[Numpy-discussion] automatic differentiation with PyAutoDiff

James Bergstra bergstrj@iro.umontreal...
Thu Jun 14 08:43:53 CDT 2012


On Thu, Jun 14, 2012 at 4:00 AM, Olivier Grisel
<olivier.grisel@ensta.org> wrote:
> 2012/6/13 James Bergstra <bergstrj@iro.umontreal.ca>:
>> Further to the recent discussion on lazy evaluation & numba, I moved
>> what I was doing into a new project:
>>
>> PyAutoDiff:
>> https://github.com/jaberg/pyautodiff
>>
>> It currently works by executing CPython bytecode with a numpy-aware
>> engine that builds a symbolic expression graph with Theano... so you
>> can do for example:
>>
>>>>> import autodiff, numpy as np
>>>>> autodiff.fmin_l_bfgs_b(lambda x: (x + 1) ** 2, [np.zeros(())])
>>
>> ... and you'll see `[array(-1.0)]` printed out.
>>
>> In the future, I think it should be able to export the
>> gradient-computing function as bytecode, which could then be optimized
>> by e.g. numba or a theano bytecode front-end. For now it just compiles
>> and runs the Theano graph that it built.
>>
>> It's still pretty rough (you'll see if you look at the code!) but I'm
>> excited about it.
>
> Very interesting. Would it be possible to use bytecode introspection
> to printout the compute and display a symbolic representation of an
> arbitrary python + numpy expression?
>
> E.g. something along the lines of:
>
>>>> g = autodiff.gradient(lambda x: (x + 1) ** 2, [np.zeros(())])
>>>> print g
> f(x) = 2 * x + 2
>>>> g(np.arrange(3))
> array[2, 4, 6]
>
> --
> Olivier
> http://twitter.com/ogrisel - http://github.com/ogrisel

So... almost?

I just hacked this gradient function to see what theano could print
out, and the first thing that happened (after my own mistakes were
sorted out) was an error because the lambda expression was defined to
work on a 0-d array, but then you evaluated g on a vector. Was this
part of the test? If so, I'm not sure I think it's a good idea, I'm
assuming it was a cut-and-paste oversight and moving on....

I settled on (https://github.com/jaberg/pyautodiff/blob/master/autodiff/tests/test_gradient.py)
```
import numpy as np
from autodiff import Gradient

def test_basic():
    g = Gradient(lambda x: ((x + 1) ** 2).sum(), [np.zeros(3)])
    print g
    print g(np.arange(3))
```

The output is ... well... ugly but correct:
Elemwise{Composite{[mul(i0, add(i1, i2))]}}(TensorConstant{(1,) of
2.0}, TensorConstant{(1,) of 1.0}, <TensorType(float64, vector)>)
[array([ 2.,  4.,  6.])]

So with some effort on pretty-printing I'm pretty confident that this
could work, at least for simple examples. Pretty-printing is always a
challenge for non-trivial examples.  One option might be to convert
the internal symbolic graph to sympy?

- James
-- 
http://www-etud.iro.umontreal.ca/~bergstrj


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