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

We derive Markovian master equations of single and interacting harmonic systems in different scenarios, including strong internal coupling. By comparing the dynamics resulting from the corresponding Markovian master equations with exact…

Novel method of reconstructing dynamical networks from empirically measured time series is proposed. By examining the variable--derivative correlation of network node pairs, we derive a simple equation that directly yields the adjacency…

This paper introduces a neural network model that learns multiple attributes as images and performs associated, sequential recall of the learned memories. Briefly, the model presented here is an associative memory model that extends…

Over past few years afterward the birth of ResNet, skip connection has become the defacto standard for the design of modern architectures due to its widespread adoption, easy optimization and proven performance. Prior work has explained the…

In the recent publication (arxiv:2007.08063v2 [cs.LG]) a fast prediction algorithm for a single recurrent network (RN) was suggested. In this manuscript we generalize this approach to a chain of RNs and show that it can be implemented in…

We first review traditional approaches to memory storage and formation, drawing on the literature of quantitative neuroscience as well as statistical physics. These have generally focused on the fast dynamics of neurons; however, there is…

Memory is a complex phenomenon that involves several distinct mechanisms. These mechanisms operate at different spatial and temporal levels. This chapter focuses on the theoretical framework and the mathematical models that have been…

The general scheme for the treatment of relaxation processes and temporal autocorrelations of dynamical variables for many particle systems is presented in framework of the recurrence relations approach. The time autocorrelation functions…

Much of interesting complex biological behaviour arises from collective properties. Important information about collective behaviour lies in the time and space structure of fluctuations around average properties, and two-point correlation…

Proteins have been empirically linked to memory. If memory relates to protein structure, then each conformation would_functionally_ code only one bit, making it difficult to explain large memories. Nor is there a simple way to relate memory…

In reinforcement learning, conducting task composition by forming cohesive, executable sequences from multiple tasks remains challenging. However, the ability to (de)compose tasks is a linchpin in developing robotic systems capable of…

Dense Associative Memories are high storage capacity variants of the Hopfield networks that are capable of storing a large number of memory patterns in the weights of the network of a given size. Their common formulations typically require…

This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is 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…

In this paper, a general framework for the analysis of a connection between the training of artificial neural networks via the dynamics of Markov chains and the approximation of conservation law equations is proposed. This framework allows…

In "Large Associative Memory Problem in Neurobiology and Machine Learning," Dmitry Krotov and John Hopfield introduced a general technique for the systematic construction of neural ordinary differential equations with non-increasing energy…

An average instantaneous cross-correlation function is introduced to quantify the interaction of the financial market of a specific time. Based on the daily data of the American and Chinese stock markets, memory effect of the average…

We extend the simply-typed guarded $\lambda$-calculus with discrete probabilities and endow it with a program logic for reasoning about relational properties of guarded probabilistic computations. This provides a framework for programming…

Strong correlation can be essentially captured with multireference wavefunction methods such as complete active space self-consistent field (CASSCF) or density matrix renormalization group (DMRG). Still, an accurate description of the…

We consider a Markov control model in discrete time with countable both state space and action space. Using the value function of a suitable long-run average reward problem, we study various reachability/controllability problems. First, we…