Related papers: Stochastically Perturbed Chains of Variable Memory

We consider binary infinite order stochastic chains perturbed by a random noise. This means that at each time step, the value assumed by the chain can be randomly and independently flipped with a small fixed probability. We show that the…

In this paper, we present a methodology to estimate the parameters of stochastically contaminated models under two contamination regimes. In both regimes, we assume that the original process is a variable length Markov chain that is…

In this article we introduce two new perfect simulation algorithms for chains with infinite memory. Both algorithms belong to the coupling of past procedures. The novelty of our approach is that it allows to include unknown states to the…

We present a new perfect simulation algorithm for stationary chains having unbounded variable length memory. This is the class of infnite memory chains for which the family of transition probabilities is represented by a probabilistic…

Assume we have two stochastic chains taking values in a finite alphabet. These chains may be of infinite order. Assume also that these chains are coupled in such a way that given the past of both chains they have a not too large probability…

Stochastic chains with memory of variable length constitute an interesting family of stochastic chains of infinite order on a finite alphabet. The idea is that for each past, only a finite suffix of the past, called context, is enough to…

This paper is composed of two main results concerning chains of infinite order which are not necessarily continuous. The first one is a decomposition of the transition probability kernel as a countable mixture of unbounded probabilistic…

This article studies the expected occupancy probabilities on an alphabet. Unlike the standard situation, where observations are assumed to be independent and identically distributed (iid), we assume that they follow a regime switching…

We investigate the capacity of transformers to learn algorithms involving their context while solely being trained using next token prediction. We set up Markov chains with random transition matrices and we train transformers to predict the…

We propose a principle for exploring context in machine learning models. Starting with a simple assumption that each observation may or may not depend on its context, a conditional probability distribution is decomposed into two parts:…

We studied the quantum state transfer in randomly coupled spin chains. By using local memories storing the information and dividing the task into transfer portion and decoding portion, conclusive transfer was ingeniously achieved with just…

Binomial distributions capture the probabilities of `heads' outcomes when a (biased) coin is tossed multiple times. The coin may be identified with a distribution on the two-element set {0,1}, where the 1 outcome corresponds to `head'. One…

A variation in the environment of a system, such as the temperature, the concentration of a chemical solution or the appearance of a magnetic field, may lead to a drift in one of the parameters. If the parameter crosses a bifurcation point,…

A new converse bound is presented for the two-user multiple-access channel under the average probability of error constraint. This bound shows that for most channels of interest, the second-order coding rate -- that is, the difference…

In distributed systems where strong consistency is costly when not impossible, causal consistency provides a valuable abstraction to represent program executions as partial orders. In addition to the sequential program order of each…

We study the problem of deinterleaving a set of finite-memory (Markov) processes over disjoint finite alphabets, which have been randomly interleaved by a finite-memory switch. The deinterleaver has access to a sample of the resulting…

Transformer architectures have achieved state-of-the-art results on a variety of sequence modeling tasks. However, their attention mechanism comes with a quadratic complexity in sequence lengths, making the computational overhead…

We consider how randomness can be made to play a useful role in quantum information processing - in particular, for decoherence control and the implementation of quantum algorithms. For a two-level system in which the decoherence channel is…

The recently proposed set-up of source coding with a side information "vending machine" allows the decoder to select actions in order to control the quality of the side information. The actions can depend on the message received from the…

We study random walk on complex networks with transition probabilities which depend on the current and previously visited nodes. By using an absorbing Markov chain we derive an exact expression for the mean first passage time between pairs…