Related papers: p-Adic Statistical Field Theory and Convolutional …
Deep feedforward neural networks (DFNNs) are a powerful tool for functional approximation. We describe flexible versions of generalized linear and generalized linear mixed models incorporating basis functions formed by a DFNN. The…
How can one analyze detailed 3D biological objects, such as neurons and botanical trees, that exhibit complex geometrical and topological variation? In this paper, we develop a novel mathematical framework for representing, comparing, and…
We present a systematic comparison between neural network (NN) architectures for inference of AC-OPF solutions. Using fully connected NNs as a baseline we demonstrate the efficacy of leveraging network topology in the models by constructing…
The algebraic structures related with integrable structure of superconformal field theory (SCFT) are introduced. The SCFT counterparts of Baxter's Q-operator are constructed. The fusion-like relations for the transfer-matrices in different…
Deep learning has arguably achieved tremendous success in recent years. In simple words, deep learning uses the composition of many nonlinear functions to model the complex dependency between input features and labels. While neural networks…
In this chapter we take a look at the universal approximation question for stochastic feedforward neural networks. In contrast to deterministic networks, which represent mappings from a set of inputs to a set of outputs, stochastic networks…
In the past decade, deep neural networks (DNNs) came to the fore as the leading machine learning algorithms for a variety of tasks. Their raise was founded on market needs and engineering craftsmanship, the latter based more on trial and…
Statistical field theory methods have been very successful with a number of random graph and random matrix problems, but it is challenging to apply these methods to graphs with prescribed degree sequences due to the extensive number of…
Spiking neural networks (SNNs) are promising in a bio-plausible coding for spatio-temporal information and event-driven signal processing, which is very suited for energy-efficient implementation in neuromorphic hardware. However, the…
This PhD Thesis is devoted to the study of Hodge structures on a special type of complex algebraic varieties, the so-called character varieties. For this purpose, we propose to use a powerful algebro-geometric tool coming from theoretical…
The need for consistent treatment of uncertainty has recently triggered increased interest in probabilistic deep learning methods. However, most current approaches have severe limitations when it comes to inference, since many of these…
Despite the latest prevailing success of deep neural networks (DNNs), several concerns have been raised against their usage, including the lack of intepretability the gap between DNNs and other well-established machine learning models, and…
Symbolic Branch Networks (SBNs) are neural models whose architecture is inherited directly from an ensemble of decision trees. Each root-to-parent-of-leaf decision path is mapped to a hidden neuron, and the matrices $W_{1}$…
We present an efficient deep learning technique for the model reduction of the Navier-Stokes equations for unsteady flow problems. The proposed technique relies on the Convolutional Neural Network (CNN) and the stochastic gradient descent…
We provide an overview of high dimensional dynamical systems driven by random matrices, focusing on applications to simple models of learning and generalization in machine learning theory. Using both cavity method arguments and path…
We introduce a new method, called CNNAS (convolutional neural networks for atomistic systems), for calculating the total energy of atomic systems which rivals the computational cost of empirical potentials while maintaining the accuracy of…
Although statistical learning theory provides a robust framework to understand supervised learning, many theoretical aspects of deep learning remain unclear, in particular how different architectures may lead to inductive bias when trained…
Deep neural networks are renowned for their ability to generalise well across diverse tasks, even when heavily overparameterized. Existing works offer only partial explanations (for example, the NTK-based task-model alignment explanation…
The structure of overlapping subdivergences, which appear in the perturbative expansions of quantum field theory, is analyzed using algebraic lattice theory. It is shown that for specific QFTs the sets of subdivergences of Feynman diagrams…
We develop a novel theoretical method for calculating spectroscopic properties of those nuclei with odd number of nucleons, that is based on the nuclear density functional theory and the particle-boson coupling scheme. Self-consistent…