Related papers: Comparison-free polyregular functions
Functional MSO transductions, deterministic two-way transducers, as well as streaming string transducers are all equivalent models for regular functions. In this paper, we show that every regular function, either on finite words or on…
Recent work has shown that purely quadratic functions can replace MLPs in transformers with no significant loss in performance, while enabling new methods of interpretability based on linear algebra. In this work, we theoretically derive…
We introduce the notion of composite growth function and provide examples that illustrate the primary properties of these growth functions. There are provided examples of Mealy automata that have composite non-monotonic growth functions of…
In this article, we explore a class of tractable interest rate models that have the property that the price of a zero-coupon bond can be expressed as a polynomial of a state diffusion process. Our results include a classification of all…
Matrix functions extend scalar function concepts to linear operators, offering a unified framework with broad applications in mathematics, science, and engineering. Classical definitions--via power series, spectral calculus, or Jordan…
Motivated by the successful application of the theory of regular languages to formal verification of finite-state systems, there is a renewed interest in developing a theory of analyzable functions from strings to numerical values that can…
We develop here a novel transfer learning methodology called Profiled Transfer Learning (PTL). The method is based on the \textit{approximate-linear} assumption between the source and target parameters. Compared with the commonly assumed…
An overview is given of the construction of a differential polynomial ring of functions on the moduli space of Calabi-Yau threefolds. These rings coincide with the rings of quasi modular forms for geometries with duality groups for which…
Multiplication layers are a key component in various influential neural network modules, including self-attention and hypernetwork layers. In this paper, we investigate the approximation capabilities of deep neural networks with…
The focus of this thesis is on (1) the role of Ka\v c-Moody (KM) algebras in string theory and the development of techniques for systematically building string theory models based on higher level ($K\geq 2$) KM algebras and (2) fractional…
We investigate a more generalized form of submodular maximization, referred to as $k$-submodular maximization, with applications across social networks and machine learning domains. In this work, we propose the multilinear extension of…
Entire functions in one complex variable are extremely relevant in several areas ranging from the study of convolution equations to special functions. An analog of entire functions in the quaternionic setting can be defined in the slice…
We investigate new graph classes of bounded mim-width, strictly extending interval graphs and permutation graphs. The graphs $K_t \boxminus K_t$ and $K_t \boxminus S_t$ are graphs obtained from the disjoint union of two cliques of size $t$,…
Learning probabilistic models over strings is an important issue for many applications. Spectral methods propose elegant solutions to the problem of inferring weighted automata from finite samples of variable-length strings drawn from an…
We discuss various formalisms to describe string-to-string transformations. Many are based on automata and can be seen as operational descriptions, allowing direct implementations when the input scanner is deterministic. Alternatively, one…
In studying the expressiveness of neural networks, an important question is whether there are functions which can only be approximated by sufficiently deep networks, assuming their size is bounded. However, for constant depths, existing…
We develop a family-based route to unicyclic graphs whose independence polynomials are unimodal but not log-concave. The paper is organized around one flagship statement: for the explicit KL-closure family $U_{k,r}$, with $r\in\{0,1,2\}$…
A cutting-plane model for a nonsmooth function is the maximum of several first-order expansions centered at different points. Using such a model in a bundle method leads to linear convergence (of serious steps) to a minimum. In smooth…
String diagrams are a powerful tool for reasoning about physical processes, logic circuits, tensor networks, and many other compositional structures. The distinguishing feature of these diagrams is that edges need not be connected to…
We study modular transformation properties of a class of indefinite theta series involved in characters of infinite-dimensional Lie superalgebras. The \textit{level-$\ell$ Appell functions} $K_\ell$ satisfy open quasiperiodicity relations…