数据挖掘 - 如何使用不可微分的损失函数？ - 吾爱随笔录

我试图在一个完全连接的神经网络的输出处找到一个码本，该网络选择的点使得如此产生的码本之间的最小距离（欧几里得范数）最大化。神经网络的输入是需要映射到输出空间更高维度的点。

例如，如果输入维度为 2，输出维度为 3，则以下映射（以及任何排列）效果最佳：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})

由于损失函数本身不可微，我得到了错误

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

我是在做一些愚蠢的事情还是有办法绕过这个？感谢您在这方面的任何帮助。提前致谢。

更新：

import tensorflow as tf
import numpy as np
import itertools
from random import shuffle


input_bits = tf.placeholder(dtype=tf.float32, shape=[None, 2], name='input_bits')
learning_rate_val = tf.placeholder(dtype=tf.float32, shape=(), name='learning_rate')


def find_code(message):
    weight1 = np.random.normal(loc=0.0, scale=0.01, size=[2, 3])
    init1 = tf.constant_initializer(weight1)
    out1 = tf.layers.dense(inputs=message, units=3, activation=tf.nn.sigmoid, kernel_initializer=init1)
    return out1


code = find_code(input_bits)

distances = []
for i in range(0, 4):
    for j in range(i+1, 4):
        distances.append(tf.linalg.norm(code[i]-code[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(9e5)
threshold = 0.5

for i in range(count):
    input_bit = [list(k) for k in itertools.product([0, 1], repeat=2)]
    shuffle(input_bit)
    input_bit = 2 * np.array(input_bit) - 1
    code_preview = sess.run(code, feed_dict={input_bits: input_bit})
    sess.run(opt, feed_dict={input_bits: input_bit, learning_rate_val: initial_learning_rate})
    train_loss_track.append(sess.run(loss, feed_dict={input_bits: input_bit}))
    if i % 5000 == 0 or i == 0 or i == count - 1:
        input_bit = [list(k) for k in itertools.product([0, 1], repeat=2)]
        input_bit = 2 * np.array(input_bit) - 1
        output, train_loss = sess.run([code, loss], feed_dict={input_bits: input_bit,
                                                               learning_rate_val: initial_learning_rate})
        print("\nEpoch: " + str(i))
        print("Code: " + str(output))
        output[output > threshold] = 1
        output[output <= threshold] = 0
        print("Code: " + str(output))
        print("Loss: " + str(train_loss) + "\n")

这似乎工作正常。但最终的输出是

Code: [[9.9976158e-01 0.0000000e+00 1.0000000e+00]
 [4.9997061e-01 0.0000000e+00 0.0000000e+00]
 [5.0000829e-01 1.0000000e+00 1.0000000e+00]
 [2.3837961e-04 1.0000000e+00 4.6849247e-11]]
Code: [[1. 0. 1.]
 [0. 0. 0.]
 [1. 1. 1.]
 [0. 1. 0.]]
Loss: -1.1179142

虽然它接近预期的输出，但它卡在这里。反正有没有达到预期的输出？