[Doubt] Would iteratively setting a non-local variable as the answer result in correct gradients

[pranv]

Suppose I had a class method that like:

def call(self, X):
    for t in range(X.shape[0]):
        self.ans = some_function(X[t], self.ans)       # some_function is a parameterized operation
        # some more computation with self.ans
        # final step has a scalar loss function

would I get correct gradients of this whole process? Meaning - will the computation graph that autograd constructs have the value of self.ans stored per iteration and use it?

[mattjj]

Yup!

Here's a test just to make sure I understand what you mean:

import autograd.numpy as np
from autograd import grad
from autograd.util import quick_grad_check


def some_function(x, y):
    return x + y + x*y

class A(object):
    def call(self, X):
        self.ans = np.zeros(X.shape)
        for t in range(X.shape[0]):
            self.ans = some_function(X[t], self.ans)

        return np.sum(self.ans**2)


a = A()
print grad(a.call)(np.random.randn(5))
quick_grad_check(a.call, np.random.randn(5))

One thing to keep in mind is that ans will come out boxed at the end:

In [1]: run issue67
[ 323.38327233  185.12997922  283.66369298  168.29411013  807.31095824]
Checking gradient of <bound method A.call of <__main__.A object at 0x10d2d9610>> at [-0.10688095  0.66919977 -0.45675244 -1.08241973 -0.91352716]
Gradient projection OK (numeric grad: -0.105982859395, analytic grad: -0.105982859699)

In [2]: print a.ans
Autograd ArrayNode with value [-1.005772 -1.005772 -1.005772 -1.005772 -1.005772] and 1 tape(s)

but its computation tape is completed and so it will act just like a regular array.

The code also works if the updated value of self.ans gets reused in future calls to call instead of getting reset to zeros like in the example I wrote. That just means the function changes every time you call it, which autograd can handle but quick_grad_check can't (because it invokes the function multiple times to check its numerical gradient):

class A(object):
    def __init__(self, ans):
        self.ans = ans

    def call(self, X):
        for t in range(X.shape[0]):
            self.ans = some_function(X[t], self.ans)

        return np.sum(self.ans**2)


a = A(5.)
print grad(a.call)(np.random.randn(3))
print grad(a.call)(np.random.randn(3))

In [1]: run issue67
[  8.91513093  60.30447614 -32.37465155]
[  2.43210897  17.48004748   5.28757384]

[pranv]

Thanks!