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I want to define a custom loss function using Keras, which contains the gradient of the difference between y_true and y_pred. I found numpy.gradient can help me get the gradient of an array. So part of my code for loss function looks like this:

def loss(y_true, y_pred):
    d   = y_true - y_pred
    gradient_x = np.gradient(d, axis=0)
    gradient_y = np.gradient(d, axis=1)

but it turns out d is a Tensorflow tensor class and numpy.gradient can't process it. I'm kind of new to Keras and Tensorflow.

Is there any other function can help me do this? Or I have to compute the gradient by myself?

Zhicheng Geng
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2 Answers2

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Tensorflow tensors are not arrays at all when they are executed, they are only references to a computational graph that is being built. You might want to review the tutorial on how Tensorflow builds graphs.

You have two problems with your loss function: first, collapsing on either axis will not yield a scalar, so it won't be possible to take a derivative and second, np.gradient doesn't appear to exist in Tensorflow.

For the first problem, you can solve it by reducing along the remaining axis of gradient_y or gradient_x. I don't know which function you might want to use because I don't know your application.

The second problem can be fixed in two ways:

  1. You could wrap np.gradient using py_func, but you plan to use this as a loss function, so you will want to take the gradient of that function, and defining the gradient of a py_func call is complicated.
  2. Write your own version of np.gradient using pure Tensorflow.

For example, here's a 1D np.gradient in tensorflow (untested):

def gradient(x):
    d = x[1:]-x[:-1]
    fd = tf.concat([x,x[-1]], 0).expand_dims(1)
    bd = tf.concat([x[0],x], 0).expand_dims(1)
    d = tf.concat([fd,bd], 1)
    return tf.reduce_mean(d,1)
gngdb
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I run into the same problem of wanting to define a loss function using np.gradient. I wrote a pure tensorflow version of the function to work around the problem.

Here's my version of it: (It has the same behavior as np.gradient with axis=-1.) If you want to make it work for arbitrary axis, you need to play around it a bit more:

def my_gradient_tf(a):
    rght = tf.concat((a[..., 1:], tf.expand_dims(a[..., -1], -1)), -1)
    left = tf.concat((tf.expand_dims(a[...,0], -1), a[..., :-1]), -1)
    ones = tf.ones_like(rght[..., 2:], tf.float64)
    one = tf.expand_dims(ones[...,0], -1)
    divi = tf.concat((one, ones*2, one), -1)
    return (rght-left) / divi
Bernat Gene
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