Related papers: Geometry and Generalization: Eigenvalues as predic…
Existing popular unsupervised embedding learning methods focus on enhancing the instance-level local discrimination of the given unlabeled images by exploring various negative data. However, the existed sample outliers which exhibit large…
The generalized Jacobi equation is a differential equation in local coordinates that describes the behavior of infinitesimally close geodesics with an arbitrary relative velocity. In this note we study some transformation properties for…
The following work presents how autoencoding all the possible hidden activations of a network for a given problem can provide insight about its structure, behavior, and vulnerabilities. The method, termed self-introspection, can show that a…
Eigenvalue analysis is widely used for linear instability analysis in both external and internal aerodynamics. It typically involves finding the steady state, linearizing around it to obtain the Jacobian, and then solving for its…
Feedforward neural networks are widely used as universal predictive models to fit data distribution. Common gradient-based learning, however, suffers from many drawbacks making the training process ineffective and time-consuming.…
In the years since Goodfellow et al. introduced Generative Adversarial Networks (GANs), there has been an explosion in the breadth and quality of generative model applications. Despite this work, GANs still have a long way to go before they…
Variational Autoencoders (VAEs) represent the given data in a low-dimensional latent space, which is generally assumed to be Euclidean. This assumption naturally leads to the common choice of a standard Gaussian prior over continuous latent…
Geodesic metric spaces support a variety of averaging constructions for given finite sets. Computing such averages has generated extensive interest in diverse disciplines. Here we consider the inverse problem of recognizing computationally…
The use of Variational Autoencoders in different Machine Learning tasks has drastically increased in the last years. They have been developed as denoising, clustering and generative tools, highlighting a large potential in a wide range of…
We consider the transmission of a Gaussian vector source over a multi-dimensional Gaussian channel where a random or a fixed subset of the channel outputs are erased. Within the setup where the only encoding operation allowed is a linear…
It is common in machine learning and statistics to use symmetries derived from expert knowledge to simplify problems or improve performance, using methods like data augmentation or penalties. In this paper we consider the unsupervised and…
Autoencoders have emerged as powerful models for visualization and dimensionality reduction based on the fundamental assumption that high-dimensional data is generated from a low-dimensional manifold. A critical challenge in autoencoder…
Increasingly many real world tasks involve data in multiple modalities or views. This has motivated the development of many effective algorithms for learning a common latent space to relate multiple domains. However, most existing…
Many problems give rise to polynomial systems. These systems often have several parameters and we are interested to study how the solutions vary when we change the values for the parameters. Using predictor-corrector methods we track the…
While much work has been devoted to understanding the implicit (and explicit) regularization of deep nonlinear networks in the supervised setting, this paper focuses on unsupervised learning, i.e., autoencoders are trained with the…
Jacobi's method is a well-known algorithm in linear algebra to diagonalize symmetric matrices by successive elementary rotations. We report about the generalization of these elementary rotations towards canonical transformations acting in…
Variational autoencoders (VAEs) learn representations of data by jointly training a probabilistic encoder and decoder network. Typically these models encode all features of the data into a single variable. Here we are interested in learning…
How can agents learn internal models that veridically represent interactions with the real world is a largely open question. As machine learning is moving towards representations containing not just observational but also interventional…
Recent results on optimization and generalization properties of neural networks showed that in a simple two-layer network, the alignment of the labels to the eigenvectors of the corresponding Gram matrix determines the convergence of the…
Prior work investigating the geometry of pre-trained word embeddings have shown that word embeddings to be distributed in a narrow cone and by centering and projecting using principal component vectors one can increase the accuracy of a…