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Functional linear regression analysis aims to model regression relations which include a functional predictor. The analog of the regression parameter vector or matrix in conventional multivariate or multiple-response linear regression…
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…
We formulate some simple conditions under which a Markov chain may be approximated by the solution to a differential equation, with quantifiable error probabilities. The role of a choice of coordinate functions for the Markov chain is…
The storage capacity of a binary classification model is the maximum number of random input-output pairs per parameter that the model can learn. It is one of the indicators of the expressive power of machine learning models and is important…
Neural network acoustic models have significantly advanced state of the art speech recognition over the past few years. However, they are usually computationally expensive due to the large number of matrix-vector multiplications and…
The notion of memory capacity, originally introduced for echo state and linear networks with independent inputs, is generalized to nonlinear recurrent networks with stationary but dependent inputs. The presence of dependence in the inputs…
Experimental and numerical results suggest that the brain can be viewed as a system acting close to a critical point, as confirmed by scale-free distributions of relevant quantities in a variety of different systems and models. Less…
In cognitive network neuroscience, the connectivity and community structure of the brain network is related to cognition. Much of this research has focused on two measures of connectivity - modularity and flexibility - which frequently have…
Many neural nets appear to represent data as linear combinations of "feature vectors." Algorithms for discovering these vectors have seen impressive recent success. However, we argue that this success is incomplete without an understanding…
We describe the impact of the intra-day activity pattern on the autocorrelation function estimator. We obtain an exact formula relating estimators of the autocorrelation functions of non-stationary process to its stationary counterpart.…
The distance of a binary operation from being associative can be "measured" by its associative spectrum, an appropriate sequence of positive integers. Particular instances and general properties of associative spectra are studied.
We consider the correlation functions of eigenvalues of a unidimensional chain of large random hermitian matrices. An asymptotic expression of the orthogonal polynomials allows to find new results for the correlations of eigenvalues of…
We first study labeled transition systems with explicit successful termination. We establish the notions of strong, weak, and branching bisimulation in terms of boolean matrix theory, introducing thus a novel and powerful algebraic…
Recurrent neural networks can learn complex transduction problems that require maintaining and actively exploiting a memory of their inputs. Such models traditionally consider memory and input-output functionalities indissolubly entangled.…
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…
We investigate a recurrent neural network model with common external and bias inputs that can retrieve branching sequences. Retrieval of memory sequences is one of the most important functions of the brain. A lot of research has been done…
We propose a minimal yet intriguing model for a relationship between two individuals. The feeling of an individual is modeled by a complex variable and hence has two degrees of freedom. The effect of memory of other individual's behavior in…
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,…
A new recursion formula is presented for the correlation functions of the integrable spin 1/2 XXX chain with inhomogeneity. It relates the correlators involving n consecutive lattice sites to those with n-1 and n-2 sites. In a series of…
We establish Bernstein's inequalities for functions of general (general-state-space and possibly non-reversible) Markov chains. These inequalities achieve sharp variance proxies and encompass the classical Bernstein inequality for…