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Bayesian computation plays an important role in modern machine learning and statistics to reason about uncertainty. A key computational challenge in Bayesian inference is to develop efficient techniques to approximate, or draw samples from…

In this paper, we present a fast implementation of the Singular Value Thresholding (SVT) algorithm for matrix completion. A rank-revealing randomized singular value decomposition (R3SVD) algorithm is used to adaptively carry out partial…

Many successful methods to learn dynamical systems from data have recently been introduced. However, ensuring that the inferred dynamics preserve known constraints, such as conservation laws or restrictions on the allowed system states,…

Very deep convolutional neural networks (CNNs) have been firmly established as the primary methods for many computer vision tasks. However, most state-of-the-art CNNs are large, which results in high inference latency. Recently, depth-wise…

Spiking Neural Networks (SNNs) have attracted growing interest in both computational neuroscience and artificial intelligence, primarily due to their inherent energy efficiency and compact memory footprint. However, achieving adversarial…

Spiking neural networks (SNNs) represent a promising approach in machine learning, combining the hierarchical learning capabilities of deep neural networks with the energy efficiency of spike-based computations. Traditional end-to-end…

The inverse problem of supervised reconstruction of depth-variable (time-dependent) parameters in a neural ordinary differential equation (NODE) is considered, that means finding the weights of a residual network with time continuous…

In many numerical simulations stochastic gradient descent (SGD) type optimization methods perform very effectively in the training of deep neural networks (DNNs) but till this day it remains an open problem of research to provide a…

Variance reduction (VR) methods employ stochastic gradients with decreasing variance, and they have been widely applied to solve large-scale optimization problems in machine learning because of their efficiency. Existing theoretical studies…

Achieving efficient and robust multi-channel data learning is a challenging task in data science. By exploiting low-rankness in the transformed domain, i.e., transformed low-rankness, tensor Singular Value Decomposition (t-SVD) has achieved…

This paper proposes the SVDNet for retrieval problems, with focus on the application of person re-identification (re-ID). We view each weight vector within a fully connected (FC) layer in a convolutional neuron network (CNN) as a projection…

Recurrent neural networks are known for their notorious exploding and vanishing gradient problem (EVGP). This problem becomes more evident in tasks where the information needed to correctly solve them exist over long time scales, because…

Normalization layers are widely used in deep neural networks to stabilize training. In this paper, we consider the training of convolutional neural networks with gradient descent on a single training example. This optimization problem…

We introduce data structures for solving robust regression through stochastic gradient descent (SGD) by sampling gradients with probability proportional to their norm, i.e., importance sampling. Although SGD is widely used for large scale…

The big breakthrough on the ImageNet challenge in 2012 was partially due to the `dropout' technique used to avoid overfitting. Here, we introduce a new approach called `Spectral Dropout' to improve the generalization ability of deep neural…

Updating a truncated Singular Value Decomposition (SVD) is crucial in representation learning, especially when dealing with large-scale data matrices that continuously evolve in practical scenarios. Aligning SVD-based models with fast-paced…

Neural operators have emerged as a promising paradigm for learning solution operators of partial differential equa- tions (PDEs) directly from data. Existing methods, such as those based on Fourier or graph techniques, make strong as-…

In real-world scenarios, complex data such as multispectral images and multi-frame videos inherently exhibit robust low-rank property. This property is vital for multi-dimensional inverse problems, such as tensor completion, spectral…

As deep neural networks (DNNs) achieve tremendous success across many application domains, researchers tried to explore in many aspects on why they generalize well. In this paper, we provide a novel perspective on these issues using the…

Convolutional Neural Networks (CNNs) have made significant progress on several computer vision benchmarks, but are fraught with numerous non-human biases such as vulnerability to adversarial samples. Their lack of explainability makes…