This paper introduces a modified variational autoencoder (VAEs) that contains an additional neural network branch. The resulting branched VAE (BVAE) contributes a classification component based on the class labels to the total loss and therefore imparts categorical information to the latent representation. As a result, the latent space distributions of the input classes are separated and ordered, thereby enhancing the classification accuracy. The degree of improvement is quantified by numerical calculations employing the benchmark MNIST dataset for both unrotated and rotated digits. The proposed technique is then compared to and then incorporated into a VAE with fixed output distributions. This procedure is found to yield improved performance for a wide range of output distributions.

In this study, we focus on sampling from the latent space of generative models built upon autoencoders so as the reconstructed samples are lifelike images. To do to, we introduce a novel post-training sampling algorithm rooted in the concept of probability mass functions, coupled with a quantization process. Our proposed algorithm establishes a vicinity around each latent vector from the input data and then proceeds to draw samples from these defined neighborhoods. This strategic approach ensures that the sampled latent vectors predominantly inhabit high-probability regions, which, in turn, can be effectively transformed into authentic real-world images. A noteworthy point of comparison for our sampling algorithm is the sampling technique based on Gaussian mixture models (GMM), owing to its inherent capability to represent clusters. Remarkably, we manage to improve the time complexity from the previous $\mathcal{O}(n\times d \times k \times i)$ associated with GMM sampling to a much more streamlined $\mathcal{O}(n\times d)$, thereby resulting in substantial speedup during runtime. Moreover, our experimental results, gauged through the Fr\'echet inception distance (FID) for image generation, underscore the superior performance of our sampling algorithm across a diverse range of models and datasets. On the MNIST benchmark dataset, our approach outperforms GMM sampling by yielding a noteworthy improvement of up to $0.89$ in FID value. Furthermore, when it comes to generating images of faces and ocular images, our approach showcases substantial enhancements with FID improvements of $1.69$ and $0.87$ respectively, as compared to GMM sampling, as evidenced on the CelebA and MOBIUS datasets. Lastly, we substantiate our methodology's efficacy in estimating latent space distributions in contrast to GMM sampling, particularly through the lens of the Wasserstein distance.

We propose the Generalized Probabilistic U-Net, which extends the Probabilistic U-Net by allowing more general forms of the Gaussian distribution as the latent space distribution that can better approximate the uncertainty in the reference segmentations. We study the effect the choice of latent space distribution has on capturing the variation in the reference segmentations for lung tumors and white matter hyperintensities in the brain. We show that the choice of distribution affects the sample diversity of the predictions and their overlap with respect to the reference segmentations.

Wasserstein autoencoder (WAE) shows that matching two distributions is equivalent to minimizing a simple autoencoder (AE) loss under the constraint that the latent space of this AE matches a pre-specified prior distribution. This latent space distribution matching is a core component of WAE, and a challenging task. In this paper, we propose to use the contrastive learning framework that has been shown to be effective for self-supervised representation learning, as a means to resolve this problem. We do so by exploiting the fact that contrastive learning objectives optimize the latent space distribution to be uniform over the unit hyper-sphere, which can be easily sampled from. We show that using the contrastive learning framework to optimize the WAE loss achieves faster convergence and more stable optimization compared with existing popular algorithms for WAE. This is also reflected in the FID scores on CelebA and CIFAR-10 datasets, and the realistic generated image quality on the CelebA-HQ dataset. The main goal of generative modeling is to learn a good approximation of the underlying data distribution from finite data samples, while facilitating an efficient way to draw samples. Popular algorithms such as variational autoencoders (VAE, Kingma & Welling (2013); Rezende et al. (2014)) and generative adversarial networks (GAN, Goodfellow et al. (2014)) are theoretically-grounded models designed to meet this goal. However, they come with some challenges. For instance, VAEs suffer from the posterior collapse problem (Chen et al., 2016; Zhao et al., 2017; Van Den Oord et al., 2017), and a mismatch between the posterior and prior distribution (Kingma et al., 2016; Tomczak & Welling, 2018; Dai & Wipf, 2019; Bauer & Mnih, 2019).

Currently end-to-end deep learning based open-domain dialogue systems remain black box models, making it easy to generate irrelevant contents with data-driven models. Specifically, latent variables are highly entangled with different semantics in the latent space due to the lack of priori knowledge to guide the training. To address this problem, this paper proposes to harness the generative model with a priori knowledge through a cognitive approach involving mesoscopic scale feature disentanglement. Particularly, the model integrates the macro-level guided-category knowledge and micro-level open-domain dialogue data for the training, leveraging the priori knowledge into the latent space, which enables the model to disentangle the latent variables within the mesoscopic scale. Besides, we propose a new metric for open-domain dialogues, which can objectively evaluate the interpretability of the latent space distribution. Finally, we validate our model on different datasets and experimentally demonstrate that our model is able to generate higher quality and more interpretable dialogues than other models.

We propose the Generalized Probabilistic U-Net, which extends the Probabilistic U-Net by allowing more general forms of the Gaussian distribution as the latent space distribution that can better approximate the uncertainty in the reference segmentations. We study the effect the choice of latent space distribution has on capturing the uncertainty in the reference segmentations using the LIDC-IDRI dataset. We show that the choice of distribution affects the sample diversity of the predictions and their overlap with respect to the reference segmentations. For the LIDC-IDRI dataset, we show that using a mixture of Gaussians results in a statistically significant improvement in the generalized energy distance (GED) metric with respect to the standard Probabilistic U-Net. We have made our implementation available at https://github.com/ishaanb92/GeneralizedProbabilisticUNet

Neural Networks play a growing role in many science disciplines, including physics. Variational Autoencoders (VAEs) are neural networks that are able to represent the essential information of a high dimensional data set in a low dimensional latent space, which have a probabilistic interpretation. In particular the so-called encoder network, the first part of the VAE, which maps its input onto a position in latent space, additionally provides uncertainty information in terms of a variance around this position. In this work, an extension to the Autoencoder architecture is introduced, the FisherNet. In this architecture, the latent space uncertainty is not generated using an additional information channel in the encoder, but derived from the decoder, by means of the Fisher information metric. This architecture has advantages from a theoretical point of view as it provides a direct uncertainty quantification derived from the model, and also accounts for uncertainty cross-correlations. We can show experimentally that the FisherNet produces more accurate data reconstructions than a comparable VAE and its learning performance also apparently scales better with the number of latent space dimensions.