Related papers: The Parallel-Sequential Duality : Matrices and Gra…

Decomposable dependency models and their graphical counterparts, i.e., chordal graphs, possess a number of interesting and useful properties. On the basis of two characterizations of decomposable models in terms of independence…

In this paper, we study discrete Lyapunov models, which consist of steady-state distributions of first-order vector autoregressive models. The parameter matrix of such a model encodes a directed graph whose vertices correspond to the…

Algebraic effects and handlers support composable and structured control-flow abstraction. However, existing designs of algebraic effects often require effects to be executed sequentially. This paper studies parallel algebraic effect…

We reveal that transformers trained in an autoregressive manner naturally encode time-delayed causal structures in their learned representations. When predicting future values in multivariate time series, the gradient sensitivities of…

This article shows a correspondence between abstract interpretation of imperative programs and the refinement calculus: in the refinement calculus, an abstract interpretation of a program is a specification which is a function. This…

One must add arrows which are forced by transitivity to form the transitive closure of a directed graph. We introduce a construction of a transitive directed graph which is formed by adding vertices instead of arrows and which preserves the…

In real world domains, most graphs naturally exhibit a hierarchical structure. However, data-driven graph generation is yet to effectively capture such structures. To address this, we propose a novel approach that recursively generates…

We extend the concept of the law of a finite graph to graphings, which are, in general, infinite graphs whose vertices are equipped with the structure of a probability space. By doing this, we obtain a vast array of new unimodular measures.…

On the Euclidean domains of classical signal processing, linking of signal samples to the underlying coordinate structure is straightforward. While graph adjacency matrices totally define the quantitative associations among the underlying…

We prove a general duality theorem for tangle-like dense objects in combinatorial structures such as graphs and matroids. This paper continues, and assumes familiarity with, the theory developed in [6]

Call graphs depict the static, caller-callee relation between "functions" in a program. With most source/target languages supporting functions as the primitive unit of composition, call graphs naturally form the fundamental control flow…

In this paper, we extend the recently introduced concept of partially dual ribbon graphs to graphs. We then go on to characterize partial duality of graphs in terms of bijections between edge sets of corresponding graphs. This result…

Neural fields offer continuous, learnable representations that extend beyond traditional discrete formats in visual computing. We study the problem of learning neural representations of repeated antiderivatives directly from a function, a…

While deep learning excels in natural image and language processing, its application to high-dimensional data faces computational challenges due to the dimensionality curse. Current large-scale data tools focus on business-oriented…

In this dissertation, we explore the structure of inversion graphs of permutations--a class of graphs that naturally arises by representing each permutation as a graph, where vertices correspond to entries and edges encode inversions.…

The (parallel linear) transports in tensor spaces generated by derivations of the tensor algebra along paths are axiomatically described. Certain their properties are investigated. Transports along paths defined by derivations of the tensor…

Many applications collect a large number of time series, for example, the financial data of companies quoted in a stock exchange, the health care data of all patients that visit the emergency room of a hospital, or the temperature sequences…

In many ways, graphs are the main modality of data we receive from nature. This is due to the fact that most of the patterns we see, both in natural and artificial systems, are elegantly representable using the language of graph structures.…

We study the computational model of polygraphs. For that, we consider polygraphic programs, a subclass of these objects, as a formal description of first-order functional programs. We explain their semantics and prove that they form a…

Traditional model-based diagnosis relies on constructing explicit system models, a process that can be laborious and expertise-demanding. In this paper, we propose a novel framework that combines concepts of model-based diagnosis with deep…