Cross entropy loss suddenly increases to infinity

问题:

I am attempting to replicate an deep convolution neural network from a research paper. I have implemented the architecture, but after 10 epochs, my cross entropy loss suddenly increases to infinity. This can be seen in the chart below. You can ignore what happens to the accuracy after the problem occurs.

Here is the github repository with a picture of the architecture

After doing some research I think using an AdamOptimizer or relu might be a problem.

x = tf.placeholder(tf.float32, shape=[None, 7168])
y_ = tf.placeholder(tf.float32, shape=[None, 7168, 3])

#Many Convolutions and Relus omitted

final = tf.reshape(final, [-1, 7168])
keep_prob = tf.placeholder(tf.float32)
W_final = weight_variable([7168,7168,3])
b_final = bias_variable([7168,3])
final_conv = tf.tensordot(final, W_final, axes=[[1], [1]]) + b_final

cross_entropy = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(labels=y_, logits=final_conv))
train_step = tf.train.AdamOptimizer(1e-5).minimize(cross_entropy)
correct_prediction = tf.equal(tf.argmax(final_conv, 2), tf.argmax(y_, 2))
accuracy = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))

EDIT If anyone is interested, the solution was that I was basically feeding in incorrect data.

回答1:

Solution: Control the solution space. This might mean using smaller datasets when training, it might mean using less hidden nodes, it might mean initializing your wb differently. Your model is reaching a point where the loss is undefined, which might be due to the gradient being undefined, or the final_conv signal.

Why: Sometimes no matter what, a numerical instability is reached. Eventually adding a machine epsilon to prevent dividing by zero (cross entropy loss here) just won't help because even then the number cannot be accurately represented by the precision you are using. (Ref: https://en.wikipedia.org/wiki/Round-off_error and https://floating-point-gui.de/basic/)

Considerations:
1) When tweaking epsilons, be sure to be consistent with your data type (Use the machine epsilon of the precision you are using, in your case float32 is 1e-6 ref: https://en.wikipedia.org/wiki/Machine_epsilon and python numpy machine epsilon.

2) Just in-case others reading this are confused: The value in the constructor for Adamoptimizer is the learning rate, but you can set the epsilon value (ref: How does paramater epsilon affects AdamOptimizer? and https://www.tensorflow.org/api_docs/python/tf/train/AdamOptimizer)

3) Numerical instability of tensorflow is there and its difficult to get around. Yes there is tf.nn.softmax_with_cross_entropy but this is too specific (what if you don't want a softmax?). Refer to Vahid Kazemi's 'Effective Tensorflow' for an insightful explanation: https://github.com/vahidk/EffectiveTensorflow#entropy

回答2:

that jump in your loss graph is very weird...

I would like you to focus on few points :

• if your images are not normalized between 0 and 1 then normalize them
• if you have normalized your values between -1 and 1 then use a sigmoid layer instead of softmax because softmax squashes the values between 0 and 1
• before using softmax add a sigmoid layer to squash your values (Highly Recommended)
• other things you can do is add dropouts for every layer
• also I would suggest you to use tf.clip so that your gradients does not explode and implode
• you can also use L2 regularization
• and experiment with the learning rate and epsilon of AdamOptimizer
• I would also suggest you to use tensor-board to keep track of the weights so that way you will come to know where the weights are exploding

• You can also use tensor-board for keeping track of loss and accuracy

• See The softmax formula below:

• Probably that e to power of x, the x is being a very large number because of which softmax is giving infinity and hence the loss is infinity
• Heavily use tensorboard to debug and print the values of the softmax so that you can figure out where you are going wrong
• One more thing I noticed you are not using any kind of activation functions after the convolution layers... I would suggest you to leaky relu after every convolution layer
• Your network is a humongous network and it is important to use leaky relu as activation function so that it adds non-linearity and hence improves the performance

回答3:

You may want to use a different value for epsilon in the Adam optimizer (e.g. 0.1 -- 1.0).This is mentioned in the documentation:

The default value of 1e-8 for epsilon might not be a good default in general. For example, when training an Inception network on ImageNet a current good choice is 1.0 or 0.1.