Tangent: Source-To-Source Autodiff for Python
research.googleblog.com
research.googleblog.com
>>> import tangent
>>> import numpy as np
>>> tangent.grad(tangent.grad(np.sin))
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "/usr/local/lib/python3.6/site-packages/tangent/grad_util.py", line 178, in grad
node, namespace = grad_tree(func, wrt, motion, mode, preserve_result, verbose)
File "/usr/local/lib/python3.6/site-packages/tangent/grad_util.py", line 97, in grad_tree
namespace.update(six.get_function_globals(func))
AttributeError: 'numpy.ufunc' object has no attribute '__globals__'So, it's not a nested differentiation problem, so much as a problem with "ufuncs". If you wrap np.sin in your own function then it takes the gradient just fine.
def sin(x): return np.sin(x)
negative_sin = tangent.grad(tangent.grad(sin))