Are gradient operations in TF themselves differentiable?

[heiz...@gmail.com]

Hello,

- > How do I find out in TF if an operation supports gradients or not (except at runtime where I will get an error if it doesn't) ?
- > Does the tf.gradients() or compute_gradients() operations support gradients? Are they differentiable? 

Tl;DR:   Can I put a gradients() operation in a cost function of some optimization? 

Thanks in advance for any answers.

[Yaroslav Bulatov]

"gradients" produces TensorFlow graphs, any part of that graph can be further differentiated.

Some gotchas:

- "gradients" takes derivatives with respect to single y, so need to call it several times for multi-dimensional y.

   (technically gradients function can take a list of ys, but it sums them up before differentiating)

- "gradients" produces Python list instead of Tensor, so need to use "tf.pack" to convert to Tensor

- "gradients" can produce None in cases when gradient is 0, but that's an illegal input to "gradients" so you need to replace None's with 0's

Here's an example of getting a Hessian matrix of loss by calling "gradients" twice

def replace_none_with_zero(l):

  return [0 if i==None else i for i in l] 

tf.reset_default_graph()

x = tf.Variable(1.)

y = tf.Variable(1.)

loss = tf.square(x) + tf.square(y)

sess = create_session()

grads = tf.gradients([loss], [x, y])

hess0 = replace_none_with_zero(tf.gradients([grads[0]], [x, y]))

hess1 = replace_none_with_zero(tf.gradients([grads[1]], [x, y]))

hessian = tf.pack([tf.pack(hess0), tf.pack(hess1)])

print hessian.eval()

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[heiz...@gmail.com]

Thanks alot for the reply and the gotchas. I will try it out tonight.

[George Dahl]

Yaroslav already covered many of the issues, but depending on what you are doing you will might get bad results. If you sum up a gradient or average it into a scalar, you can probably differentiate again without too many issues. But if you aren't careful you can get a very large and expensive graph, or hit one of the issues Yaroslav mentioned.

[heiz...@gmail.com]

Unfortunately I have not had any success so far. I'm getting an error of  'LookupError: No gradient defined for operation 'gradients/MaxPool_grad/MaxPoolGrad'

which I guess means that there is no gradient for the maxpool_gradient operation.

What I basically want to do is input an image X and forward propagate it up to a layer L , then set the gradient equal to the predictionvector and backpropagating it back into pixelspace.
Now I want to calculate gradients of the costfunction of the backpropagated heatmap and a binary mask and update the weights in layer l. 

py_x = model(X,weights) # Prediction at layer l

# Evaluate model
predict_op = tf.argmax(py_x, 1)
scores_pred = tf.round(py_x)

# Project gradients back to pixelspace
heatMap_grads_op = tf.reduce_max(tf.abs(tf.gradients(scores_pred, X, scores_pred)[0]), reduction_indices=[3],keep_dims=True)

# Numerically stable  cost
cost = tf.reduce_mean(tf.square(Y - heatMap_grads_op)) # Cost function of the backpropagated gradient heat-map and an annotated binary mask Y

# Optimization
optimizer = tf.train.AdamOptimizer(1e-4)
train_op = optimizer.minimize(cost)

As you can see this is similar to if I just forwarded the activations to layer L and then constructed a 'deconv' network with transposed weights and passed it through to reconstruct the image. 
The problem though I don't know how to (or if it's possible) in TF to copy pooling activation maps because I upon pooling alot of spacial information is lost and I would like to use the downpooled activation

maps for the uppooling.

[Yaroslav Bulatov]

I suspect that grad of maxpool_gradient is maxpool_gradient so maybe register that as the gradient function and see what happens? (maxpool backprop sends first-order sensitivities back to the largest element of the pool, second-order sensitivities should propagate in the same way)

But, I won't be surprised if there are more specialized operations which don't have gradient implemented

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