Related papers: Compositional Growth Models
In tasks like semantic parsing, instruction following, and question answering, standard deep networks fail to generalize compositionally from small datasets. Many existing approaches overcome this limitation with model architectures that…
The logistic equation is ubiquitous in applied mathematics as a minimal model of saturating growth. Here, we examine a broad generalisation of the logistic growth model to discretely structured populations, motivated by examples that range…
Continuum models for the spatial dynamics of growing cell populations have been widely used to investigate the mechanisms underpinning tissue development and tumour invasion. These models consist of nonlinear partial differential equations…
For language models to generalize correctly to novel expressions, it is critical that they exploit access compositional meanings when this is justified. Even if we don't know what a "pelp" is, we can use our knowledge of numbers to…
This paper studies the bounded confidence model on growing fully-mixed populations. In this model, in addition to the usual opinion clusters, significant secondary clusters of smaller size appear systematically, while those secondary…
To analyze the evolutionary emergence of structural complexity in physical processes we introduce a general, but tractable, model of objects that interact to produce new objects. Since the objects--\emph{$epsilon$-machines}--have well…
Addressing health disparities among different demographic groups is a key challenge in public health. Despite many efforts, there is still a gap in understanding how these disparities unfold over time. Our paper focuses on this overlooked…
We develop a novel Bayesian framework for dynamic modeling of mixed frequency data to nowcast quarterly U.S. GDP growth. The introduced framework utilizes foundational Bayesian theory and treats data sampled at different frequencies as…
We are concerned with how the implementation of growth determines the expected number of state-changes in a growing self-organizing process. With this problem in mind, we examine two versions of the voter model on a one-dimensional growing…
Urban systems are composed by complex couplings of several components, and more particularly between the built environment and transportation networks. Their interaction is involved in the emergence of the urban form. We propose in this…
These lecture notes discuss several related features of the exactly solvable two-dimensional corner growth model with exponentially distributed weights. A key property of this model is the availability of a fairly explicit stationary…
Growth patterns of complex systems predict how they change in sizes, numbers, masses, etc. Understanding growth is important, especially for many biological, ecological, urban, and socioeconomic systems. One noteworthy growth behavior is…
Composed ensembles of random unitary matrices are defined via products of matrices, each pertaining to a given canonical circular ensemble of Dyson. We investigate statistical properties of spectra of some composed ensembles and demonstrate…
We propose flexible Gaussian representations for conditional cumulative distribution functions and give a concave likelihood criterion for their estimation. Optimal representations satisfy the monotonicity property of conditional cumulative…
Many complex systems are characterized by broad distributions capturing, for example, the size of firms, the population of cities or the degree distribution of complex networks. Typically this feature is explained by means of a preferential…
We compute the growth fluctuations in equilibrium of a wide class of deposition models. These models also serve as general frame to several nearest-neighbor particle jump processes, e.g. the simple exclusion or the zero range process, where…
Growth of monetary assets and debts is commonly described by the formula of compound interest which for the case of continuous compounding is the exponential growth law. Its differential form is dc/dt = i c where dc/dt describes the rate of…
We are entering a new era in which software systems are becoming more and more complex and larger. So, the composition of such systems is becoming infeasible by manual means. To address this challenge, self-organising software models…
This is an evolving document. It is devoted to summarizing patterns and laws of knowledge growth. By examining a variety of parameters in data sources such as Wikipedia and Microsoft Academic Graph, we can get deeper insights of how…
A punctuated equilibrium model of biological evolution with relative fitness between different species being the fundamental driving force of evolution is introduced. Mutation is modeled as a fitness updating cellular automaton process…