Related papers: Random Operator Approach for Word Enumeration in B…
In many data analysis pipelines, a basic and time-consuming process is to produce join results and feed them into downstream tasks. Numerous enumeration algorithms have been developed for this purpose. To be a statistically meaningful…
Large Language Model (LLM) has demonstrated significant ability in various Natural Language Processing tasks. However, their effectiveness is highly dependent on the phrasing of the task prompt, leading to research on automatic prompt…
The direct parametrisation method for invariant manifold is a model-order reduction technique that can be applied to nonlinear systems described by PDEs and discretised e.g. with a finite element procedure in order to derive efficient…
Nominal automata models serve as a formalism for data languages, and in fact often relate closely to classical register models. The paradigm of name allocation in nominal automata helps alleviate the pervasive computational hardness of…
We develop a combinatorial approach to the study of semigroups and monoids with finite presentations satisfying small overlap conditions. In contrast to existing geometric methods, our approach facilitates a sequential left-right analysis…
Interval scheduling is a basic problem in the theory of algorithms and a classical task in combinatorial optimization. We develop a set of techniques for partitioning and grouping jobs based on their starting and ending times, that enable…
Symbolic regression is a type of discrete optimization problem that involves searching expressions that fit given data points. In many cases, other mathematical constraints about the unknown expression not only provide more information…
We investigate a learning algorithm in the context of nominal automata, an extension of classical automata to alphabets featuring names. This class of automata captures nominal regular languages; analogously to the classical language…
We present a new optimization method for the group selection problem in linear regression. In this problem, predictors are assumed to have a natural group structure and the goal is to select a small set of groups that best fits the…
We introduce classical and non-deterministic finite automata associated with representations of the braid group. After briefly reviewing basic definitions on finite automata, Coxeter's groups and the associated word problem, we turn to the…
We study the complexity of computation in finitely generated free left, right and two-sided adequate semigroups and monoids. We present polynomial time (quadratic in the RAM model of computation) algorithms to solve the word problem and…
We combine concepts from random matrix theory and free probability together with ideas from the theory of commutator length in groups and maps from surfaces, and establish new connections between the two. More particularly, we study…
This work studies the problem of sparse signal recovery with automatic grouping of variables. To this end, we investigate sorted nonsmooth penalties as a regularization approach for generalized linear models. We focus on a family of sorted…
Given a locally finite graph $\Gamma$, an amenable subgroup $G$ of graph automorphisms acting freely and almost transitively on its vertices, and a $G$-invariant activity function $\lambda$, consider the free energy $f_G(\Gamma,\lambda)$ of…
Recently the third named author defined a 2-parametric family of groups $G_n^k$ \cite{gnk}. Those groups may be regarded as a certain generalisation of braid groups. Study of the connection between the groups $G_n^k$ and dynamical systems…
Data trees serve as an abstraction of structured data, such as XML documents. A number of specification formalisms for languages of data trees have been developed, many of them adhering to the paradigm of register automata, which is based…
For random operators it is conjectured that spectral properties of an infinite-volume operator are related to the distribution of spectral gaps of finite-volume approximations. In particular, localization and pure point spectrum in infinite…
We present a formal operator-theoretic framework for analyzing Transformer-based language models using free probability theory. By modeling token embeddings and attention mechanisms as self-adjoint operators in a tracial \( W^*…
Word segmentation is the task of inserting or deleting word boundary characters in order to separate character sequences that correspond to words in some language. In this article we propose an approach based on a beam search algorithm and…
We study the task, for a given language $L$, of enumerating the (generally infinite) sequence of its words, without repetitions, while bounding the delay between two consecutive words. To allow for delay bounds that do not depend on the…