Related papers: Nonlinear Schr\"odinger Kernel for hardware accele…
Optical neural networks present distinct advantages over traditional electrical counterparts, such as accelerated data processing and reduced energy consumption. While coherent light is conventionally employed in optical neural networks,…
We introduce photonic kernel machines, a scheme for ultrafast spectral analysis of noisy radio-frequency signals from single-shot optical intensity measurements. The approach combines the versatility of machine learning and the speed of…
We introduce a data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves…
Many scientific problems involve data exhibiting both temporal and cross-sectional dependencies. While linear dependencies have been extensively studied, the theoretical analysis of regression estimators under nonlinear dependencies remains…
Incorporating nonlinearity into quantum machine learning is essential for learning a complicated input-output mapping. We here propose quantum algorithms for nonlinear regression, where nonlinearity is introduced with feature maps when…
We propose a new method for input variable selection in nonlinear regression. The method is embedded into a kernel regression machine that can model general nonlinear functions, not being a priori limited to additive models. This is the…
Nonlinear optical processing of ambient natural light is highly desired in computational imaging and sensing applications. A strong optical nonlinear response that can work under weak broadband incoherent light is essential for this…
Digital signal processing is the cornerstone of several modern-day technologies, yet in multiple applications it faces critical bottlenecks related to memory and speed constraints. Thanks to recent advances in metasurface design and…
This paper presents a kernel-based framework for physics-informed nonlinear system identification. The key contribution is a structured methodology that extends kernel-based techniques to seamlessly embed partially known physics-based…
Spiking neural networks encode information in spike timing and offer a pathway toward energy efficient artificial intelligence. However, a key challenge in spiking neural networks is realizing nonlinear and expressive computation in…
High-dimensional nonlinear dynamical systems including neural networks can be utilized as a computational resource for information processing. In this sense, nonlinear wave systems are good candidate for such a computational resource. Here,…
We conduct an experimental investigation of nonlinearity management in optics using femtosecond pulses and layered Kerr media consisting of glass and air. By examining the propagation properties over several diffraction lengths, we show…
We propose a kernel-spectral embedding algorithm for learning low-dimensional nonlinear structures from high-dimensional and noisy observations, where the datasets are assumed to be sampled from an intrinsically low-dimensional manifold and…
Plasmon-induced transparency (PIT) displays complex nonlinear dynamics that find critical phenomena in areas such as nonlinear waves. However, such a nonlinear solution depends sensitively on the selection of parameters and different…
Optical neural networks promise ultrafast, low-energy information processing by performing computation directly with photons. Current implementations, however, are largely restricted to steady-state operation and rely on high-latency…
Neural networks find widespread use in scientific and technological applications, yet their implementations in conventional computers have encountered bottlenecks due to ever-expanding computational needs. Photonic neuromorphic hardware,…
Modern machine learning models use an ever-increasing number of parameters to train (175 billion parameters for GPT-3) with large datasets to obtain better performance. Bigger is better has been the norm. Optical computing has been…
A key question in modern statistics is how to make fast and reliable inferences for complex, high-dimensional data. While there has been much interest in sparse techniques, current methods do not generalize well to data with nonlinear…
Optical approaches have made great strides towards the goal of high-speed, energy-efficient computing necessary for modern deep learning and AI applications. Read-in and read-out of data, however, limit the overall performance of existing…
Nonlinear spectroscopy employs a series of laser pulses to interrogate dynamics in large interacting many-body systems, and has become a highly successful method for experiments in chemical physics. Current quantum optical experiments…