Related papers: p-Adic Statistical Field Theory and Deep Belief Ne…

This paper contributes to a development of randomized methods for neural networks. The proposed learner model is generated incrementally by stochastic configuration (SC) algorithms, termed as Stochastic Configuration Networks (SCNs). In…

Reservoir computers (RCs) and recurrent neural networks (RNNs) can mimic any finite-state automaton in theory, and some workers demonstrated that this can hold in practice. We test the capability of generalized linear models, RCs, and Long…

Deep neural networks (DNN) consist of layers of neurons interconnected by synaptic weights. A high bit-precision in weights is generally required to guarantee high accuracy in many applications. Minimizing error accumulation between layers…

Restricted Boltzmann Machines (RBMs) and Deep Belief Networks have been demonstrated to perform efficiently in a variety of applications, such as dimensionality reduction, feature learning, and classification. Their implementation on…

Combining additive models and neural networks allows to broaden the scope of statistical regression and extend deep learning-based approaches by interpretable structured additive predictors at the same time. Existing attempts uniting the…

Large neural networks are typically trained for a fixed computational budget, creating a rigid trade-off between performance and efficiency that is ill-suited for deployment in resource-constrained or dynamic environments. Existing…

Kohn-Sham density functional theory (DFT) has long struggled with the accurate description of strongly correlated and open shell systems and improvements have been minor even in the newest hybrid functionals. In this Letter we treat the…

Foundation models are deep neural networks (such as GPT-5, Gemini~3, and Opus~4) trained on large datasets that can perform diverse downstream tasks -- text and code generation, question answering, summarization, image classification, and…

The study of critical quantum many-body systems through conformal field theory (CFT) is one of the pillars of modern quantum physics. Certain CFTs are also understood to be dual to higher-dimensional theories of gravity via the anti-de…

In this paper we consider the limiting case of neural networks (NNs) architectures when the number of neurons in each hidden layer and the number of hidden layers tend to infinity thus forming a continuum, and we derive approximation errors…

Spiking neural networks (SNNs) offer a promising energy-efficient alternative to artificial neural networks (ANNs), in virtue of their high biological plausibility, rich spatial-temporal dynamics, and event-driven computation. The direct…

Despite the remarkable performance, Deep Neural Networks (DNNs) behave as black-boxes hindering user trust in Artificial Intelligence (AI) systems. Research on opening black-box DNN can be broadly categorized into post-hoc methods and…

Building a good generative model for image has long been an important topic in computer vision and machine learning. Restricted Boltzmann machine (RBM) is one of such models that is simple but powerful. However, its restricted form also has…

There exists a dichotomy between classical probabilistic graphical models, such as Bayesian networks (BNs), and modern tractable models, such as sum-product networks (SPNs). The former generally have intractable inference, but provide a…

Conditional belief networks introduce stochastic binary variables in neural networks. Contrary to a classical neural network, a belief network can predict more than the expected value of the output $Y$ given the input $X$. It can predict a…

Density functional theory is a successful branch of numerical simulations of quantum systems. While the foundations are rigorously defined, the universal functional must be approximated resulting in a `semi'-ab initio approach. The search…

Deep neural network (DNN) models have demonstrated impressive performance in various domains, yet their application in cognitive neuroscience is limited due to their lack of interpretability. In this study we employ two structurally…

Nowadays this is very popular to use deep architectures in machine learning. Deep Belief Networks (DBNs) are deep architectures that use stack of Restricted Boltzmann Machines (RBM) to create a powerful generative model using training data.…

Approximation capabilities of shallow neural networks (SNNs) form an integral part in understanding the properties of deep neural networks (DNNs). In the study of these approximation capabilities some very popular classes of target…

Deep learning has delivered its powerfulness in many application domains, especially in image and speech recognition. As the backbone of deep learning, deep neural networks (DNNs) consist of multiple layers of various types with hundreds to…