Related papers: Distributed Computation over MAC via Kolmogorov-Ar…

Function computation of arbitrarily correlated discrete sources over Gaussian networks with orthogonal components is studied. Two classes of functions are considered: the arithmetic sum function and the type function. The arithmetic sum…

Dimensionality reduction, a form of compression, can simplify representations of information to increase efficiency and reveal general patterns. Yet, this simplification also forfeits information, thereby reducing representational capacity.…

Specifying a computational problem requires fixing encodings for input and output: encoding graphs as adjacency matrices, characters as integers, integers as bit strings, and vice versa. For such discrete data, the actual encoding is…

We propose a novel approach for computing committor functions, which describe transitions of a stochastic process between metastable states. The committor function satisfies a backward Kolmogorov equation, and in typical high-dimensional…

Multivariate functions emerge naturally in a wide variety of data-driven models. Popular choices are expressions in the form of basis expansions or neural networks. While highly effective, the resulting functions tend to be hard to…

This work presents an abstract model for the computations performed by analytic column stores or columnar query processors. The model is based on circuits whose wires carry columns rather than scalar values, and whose nodes apply operators…

One open problem in source coding is to characterize the limits of representing losslessly a non-identity discrete function of the data encoded independently by the encoders of several correlated sources with memory. This paper investigates…

In this paper, we propose to use Sinc interpolation in the context of Kolmogorov-Arnold Networks, neural networks with learnable activation functions, which recently gained attention as alternatives to Multilayer Perceptron. Many different…

In science and engineering, intelligent processing of complex signals such as images, sound or language is often performed by a parameterized hierarchy of nonlinear processing layers, sometimes biologically inspired. Hierarchical systems…

This paper explores alternative formulations of the Kolmogorov Superposition Theorem (KST) as a foundation for neural network design. The original KST formulation, while mathematically elegant, presents practical challenges due to its…

A central question in cognitive science is whether conceptual representations converge onto a shared manifold to support generalization, or diverge into orthogonal subspaces to minimize task interference. While prior work has discovered…

The Convolutional Neural Networks (CNNs) have been the dominant and effective approach for general computer vision tasks. Recently, Kolmogorov-Arnold neural networks (KANs), based on the Kolmogorov-Arnold representation theorem, have shown…

In current molecular communication (MC) systems, performing computational operations at the nanoscale remains challenging, restricting their applicability in complex scenarios such as adaptive biochemical control and advanced nanoscale…

In this paper, it is shown that the rank function of a matroid can be represented by a "mutual information function" if and only if the matroid is binary. The mutual information function considered is the one measuring the amount of…

Coded distributed matrix multiplication (CDMM) schemes, such as MatDot codes, seek efficient ways to distribute matrix multiplication task(s) to a set of $N$ distributed servers so that the answers returned from any $R$ servers are…

Multimodal representation learning has demonstrated remarkable potential in enabling models to process and integrate diverse data modalities, such as text and images, for improved understanding and performance. While the medical domain can…

Multilayer Perceptron (MLP), as a simple yet powerful model, continues to be widely used in classification and regression tasks. However, traditional MLPs often struggle to efficiently capture nonlinear relationships in load data when…

Learning representations of nodes in a low dimensional space is a crucial task with numerous interesting applications in network analysis, including link prediction, node classification, and visualization. Two popular approaches for this…

We study communication over a Gaussian multiple-access channel (MAC) with two types of transmitters: Digital transmitters hold a message from a discrete set that needs to be communicated to the receiver with vanishing error probability.…

The widespread use of multi-sensor technology and the emergence of big datasets has highlighted the limitations of standard flat-view matrix models and the necessity to move towards more versatile data analysis tools. We show that…