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This work presents an analysis of the hidden representations of Variational Autoencoders (VAEs) using the Intrinsic Dimension (ID) and the Information Imbalance (II). We show that VAEs undergo a transition in behaviour once the bottleneck…
Classical methods for model order selection often fail in scenarios with low SNR or few snapshots. Deep learning-based methods are promising alternatives for such challenging situations as they compensate lack of information in the…
Variational autoencoders (VAEs) are powerful deep generative models widely used to represent high-dimensional complex data through a low-dimensional latent space learned in an unsupervised manner. In the original VAE model, the input data…
The variational auto-encoder (VAE) is a popular method for learning a generative model and embeddings of the data. Many real datasets are hierarchically structured. However, traditional VAEs map data in a Euclidean latent space which cannot…
Recent advances in deep learning have shown their ability to learn strong feature representations for images. The task of image clustering naturally requires good feature representations to capture the distribution of the data and…
Selective manipulation of data attributes using deep generative models is an active area of research. In this paper, we present a novel method to structure the latent space of a Variational Auto-Encoder (VAE) to encode different…
We propose a new class of physics-informed neural networks, called physics-informed Variational Autoencoder (PI-VAE), to solve stochastic differential equations (SDEs) or inverse problems involving SDEs. In these problems the governing…
In this article we introduce the notion of Split Variational Autoencoder (SVAE), whose output $\hat{x}$ is obtained as a weighted sum $\sigma \odot \hat{x_1} + (1-\sigma) \odot \hat{x_2}$ of two generated images $\hat{x_1},\hat{x_2}$, and…
In this paper, we explore the use of a variational autoencoder (VAE), a deep generative model, to compress and generate images of dark matter density fields from $\Lambda$CDM like cosmological simulations. The VAE learns a compact,…
Normalizing flows, autoregressive models, variational autoencoders (VAEs), and deep energy-based models are among competing likelihood-based frameworks for deep generative learning. Among them, VAEs have the advantage of fast and tractable…
3D shape analysis is an important research topic in computer vision and graphics. While existing methods have generalized image-based deep learning to meshes using graph-based convolutions, the lack of an effective pooling operation…
Deep metric learning has been demonstrated to be highly effective in learning semantic representation and encoding information that can be used to measure data similarity, by relying on the embedding learned from metric learning. At the…
We present the Material Masked Autoencoder (MMAE), a self-supervised Vision Transformer pretrained on a large corpus of short-fiber composite images via masked image reconstruction. The pretrained MMAE learns latent representations that…
In this work we study Variational Autoencoders (VAEs) from the perspective of harmonic analysis. By viewing a VAE's latent space as a Gaussian Space, a variety of measure space, we derive a series of results that show that the encoder…
In this paper, we present a multimodal and dynamical VAE (MDVAE) applied to unsupervised audio-visual speech representation learning. The latent space is structured to dissociate the latent dynamical factors that are shared between the…
This paper reviews the novel concept of controllable variational autoencoder (ControlVAE), discusses its parameter tuning to meet application needs, derives its key analytic properties, and offers useful extensions and applications.…
Group-equivariant neural networks have emerged as a data-efficient approach to solve classification and regression tasks, while respecting the relevant symmetries of the data. However, little work has been done to extend this paradigm to…
A novel framework for Bayesian structural model updating is presented in this study. The proposed method utilizes the surrogate unimodal encoders of a multimodal variational autoencoder (VAE). The method facilitates an approximation of the…
Masked Autoencoder (MAE) has recently been shown to be effective in pre-training Vision Transformers (ViT) for natural image analysis. By reconstructing full images from partially masked inputs, a ViT encoder aggregates contextual…
In just three years, Variational Autoencoders (VAEs) have emerged as one of the most popular approaches to unsupervised learning of complicated distributions. VAEs are appealing because they are built on top of standard function…