Related papers: Representations of Stream Processors Using Nested …
An analogue of Burnside's Lemma for 2-transitive groups is shown to hold for a class of topological groups. If the group is compact the representation is finite and splits into an irreducible and the constant functions. If both the group…
Tensor networks and circuits are widely used data structures to represent pseudo-Boolean functions. These two formalisms have been studied primarily in separate communities, and this paper aims to establish equivalences between them. We…
Representing 3D surfaces as level sets of continuous functions over $\mathbb{R}^3$ is the common denominator of neural implicit representations, which recently enabled remarkable progress in geometric deep learning and computer vision…
Diffusion models have established themselves as state-of-the-art generative models across various data modalities, including images and videos, due to their ability to accurately approximate complex data distributions. Unlike traditional…
We introduce a definition of a quasiconvex function on an infinite directed regular tree that depends on what we understood by a segment on the tree. Our definition is based on thinking on segments as sub-trees with the root as the midpoint…
A prominent goal of representation learning research is to achieve representations which are factorized in a useful manner with respect to the ground truth factors of variation. The fields of disentangled and equivariant representation…
There is a growing demand for live, on-the-fly processing of increasingly large amounts of data. In order to ensure the timely and reliable processing of streaming data, a variety of distributed stream processing architectures and platforms…
An efficient and flexible engine for computing fixed points is critical for many practical applications. In this paper, we firstly present a goal-directed fixed point computation strategy in the logic programming paradigm. The strategy…
Mounting evidence in neuroscience suggests the possibility of neuronal representations that individual neurons serve as the substrates of different mental representations in a point-to-point way. Combined with associationism, it can…
Kolmogorov's representation theorem provides a framework for decomposing any arbitrary real-valued, multivariate, and continuous function into a two-layer nested superposition of a finite number of functions. The functions at these two…
We introduce monoidal streams: a generalization of causal stream functions to monoidal categories. In the same way that streams provide semantics to dataflow programming with pure functions, monoidal streams provide semantics to dataflow…
We construct compositional continuous approximations for an interconnection of infinitely many discrete-time switched systems. An approximation (known as abstraction) is itself a continuous-space system, which can be used as a replacement…
We consider the problem of representation of a bivariate function by sums of ridge functions. We show that if a function of a certain smoothness class is represented by a sum of finitely many, arbitrarily behaved ridge functions, then it…
Given $m$ distributed data streams $A_1, \dots, A_m$, we consider the problem of estimating the number of unique identifiers in streams defined by set expressions over $A_1, \dots, A_m$. We identify a broad class of algorithms for solving…
We introduce a change of perspective on tensor network states that is defined by the computational graph of the contraction of an amplitude. The resulting class of states, which we refer to as tensor network functions, inherit the…
We study properties of strongly separately continuous mappings defined on subsets of products of topological spaces equipped with the topology of pointwise convergence. In particular, we give a necessary and sufficient condition for a…
In this paper, C1-conforming element methods are analyzed for the stream function formulation of a single layer non-stationary quasi-geostrophic equation in the ocean circulation model. In its first part, some new regularity results are…
Terminal coalgebras for a functor serve as semantic domains for state-based systems of various types. For example, behaviors of CCS processes, streams, infinite trees, formal languages and non-well-founded sets form terminal coalgebras. We…
A neural network computes a function. A central property of neural networks is that they are "universal approximators:" for a given continuous function, there exists a neural network that can approximate it arbitrarily well, given enough…
We consider the problem of the representation of real continuous functions by linear superpositions $\sum_{i=1}^{k}g_{i}\circ p_{i}$ with continuous $g_{i}$ and $p_{i}$. This problem was considered by many authors. But complete, and at the…