Related papers: Expregular functions

Idempotent Boolean functions form a highly structured subclass of Boolean functions that is closely related to rotation symmetry under a normal-basis representation and to invariance under a fixed linear map in a polynomial basis. These…

The theory of regular cost functions is a quantitative extension to the classical notion of regularity. A cost function associates to each input a non-negative integer value (or infinity), as opposed to languages which only associate to…

Despite the great success of Transformer networks in various applications such as natural language processing and computer vision, their theoretical aspects are not well understood. In this paper, we study the approximation and estimation…

This paper examines the characterization and learning of grammars defined with enriched representational models. Model-theoretic approaches to formal language theory traditionally assume that each position in a string belongs to exactly one…

We study various regularization operators on plurisubharmonic functions that preserve Lelong classes with growth given by certain compact convex sets. The purpose is to show that the weighted Siciak-Zakharyuta functions associated with…

Polynomial functions have plenty of useful analytical properties, but they are rarely used as learning models because their function class is considered to be restricted. This work shows that when trained properly polynomial functions can…

Inspired by prior work of Bruinier and Ono and Mertens and Rolen, we study class polynomials for non-holomorphic modular functions arising from modular forms of negative weight. In particular, we give general conditions for the…

Large language and music models are increasingly used for constrained generation: rhyming lines, fixed meter, inpainting or infilling, positional endings, and other global form requirements. These systems often perform strikingly well, but…

Multi-task learning, as it is understood nowadays, consists of using one single model to carry out several similar tasks. From classifying hand-written characters of different alphabets to figuring out how to play several Atari games using…

For any measure preserving system $(X,\mathcal{B},\mu,T_1,\ldots,T_d),$ where we assume no commutativity on the transformations $T_i,$ $1\leq i\leq d,$ we study the pointwise convergence of multiple ergodic averages with iterates of…

We establish strong well-posedness for a class of degenerate SDEs of kinetic type with autonomous diffusion driven by a symmetric $\alpha$-stable process under H\"older regularity conditions for the drift term. We partially recover the…

Fast-growing hierarchies are sequences of functions obtained through various processes similar to the ones that yield multiplication from addition, exponentiation from multiplication, etc. We observe that fast-growing hierarchies can be…

We say that a positively homogeneous function admits a saddle representation by linear functions iff it admits both an inf-sup-representation and a sup-inf-representation with the same two-index family of linear functions. In the paper we…

We give estimates for the convolution product of an arbitrary number of endlessly continuable functions. This allows us to deal with nonlinear operations for the corresponding resurgent series, e.g. substitution into a convergent power…

Compounding submodular monotone (i.e. 2-alternating) set functions on a finite set preserves this property, as shown in 2010. A natural generalization to k-alternating functions was presented in 2018, however hardly readable because of page…

We propose a multi-resolution convolutional autoencoder (MrCAE) architecture that integrates and leverages three highly successful mathematical architectures: (i) multigrid methods, (ii) convolutional autoencoders and (iii) transfer…

We investigate combinatorial properties of a kind of insets we defined in an earlier paper, interpreting them now in terms of restricted ternary words. This allows us to give new combinatorial interpretations of a number of known integer…

In mathematical logic there are two seemingly distinct kinds of principles called "reflection principles." Semantic reflection principles assert that if a formula holds in the whole universe, then it holds in a set-sized model. Syntactic…

We present a family of neural-network--inspired models for computing continuous word representations, specifically designed to exploit both monolingual and multilingual text. This framework allows us to perform unsupervised training of…

Dominant sequence models like the Transformer represent structure implicitly through dense attention weights, incurring quadratic complexity. We propose RewriteNets, a novel neural architecture built on an alternative paradigm: explicit,…