In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.
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Question: The Variational Auto Encoder (VAE) is a popular generative
latent variable model that is often
applied for representation learning.
Standard VAEs assume continuous valued
latent variables and are trained by maximization
of the evidence lower bound (ELBO). Conventional methods obtain a
differentiable estimate of the ELBO with reparametrized sampling and
optimize it with Stochastic Gradient Descend (SGD). However, this is not possible if
we want to train VAEs with discrete valued latent variables,
since reparametrized sampling is not possible. Till now, there
exist no simple solutions to circumvent this problem.
In this paper, we propose an easy method to train VAEs
with binary or categorically valued latent representations. Therefore, we use a differentiable
estimator for the ELBO which is based on importance sampling. In experiments, we verify the approach and
train two different VAEs architectures with Bernoulli and
Categorically distributed latent representations on two different benchmark
datasets.

Answer: We propose an easy method to train Variational Auto Encoders (VAE) with discrete latent representations, using importance sampling

Question: The softmax function is widely used to train deep neural networks for multi-class classification. Despite its outstanding performance in classification tasks, the features derived from the supervision of softmax are usually sub-optimal in some scenarios where Euclidean distances apply in feature spaces. To address this issue, we propose a new loss, dubbed the isotropic loss, in the sense that the overall distribution of data points is regularized to approach the isotropic normal one. Combined with the vanilla softmax, we formalize a novel criterion called the isotropic softmax, or isomax for short, for supervised learning of deep neural networks. By virtue of the isomax, the intra-class features are penalized by the isotropic loss while inter-class distances are well kept by the original softmax loss. Moreover, the isomax loss does not require any additional modifications to the network, mini-batches or the training process. Extensive experiments on classification and clustering are performed to demonstrate the superiority and robustness of the isomax loss.

Answer: The discriminative capability of softmax for learning feature vectors of objects is effectively enhanced by virture of isotropic normalization on global distribution of data points.

Question: Due to the phenomenon of "posterior collapse," current latent variable generative models pose a challenging design choice that either weakens the capacity of the decoder or requires altering the training objective. We develop an alternative that utilizes the most powerful generative models as decoders, optimize the variational lower bound, and ensures that the latent variables preserve and encode useful information. Our proposed -VAEs achieve this by constraining the variational family for the posterior to have a minimum distance to the prior. For sequential latent variable models, our approach resembles the classic representation learning approach of slow feature analysis. We demonstrate our method's efficacy at modeling text on LM1B and modeling images: learning representations, improving sample quality, and achieving state of the art log-likelihood on CIFAR-10 and ImageNet 32 32.

Answer:
Avoid posterior collapse by lower bounding the rate.