Related papers: Stable variation in multidimensional competition
In order to analyze the dynamics of two languages in competition, one approach is to fit historical data on their numbers of speakers with a mathematical model in which the parameters are interpreted as the similarity between those…
Many languages' inflectional morphological systems are replete with irregulars, i.e., words that do not seem to follow standard inflectional rules. In this work, we quantitatively investigate the conditions under which irregulars can…
This paper measures variation in embedding spaces which have been trained on different regional varieties of English while controlling for instability in the embeddings. While previous work has shown that it is possible to distinguish…
I survey some recent approaches to studying change in the lexicon, particularly change in meaning across phylogenies. I briefly sketch an evolutionary approach to language change and point out some issues in recent approaches to studying…
Grammatical forms are said to evolve via two main mechanisms. These are, respectively, the `descent' mechanism, where current forms can be seen to have descended (albeit with occasional modifications) from their roots in ancient languages,…
We introduce a language competition model that is based on the Abrams-Strogatz model and incorporates the effects of memory and learning in the language shift dynamics. On a coarse grained time scale, the effects of memory and learning can…
Natural languages display a trade-off among different strategies to convey syntactic structure, such as word order or inflection. This trade-off, however, has not appeared in recent simulations of iterated language learning with neural…
Word embeddings are powerful representations that form the foundation of many natural language processing architectures, both in English and in other languages. To gain further insight into word embeddings, we explore their stability (e.g.,…
The processes leading to change in languages are manifold. In order to reduce ambiguity in the transmission of information, agreement on a set of conventions for recurring problems is favored. In addition to that, speakers tend to use…
There has been a long-standing and at times fractious debate whether complex and large systems can be stable. In ecology, the so-called `diversity-stability debate' arose because mathematical analyses of ecosystem stability were either…
Features in machine learning problems are often time-varying and may be related to outputs in an algebraic or dynamical manner. The dynamic nature of these machine learning problems renders current higher order accelerated gradient descent…
Resource competition is a fundamental interaction in natural communities.However little is known about competition in spatial environments where organisms are able to regulate resource distributions. Here, we analyze the competition of two…
Toward explaining the persistence of biased inferences, we propose a framework to evaluate competing (mis)specifications in strategic settings. Agents with heterogeneous (mis)specifications coexist and draw Bayesian inferences about their…
We extend the Abrams-Strogatz model for competition between two languages [Nature 424, 900 (2003)] to the case of n(>=2) competing states (i.e., languages). Although the Abrams-Strogatz model for n=2 can be interpreted as modeling either…
For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…
We study learning under regime variation, where the learner, its memory state, and the evaluative conditions may evolve over time. This paper is a foundational and structural contribution: its goal is to define the core learning-theoretic…
Environmental variation can play an important role in ecological competition by influencing the relative advantage between competing species. Here, we consider such effects by extending a classical, competitive Moran model to incorporate an…
In a stable matching setting, we consider a query model that allows for an interactive learning algorithm to make precisely one type of query: proposing a matching, the response to which is either that the proposed matching is stable, or a…
Given only observational data $X = g(Z)$, where both the latent variables $Z$ and the generating process $g$ are unknown, recovering $Z$ is ill-posed without additional assumptions. Existing methods often assume linearity or rely on…
In this work the stability of perturbed linear time-varying systems is studied. The main features of the problem are threefold. Firstly, the time-varying dynamics is not required to be continuous but allowed to have jumps. Also the system…