Related papers: Generating sequences of rank 1 valuations

Neural sequence generation is typically performed token-by-token and left-to-right. Whenever a token is generated only previously produced tokens are taken into consideration. In contrast, for problems such as sequence classification,…

Generative models reliant on sequential autoregression have been at the forefront of language generation for an extensive period, particularly following the introduction of widely acclaimed transformers. Despite its excellent performance,…

For an arbitrary ideal $I$ in a polynomial ring $R$ we define the notion of initially regular sequences on $R/I$. These sequences share properties with regular sequences. In particular, the length of an initially regular sequence provides a…

In this paper we define and study self-similar ranked fragmentations. We first show that any ranked fragmentation is the image of some partition-valued fragmentation, and that there is in fact a one-to-one correspondence between the laws of…

We give a new algorithm for constructing Picard curves over a finite field with a given endomorphism ring. This has important applications in cryptography since curves of genus 3 allow for smaller key sizes than elliptic curves. For a…

Reranking is attracting incremental attention in the recommender systems, which rearranges the input ranking list into the final rank-ing list to better meet user demands. Most existing methods greedily rerank candidates through the rating…

Let us consider a polynomial algebra in three variables equipped with an integer grading. We construct a system of group-generating automorphisms that preserve a given grading.

Suppose that $R$ is a 2 dimensional excellent local domain with quotient field $K$, $K^*$ is a finite separable extension of $K$ and $S$ is a 2 dimensional local domain with quotient field $K^*$ such that $S$ dominates $R$. Suppose that…

In the combinatorial recommender systems, multiple items are fed to the user at one time in the result page, where the correlations among the items have impact on the user behavior. In this work, we model the combinatorial recommendation as…

We present a simple, yet useful result about the expected value of the determinant of random sum of rank-one matrices. Computing such expectations in general may involve a sum over exponentially many terms. Nevertheless, we show that an…

We give new and efficient black-box reconstruction algorithms for some classes of depth-$3$ arithmetic circuits. As a consequence, we obtain the first efficient algorithm for computing the tensor rank and for finding the optimal tensor…

In this paper, we consider the rank-one tensor completion problem. We address the question of existence and uniqueness of the rank-one solution. In particular we show that the global uniqueness over the field of real numbers can be verified…

Let f be a real or complex polynomial. We give an algorithm to compute the set of generalized critical values. The algorithm uses a finite dimensional space of rational arcs along which we can reach all generalized critical values of f.

A Skolem sequence is a linear arrangement of the multiset, {1, 1, 2, 2, ..., n, n} such that if r in [n] appears in positions i and j, then |i-j| = r. We first translate the problem to a particular set of perfect matchings, then apply the…

A valuation theory for superrings is developed, extending classical constructions from commutative algebra to the $\mathbb Z_2$-graded and supercommutative setting. We define valuations on superrings, investigate their fundamental…

$\newcommand{\R}{\mathbb R} \newcommand{\rweyl}{\mathcal{A}_1(\R)}$ The first Weyl algebra $\mathcal{A}_1(k)$ over a field $k$ is the $k$-algebra with two generators $x, y$ subject to $[y, x] = 1$ and was first introduced during the…

We study whether visual embedding models capture continuous, ordinal attributes along linear directions, which we term _rank axes_. We define a model as _rankable_ for an attribute if projecting embeddings onto such an axis preserves the…

Non-linear recurrences which generate integers in a surprising way have been studied by many people. Typically people study recurrences that are linear in the highest order term. In this paper I consider what happens when the recurrence is…

Sequence generation with reinforcement learning (RL) has received significant attention recently. However, a challenge with such methods is the sparse-reward problem in the RL training process, in which a scalar guiding signal is often only…

Given an undirected graph representing similarities between a set of items and an additive measure evaluating the items, we treat the position of a special subset of items in an ordinal ranking through a collection of combinatorial…