Related papers: A multiscale neural network based on hierarchical …

With the emergence of Artificial Intelligence, numerical algorithms are moving towards more approximate approaches. For methods such as PCA or diffusion maps, it is necessary to compute eigenvalues of a large matrix, which may also be dense…

This paper proposes a novel face recognition algorithm based on large-scale supervised hierarchical feature learning. The approach consists of two parts: hierarchical feature learning and large-scale model learning. The hierarchical feature…

A fully tensorial theoretical framework for hypercomplex-valued neural networks is presented. The proposed approach enables neural network architectures to operate on data defined over arbitrary finite-dimensional algebras. The central…

A novel hierarchical Deep Neural Network (DNN) model is presented to address the task of end-to-end driving. The model consists of a master classifier network which determines the driving task required from an input stereo image and directs…

We introduce an architecture based on deep hierarchical decompositions to learn effective representations of large graphs. Our framework extends classic R-decompositions used in kernel methods, enabling nested part-of-part relations. Unlike…

We propose an adaptive scheme for distributed learning of nonlinear functions by a network of nodes. The proposed algorithm consists of a local adaptation stage utilizing multiple kernels with projections onto hyperslabs and a diffusion…

Deep learning has been widely used for hyperspectral pixel classification due to its ability of generating deep feature representation. However, how to construct an efficient and powerful network suitable for hyperspectral data is still…

In deep learning theory, a critical question is to understand how neural networks learn hierarchical features. In this work, we study the learning of hierarchical polynomials of \textit{multiple nonlinear features} using three-layer neural…

Nonlinear hyperspectral unmixing has recently received considerable attention, as linear mixture models do not lead to an acceptable resolution in some problems. In fact, most nonlinear unmixing methods are designed by assuming specific…

An object-oriented approach to implementing artificial neural networks is introduced in this article. The networks obtained in this way are highly connected in that they admit edges between nodes in any layers of the network, and dynamic,…

In the present work, a multi-scale framework for neural network enhanced methods is proposed for approximation of function and solution of partial differential equations (PDEs). By introducing the multi-scale concept, the total solution of…

Multilayer switch networks are proposed as artificial generators of high-dimensional discrete data (e.g., binary vectors, categorical data, natural language, network log files, and discrete-valued time series). Unlike deconvolution networks…

Rapid development in numerical modelling of materials and the complexity of new models increases quickly together with their computational demands. Despite the growing performance of modern computers and clusters, calibration of such models…

We use explicit representation formulas to show that solutions to certain partial differential equations lie in Barron spaces or multilayer spaces if the PDE data lie in such function spaces. Consequently, these solutions can be represented…

Kernel matrices are ubiquitous in computational mathematics, often arising from applications in machine learning and scientific computing. In two or three spatial or feature dimensions, such problems can be approximated efficiently by a…

We present a new paradigm for speeding up randomized computations of several frequently used functions in machine learning. In particular, our paradigm can be applied for improving computations of kernels based on random embeddings. Above…

Analyzing and understanding the structure of complex relational data is important in many applications including analysis of the connectivity in the human brain. Such networks can have prominent patterns on different scales, calling for a…

We present a distributed-memory library for computations with dense structured matrices. A matrix is considered structured if its off-diagonal blocks can be approximated by a rank-deficient matrix with low numerical rank. Here, we use…

We introduce a distributed spatio-temporal artificial neural network architecture (DISTANA). It encodes mesh nodes using recurrent, neural prediction kernels (PKs), while neural transition kernels (TKs) transfer information between…

We describe four algorithms for neural network training, each adapted to different scalability constraints. These algorithms are mathematically principled and invariant under a number of transformations in data and network representation,…