Related papers: Nonlinear Schr\"odinger Kernel for hardware accele…
We study artificial neural networks with nonlinear waves as a computing reservoir. We discuss universality and the conditions to learn a dataset in terms of output channels and nonlinearity. A feed-forward three-layer model, with an…
The Regularized Nonlinear Acceleration (RNA) algorithm is an acceleration method capable of improving the rate of convergence of many optimization schemes such as gradient descend, SAGA or SVRG. Until now, its analysis is limited to convex…
Standard deep learning algorithms require differentiating large nonlinear networks, a process that is slow and power-hungry. Electronic learning metamaterials offer potentially fast, efficient, and fault-tolerant hardware for analog machine…
We introduce a new, reduced nonlinear oscillator model governing the spontaneous creation of sharp pulses in a damped, driven, cubic nonlinear Schroedinger equation. The reduced model embodies the fundamental connection between mode…
Existing permanental processes often impose constraints on kernel types or stationarity, limiting the model's expressiveness. To overcome these limitations, we propose a novel approach utilizing the sparse spectral representation of…
This work introduces a novel nonlinear optimal filtering method, termed the Ensemble Schr{\"o}dinger Bridge nonlinear filter. The proposed filter combines the standard prediction step with a diffusion-generative-modeling-based analysis…
Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject…
Deep learning has rapidly become a widespread tool in both scientific and commercial endeavors. Milestones of deep learning exceeding human performance have been achieved for a growing number of tasks over the past several years, across…
Deep neural networks with applications from computer vision and image processing to medical diagnosis are commonly implemented using clock-based processors, where computation speed is limited by the clock frequency and the memory access…
This paper introduces a computational framework to identify nonlinear input-output operators that fit a set of system trajectories while satisfying incremental integral quadratic constraints. The data fitting algorithm is thus regularized…
We theoretically propose and experimentally demonstrate optically tunable nonlinear mechanical damping in a cavity optomechanical system utilizing a partly resolved sideband regime. Optomechanical coupling provides a delayed nonlinear…
Recent advances in nonlinear dynamical systems theory provide a new insight into numerical properties of discrete algorithms developed to solve nonlinear initial value problems. Basic features like accuracy and stability are well pointed…
This project explores the use of non-volatile synapses in neuromorphic computing for pattern recognition tasks through a comprehensive simulation-based approach. The main approach is through spintronic synapses, which leverage the…
Frequency conversion of non-classical light enables robust encoding of quantum information based upon spectral multiplexing that is particularly well-suited to integrated-optics platforms. Here we present an intrinsically deterministic…
We apply machine learning techniques in an attempt to predict and classify stellar properties from noisy and sparse time series data. We preprocessed over 94 GB of Kepler light curves from MAST to classify according to ten distinct physical…
It is demonstrated that nonlinear dynamical systems with analytic nonlinearities can be brought down to the abstract Schr\"odinger equation in Hilbert space with boson Hamiltonian. The Fourier coefficients of the expansion of solutions to…
Nonlinear optical effects provide a natural way of light manipulation and interaction, and form the foundation of applied photonics -- from high-speed signal processing and telecommunication, to ultra-high bandwidth interconnects and…
Optically detected magnetic resonance (ODMR) has become a well-established and powerful technique for measuring the spin state of solid-state quantum emitters, at room temperature. Relying on spin-dependent recombination processes involving…
Nonlinear computation is essential for a wide range of information processing tasks, yet implementing nonlinear functions using optical systems remains a challenge due to the weak and power-intensive nature of optical nonlinearities.…
We propose data-driven nonlinear smoother (DNS) to estimate a hidden state sequence of a complex dynamical process from a noisy, linear measurement sequence. The dynamical process is model-free, that is, we do not have any knowledge of the…