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Many measurements in computer vision and machine learning manifest as non-Euclidean data samples. Several researchers recently extended a number of deep neural network architectures for manifold valued data samples. Researchers have…

Analyzing large volumes of high-dimensional data requires dimensionality reduction: finding meaningful low-dimensional structures hidden in their high-dimensional observations. Such practice is needed in atomistic simulations of complex…

Understanding how cities visually differ from each others is interesting for planners, residents, and historians. We investigate the interpretation of deep features learned by convolutional neural networks (CNNs) for city recognition. Given…

Data living on manifolds commonly appear in many applications. Often this results from an inherently latent low-dimensional system being observed through higher dimensional measurements. We show that under certain conditions, it is possible…

Despite significant advances in the field of deep learning in ap-plications to various areas, an explanation of the learning pro-cess of neural network models remains an important open ques-tion. The purpose of this paper is a comprehensive…

We propose a new family of neural networks to predict the behaviors of physical systems by learning their underpinning constraints. A neural projection operator lies at the heart of our approach, composed of a lightweight network with an…

The present phase of Machine Learning is characterized by supervised learning algorithms relying on large sets of labeled examples ($n \to \infty$). The next phase is likely to focus on algorithms capable of learning from very few labeled…

Concept learning is a fundamental aspect of human cognition and plays a critical role in mental processes such as categorization, reasoning, memory, and decision-making. Researchers across various disciplines have shown consistent interest…

Object detection and recognition are fundamental functions underlying the success of species. Because the appearance of an object exhibits a large variability, the brain has to group these different stimuli under the same object identity, a…

Protein representation learning is critical in various tasks in biology, such as drug design and protein structure or function prediction, which has primarily benefited from protein language models and graph neural networks. These models…

In this paper we revisit one of the classical perceptron problems from the neural networks and statistical physics. In \cite{Gar88} Gardner presented a neat statistical physics type of approach for analyzing what is now typically referred…

Deep convolutional neural networks (DCNNs) and the ventral visual pathway share vast architectural and functional similarities in visual challenges such as object recognition. Recent insights have demonstrated that both hierarchical…

Deep learning models develop successive representations of their input in sequential layers, the last of which maps the final representation to the output. Here we investigate the informational content of these representations by observing…

Deep neural networks implement a sequence of layer-by-layer operations that are each relatively easy to understand, but the resulting overall computation is generally difficult to understand. We consider a simple hypothesis for interpreting…

We propose Lie group embedded dynamical neural networks (LieEDNN) and the corresponding learning algorithms based on gradient descent and metric projection on smooth manifold, where we treat Lie group as an intrinsic representation for…

In this thesis, we develop various techniques for working with sets in machine learning. Each input or output is not an image or a sequence, but a set: an unordered collection of multiple objects, each object described by a feature vector.…

In this paper, we will study the following pattern recognition problem: Every pattern is a 3-dimensional graph, its surface can be split up into some regions, every region is composed of the pixels with the approximately same colour value…

Modern machine learning systems are increasingly trained on large amounts of data embedded in high-dimensional spaces. Often this is done without analyzing the structure of the dataset. In this work, we propose a framework to study the…

Deep Convolutional Neural Networks (DCNN) have been proven to be effective for various computer vision problems. In this work, we demonstrate its effectiveness on a continuous object orientation estimation task, which requires prediction of…

Given a collection of images, humans are able to discover landmarks by modeling the shared geometric structure across instances. This idea of geometric equivariance has been widely used for the unsupervised discovery of object landmark…