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The characterization of a unitary gate is experimentally accomplished via Quantum Process Tomography, which combines the outcomes of different projective measurements to reconstruct the underlying operator. The process matrix is typically…

Often in applications such as rare events estimation or optimal control it is required that one calculates the principal eigen-function and eigen-value of a non-negative integral kernel. Except in the finite-dimensional case, usually…

On-chip optical neural networks (ONNs) have recently emerged as an attractive hardware accelerator for deep learning applications, characterized by high computing density, low latency, and compact size. As these networks rely heavily on…

Integrated photonic convolution processors make optical neural networks (ONNs) a transformative solution for artificial intelligence applications such as machine vision. To enhance the parallelism, throughput, and energy efficiency of ONNs,…

We present in this work a new methodology to design kernels on data which is structured with smaller components, such as text, images or sequences. This methodology is a template procedure which can be applied on most kernels on measures…

Deep neural network with rectified linear units (ReLU) is getting more and more popular recently. However, the derivatives of the function represented by a ReLU network are not continuous, which limit the usage of ReLU network to situations…

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…

Measuring similarity between two objects is the core operation in existing clustering algorithms in grouping similar objects into clusters. This paper introduces a new similarity measure called point-set kernel which computes the similarity…

Superpixels provide a compact region-based representation that preserves object boundaries and local structures, and have therefore been widely used in a variety of vision tasks to reduce computational cost. However, most existing…

In recent years, deep neural networks (DNN) have demonstrated significant business impact in large scale analysis and classification tasks such as speech recognition, visual object detection, pattern extraction, etc. Training of large DNNs,…

Gaussian process regression is a widely-applied method for function approximation and uncertainty quantification. The technique has gained popularity recently in the machine learning community due to its robustness and interpretability. The…

We consider fast kernel summations in high dimensions: given a large set of points in $d$ dimensions (with $d \gg 3$) and a pair-potential function (the {\em kernel} function), we compute a weighted sum of all pairwise kernel interactions…

The ability to identify useful features or representations of the input data based on training data that achieves low prediction error on test data across multiple prediction tasks is considered the key to multitask learning success. In…

This whitepaper proposes the design and adoption of a new generation of Tensor Processing Unit which has the performance of Google's TPU, yet performs operations on wide precision data. The new generation TPU is made possible by…

Deep Convolutional Neural Networks (CNNs) are widely employed in modern computer vision algorithms, where the input image is convolved iteratively by many kernels to extract the knowledge behind it. However, with the depth of convolutional…

Neural kernels have drastically increased performance on diverse and nonstandard data modalities but require significantly more compute, which previously limited their application to smaller datasets. In this work, we address this by…

Optical neural networks are emerging as a powerful and versatile tool for processing optical signals directly in the optical domain with superior speed, integrability, and functionality. Their application to optical polarization enables…

The paper describes an application of Aggregating Algorithm to the problem of regression. It generalizes earlier results concerned with plain linear regression to kernel techniques and presents an on-line algorithm which performs nearly as…

Multiple kernel learning algorithms are proposed to combine kernels in order to obtain a better similarity measure or to integrate feature representations coming from different data sources. Most of the previous research on such methods is…

The widespread adoption of machine learning and other matrix intensive computing algorithms has inspired renewed interest in analog optical computing, which has the potential to perform large-scale matrix multiplications with superior…