相关论文: Memory Functions of the Additive Markov chains: Ap…

Markov Chains offer ideal conditions for the study and mathematical modelling of a certain kind of situations depending on random variables. The basic concepts of the corresponding theory were introduced by Markov in 1907 on coding literary…

Recent empirical studies have demonstrated long-memory in the signs of orders to buy or sell in financial markets [2, 19]. We show how this can be caused by delays in market clearing. Under the common practice of order splitting, large…

Complex network theory provides a unifying framework for the study of structured dynamic systems. The current literature emphasizes a widely reported phenomenon of intermittent interaction among network vertices. In this paper, we introduce…

In this paper we present the concept of description of random processes in complex systems with the discrete time. It involves the description of kinetics of discrete processes by means of the chain of finite-difference non-Markov equations…

Markov models have been widely used to represent and analyse user web navigation data. In previous work we have proposed a method to dynamically extend the order of a Markov chain model and a complimentary method for assessing the…

Identifying and quantifying memory are often critical steps in developing a mechanistic understanding of stochastic processes. These are particularly challenging and necessary when exploring processes that exhibit long-range correlations.…

We propose a novel framework for the Lyapunov analysis of an important class of hybrid systems, inspired by the theory of symbolic dynamics and earlier results on the restricted class of switched systems. This new framework allows us to…

We investigate how feature correlations influence the capacity of Dense Associative Memory (DAM), a Transformer attention-like model. Practical machine learning scenarios involve feature-correlated data and learn representations in the…

We develop a practical approach to establish the stability, that is, the recurrence in a given set, of a large class of controlled Markov chains. These processes arise in various areas of applied science and encompass important numerical…

Memory plays a pivotal role in enabling large language model~(LLM)-based agents to engage in complex and long-term interactions, such as question answering (QA) and dialogue systems. While various memory modules have been proposed for these…

Memory retention challenges in deep neural architectures have ongoing limitations in the ability to process and recall extended contextual information. Token dependencies degrade as sequence length increases, leading to a decline in…

Long range dependence or long memory is a feature of many processes in the natural world, which provides important insights on the underlying mechanisms that generate the observed data. The usual tools available to characterize the…

We show that long-term memory effects, present in the chaotic dispersion process generated by a meandering jet model, can be nonetheless taken into account by a first order Markov process, provided that the states of the phase space…

The dynamics by iteration of a function on a compact metric space, sometimes called a cascade, can be extended to the dynamics of a closed relation on such a space. Here we apply this relation dynamics to study semiflows (and their relation…

The angular and frequency correlation functions of the transmission coefficient for light propagation through a strongly scattering amplifying medium are considered. It is found that just as in the case of an elastic scattering medium the…

Memory-based neural networks model temporal data by leveraging an ability to remember information for long periods. It is unclear, however, whether they also have an ability to perform complex relational reasoning with the information they…

Markov decision processes are typically used for sequential decision making under uncertainty. For many aspects however, ranging from constrained or safe specifications to various kinds of temporal (non-Markovian) dependencies in task and…

We study the effect of temporal correlation in a Langevin equation describing non-adiabatic dynamics at metal surfaces. For a harmonic oscillator the Langevin equation preserves the quantum dynamics exactly and it is demonstrated that…

We complement our previous work [arxiv: 0707.0565] with the full (non diluted) solution describing the stable states of an attractor network that stores correlated patterns of activity. The new solution provides a good fit of simulations of…

We set out a general procedure which allows the approximation of certain Markov chains by the solutions of differential equations. The chains considered have some components which oscillate rapidly and randomly, while others are close to…