Tensorflow cost function based on binary xor operation

Question

I am trying to create a cost function that is based on the xor operation of x & y.

x and y are tf.float32 tensors and both have the same shape.

x --> ... --> y auto-encoder network

I have tried doing the following:

x_value = tf.cast(x, tf.int32)
y_value = tf.cast(y, tf.int32)
xor_bitwise_result = tf.bitwise.bitwise_xor(x_value, y_value)   
cost_value = tf.cast(xor_bitwise_result, tf.float32)
cost = tf.reduce_mean(cost_value)

but I am getting an error:

ValueError: No gradients provided for any variable, check your graph for ops that do not support gradient.

if I try to do the following I will get the same error as well

cost = tf.sqrt(tf.reduce_mean(tf.square(x_value-y_value)))

It might be the way I am casting is not good, it is possible my understanding of the process is lacking so any pointers would be greatly appreciated.