Converting theano tensor types - python-2.7

Question

I have a computation graph built with Theano. It goes like this:
import theano
from theano import tensor as T
import numpy as np
W1 = theano.shared( np.random.rand(45,32).astype('float32'), 'W1')
b1 = theano.shared( np.random.rand(32).astype('float32'), 'b1')
W2 = theano.shared( np.random.rand(32,3).astype('float32'), 'W2')
b2 = theano.shared( np.random.rand(3).astype('float32'), 'b2')
input = T.matrix('input')
hidden = T.tanh(T.dot(input, W1)+b1)
output = T.nnet.softmax(T.dot(hidden, W2)+b2)
Now, the mapping from a vector to a vector. However, input is set as a matrix type so I can pass many vectors through the mapping simultaneously. I'm doing some machine learning and this makes the learning phase more efficient.
The problem is that after the learning phase, I'd like to view the mapping as vector to vector so I can compute:
jac = theano.gradient.jacobian(output, wrt=input)
jacobian complains that input is not TensorType(float32, vector). Is there a way I can change the input tensor type without rebuilding the whole computation graph?

Answer 1

Technically, this a possible solution:
import theano
from theano import tensor as T
import numpy as np
W1 = theano.shared( np.random.rand(45,32).astype('float32'), 'W1')
b1 = theano.shared( np.random.rand(32).astype('float32'), 'b1')
W2 = theano.shared( np.random.rand(32,3).astype('float32'), 'W2')
b2 = theano.shared( np.random.rand(3).astype('float32'), 'b2')
input = T.vector('input') # it will be reshaped!
hidden = T.tanh(T.dot(input.reshape((-1, 45)), W1)+b1)
output = T.nnet.softmax(T.dot(hidden, W2)+b2)
#Here comes the trick
jac = theano.gradient.jacobian(output.reshape((-1,)), wrt=input).reshape((-1, 45, 3))
In this way jac.eval({input: np.random.rand(10*45)}).shape will result (100, 45, 3)!
The problem is that it calculates the derivative across the batch index. So in theory the first 1x45 number can effect all the 10x3 outputs (in a batch of length 10).
For that, there are several solutions.
You could take the diagonal across the first two axes, but unfortunately Theano does not implement it, numpy does!
I think it can be done with a scan, but this is an other matter.