相关论文: The Filtration of the split-words process
Previous approaches to robustness in natural language processing usually treat deviant input by relaxing grammatical constraints whenever a successful analysis cannot be provided by ``normal'' means. This schema implies, that error…
We study the dynamics of erasing randomly chosen letters from words by introducing a certain class of discrete-time stochastic processes, general erased-word processes(GEWPs), and investigating three closely related topics: Representation,…
For over a decade, researchers in formal methods tried to create formalisms that permit natural specification of systems and allow mathematical reasoning about their correctness. The availability of fully-automated reasoning tools enables…
In this paper, we consider a nonlinear filtering model with observations driven by correlated Wiener processes and point processes. We first derive a Zakai equation whose solution is a unnormalized probability density function of the filter…
The particle filter is a popular Bayesian filtering algorithm for use in cases where the state-space model is nonlinear and/or the random terms (initial state or noises) are non-Gaussian distributed. We study the behavior of the error in…
In this paper, we extend the notion of Lyndon word to transfinite words. We prove two main results. We first show that, given a transfinite word, there exists a unique factorization in Lyndon words that are densely non-increasing, a…
The use of terms from natural and social scientific titles and abstracts is studied from the perspective of sublanguages and their specialized dictionaries. Different notions of sublanguage distinctiveness are explored. Objective methods…
Let $X$ be a stationary process with values in some $\sigma$-finite measured state space $(E,\mathcal{E},\pi)$, indexed by ${\mathbb Z}$. Call ${\mathcal F}^X$ its natural filtration. In \cite{ceillierstationary}, sufficient conditions were…
The Swadesh approach for determining the temporal separation between two languages relies on the stochastic process of words replacement (when a complete new word emerges to represent a given concept). It is well known that the basic…
The survey is devoted to the combinatorial and metric theory of filtrations, i.\,e., decreasing sequences of $\sigma$-algebras in measure spaces or decreasing sequences of subalgebras of certain algebras. One of the key notions, that of…
Filtering and parameter estimation under partial information for multiscale problems is studied in this paper. After proving mean square convergence of the nonlinear filter to a filter of reduced dimension, we establish that the conditional…
Unsupervised word segmentation in audio utterances is challenging as, in speech, there is typically no gap between words. In a preliminary experiment, we show that recent deep self-supervised features are very effective for word…
Today's probabilistic language generators fall short when it comes to producing coherent and fluent text despite the fact that the underlying models perform well under standard metrics, e.g., perplexity. This discrepancy has puzzled the…
Variation in language use, shaped by speakers' sociocultural background and specific context of use, offers a rich lens into cultural perspectives, values, and opinions. For example, Chinese students discuss "healthy eating" with words like…
A polarized version of Girard, Scedrov and Scott's Bounded Linear Logic is introduced and its normalization properties studied. Following Laurent, the logic naturally gives rise to a type system for the lambda-mu-calculus, whose derivations…
We analyse a class of time discretizations for solving the nonlinear Schr\"odinger equation with non-smooth potential and at low-regularity on an arbitrary Lipschitz domain $\Omega \subset \mathbb{R}^d$, $d \le 3$. We show that these…
Without prior knowledge, distinguishing different languages may be a hard task, especially when their borders are permeable. We develop an extension of spectral clustering -- a powerful unsupervised classification toolbox -- that is shown…
The Neyman-Pearson (NP) binary classification paradigm constrains the more severe type of error (e.g., the type I error) under a preferred level while minimizing the other (e.g., the type II error). This paradigm is suitable for…
Large language models (LLMs) can explain grammatical rules, yet they often fail to apply those rules when judging sentence acceptability. We present "grammar prompting", an explain-then-process paradigm: a large LLM first produces a concise…
We study word series and extended word series, classes of formal series for the analysis of some dynamical systems and their discretizations. These series are similar to but more compact than B-series. They may be composed among themselves…