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Convolutional neural networks (CNNs) are important in a wide variety of machine learning tasks and applications, so optimizing their performance is essential. Moving words of data between levels of a memory hierarchy or between processors…

The random Fourier method (RFM) is widely employed for synthetic turbulence due to its mathematical clarity and simplicity. However, deviations remain between prescribed inputs and synthetic results, and the origin of these errors has not…

The research on spectral inequalities for discrete Schrodinger Operators has proved fruitful in the last decade. Indeed, several authors analysed the operator's canonical relation to a tridiagonal Jacobi matrix operator. In this paper, we…

We investigate the radiative decay of the cosmic neutrino background, and its impact on the spectrum of the cosmic microwave background (CMB) that is known to be a nearly perfect black body. We derive exact formulae for the decay of a…

In modern artificial intelligence, convolutional neural networks (CNNs) have become a cornerstone for visual and perceptual tasks. However, their implementation on conventional electronic hardware faces fundamental bottlenecks in speed and…

In this note, we propose a framework for proving computational lower bounds in norm approximation by leveraging a reverse detection--estimation gap. The starting point is a testing problem together with an estimator whose error is…

Efficiently executing convolutional neural nets (CNNs) is important in many machine-learning tasks. Since the cost of moving a word of data, either between levels of a memory hierarchy or between processors over a network, is much higher…

In this paper, we study the convergence of the spectral embeddings obtained from the leading eigenvectors of certain similarity matrices to their population counterparts. We opt to study this convergence in a uniform (instead of average)…

Atomic norm methods have recently been proposed for spectral super-resolution with flexibility in dealing with missing data and miscellaneous noises. A notorious drawback of these convex optimization methods however is their lower…

To compress deep convolutional neural networks (CNNs) with large memory footprint and long inference time, this paper proposes a novel pruning criterion using layer-wised Ln-norm of feature maps. Different from existing pruning criteria,…

CoVariance Neural Networks (VNNs) perform convolutions on the graph determined by the covariance matrix of the data, which enables expressive and stable covariance-based learning. However, covariance matrices are typically dense, fail to…

Deep convolutional neural networks (CNNs) have been shown to be able to fit a random labeling over data while still being able to generalize well for normal labels. Describing CNN capacity through a posteriori measures of complexity has…

Hyperspectral imaging sensors are becoming increasingly popular in robotics applications such as agriculture and mining, and allow per-pixel thematic classification of materials in a scene based on their unique spectral signatures.…

We study performance characteristics of convolutional neural networks (CNN) for mobile computer vision systems. CNNs have proven to be a powerful and efficient approach to implement such systems. However, the system performance depends…

Previous work generally believes that improving the spatial invariance of convolutional networks is the key to object counting. However, after verifying several mainstream counting networks, we surprisingly found too strict pixel-level…

This work investigates use of equivariant neural networks as efficient and high-performance frameworks for image reconstruction and denoising in nuclear medicine. Our work aims to tackle limitations of conventional Convolutional Neural…

Existing Rademacher complexity bounds for neural networks rely only on norm control of the weight matrices and depend exponentially on depth via a product of the matrix norms. Lower bounds show that this exponential dependence on depth is…

While dark transitions made bright by molecular motions determine the optoelectronic properties of many materials, simulating such non-Condon effects in condensed-phase spectroscopy remains a fundamental challenge. We derive a Gaussian…

The convolution potential arises in a wide variety of application areas, and its efficient and accurate evaluation encounters three challenges: singularity, nonlocality and anisotropy. We introduce a fast algorithm based on a far-field…

Complex demodulation of evolutionary spectra is formulated as a two-dimensional kernel smoother in the time-frequency domain. In the first stage, a tapered Fourier transform, $y_{nu}(f,t)$, is calculated. Second, the log-spectral estimate,…