Related papers: Memory functions and Correlations in Additive Bina…

World models enable agents to plan within imagined environments by predicting future states conditioned on past observations and actions. However, their ability to plan over long horizons is limited by the effective memory span of the…

A theory of systems with long-range correlations based on the consideration of binary N-step Markov chains is developed. In the model, the conditional probability that the i-th symbol in the chain equals zero (or unity) is a linear function…

The relative timing of action potentials in neurons recorded from local cortical networks often shows a non-trivial dependence, which is then quantified by cross-correlation functions. Theoretical models emphasize that such spike train…

We introduce a Vasicek-type short rate model which has two additional parameters representing memory effect. This model presents better results in yield curve fitting than the classical Vasicek model. We derive closed-form expressions for…

We consider a sequence of additive functionals {\phi_n}, set on a sequence of Markov chains {X_n} that weakly converges to a Markov process X. We give sufficient condition for such a sequence to converge in distribution, formulated in terms…

Beyond the conventional quantum regression theorem, a general formula for non-Markovian correlation functions of arbitrary system operators both in the time- and frequency-domain is given. We approach the problem by transforming the…

Memory effects are ubiquitous in small-scale systems. They emerge from interactions between accessible and inaccessible degrees of freedom and give rise to evolution equations that are non-local in time. If the characteristic time scales of…

We examine a previouly introduced attractor neural network model that explains the persistent activities of neurons in the anterior ventral temporal cortex of the brain. In this model, the coexistence of several attractors including…

In the paper we study continuous time controlled Markov processes using discrete time controlled Markov processes. We consider long run functionals: average reward per unit time or long run risk sensitive functional. We also investigate…

We propose a method to probe time dependent correlations of non trivial observables in many-body ultracold lattice gases. The scheme uses a quantum non-demolition matter-light interface, first, to map the observable of interest on the many…

This paper proposes an information-theoretic cost function for aggregating a Markov chain via a (possibly stochastic) mapping. The cost function is motivated by two objectives: 1) The process obtained by observing the Markov chain through…

One successful model of interacting biological systems is the Boolean network. The dynamics of a Boolean network, controlled with Boolean functions, is usually considered to be a Markovian (memory-less) process. However, both self…

Replay buffers are a key component in many reinforcement learning schemes. Yet, their theoretical properties are not fully understood. In this paper we analyze a system where a stochastic process X is pushed into a replay buffer and then…

Residual connections have been proposed as an architecture-based inductive bias to mitigate the problem of exploding and vanishing gradients and increased task performance in both feed-forward and recurrent networks (RNNs) when trained with…

In spite of remarkable progress in machine learning techniques, the state-of-the-art machine learning algorithms often keep machines from real-time learning (online learning) due in part to computational complexity in parameter…

We calculate in an exact way the conditional past-future correlation for the decay dynamics of a two-level system in a bosonic bath. Different measurement processes are considered. In contrast to quantum memory measures based solely on…

Learning auxiliary tasks, such as multiple predictions about the world, can provide many benefits to reinforcement learning systems. A variety of off-policy learning algorithms have been developed to learn such predictions, but as yet there…

Neural dynamical systems with stable attractor structures, such as point attractors and continuous attractors, are hypothesized to underlie meaningful temporal behavior that requires working memory. However, working memory may not support…

The computational complexity of the self-attention mechanism in Transformer models significantly limits their ability to generalize over long temporal durations. Memory-augmentation, or the explicit storing of past information in external…

Many Reinforcement Learning algorithms assume a Markov reward function to guarantee optimality. However, not all reward functions are Markov. This paper proposes a framework for mapping non-Markov reward functions into equivalent Markov…