Related papers: Uniqueness of Normal Forms for Shallow Term Rewrit…
We present a functional form (that we refer to as a Unified Neural Scaling Law (UNSL)) that accurately models and extrapolates the scaling behaviors of deep neural networks as multiple dimensions all vary simultaneously (i.e. how the…
The importance of subtyping to enable a wider range of well-typed programs is undeniable. However, the interaction between subtyping, recursion, and polymorphism is not completely understood yet. In this work, we explore subtyping in a…
This paper examines the potential role of unit consistency as a system design principle. Unit-consistent generalized matrix inverses and unit-invariant matrix decompositions are derived in support of this principle. Applications of the…
The formal degree of a unipotent discrete series character of a simple linear algebraic group over a non-archimedean local field (in the sense of Lusztig), is a rational function of the cardinality q of the residue field. The irreducible…
Hyperuniform materials, characterized by their suppressed density fluctuations and vanishing structure factors as the wave number approaches zero, represent a unique state of matter that straddles the boundary between order and randomness.…
We study the fundamental issue of decidability of satisfiability over string logics with concatenations and finite-state transducers as atomic operations. Although restricting to one type of operations yields decidability, little is known…
The normal form for a system of ode's is constructed from its polynomial symmetries of the linear part of the system, which is assumed to be semi-simple. The symmetries are shown to have a simple structure such as invariant function times…
A relational structure $\mathbb{X}$ is called reversible iff each bijective homomorphism from $\mathbb{X}$ onto $\mathbb{X}$ is an isomorphism, and linear orders are prototypical examples of such structures. One way to detect new reversible…
Minimal surfaces are ubiquitous in nature. Here they are considered as geometric objects that bear a deformation content. By refining the resolution of the surface deformation gradient afforded by the polar decomposition theorem, we…
Recent work on the use of dimensional reduction for the regularisation of non--supersymmetric theories is reviewed. It is then shown that there exists a class of theories for which a universal form of the soft supersymmetry breaking terms…
A deflatable permutation class is one in which the simple permutations are contained in a proper subclass. Deflatable permutation classes are often easier to describe and enumerate than non-deflatable ones. Some theorems which guarantee…
For a set $S$ of (positive definite and integral) quadratic forms with bounded rank, a quadratic form $f$ is called $S$-universal if it represents all quadratic forms in $S$. A subset $S_0$ of $S$ is called an $S$-universality criterion set…
Let $\mathscr{X}\to W$ be a flat family of generically irreducible hypersurfaces of degree $d\geq 2$ in $\PP^n$ with singular locus of dimension $t$, with $W$ unirational of dimension $r$. We prove that if $n$ is large enough with respect…
The HOM problem, which asks whether the image of a regular tree language under a given tree homomorphism is again regular, is known to be decidable [Godoy & Gim\'enez: The HOM problem is decidable. JACM 60(4), 2013]. However, the problem…
Regular synchronization languages can be used to define rational relations of finite words, and to characterize subclasses of rational relations, like automatic or recognizable relations. We provide a systematic study of the decidability of…
This paper tackles the problem of the existence of solutions for recursive systems of Horn clauses with second-order variables interpreted as integer relations, and harnessed by quantifier-free difference bounds arithmetic. We start by…
We study the problem of completely automatically verifying uninterpreted programs---programs that work over arbitrary data models that provide an interpretation for the constants, functions and relations the program uses. The verification…
In this manuscript we present a detailed proof for undecidability of the equivalence of finite substitutions on regular language $b\{0,1\}^*c$. The proof is based on the works of Leonid P. Lisovik.
List-wise reranking arranges a request-specific pool of candidate items into an ordered slate that maximizes user satisfaction. Existing generative rerankers fall into two paradigms: Autoregressive (AR) rerankers construct the slate left to…
The present work establishes necessary and sufficient conditions for a nonlinear system with two inputs to be described by a specific triangular form. Except for some regularity conditions, such triangular form is flat. This may lead to the…