Related papers: Skolem Functions for Factored Formulas
Polylogrithmic functions, such as the logarithm or dilogarithm, satisfy a number of algebraic identities. For the logarithm, all the identities follow from the product rule. For the dilogarithm and higher-weight classical polylogarithms,…
Since its inception in 2016, Federated Learning (FL) has been gaining tremendous popularity in the machine learning community. Several frameworks have been proposed to facilitate the development of FL algorithms, but researchers often…
To avoid the "meaning conflation deficiency" of word embeddings, a number of models have aimed to embed individual word senses. These methods at one time performed well on tasks such as word sense induction (WSI), but they have since been…
Let X be an affine real algebraic set . We investigate on the theory of algebraically constructible functions on X and the description of the semi-algebraic subsets of X when we replace the polynomial functions on X by some rational…
Federated Learning (FL) has gained prominence as a decentralized machine learning paradigm, allowing clients to collaboratively train a global model while preserving data privacy. Despite its potential, FL faces significant challenges in…
We propose the Factorized Fourier Neural Operator (F-FNO), a learning-based approach for simulating partial differential equations (PDEs). Starting from a recently proposed Fourier representation of flow fields, the F-FNO bridges the…
Quantum signal processing is a framework for implementing polynomial functions on quantum computers. To implement a given polynomial $P$, one must first construct a corresponding complementary polynomial $Q$. Existing approaches to this…
There are many approaches to nonlinear SEM (structural equation modeling) but it seems that a rather straightforward approach using Isserlis' theorem has not yet been investigated although it allows the direct extension of the standard…
This paper studies how to sketch element-wise functions of low-rank matrices. Formally, given low-rank matrix A = [Aij] and scalar non-linear function f, we aim for finding an approximated low-rank representation of the (possibly high-rank)…
We study the algebraic theory of computable functions, which can be viewed as arising from possibly non-halting computer programs or algorithms, acting on some state space, equipped with operations of composition, {\em if-then-else} and…
The main objective of this paper is to introduce an algorithm for solving fractional and classical differential equations based on a new generalized fractional power series. The algorithm relies on expanding the solution of an FDE or an ODE…
We begin with the observation that the signed generalized Stirling polynomials $P_k(m,x)$, which occur in a generalization of Malmsten's integral, reduce to the falling factorials when $k=m$. The structure of these generalized Stirling…
We present a new probabilistic model to address semi-nonnegative matrix factorization (SNMF), called Skellam-SNMF. It is a hierarchical generative model consisting of prior components, Skellam-distributed hidden variables and observed data.…
We present a prototype of an integrated reasoning environment for educational purposes. The presented tool is a fragment of a proof assistant and automated theorem prover. We describe the existing and planned functionality of the theorem…
In this article, we prove some factorization results for several classes of polynomials having integer coefficients, which in particular yield several classes of irreducible polynomials. Such classes of polynomials are devised by imposing…
Submodular function minimization (SFM) is a fundamental and efficiently solvable problem class in combinatorial optimization with a multitude of applications in various fields. Surprisingly, there is only very little known about constraint…
The monadic second-order theory of trees allows quantification over elements and over arbitrary subsets. We classify the class of trees with respect to the question: does a tree T have definable Skolem functions (by a monadic formula with…
These days, Key-Value Stores are widely used for scalable data storage. In this environment, Bloom filter (BF) serves as an efficient probabilistic data structure for representing sets of keys. They allow for set membership queries with no…
This paper describes learning in a compiler for algorithms solving classes of the logic minimization problem MINSAT, where the underlying propositional formula is in conjunctive normal form (CNF) and where costs are associated with the…
Let G be a block matrix function with one diagonal block A being positive definite and the off diagonal blocks complex conjugates of each other. Conditions are obtained for G to be factorable (in particular, with zero partial indices) in…