Related papers: An optimal Q-state neural network using mutual inf…
In this paper we propose a new computational method for designing optimal regulators for high-dimensional nonlinear systems. The proposed approach leverages physics-informed machine learning to solve high-dimensional Hamilton-Jacobi-Bellman…
We consider the problem of determining the spatial phase profile of a single-mode electromagnetic field. Our attention is on input states that are a statistical mixture of displaced and squeezed number states, a superset of Gaussian states.…
We study pairwise Ising models for describing the statistics of multi-neuron spike trains, using data from a simulated cortical network. We explore efficient ways of finding the optimal couplings in these models and examine their…
In this paper new descent line search iterative schemes for unconstrained as well as constrained optimization problems are developed using q-derivative. At every iteration of the scheme, a positive definite matrix is provided which is…
We revisit quantum tomography in an informationally incomplete scenario and propose improved state reconstruction methods using deep neural networks. In the first approach, the trained network predicts an optimal linear or quadratic…
We discuss efficient methods to optimize the metrological performance over local Hamiltonians in a bipartite quantum system. For a given quantum state, our methods find the best local Hamiltonian for which the state outperforms separable…
Entanglement is one of the key resources of quantum information science which makes identification of entangled states essential to a wide range of quantum technologies and phenomena. This problem is however both computationally and…
In neural network's Literature, Hebbian learning traditionally refers to the procedure by which the Hopfield model and its generalizations store archetypes (i.e., definite patterns that are experienced just once to form the synaptic…
The objective is to study an on-line Hidden Markov model (HMM) estimation-based Q-learning algorithm for partially observable Markov decision process (POMDP) on finite state and action sets. When the full state observation is available,…
We study analytically and numerically a Hopfield fully-connected network with $d$-dimensional vector spins. These networks are models of associative memory that generalize the standard Hopfield with Ising spins, where $P$ examples are…
The restricted Boltzmann machine (RBM) has been successfully applied to solve the many-electron Schr$\ddot{\text{o}}$dinger equation. In this work we propose a single-layer fully connected neural network adapted from RBM and apply it to…
We study variants of hierarchical modular network models suggested by Kaiser and Hilgetag [Frontiers in Neuroinformatics, 4 (2010) 8] to model functional brain connectivity, using extensive simulations and quenched mean-field theory (QMF),…
The structure of continuous Hopfield networks is revisited from a system-theoretic point of view. After adopting a novel electrical network interpretation involving nonlinear capacitors, it is shown that Hopfield networks admit a…
Hopfield networks are artificial neural networks which store memory patterns on the states of their neurons by choosing recurrent connection weights and update rules such that the energy landscape of the network forms attractors around the…
Through a redefinition of patterns in an Hopfield-like model, we introduce and develop an approach to model discrete systems made up of many, interacting components with inner degrees of freedom. Our approach clarifies the intrinsic…
We develop a constructive approach to generate artificial neural networks representing the exact ground states of a large class of many-body lattice Hamiltonians. It is based on the deep Boltzmann machine architecture, in which two layers…
Deep reinforcement learning techniques have demonstrated superior performance in a wide variety of environments. As improvements in training algorithms continue at a brisk pace, theoretical or empirical studies on understanding what these…
The influence of a macroscopic time-dependent threshold on the retrieval process of three-state extremely diluted neural networks is examined. If the threshold is chosen appropriately in function of the noise and the pattern activity of the…
Higher-order interactions underlie complex phenomena in systems such as biological and artificial neural networks, but their study is challenging due to the scarcity of tractable models. By leveraging a generalisation of the maximum entropy…
We prove that a single-layer neural network trained with the Q-learning algorithm converges in distribution to a random ordinary differential equation as the size of the model and the number of training steps become large. Analysis of the…