Related papers: Representations of Stream Processors Using Nested …

Neural networks successfully capture the computational power of the human brain for many tasks. Similarly inspired by the brain architecture, Nearest Neighbor (NN) representations is a novel approach of computation. We establish a firmer…

We completely describe a new domain for abstract interpretation of numerical programs. Fixpoint iteration in this domain is proved to converge to finite precise invariants for (at least) the class of stable linear recursive filters of any…

Deep learning is currently the subject of intensive study. However, fundamental concepts such as representations are not formally defined -- researchers "know them when they see them" -- and there is no common language for describing and…

This work provides the first unifying theoretical framework for node (positional) embeddings and structural graph representations, bridging methods like matrix factorization and graph neural networks. Using invariant theory, we show that…

We investigate the hierarchical structure of processes using the mathematical theory of operads. Information or material enters a given process as a stream of inputs, and the process converts it to a stream of outputs. Output streams can…

We have a set of processors (or agents) and a set of graph networks defined over some vertex set. Each processor can access a subset of the graph networks. Each processor has a demand specified as a pair of vertices $<u, v>$, along with a…

We recently introduced a formalism for the modeling of temporal networks, that we call stream graphs. It emphasizes the streaming nature of data and allows rigorous definitions of many important concepts generalizing classical graphs. This…

Molecules have various computational representations, including numerical descriptors, strings, graphs, point clouds, and surfaces. Each representation method enables the application of various machine learning methodologies from linear…

The representation of graphs is commonly based on the adjacency matrix concept. This formulation is the foundation of most algebraic and computational approaches to graph processing. The advent of deep learning language models offers a wide…

This paper intends to lay the theoretical foundation for the method of functional maps, first presented in 2012 by Ovsjanikov, Ben-Chen, Solomon, Butscher and Guibas in the field of the theory and numerics of maps between shapes. We show…

Stochastic line integrals provide a useful tool for quantitatively characterizing irreversibility and detailed balance violation in noise-driven dynamical systems. A particular realization is the stochastic area, recently studied in coupled…

Finite (word) state transducers extend finite state automata by defining a binary relation over finite words, called rational relation. If the rational relation is the graph of a function, this function is said to be rational. The class of…

In a number of papers, Y. Sternfeld investigated the problems of representation of continuous and bounded functions by linear superpositions. In particular, he proved that if such representation holds for continuous functions, then it holds…

Coordination is essential for dynamic distributed systems whose components exhibit interactive and autonomous behaviors. Spatially distributed, locally interacting, propagating computational fields are particularly appealing for allowing…

Connected operators are filtering tools that act by merging elementary regions of an image. A popular strategy is based on tree-based image representations: for example, one can compute an attribute on each node of the tree and keep only…

In this paper, we propose a convolutional layer inspired by optical flow algorithms to learn motion representations. Our representation flow layer is a fully-differentiable layer designed to capture the `flow' of any representation channel…

Theoretical studies show that for any differentiable function on a compact domain, there exists a neural network that approximates both the function values and gradients. However, such a result cannot be used in practice since it assumes…

Based on a new coinductive characterization of continuous functions we extract certified programs for exact real number computation from constructive proofs. The extracted programs construct and combine exact real number algorithms with…

A major problem in system identification is the incorporation of prior knowledge about the physical properties of the given system, such as stability, positivity and passivity. In this paper, we present first steps towards tackling this…

Concept-based interpretability for Convolutional Neural Networks (CNNs) aims to align internal model representations with high-level semantic concepts, but existing approaches largely overlook the semantic roles of individual filters and…