相关论文: Distributed Computation over MAC via Kolmogorov-Ar…

The multi-user linearly-separable distributed computing problem is considered here, in which $N$ servers help to compute the real-valued functions requested by $K$ users, where each function can be written as a linear combination of up to…

This paper considers an $N$-server distributed computing setting with $K$ users requesting functions that are arbitrary multivariable polynomial evaluations of $L$ real (potentially non-linear) basis subfunctions, where each function output…

Recent advancements in both representation learning and function learning have demonstrated substantial promise across diverse domains of artificial intelligence. However, the effective integration of these paradigms poses a significant…

Many computational problems can be formulated in terms of high-dimensional functions. Simple representations of such functions and resulting computations with them typically suffer from the "curse of dimensionality", an exponential cost…

For years, many neural networks have been developed based on the Kolmogorov-Arnold Representation Theorem (KART), which was created to address Hilbert's 13th problem. Recently, relying on KART, Kolmogorov-Arnold Networks (KANs) have…

We develop and investigate a general theory of representations of second-order functionals, based on a notion of a right comodule for a monad on the category of containers. We show how the notion of comodule representability naturally…

We develop the notion of a locally homomorphic channel and prove an approximate equivalence between those and codes for computing functions. Further, we derive decomposition properties of locally homomorphic channels which we use to analyze…

We introduce combinatorial interpretability, a methodology for understanding neural computation by analyzing the combinatorial structures in the sign-based categorization of a network's weights and biases. We demonstrate its power through…

We propose a compact and effective framework to fuse multimodal features at multiple layers in a single network. The framework consists of two innovative fusion schemes. Firstly, unlike existing multimodal methods that necessitate…

Neural compression algorithms are typically based on autoencoders that require specialized encoder and decoder architectures for different data modalities. In this paper, we propose COIN++, a neural compression framework that seamlessly…

We propose a federated methodology to learn low-dimensional representations from a dataset that is distributed among several clients. In particular, we move away from the commonly-used cross-entropy loss in federated learning, and seek to…

Aiming at better representing multivariate relationships, this paper investigates a motif dimensional framework for higher-order graph learning. The graph learning effectiveness can be improved through OFFER. The proposed framework mainly…

Beginning with the projectively invariant method for linear programming, interior point methods have led to powerful algorithms for many difficult computing problems, in combinatorial optimization, logic, number theory and non-convex…

Symbolic discovery of governing equations is a long-standing goal in scientific machine learning, yet a fundamental trade-off persists between interpretability and scalable learning. Classical symbolic regression methods yield explicit…

We provide extension procedures for nonlinear expectations to the space of all bounded measurable functions. We first discuss a maximal extension for convex expectations which have a representation in terms of finitely additive measures.…

Proximal operators with affine constraints arise in numerous models in nonconvex projection, composite optimization, and structured regularization. However, their efficient computation remains challenging due to the simultaneous presence of…

We study the limits of communication efficiency for function computation in collocated networks within the framework of multi-terminal block source coding theory. With the goal of computing a desired function of sources at a sink, nodes…

Distributed computing is fundamental to multi-agent systems, with solving distributed linear equations as a typical example. In this paper, we study distributed solvers for network linear equations over a network with node-to-node…

We propose a model for deterministic distributed function computation by a network of identical and anonymous nodes, with bounded computation and storage capabilities that do not scale with the network size. Our goal is to characterize the…

Representation of data on mixed variables, numerical and categorical types to get suitable feature map is a challenging task as important information lies in a complex non-linear manifold. The feature transformation should be able to…