Related papers: Continuous Sentences Preserved Under Reduced Produ…
A lot of work has been done in the field of image compression via machine learning, but not much attention has been given to the compression of natural language. Compressing text into lossless representations while making features easily…
In this work some results on the structure-preserving diagonalization of selfadjoint and skewadjoint matrices in indefinite inner product spaces are presented. In particular, necessary and sufficient conditions on the symplectic…
Autoregressive language models (LMs) generate one token at a time, yet human reasoning operates over higher-level abstractions - sentences, propositions, and concepts. This contrast raises a central question- Can LMs likewise learn to…
We show stability of spherical caps (SCs) lying on a flat surface, where the motion is governed by the volume-preserving Mean Curvature Flow (MCF). Moreover, we introduce a dynamic boundary condition that models a line tension effect on the…
We highlight some facts about continued fractions of real cubic irrationalities. This may be thought as a small section in a textbook on continued fractions.
Contextualized representation models such as ELMo (Peters et al., 2018a) and BERT (Devlin et al., 2018) have recently achieved state-of-the-art results on a diverse array of downstream NLP tasks. Building on recent token-level probing work,…
The theory of persistence modules is an emerging field of algebraic topology which originated in topological data analysis. In these notes we provide a concise introduction into this field and give an account on some of its interactions…
The semantics of the Prolog ``cut'' construct is explored in the context of some desirable properties of logic programming systems, referred to as the witness properties. The witness properties concern the operational consistency of…
We combine aspects of the notions of finite decomposition complexity and asymptotic property C into a notion that we call finite APC-decomposition complexity. Any space with finite decomposition complexity has finite APC-decomposition…
Intuitionistic grammar logics fuse constructive and multi-modal reasoning while permitting the use of converse modalities, serving as a generalization of standard intuitionistic modal logics. In this paper, we provide definitions of these…
Word embedding models offer continuous vector representations that can capture rich contextual semantics based on their word co-occurrence patterns. While these word vectors can provide very effective features used in many NLP tasks such as…
We examine conditions on a (compact metrizable) space $X$ such that for any space $Y$ and closed subspace $Z$, the set of continuous functions from $Z$ to $X$ which extend to $Y$ is either open or closed in the set of continuous functions…
Traditional sentence embedding models encode sentences into vector representations to capture useful properties such as the semantic similarity between sentences. However, in addition to similarity, sentence semantics can also be…
We look at spaces of infinite-by-infinite matrices, and consider closed subsets that are stable under simultaneous row and column operations. We prove that up to symmetry, any of these closed subsets is defined by finitely many equations.
The fusion of speech and language in the era of large language models has garnered significant attention. Discrete speech token is often utilized in text-to-speech tasks for speech compression and portability, which is convenient for joint…
Counters that hold natural numbers are ubiquitous in modeling and verifying software systems; for example, they model dynamic creation and use of resources in concurrent programs. Unfortunately, such discrete counters often lead to…
In this article we present ways to evaluate certain sums, products and continued fractions using tools from the theory of elliptic functions. The specific results appear to be new, although similar ones can be found in the leterature; in…
In some scientific fields, a scaling is able to modify the topology of an observed object. Our goal in the present work is to introduce a new formalism adapted to the mathematical representation of this kind of phenomenon. To this end, we…
Sequence representations supporting not only direct access to their symbols, but also rank/select operations, are a fundamental building block in many compressed data structures. Several recent applications need to represent highly…
We generalize the lexicographic product of first-order structures by presenting a framework for constructions which, in a sense, mimic iterating the lexicographic product infinitely and not necessarily countably many times. We then define…