ValueError：Theano中的尺寸不匹配错误

Question

I'm trying to implement AND operation via Neural network using Theano library in python. Here is my code:

import theano
import theano.tensor as T
import numpy as np
import matplotlib.pyplot as plt

#Define variables:
x = T.matrix('x')
w1 = theano.shared(np.random.uniform(0,1,(3,3)))
w2 = theano.shared(np.random.uniform(0,1,(1,3)))

learning_rate = 0.01

#Define mathematical expression:c for forward pass
z1 = T.dot(x,w1)
a1 = 1/(1+T.exp(-z1))
z2 = T.dot(a1,w2.T)
a2 = 1/(1 + T.exp(-z2))
#Let’s determine the cost as follows:
a_hat = T.vector('a_hat') #Actual output
cost = -(a_hat*T.log(a2) + (1-a_hat)*T.log(1-a2)).sum()
dw2,dw1 = T.grad(cost,[w2,w1])

train = theano.function(
inputs = [x,a_hat],
outputs = [a2,cost],
updates = [
    [w1, w1-learning_rate*dw1],
    [w2, w2-learning_rate*dw2]
]
)

#Define inputs and weights
inputs = np.array([
 [0, 0],
 [0, 1],
 [1, 0],
 [1, 1]
])

inputs = np.append( np.ones((inputs.shape[0],1)), inputs, axis=1)

outputs = np.array([0,0,0,1]).T

#Iterate through all inputs and find outputs:
cost = []
for iteration in range(30000):
    pred, cost_iter = train(inputs, outputs)
    cost.append(cost_iter)

I'm not able to trace back the error ValueError: Dimension mismatch; shapes are (*, *), (*, 4), (4, 1), (*, *), (*, 4), (4, 1) Apply node that caused the error: ValueError: Dimension mismatch; shapes are (*, *), (*, 4), (4, 1), (*, *), (*, 4), (4, 1) Apply node that caused the error: . Even if I change the dimension of the weight vectors w1 and w2 , error remains the same. I'm new to Theano and don't know much about debugging it. Can someone help me out? Thanks.

Answer 1

Your have an input dimension mismatch as you can see in the error message :

ValueError: Input dimension mis-match. (input[1].shape[1] = 4, input[2].shape[1] = 1)

More precisely here :

Inputs values: [array([[-1.]]), array([[ 0.,  0.,  0.,  1.]]), array([[-1.13961476],
       [-1.28500784],
       [-1.3082276 ],
       [-1.4312266 ]]), array([[-1.]]), array([[ 1.,  1.,  1.,  0.]]), array([[ 1.13961476],
       [ 1.28500784],
       [ 1.3082276 ],
       [ 1.4312266 ]])]

You can get inspiration on the XOR neural network, this example has been treated here , and going through this tutorial will help you a lot understanding theano.

I also had tough times when I first tried using theano. Very few examples and tutorials. Maybe you can also check Lasagne , it is a library based on Theano, however I felt like it was easier to take in hand.

I hope this will help you.

[EDIT]

Use the following flags to help you find where the error comes from

theano.config.exception_verbosity='high'
theano.config.optimizer='None'

In your case we can find this interesting lines in the output :

Backtrace when the node is created(use Theano flag traceback.limit=N to make it longer):
  File "SO.py", line 30, in <module>
    cost = -(a_hat*T.log(a2) + (1-a_hat)*T.log(1-a2)).T.sum()

So, here are the weights we wanted :

w1 = theano.shared(np.random.uniform(0,1,(3,3)))
w2 = theano.shared(np.random.uniform(0,1,(3,1)))

With this cost function :

cost = -(a_hat*T.log(a2.T) + (1-a_hat)*T.log(1-a2.T)).sum()

This way we get a1 of shape (4,3) (same as 1st layer input) and a2 (4,1) as the expected output.

x * w1 = (4,3) * (3,3) = (4,3) = a1.shape

a1 * w2 = (4,3) * (3,1) = (4,1) = a2.shape

You will also have to add this line :

from random import random

It will give you, with 30000 iterations :

The outputs of the NN are:
The output for x1=0 | x2=0 is 0.0001
The output for x1=0 | x2=1 is 0.0029
The output for x1=1 | x2=0 is 0.0031
The output for x1=1 | x2=1 is 0.9932