Related papers: Learning Tangent Bundles and Characteristic Classe…
Artificial neural networks have become important to improve the search for admissible string compactifications and characterize them. In this paper we construct the heterotic orbiencoder, a general deep autoencoder to study heterotic…
Sensory data are often comprised of independent content and transformation factors. For example, face images may have shapes as content and poses as transformation. To infer separately these factors from given data, various…
We describe a novel weakly supervised deep learning framework that combines both the discriminative and generative models to learn meaningful representation in the multiple instance learning (MIL) setting. MIL is a weakly supervised…
Latent space geometry provides a rigorous and empirically valuable framework for interacting with the latent variables of deep generative models. This approach reinterprets Euclidean latent spaces as Riemannian through a pull-back metric,…
The tangent bundle $T^kM$ of order $k$, of a smooth Banach manifold $M$ consists of all equivalent classes of curves that agree up to their accelerations of order $k$. In the previous work of the author he proved that $T^kM$, $1\leq k\leq…
We explain the relationship between various characteristic classes for smooth manifold bundles known as ``higher torsion'' classes. We isolate two fundamental properties that these cohomology classes may or may not have: additivity and…
Causal structure learning has been a challenging task in the past decades and several mainstream approaches such as constraint- and score-based methods have been studied with theoretical guarantees. Recently, a new approach has transformed…
We propose a principled method for autoencoding with random forests. Our strategy builds on foundational results from nonparametric statistics and spectral graph theory to learn a low-dimensional embedding of the model that optimally…
We propose to learn a hierarchical prior in the context of variational autoencoders to avoid the over-regularisation resulting from a standard normal prior distribution. To incentivise an informative latent representation of the data, we…
Bi-linear feature learning models, like the gated autoencoder, were proposed as a way to model relationships between frames in a video. By minimizing reconstruction error of one frame, given the previous frame, these models learn "mapping…
An autoencoder is a neural network which data projects to and from a lower dimensional latent space, where this data is easier to understand and model. The autoencoder consists of two sub-networks, the encoder and the decoder, which carry…
To achieve near-zero training error in a classification problem, the layers of a feed-forward network have to disentangle the manifolds of data points with different labels, to facilitate the discrimination. However, excessive class…
Autoencoders are widely used in machine learning applications, in particular for anomaly detection. Hence, they have been introduced in high energy physics as a promising tool for model-independent new physics searches. We scrutinize the…
A stratified space is a kind of topological space together with a partition into smooth manifolds. These kinds of spaces naturally arise in the study of singular algebraic varieties, symplectic reduction, and differentiable stacks. In this…
Adaptive cognition requires structured internal models of objects and their relations. Predictive neural networks are often proposed to learn such world models, but how these are instantiated and how they support prediction remain unclear.…
We treat shape co-segmentation as a representation learning problem and introduce BAE-NET, a branched autoencoder network, for the task. The unsupervised BAE-NET is trained with a collection of un-segmented shapes, using a shape…
The classification of electron systems according to their topology has been at the forefront of condensed matter research in recent years. It has been found that systems of the same symmetry, previously thought of as equivalent, may in fact…
Variational autoencoders (VAEs) and generative adversarial networks (GANs) enjoy an intuitive connection to manifold learning: in training the decoder/generator is optimized to approximate a homeomorphism between the data distribution and…
The dynamics of a turbulent flow tend to occupy only a portion of the phase space at a statistically stationary regime. From a dynamical systems point of view, this portion is the attractor. The knowledge of the turbulent attractor is…
Autoencoders are able to learn useful data representations in an unsupervised matter and have been widely used in various machine learning and computer vision tasks. In this work, we present methods to train Invertible Neural Networks…