Related papers: Another look at the Gardner problem
Convolutional Neural Networks (CNNs) have recently emerged as the dominant model in computer vision. If provided with enough training data, they predict almost any visual quantity. In a discrete setting, such as classification, CNNs are not…
In this research we address the problem of capturing recurring concepts in a data stream environment. Recurrence capture enables the re-use of previously learned classifiers without the need for re-learning while providing for better…
This paper presents enhanced reductions of the bounded-weight and exact-weight Syndrome Decoding Problem (SDP) to a system of quadratic equations. Over $\mathbb{F}_2$, we improve on a previous work and study the degree of regularity of the…
We consider the Bayesian optimal filtering problem: i.e. estimating some conditional statistics of a latent time-series signal from an observation sequence. Classical approaches often rely on the use of assumed or estimated transition and…
Stochasticity and limited precision of synaptic weights in neural network models are key aspects of both biological and hardware modeling of learning processes. Here we show that a neural network model with stochastic binary weights…
This paper proposes a new Quantum Spatial Graph Convolutional Neural Network (QSGCNN) model that can directly learn a classification function for graphs of arbitrary sizes. Unlike state-of-the-art Graph Convolutional Neural Network (GCNN)…
This work is concerned with an inverse elastic scattering problem of identifying the unknown rigid obstacle embedded in an open space filled with a homogeneous and isotropic elastic medium. A Newton-type iteration method relying on the…
Important information on the structure of complex systems, consisting of more than one component, can be obtained by measuring to which extent the individual components exchange information among each other. Such knowledge is needed to…
The regression of multiple inter-connected sequence data is a problem in various disciplines. Formally, we name the regression problem of multiple inter-connected data entities as the "dynamic network regression" in this paper. Within the…
Typical-case computation complexity is a research topic at the boundary of computer science, applied mathematics, and statistical physics. In the last twenty years the replica-symmetry-breaking mean field theory of spin glasses and the…
We present results for two different kinds of high order connections between neurons acting as corrections to the Hopfield model. Equilibrium properties are analyzed using the replica mean-field theory and compared with numerical…
We explore the problem of inferring the graph Laplacian of a weighted, undirected network from snapshots of a single or multiple discrete-time consensus dynamics, subject to parameter uncertainty, taking place on the network. Specifically,…
Inference algorithms based on evolving interactions between replicated solutions are introduced and analyzed on a prototypical NP-hard problem - the capacity of the binary Ising perceptron. The efficiency of the algorithm is examined…
The notion of concept drift refers to the phenomenon that the distribution, which is underlying the observed data, changes over time; as a consequence machine learning models may become inaccurate and need adjustment. While there do exist…
Ordinal regression is an important type of learning, which has properties of both classification and regression. Here we describe a simple and effective approach to adapt a traditional neural network to learn ordinal categories. Our…
We offer a solution to a long-standing problem in the physics of networks, the creation of a plausible, solvable model of a network that displays clustering or transitivity -- the propensity for two neighbors of a network node also to be…
Controlling network systems has become a problem of paramount importance. In this paper, we consider a distributed linear-quadratic problem and propose the use of graph neural networks (GNNs) to parametrize and design a distributed…
Recurrent Neural Networks (RNNs), which are a powerful scheme for modeling temporal and sequential data need to capture long-term dependencies on datasets and represent them in hidden layers with a powerful model to capture more information…
In artificial neural networks trained with gradient descent, the weights used for processing stimuli are also used during backward passes to calculate gradients. For the real brain to approximate gradients, gradient information would have…
The Gardner method, traditionally used to generate conservation laws of integrable equations, is generalized to generate symmetries. The method is demonstrated for the KdV, Camassa-Holm and Sine-Gordon equations. The method involves…