Related papers: Briefly on Bottom-up
We introduce a top-down approach to discourse parsing that is conceptually simpler than its predecessors (Kobayashi et al., 2020; Zhang et al., 2020). By framing the task as a sequence labelling problem where the goal is to iteratively…
LoRA (Low-Rank Adaptation) has emerged as a preferred method for efficiently adapting Large Language Models (LLMs) with remarkable simplicity and efficacy. This note extends the original LoRA paper by offering new perspectives that were not…
In this short note, we briefly discuss the Borel-Cantelli lemma and propose a new generalization of the first part of it.
The aim of this note is to share the observation that the set of elementary operations of Turing on lattice knots can be reduced to just one type of simple local switches.
These notes give an elementary introduction to Lie groups, Lie algebras, and their representations. Designed to be accessible to graduate students in mathematics or physics, they have a minimum of prerequisites. Topics include definitions…
The design of an LR parser based on interleaving the atomic symbol processing of a context-free backbone grammar with the full constraints of the underlying unification grammar is described. The parser employs a set of reduced constraints…
The notes provide a short introduction to de Branges--Rovnyak spaces. They cover some basic facts and are intended to give the reader a taste of the theory, providing sufficient motivation to make it interesting.
Bottom-up layout algorithms for compound graphs are suitable for presenting the microscale view of models and are often used in model-driven engineering. However, they have difficulties at the macroscale where maintaining the overview of…
The purpose of these notes is to introduce some of the problems the enumeration of lattice walks is dedicated to and familiarize with some of the arguments they can be addressed with. We discuss the enumeration of lattice walks, their…
This paper provides a self-contained first introduction to description logics (DLs). The main concepts and features are explained with examples before syntax and semantics of the DL SROIQ are defined in detail. Additional sections review…
This short note is an "elementary'' introduction to the conjectural theory of motives.
Throughout the papers of E.B. Vinberg some non-abelian gradings of simple Lie algebras were introduced and investigated, namely short $SO_3 -$ and $SL_3$ - structures. We study another kind of them -- short $SL_2$ - structures. The main…
Expanded lecture notes. Preliminary version, comments are welcome.
We categorify one half of the small quantum sl(2) at a prime root of unity. An extension of this construction to an arbitrary simply-laced case is proposed.
Many algorithms in scientific computing and data science take advantage of low-rank approximation of matrices and kernels, and understanding why nearly-low-rank structure occurs is essential for their analysis and further development. This…
Here I share a few notes I used in various course lectures, talks, etc. Some may be just calculations that in the textbooks are more complicated, scattered, or less specific; others may be simple observations I found useful or curious.
Tabular data are crucial in many fields and their understanding by large language models (LLMs) under high parameter efficiency paradigm is important. However, directly applying parameter-efficient fine-tuning (PEFT) techniques to tabular…
These notes are a brief introduction to the RSA algorithm and modular arithmetic. They are intended for an undergraduate audience.
Table reasoning (TR) requires structured reasoning over semi-structured tabular data and remains challenging, particularly for small language models (SLMs, e.g., LLaMA-8B) due to their limited capacity compared to large LMs (LLMs, e.g.,…
In the present paper we discuss the lattice of reducts of $\langle \mathbb{Q}, \{$+$\} \rangle$