Autograd
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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.
Example use:
>>> import autograd.numpy as np
>>> from autograd import grad
>>>
>>> def tanh(x):
... y = np.exp(-2.0 * x)
... return (1.0 - y) / (1.0 + y)
...
>>> grad_tanh = grad(tanh)
>>> grad_tanh(1.0)
0.41997434161402603
>>> (tanh(1.0001) - tanh(0.9999)) / 0.0002
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
>>> import matplotlib.pyplot as plt
>>> x = np.linspace(-7, 7, 200)
>>> plt.plot(x, tanh(x),
... x, egrad(tanh)(x),
... x, egrad(egrad(tanh))(x),
... x, egrad(egrad(egrad(tanh)))(x),
... x, egrad(egrad(egrad(egrad(tanh))))(x),
... x, egrad(egrad(egrad(egrad(egrad(tanh)))))(x),
... x, egrad(egrad(egrad(egrad(egrad(egrad(tanh))))))(x))
>>> plt.show()
See the tanh example file for the code.
Documentation
You can find a tutorial here.
End-to-end examples
How to install
Install Autograd using Pip:
pip install autograd
Some features require SciPy, which you can install separately or as an
optional dependency along with Autograd:
pip install "autograd[scipy]"
Authors and maintainers
Autograd was written by Dougal Maclaurin,
David Duvenaud,
Matt Johnson,
Jamie Townsend
and many other contributors. The package is currently being maintained by
Agriya Khetarpal,
Fabian Joswig and
Jamie Townsend.
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.