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Deep Neural Networks (DNNs) are generated by sequentially performing linear and non-linear processes. Using a combination of linear and non-linear procedures is critical for generating a sufficiently deep feature space. The majority of…

The modern digital engineering design often requires costly repeated simulations for different scenarios. The prediction capability of neural networks (NNs) makes them suitable surrogates for providing design insights. However, only a few…

Kolmogorov-Arnold Networks (KAN) \cite{liu2024kan} were very recently proposed as a potential alternative to the prevalent architectural backbone of many deep learning models, the multi-layer perceptron (MLP). KANs have seen success in…

The 3-hinge gyrus (3HG) is a newly defined folding pattern, which is the conjunction of gyri coming from three directions in cortical folding. Many studies demonstrated that 3HGs can be reliable nodes when constructing brain networks or…

Kolmogorov-Arnold networks (KANs) offer a potent combination of accuracy and interpretability, thanks to their compositions of learnable univariate activation functions. However, the activations of well-fitting KANs tend to exhibit…

Tensor train (TT) decomposition is a powerful representation for high-order tensors, which has been successfully applied to various machine learning tasks in recent years. However, since the tensor product is not commutative, permutation of…

Multimodal learning is a framework for building models that make predictions based on different types of modalities. Important challenges in multimodal learning are the inference of shared representations from arbitrary modalities and…

The key to success in machine learning (ML) is the use of effective data representations. Traditionally, data representations were hand-crafted. Recently it has been demonstrated that, given sufficient data, deep neural networks can learn…

Algorithmic speedup of training common neural architectures is made difficult by the lack of structure guaranteed by the function compositions inherent to such networks. In contrast to multilayer perceptrons (MLPs), Kolmogorov-Arnold…

Developing surrogates for computer models has become increasingly important for addressing complex problems in science and engineering. This article introduces an artificial intelligent (AI) surrogate, referred to as the DeepSurrogate, for…

In an ever expanding set of research and application areas, deep neural networks (DNNs) set the bar for algorithm performance. However, depending upon additional constraints such as processing power and execution time limits, or…

In traditional software programs, it is easy to trace program logic from variables back to input, apply assertion statements to block erroneous behavior, and compose programs together. Although deep learning programs have demonstrated…

We report a method to convert discrete representations of molecules to and from a multidimensional continuous representation. This model allows us to generate new molecules for efficient exploration and optimization through open-ended…

Many problems in real-world applications involve predicting several random variables which are statistically related. Markov random fields (MRFs) are a great mathematical tool to encode such relationships. The goal of this paper is to…

In lifelong learning, a learner faces a sequence of tasks with shared structure and aims to identify and leverage it to accelerate learning. We study the setting where such structure is captured by a common representation of data. Unlike…

This work shows that for rational multivariate functions, the Kolmogorov Superposition Theorem (KST) involves several single-variable functions, which can be written down by inspection. In other words, no computation is required for…

Data-driven model discovery of complex dynamical systems is typically done using sparse optimization, but it has a fundamental limitation: sparsity in that the underlying governing equations of the system contain only a small number of…

We propose a novel approach that enhances multivariate function approximation using learnable path signatures and Kolmogorov-Arnold networks (KANs). We enhance the learning capabilities of these networks by weighting the values obtained by…

Modern machine learning, grounded in the Universal Approximation Theorem, has achieved significant success in the study of phase transitions in both equilibrium and non-equilibrium systems. However, identifying the critical points of…

Recently proposed budding tree is a decision tree algorithm in which every node is part internal node and part leaf. This allows representing every decision tree in a continuous parameter space, and therefore a budding tree can be jointly…