to be usable, extensive and extensible, efficient, scalable, stable, portable, and redistributable in order to facilitate the construction and utilization of algorithms that utilize derivatives. The Stan Math Library is licensed under the new BSD license.

stan stan-math-library math eigen boost automatic-differentiation cvode
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