Related papers: Briefly on Bottom-up
In this paper a list of $R$-matrices on a certain coupled Lie algebra is obtained. With one of these $R$-matrices, we construct infinitely many bi-Hamiltonian structures for each of the two-component BKP and the Toda lattice hierarchies. We…
These informal notes are concerned with sums and averages in various situations in analysis.
This paper describes an algorithm for the compilation of a two (or more) level orthographic or phonological rule notation into finite state transducers. The notation is an alternative to the standard one deriving from Koskenniemi's work: it…
In this paper we relate a number of parsing algorithms which have been developed in very different areas of parsing theory, and which include deterministic algorithms, tabular algorithms, and a parallel algorithm. We show that these…
In this review, we examine the recent progress in saliency prediction and proposed several avenues for future research. In spite of tremendous efforts and huge progress, there is still room for improvement in terms finer-grained analysis of…
These informal notes concern some basic themes of harmonic analysis related to representations of groups.
We investigate the definability (reducts) lattice of the order of integers and describe a sublattice generated by relations 'between', 'cycle', 'separation', 'neighbor', '1-codirection', 'order' and equality'. Some open questions are…
This short note gives questions and examples of points on X1(N) defined over number fields whose degrees are lower than the gonality.
Consider a finite-dimensional, complex Lie algebra G and a semi-simple automorphism {\alpha}. This note aims to give a short and simple proof for explicit upper bounds for the derived length of the radical R and the rank of a Levi…
Perspective on cond-mat/0303289
A general method for calculating or constructing lower central factors of groups is presented. {\it Relative basic commutators} are defined.
These notes deal with a few aspects of Lie algebras and Lie groups, including some matters related to exponentiation.
Motivated by re-weighted $\ell_1$ approaches for sparse recovery, we propose a lifted $\ell_1$ (LL1) regularization which is a generalized form of several popular regularizations in the literature. By exploring such connections, we discover…
Coreference annotation and resolution is a vital component of computational literary studies. However, it has previously been difficult to build high quality systems for fiction. Coreference requires complicated structured outputs, and…
As for semantic role labeling (SRL) task, when it comes to utilizing parsing information, both traditional methods and recent recurrent neural network (RNN) based methods use the feature engineering way. In this paper, we propose Syntax…
Named entity recognition (NER) models are typically based on the architecture of Bi-directional LSTM (BiLSTM). The constraints of sequential nature and the modeling of single input prevent the full utilization of global information from…
Sentence-level classification and sequential labeling are two fundamental tasks in language understanding. While these two tasks are usually modeled separately, in reality, they are often correlated, for example in intent classification and…
An exposition of the mathematics underpinning the neural network architecture of a GPT-3-style LLM.
Recent work in NLP shows that LSTM language models capture hierarchical structure in language data. In contrast to existing work, we consider the \textit{learning} process that leads to their compositional behavior. For a closer look at how…
These are notes on adic spaces. They are made available upon some requests in order to make quoting them easier.