Autograd 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.
>>> import autograd.numpy as np # Thinly-wrapped numpy >>> from autograd import grad # The only autograd function you may ever need >>> >>> def tanh(x): # Define a function ... y = np.exp(-2.0 * x) ... return (1.0 - y) / (1.0 + y) ... >>> grad_tanh = grad(tanh) # Obtain its gradient function >>> grad_tanh(1.0) # Evaluate the gradient at x = 1.0 0.41997434161402603 >>> (tanh(1.0001) - tanh(0.9999)) / 0.0002 # Compare to finite differences 0.41997434264973155
We can continue to differentiate as many times as we like, and use numpy's vectorization of scalar-valued functions across many different input values:
>>> from autograd import elementwise_grad as egrad # for functions that vectorize over inputs >>> import matplotlib.pyplot as plt >>> x = np.linspace(-7, 7, 200) >>> plt.plot(x, tanh(x), ... x, egrad(tanh)(x), # first derivative ... x, egrad(egrad(tanh))(x), # second derivative ... x, egrad(egrad(egrad(tanh)))(x), # third derivative ... x, egrad(egrad(egrad(egrad(tanh))))(x), # fourth derivative ... x, egrad(egrad(egrad(egrad(egrad(tanh)))))(x), # fifth derivative ... x, egrad(egrad(egrad(egrad(egrad(egrad(tanh))))))(x)) # sixth derivative >>> plt.show()
See the tanh example file for the code.
You can find a tutorial here.
- Simple neural net
- Convolutional neural net
- Recurrent neural net
- Neural Turing Machine
- Backpropagating through a fluid simulation
- Variational inference in Bayesian neural network
- Gaussian process regression
- Sampyl, a pure Python MCMC package with HMC and NUTS
How to install
pip install autograd
Autograd was written by Dougal Maclaurin, David Duvenaud, Matt Johnson, Jamie Townsend and many other contributors, and we're actively developing it. Please feel free to submit any bugs or feature requests. We'd also love to hear about your experiences with autograd in general. Drop us an email!
We want to thank Jasper Snoek and the rest of the HIPS group (led by Prof. Ryan P. Adams) for helpful contributions and advice; Barak Pearlmutter for foundational work on automatic differentiation and for guidance on our implementation; and Analog Devices Inc. (Lyric Labs) and Samsung Advanced Institute of Technology for their generous support.