Defining a gradient with respect to a subtensor in Theano

问题

I have what is conceptually a simple question about Theano but I haven't been able to find the answer (I'll confess upfront to not really understanding how shared variables work in Theano, despite many hours with the tutorials).

I'm trying to implement a "deconvolutional network"; specifically I have a 3-tensor of inputs (each input is a 2D image) and a 4-tensor of codes; for the ith input codes[i] represents a set of codewords which together code for input i.

I've been having a lot of trouble figuring out how to do gradient descent on the codewords. Here are the relevant parts of my code:

idx = T.lscalar()
pre_loss_conv = conv2d(input = codes[idx].dimshuffle('x', 0, 1,2),
                       filters = dicts.dimshuffle('x', 0,1, 2),
                       border_mode = 'valid')
loss_conv = pre_loss_conv.reshape((pre_loss_conv.shape[2], pre_loss_conv.shape[3]))
loss_in = inputs[idx]
loss = T.sum(1./2.*(loss_in - loss_conv)**2) 

del_codes = T.grad(loss, codes[idx])
delc_fn = function([idx], del_codes)
train_codes = function([input_index], loss, updates = [
    [codes, T.set_subtensor(codes[input_index], codes[input_index] - 
                            learning_rate*del_codes[input_index])     ]])

(here codes and dicts are shared tensor variables). Theano is unhappy with this, specifically with defining

del_codes = T.grad(loss, codes[idx])

The error message I'm getting is: theano.gradient.DisconnectedInputError: grad method was asked to compute the gradient with respect to a variable that is not part of the computational graph of the cost, or is used only by a non-differentiable operator: Subtensor{int64}.0

I'm guessing that it wants a symbolic variable instead of codes[idx]; but then I'm not sure how to get everything connected to get the intended effect. I'm guessing I'll need to change the final line to something like

learning_rate*del_codes)     ]])

Can someone give me some pointers as to how to define this function properly? I think I'm probably missing something basic about working with Theano but I'm not sure what.

Thanks in advance!

-Justin

Update: Kyle's suggestion worked very nicely. Here's the specific code I used

current_codes = T.tensor3('current_codes')
current_codes = codes[input_index]
pre_loss_conv = conv2d(input = current_codes.dimshuffle('x', 0, 1,2),
                       filters = dicts.dimshuffle('x', 0,1, 2),
                       border_mode = 'valid')
loss_conv = pre_loss_conv.reshape((pre_loss_conv.shape[2], pre_loss_conv.shape[3]))
loss_in = inputs[input_index]
loss = T.sum(1./2.*(loss_in - loss_conv)**2)  

del_codes = T.grad(loss, current_codes)
train_codes = function([input_index], loss)
train_dicts = theano.function([input_index], loss, updates = [[dicts, dicts - learning_rate*del_dicts]])
codes_update = ( codes, T.set_subtensor(codes[input_index], codes[input_index] - learning_rate*del_codes) )
codes_update_fn = function([input_index], updates = [codes_update])

for i in xrange(num_inputs):
     current_loss = train_codes(i)
     codes_update_fn(i)

回答1:

To summarize the findings:

Assigning grad_var = codes[idx], then making a new variable such as: subgrad = T.set_subtensor(codes[input_index], codes[input_index] - learning_rate*del_codes[input_index])

Then calling train_codes = function([input_index], loss, updates = [[codes, subgrad]])

seemed to do the trick. In general, I try to make variables for as many things as possible. Sometimes tricky problems can arise from trying to do too much in a single statement, plus it is hard to debug and understand later! Also, in this case I think theano needs a shared variable, but has issues if the shared variable is created inside the function that requires it.

Glad this worked for you!

来源：https://stackoverflow.com/questions/24468482/defining-a-gradient-with-respect-to-a-subtensor-in-theano

标签

python

machine-learning

theano