Related papers: Comparison-free polyregular functions

This work concerns random dynamics of hyperbolic entire and meromorphic functions of finite order and whose derivative satisfies some growth condition at infinity. This class contains most of the classical families of transcendental…

We study the notion of tangent-like maps, which is a transcendental analogue of polynomial-like maps. We introduce a model family analogous to quadratic polynomials, with only one free asymptotic value, and define the "Tandelbrot set" as…

This paper proposes a novel method for learning highly nonlinear, multivariate functions from examples. Our method takes advantage of the property that continuous functions can be approximated by polynomials, which in turn are representable…

In context of the Wolfram Physics Project, a certain class of abstract rewrite systems known as "multiway systems" have played an important role in discrete models of spacetime and quantum mechanics. However, as abstract mathematical…

A new class of regular quaternionic functions, defined by power series in a natural fashion, has been introduced in recent years. Several results of the theory recall the classical complex analysis, whereas other results reflect the…

We study the dynamics of supervised on-line learning of realizable tasks in feed-forward neural networks. We focus on the regime where the number of examples used for training is proportional to the number of input channels N. Using…

In this thesis, we consider the problem of characterizing and enumerating sets of polyominoes described in terms of some constraints, defined either by convexity or by pattern containment. We are interested in a well known subclass of…

This paper considers submodular function minimization (SFM) restricted to a family of subsets. We show that SFM over complements of families with certain hierarchical structures can be solved in polynomial-time. This yields a…

We define two classes of functions, called regular (respectively, first-order) list functions, which manipulate objects such as lists, lists of lists, pairs of lists, lists of pairs of lists, etc. The definition is in the style of regular…

A Stein manifold X is called S-parabolic if it possesses a plurisub- harmonic exhaustion function p that is maximal outside a compact subset of X: In analogy with (Cn; ln jzj), one defines the space of polynomials on a S- parabolic manifold…

The notion of delay between finite transducers is a core element of numerous fundamental results of transducer theory. The goal of this work is to provide a similar notion for more complex abstract machines: we introduce a new notion of…

Modular graph functions arise in the calculation of the low-energy expansion of closed-string scattering amplitudes. For toroidal world-sheets, they are ${\rm SL}(2,\mathbb{Z})$-invariant functions of the torus complex structure that have…

Linear extended top-down tree transducers (or synchronous tree-substitution grammars) are popular formal models of tree transformations. The expressive power of compositions of such transducers with and without regular look-ahead is…

We introduce the concept of a prime band in a string algebra $\Lambda$ and use it to associate to $\Lambda$ its finite bridge quiver. Then we introduce a new technique of `recursive systems' for showing that a graph map between finite…

This paper presents a noncommutative theory of symmetric functions, based on the notion of quasi-determinant. We begin with a formal theory, corresponding to the case of symmetric functions in an infinite number of independent variables.…

Little string theories (LSTs) are UV complete non-local 6D theories decoupled from gravity in which there is an intrinsic string scale. In this paper we present a systematic approach to the construction of supersymmetric LSTs via the…

Standard neural network architectures are non-linear only by virtue of a simple element-wise activation function, making them both brittle and excessively large. In this paper, we consider methods for making the feed-forward layer more…

It is open whether equivalence ( f = g ) is decidable for string-to-string polyregular functions. We consider their higher-order extension based on the {\lambda}-calculus definition of polyregular functions from Boja\'nczyk (2018). In this…

This paper proposes a definition of recognizable transducers over monads and comonads, which bridges two important ongoing efforts in the current research on regularity. The first effort is the study of regular transductions, which extends…

We present a system that enables rapid model experimentation for tera-scale machine learning with trillions of non-zero features, billions of training examples, and millions of parameters. Our contribution to the literature is a new method…