如何使用不可微的损失函数？

Question

I am trying to find a codebook at the output of a fully connected neural network which chooses points such that the minimum distance (Euclidean norm) between the so produced codebook is maximized. The input to the neural network is the points that need to be mapped into higher dimension of the output space.

For instance, if the input dimension is 2 and output dimension is 3, the following mapping (and any permutations) works best: 00 - 000, 01 - 011, 10 - 101, 11 - 110

import tensorflow as tf
import numpy as np
import itertools


input_bits = tf.placeholder(dtype=tf.float32, shape=[None, 2], name='input_bits')
code_out = tf.placeholder(dtype=tf.float32, shape=[None, 3], name='code_out')
np.random.seed(1331)


def find_code(message):
    weight1 = np.random.normal(loc=0.0, scale=0.01, size=[2, 3])
    init1 = tf.constant_initializer(weight1)
    out = tf.layers.dense(inputs=message, units=3, activation=tf.nn.sigmoid, kernel_initializer=init1)
    return out


code = find_code(input_bits)

distances = []
for i in range(0, 3):
    for j in range(i+1, 3):
        distances.append(tf.linalg.norm(code_out[i]-code_out[j]))
min_dist = tf.reduce_min(distances)
# avg_dist = tf.reduce_mean(distances)

loss = -min_dist

opt = tf.train.AdamOptimizer().minimize(loss)

init_variables = tf.global_variables_initializer()
sess = tf.Session()
sess.run(init_variables)

saver = tf.train.Saver()

count = int(1e4)

for i in range(count):
    input_bit = [list(k) for k in itertools.product([0, 1], repeat=2)]
    code_preview = sess.run(code, feed_dict={input_bits: input_bit})
    sess.run(opt, feed_dict={input_bits: input_bit, code_out: code_preview})

Since the loss function itself is not differentiable, I am getting the error

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

Am I doing something silly or is there a way to circumvent this? Any help in this regard is appreciated. Thanks in advance.

Answer 1

Your loss function has to be differentiable with respect to some parameters. In your case, there are no parameters therefore you would be computing a derivative of a constant function which is 0. Moreover, in your code you have the following line:

code = find_code(input_bits)

which is not used any further. Based on the code, I assume that you want to change this line:

distances.append(tf.linalg.norm(code_out[i]-code_out[j]))

to:

distances.append(tf.linalg.norm(code[i]-code_out[j]))

Therefore, you would be using the tf.layers.dense that you have, thus include a parameter which can be used to compute the gradient of the loss with respect to that parameter.

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Moreover, you don't need to worry whether a TF operation is differentiable or not. In fact, all TF ops are differentiable. When it comes to the tf.reduce_min() , please check this link .