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We study the on-line AdaTron learning of linearly non-separable rules by a simple perceptron. Training examples are provided by a perceptron with a non-monotonic transfer function which reduces to the usual monotonic relation in a certain…
In this paper we consider the classical spherical perceptron problem. This problem and its variants have been studied in a great detail in a broad literature ranging from statistical physics and neural networks to computer science and pure…
We consider the problem of neural association for a network of non-binary neurons. Here, the task is to first memorize a set of patterns using a network of neurons whose states assume values from a finite number of integer levels. Later,…
Reaction Coordinates (RCs) are indicators of hidden, low-dimensional mechanisms that govern the long-term behavior of high-dimensional stochastic processes. We present a novel and general variational characterization of optimal RCs and…
The performance of a lossy data compression scheme for uniformly biased Boolean messages is investigated via methods of statistical mechanics. Inspired by a formal similarity to the storage capacity problem in the research of neural…
We consider correlated and distributed sources without cooperation at the encoder. For these sources, we derive the best achievable performance in the rate-distortion sense of any distributed compressed sensing scheme, under the constraint…
In this paper, designs and analyses of compressive recognition systems are discussed, and also a method of establishing a dual connection between designs of good communication codes and designs of recognition systems is presented. Pattern…
The recent demonstration of neuromorphic computing with spin-torque nano-oscillators has opened a path to energy efficient data processing. The success of this demonstration hinged on the intrinsic short-term memory of the oscillators. In…
We review the physics and some applications of photonic structures designed for the realisation of strong $\textit{nonlinear chiroptical response}$. We pay much attention to the recent strategy of utilizing different types of…
We study a relation between Hadamard powers and polynomial kernel perceptrons. The rank of Hadamard powers for the special case of a Boolean matrix and for the generic case of a real matrix is computed explicitly. These results are…
We introduce simple group-theoretic techniques for classifying conformally-invariant tensor-structures. With them, we classify tensor structures of general n-point functions of non-conserved operators, and $n\geq 4$-point functions of…
We complement our previous work [arxiv: 0707.0565] with the full (non diluted) solution describing the stable states of an attractor network that stores correlated patterns of activity. The new solution provides a good fit of simulations of…
Superconductivity in the cuprates is characterized by spatial inhomogeneity and an anisotropic electronic gap of d-wave symmetry. The aim of this work is to understand how this anisotropy affects the non-equilibrium electronic response of…
The performance of attractor neural networks has been shown to depend crucially on the heterogeneity of the underlying topology. We take this analysis a step further by examining the effect of degree-degree correlations -- or assortativity…
This paper investigates the problem of recovering the support of structured signals via adaptive compressive sensing. We examine several classes of structured support sets, and characterize the fundamental limits of accurately recovering…
This work focuses on the construction of optimized binary signaling schemes for two-sender uncoded transmission of correlated sources over non-orthogonal Gaussian multiple access channels. Specifically, signal constellations with binary…
Many real-world applications are associated with structured data, where not only input but also output has interplay. However, typical classification and regression models often lack the ability of simultaneously exploring high-order…
We study the problem of learning the input-output map of a controlled vibrating plate with a composite structure from experimental measurements. Analytical modeling of this control system faces challenges due to the essential orthotropy and…
We study photon, phonon statistics and the cross-correlation between photons and phonons in a quadratically coupled optomechanical system. Photon blockade, phonon blockade and strongly anticorrelated photons and phonons can be observed in…
We investigate the composability of soft-rules learned by relational neural architectures when operating over object-centric (slot-based) representations, under a variety of sparsity-inducing constraints. We find that increasing sparsity,…