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We consider an ensemble of $K$ single-layer perceptrons exposed to random inputs and investigate the conditions under which the couplings of these perceptrons can be chosen such that prescribed correlations between the outputs occur. A…
We propose a sample-based, sequential method to abstract a (potentially black-box) dynamical system with a sequence of memory-dependent Markov chains of increasing size. We show that this approximation allows to alleviating a correlation…
We consider a Markov chain of point processes such that each state is a super position of an independent cluster process with the previous state as its centre process together with some independent noise process. The model extends earlier…
Non-Markovian quantum processes exhibit different memory effects when measured in different ways; an unambiguous characterization of memory length requires accounting for the sequence of instruments applied to probe the system dynamics.…
One of the challenges in using numerical methods to address many-body problems is the multi-dimensional integration over poles. More often that not, one needs such integrations to be evaluated as a function of an external variable. An…
A fundamental problem in neuroscience is understanding how working memory -- the ability to store information at intermediate timescales, like 10s of seconds -- is implemented in realistic neuronal networks. The most likely candidate…
We introduce LAMP: the Linear Additive Markov Process. Transitions in LAMP may be influenced by states visited in the distant history of the process, but unlike higher-order Markov processes, LAMP retains an efficient parametrization. LAMP…
In this research the technology of complex Markov chains is applied to predict financial time series. The main distinction of complex or high-order Markov Chains and simple first-order ones is the existing of aftereffect or memory. The…
We study additive function-on-function regression where the mean response at a particular time point depends on the time point itself as well as the entire covariate trajectory. We develop a computationally efficient estimation methodology…
We consider the problem of reward learning for temporally extended tasks. For reward learning, inverse reinforcement learning (IRL) is a widely used paradigm. Given a Markov decision process (MDP) and a set of demonstrations for a task, IRL…
Stochastic processes find applications in modelling systems in a variety of disciplines. A large number of stochastic models considered are Markovian in nature. It is often observed that higher order Markov processes can model the data…
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…
Multivariate time series (MTS) analysis prevails in real-world applications such as finance, climate science and healthcare. The various self-attention mechanisms, the backbone of the state-of-the-art Transformer-based models, efficiently…
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…
A prediction makes a claim about a system's future given knowledge of its past. A retrodiction makes a claim about its past given knowledge of its future. The bidirectional machine is an ambidextrous hidden Markov chain that does both…
We identify a nonlocal correlation structure in L-functions. This structure involves very long and infinite-range correlations between values of logarithmic L-functions, where the correlation strongly depends upon the presence of a…
The generalized Langevin equation is a model for the motion of coarse-grained particles where dissipative forces are represented by a memory term. The numerical realization of such a model requires the implementation of a stochastic…
The features of the response of frustrated states to the external field are considered on the example of a diluted Ising chain. In the ferromagnetic case, partial ordering occurs, which leads to a decrease in entropy. In the…
In this paper, we propose a novel control architecture, inspired from neuroscience, for adaptive control of continuous-time systems. The proposed architecture, in the setting of standard Neural Network (NN) based adaptive control, augments…
The performance of Markov chain Monte Carlo calculations is determined by both ensemble variance of the Monte Carlo estimator and autocorrelation of the Markov process. In order to study autocorrelation, binning analysis is commonly used,…