google/jax: GPU- and TPU-backed NumPy with differentiation and JIT compilation.
JAX is a Python library for accelerator-oriented array computation and program transformation, designed for high-performance numerical computing and large-scale machine learning. With its updated version of Autograd, JAX can automatically differentiate native Python and NumPy functions. It can differentiate through loops, branches, recursion, and closures, and it can take derivatives of derivative
自動微分パッケージ ForwardDiff · julia について
Julia の便利なパッケージの一つがこの ForwardDiff. いや～、ありがたやありがたや． なんとこいつは、関数 $f$ を与えると自動微分をしてくれる． 自動微分ってのは、関数計算を tree に展開して、その枝に各計算要素の微分係数を重みとして貼り付けることによって、関数計算のわずか数倍程度の計算量で偏微分値関数を生成するという手法 1 で、数値解析のきちんとした本なんかに載っているやつだ． つまり、$\mbox{grad } f ( = \nabla f)$ やら Hessian やら Jacobian やらを計算してくれるのだ． これらの量は重要で、例えば非線形連立方程式を解くために Newton 法を使おうとすると 2 、その方程式を関数とみなしたときの Jacobian が必要になる． こうした場合、連立の次元数 $N$ は普通に 1000 とか 10000 などとい
Automatic differentiation for machine learning in Julia - int8.io
Automatic differentiation is a term I first heard of while working on (as it turns out now, a bit cumbersome) implementation of backpropagation algorithm – after all it caused lots of headaches as I had to handle all derivatives myself with almost pen-and-paper like approach. Obviously I made many mistakes until I got my final solution working. At that time, I was aware some libraries like Theano
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 "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
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Introduction to Automatic Differentiation Variational Inference
JSoC 2015 project: Automatic Differentiation in Julia with ForwardDiff.jl
