Related papers: Herding as a Learning System with Edge-of-Chaos Dy…
The dynamics of learning in modern large AI systems is hierarchical, often characterized by abrupt, qualitative shifts akin to phase transitions observed in physical systems. While these phenomena hold promise for uncovering the mechanisms…
Spatiotemporal chaotic systems are difficult to characterize in a model-free manner because of their high dimensionality, strong nonlinearity, and sensitivity to initial conditions. Coupled map lattices, as a representative class of…
This article presents a theoretical investigation of computation beyond the Turing barrier from emergent behavior in distributed systems. In particular, we present an algorithmic network that is a mathematical model of a networked…
It has long been suggested that the biological brain operates at some critical point between two different phases, possibly order and chaos. Despite many indirect empirical evidence from the brain and analytical indication on simple neural…
By means of a novel variational approach we study ergodic properties of a model of a multi lane traffic flow, considered as a (deterministic) wandering of interacting particles on an infinite lattice. For a class of initial configurations…
This paper studies how complicated and irregular behavior, known as chaos, can arise in a simple mathematical model that includes time delays. The model is a delay differential equation in which the present rate of change depends not only…
In this paper we are concerned with multiscale modeling, control, and simulation of self-organizing agents leaving an unknown area under limited visibility, with special emphasis on crowds. We first introduce a new microscopic model…
Dynamics in biological networks are in general robust against several perturbations. We investigate a coupled map network as a model motivated by gene regulatory networks and design systems which are robust against phenotypic perturbations…
Individual choices are either based on personal experience or on information provided by peers. The latter case, causes individuals to conform to the majority in their neighborhood. Such herding behavior may be very efficient in aggregating…
Sequential and temporal data arise in many fields of research, such as quantitative finance, medicine, or computer vision. A novel approach for sequential learning, called the signature method and rooted in rough path theory, is considered.…
In this paper we develop theory of sequential parametrized motion planning which generalises the approach of parametrized motion planning, which was introduced recently in [3]. A sequential parametrized motion planning algorithm produced a…
We study a sequential-learning model featuring a network of naive agents with Gaussian information structures. Agents apply a heuristic rule to aggregate predecessors' actions. They weigh these actions according the strengths of their…
Large animal groups -- bird flocks, fish schools, insect swarms -- are often assumed to form by gradual aggregation of sparsely distributed individuals. Using a mathematically precise framework based on time-varying directed interaction…
Widespread deployment of societal-scale machine learning systems necessitates a thorough understanding of the resulting long-term effects these systems have on their environment, including loss of trustworthiness, bias amplification, and…
We provide evidence that for some values of the parameters a simple agent based model, describing herding behavior, yields signals with 1/f power spectral density. We derive a non-linear stochastic differential equation for the ratio of…
This work studies networked agents cooperating to track a dynamical state of nature under partial information. The proposed algorithm is a distributed Bayesian filtering algorithm for finite-state hidden Markov models (HMMs). It can be used…
We provide a theoretical analysis for end-to-end training Discrete Flow Matching (DFM) generative models. DFM is a promising discrete generative modeling framework that learns the underlying generative dynamics by training a neural network…
Diffusion Models represent a significant advancement in generative modeling, employing a dual-phase process that first degrades domain-specific information via Gaussian noise and restores it through a trainable model. This framework enables…
Evolutionary game theory has traditionally employed deterministic models to describe population dynamics. These models, due to their inherent nonlinearities, can exhibit deterministic chaos, where population fluctuations follow complex,…
The paper deals with the theoretical analysis of a logistic system composed of at least two elements with distributed parameters. It has been shown that such a system may generate specific oscillations in spite of the fact that the…