变分自动编码器：InvalidArgumentError：不兼容的形状：[100,5] 与 [100]

Question

我尝试使用 LSTM 运行变分自动编码器。所以我用LSTM 层替换了dense 层。但它不起作用。这个例子：

# generate data
data = generate_example(length = 560,seed=253)
normal_data = data[1:400,:]
fault_data = data[400:,:]
timesteps = 5

# data prepare
# define the normalize function
# normalize function
def normalize(normal, fault):
    normal_mean = normal.mean(axis = 0)
    normal_std = normal.std(axis = 0)
    # normalize
    fault_normalize = np.array(fault).reshape(fault.shape)
    for i in np.linspace(0,fault.shape[1]-1):
        i = int(i)
        fault_normalize[:,i] = (fault[:,i] - normal_mean[i])/normal_std[i]
    return(fault_normalize)
# define the lag function
# lag function
def lag(data, timesteps = 10):
    # define the shape of return data
    data_row = data.shape[0]
    data_col = data.shape[1]
    data_len = data_row - timesteps

    data_lag = np.repeat(0,data_len*timesteps*data_col).reshape(data_len,timesteps,data_col).astype("float")
    for i in np.arange(0,data_len):
        data_lag[i,:,:] = data[i:(i+timesteps),:]
    return(data_lag)

normal_scale = normalize(normal = normal_data, fault = normal_data)
normal_scale = lag(data=normal_scale, timesteps = timesteps)

这是变分自动编码器

from __future__ import print_function

import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import norm

from keras.layers import Input, Dense, Lambda, LSTM, RepeatVector, TimeDistributed
from keras.models import Model
from keras import backend as K
from keras import metrics
from keras.datasets import mnist

batch_size = 100
original_dim = 3
latent_dim = 2
intermediate_dim = 5
epochs = 100
epsilon_std = 1.0


x = Input(shape=(timesteps,original_dim))
h = LSTM(intermediate_dim,return_sequences=False)(x)
z_mean = Dense(latent_dim)(h)
z_log_var = Dense(latent_dim)(h)


def sampling(args):
    z_mean, z_log_var = args
    epsilon = K.random_normal(shape=(K.shape(z_mean)[0], latent_dim), mean=0.,
                              stddev=epsilon_std)
    return z_mean + K.exp(z_log_var / 2) * epsilon

# note that "output_shape" isn't necessary with the TensorFlow backend
z = Lambda(sampling, output_shape=(latent_dim,))([z_mean, z_log_var])

# we instantiate these layers separately so as to reuse them later
decoded_repeat = RepeatVector(timesteps)
decoder_h = LSTM(intermediate_dim, activation='tanh',return_sequences=True)
decoder_mean = TimeDistributed(Dense(original_dim, activation='sigmoid'))

h_repeat = decoded_repeat(z)
h_decoded = decoder_h(h_repeat)
x_decoded_mean = decoder_mean(h_decoded)

# instantiate VAE model
vae = Model(x, x_decoded_mean)

# Compute VAE loss
xent_loss = original_dim * metrics.binary_crossentropy(x, x_decoded_mean)
kl_loss = - 0.5 * K.sum(1 + z_log_var - K.square(z_mean) - K.exp(z_log_var), axis=-1)
vae_loss = K.mean(xent_loss + kl_loss)

vae.add_loss(vae_loss)
vae.compile(optimizer='rmsprop',loss=None)
vae.summary()


x_train = normal_scale
x_test = normal_scale

vae.fit(x_train,
        shuffle=True,
        epochs=epochs,
        batch_size=batch_size)

# build a model to project inputs on the latent space
encoder = Model(x, z_mean)

但我得到了错误InvalidArgumentError: Incompatible shapes: [100,5] vs. [100]，我认为没有不兼容的形状。这是变分自编码器的结构

____________________________________________________________________________________________________
Layer (type)                     Output Shape          Param #     Connected to                     
====================================================================================================
input_76 (InputLayer)            (None, 5, 3)          0                                            
____________________________________________________________________________________________________
lstm_42 (LSTM)                   (None, 5)             180         input_76[0][0]                   
____________________________________________________________________________________________________
dense_317 (Dense)                (None, 2)             12          lstm_42[0][0]                    
____________________________________________________________________________________________________
dense_318 (Dense)                (None, 2)             12          lstm_42[0][0]                    
____________________________________________________________________________________________________
lambda_72 (Lambda)               (None, 2)             0           dense_317[0][0]                  
                                                                   dense_318[0][0]                  
____________________________________________________________________________________________________
repeat_vector_20 (RepeatVector)  (None, 5, 2)          0           lambda_72[0][0]                  
____________________________________________________________________________________________________
lstm_43 (LSTM)                   (None, 5, 5)          160         repeat_vector_20[0][0]           
____________________________________________________________________________________________________
time_distributed_18 (TimeDistrib (None, 5, 3)          18          lstm_43[0][0]                    
====================================================================================================
Total params: 382
Trainable params: 382
Non-trainable params: 0

Answer 1

损失函数的计算出现错误：

vae_loss = K.mean(xent_loss + kl_loss)

这里，xent_loss 是一个形状为(100, 5) 的张量，而kl_loss 的形状为(100,)。扩展kl_loss 的维度将启用广播（我想这就是您的意图）：

vae_loss = K.mean(xent_loss + kl_loss[:, None])