```python 
       encoder_input = Input(shape=self.input_dim, name='encoder_input')

        x = encoder_input

        for i in range(self.n_layers_encoder):
            conv_layer = Conv2D(
                filters = self.encoder_conv_filters[i]
                , kernel_size = self.encoder_conv_kernel_size[i]
                , strides = self.encoder_conv_strides[i]
                , padding = 'same'
                , name = 'encoder_conv_' + str(i)
                )

            x = conv_layer(x)

            if self.use_batch_norm:
                x = BatchNormalization()(x)

            x = LeakyReLU()(x)

            if self.use_dropout:
                x = Dropout(rate = 0.25)(x)

        shape_before_flattening = K.int_shape(x)[1:]

        x = Flatten()(x)
        #<1> Instead of connecting the flattened layer 
        # directly to the 2D latent space, we connect 
        # it to layers mu and log_var .
        self.mu = Dense(self.z_dim, name='mu')(x)
        self.log_var = Dense(self.z_dim, name='log_var')(x)
         
        #<2> The Keras model that outputs the values 
        # of mu and log_var for a given input image.
        self.encoder_mu_log_var = Model(encoder_input, (self.mu, self.log_var))

        def sampling(args):
            mu, log_var = args
            epsilon = K.random_normal(shape=K.shape(mu), mean=0., stddev=1.)
            return mu + K.exp(log_var / 2) * epsilon
        #This Lambda layer samples a point z in 
        # the latent space from the normal distribution 
        #defined by the parameters mu and log_var .
        encoder_output = Lambda(sampling, name='encoder_output')([self.mu, self.log_var])

        self.encoder = Model(encoder_input, encoder_output)```

Code for Variational AutoEncoder Encoder

Unlike standard autoencoders where the latent space does not need to be continuous, a variational autoencoder (VAE) maps inputs to a probability distribution. Sampling from the neighborhood of the mean vector ($$\mu$$) forces the decoder to reconstruct similar outputs for nearby points. This continuity in the latent space helps the model generalize better and reduces the reconstruction loss during training.

Impact of Continuous Latent Space Mapping on Variational Autoencoder Reconstruction Loss

A variational autoencoder encoder maps an input to a probability distribution in the latent space rather than to a single fixed point. Under the no-correlation parameterization described here, the encoder outputs two vectors: a mean vector $$\mu$$ and a log-variance vector $$\log\_var$$. The mean locates the distribution, while each log-variance value describes the variance of one latent dimension.

Google

San Diego State University

In a standard **autoencoder**, each input (such as an image) is mapped to a single point in the latent space. In contrast, in a **variational autoencoder** (VAE), each input is mapped to a multivariate normal distribution around a mean point in that space. The following diagram illustrates this difference:

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Related

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