Related papers: The algebra and the geometry aspect of Deep learni…

Particle physics classification often assumes flat geometry, ignoring the curved statistical structure of collision data. We present a geometric framework for Vector Boson Fusion Higgs classification that combines physics-inspired…

Deep learning has become the dominant approach for creating high capacity, scalable models across diverse data modalities. However, because these models rely on a large number of learned parameters, tightly couple feature extraction with…

Symmetry is a fundamental tool in the exploration of a broad range of complex systems. In machine learning symmetry has been explored in both models and data. In this paper we seek to connect the symmetries arising from the architecture of…

Machine learning often aims to produce latent embeddings of inputs which lie in a larger, abstract mathematical space. For example, in the field of 3D modeling, subsets of Euclidean space can be embedded as vectors using implicit neural…

Recently there has been a dramatic increase in the performance of recognition systems due to the introduction of deep architectures for representation learning and classification. However, the mathematical reasons for this success remain…

Whether it be in a man-made machine or a biological system, form and function are often directly related. In the latter, however, this particular relationship is often unclear due to the intricate nature of biology. Here we developed a…

Geometric Deep Learning techniques have become a transformative force in the field of Computer-Aided Design (CAD), and have the potential to revolutionize how designers and engineers approach and enhance the design process. By harnessing…

In this paper, we introduce a novel analysis of neural networks based on geometric (Clifford) algebra and convex optimization. We show that optimal weights of deep ReLU neural networks are given by the wedge product of training samples when…

The clear understanding of the non-convex landscape of neural network is a complex incomplete problem. This paper studies the landscape of linear (residual) network, the simplified version of the nonlinear network. By treating the gradient…

Neural representations of 3D data have been widely adopted across various applications, particularly in recent work leveraging coordinate-based networks to model scalar or vector fields. However, these approaches face inherent challenges,…

Deep learning models have gained great popularity in statistical modeling because they lead to very competitive regression models, often outperforming classical statistical models such as generalized linear models. The disadvantage of deep…

Machine learning is increasingly targeting areas where input data cannot be accurately described by a single vector, but can be modeled instead using the more flexible concept of random vectors, namely probability measures or more simply…

Deep neural networks (DNN) are black box algorithms. They are trained using a gradient descent back propagation technique which trains weights in each layer for the sole goal of minimizing training error. Hence, the resulting weights cannot…

One of the most prominent attributes of Neural Networks (NNs) constitutes their capability of learning to extract robust and descriptive features from high dimensional data, like images. Hence, such an ability renders their exploitation as…

Computing latent representations for graph-structured data is an ubiquitous learning task in many industrial and academic applications ranging from molecule synthetization to social network analysis and recommender systems. Knowledge graphs…

Starting from the Fermat's principle of least action, which governs classical and quantum mechanics and from the theory of exterior differential forms, which governs the geometry of curved manifolds, we show how to derive the equations…

Decomposing a deep neural network's learned representations into interpretable features could greatly enhance its safety and reliability. To better understand features, we adopt a geometric perspective, viewing them as a learned coordinate…

Graph-structured data arise in many scenarios. A fundamental problem is to quantify the similarities of graphs for tasks such as classification. R-convolution graph kernels are positive-semidefinite functions that decompose graphs into…

We present a new distributed representation in deep neural nets wherein the information is represented in native form as a matrix. This differs from current neural architectures that rely on vector representations. We consider matrices as…

Accurately modeling and designing protein complex structures is a central problem in computational structural biology, with broad implications for understanding cellular function and developing therapeutics. This thesis investigates two…