Related papers: Computing ground states of Bose-Einstein condensat…
Batch Normalization (BN) is a commonly used technique to accelerate and stabilize training of deep neural networks. Despite its empirical success, a full theoretical understanding of BN is yet to be developed. In this work, we analyze BN…
We analyze a proposed experiment [Boixo et al., Phys. Rev. Lett. 101, 040403 (2008)] for achieving sensitivity scaling better than $1/N$ in a nonlinear Ramsey interferometer that uses a two-mode Bose-Einstein condensate (BEC) of $N$ atoms.…
Deep neural networks (DNNs) have set benchmarks on a wide array of supervised learning tasks. Trained DNNs, however, often lack robustness to minor adversarial perturbations to the input, which undermines their true practicality. Recent…
Deep neural networks (DNNs) used for brain-computer-interface (BCI) classification are commonly expected to learn general features when trained across a variety of contexts, such that these features could be fine-tuned to specific contexts.…
Modern laboratory techniques like ultrafast laser excitation and shock compression can bring matter into highly nonequilibrium states with complex structural transformation, metallization and dissociation dynamics. To understand and model…
Deep learning has revolutionized the computer vision and image classification domains. In this context Convolutional Neural Networks (CNNs) based architectures are the most widely applied models. In this article, we introduced two…
We present a new, simple renormalization group method of investigating groundstate properties of interacting bosonic systems. Our method reduces the number of particles in a system, which makes numerical calculations possible for large…
Deep Neural Networks (DNNs) have begun to thrive in the field of automation systems, owing to the recent advancements in standardising various aspects such as architecture, optimization techniques, and regularization. In this paper, we take…
Deep Neural Networks (DNNs) are powerful tools for various computer vision tasks, yet they often struggle with reliable uncertainty quantification - a critical requirement for real-world applications. Bayesian Neural Networks (BNN) are…
Dilute Bose gases, cooled down to low temperatures below the Bose-Einstein condensation temperature, form coherent ensembles described by the Gross-Pitaevskii equation. Stationary solutions to the latter are topological coherent modes. The…
Batch Normalization (BN)(Ioffe and Szegedy 2015) normalizes the features of an input image via statistics of a batch of images and hence BN will bring the noise to the gradient of the training loss. Previous works indicate that the noise is…
We demonstrate that the ground state of a trapped spin-1 and spin-2 spinor ferromagnetic Bose-Einstein condensate (BEC) can be well approximated by a single decoupled Gross-Pitaevskii (GP) equation. Useful analytic models for the…
We study analytically and asymptotically as well as numerically ground states and dynamics of two-component spin-orbit-coupled Bose-Einstein condensates (BECs) modeled by the coupled Gross-Pitaevskii equations (CGPEs). In fact, due to the…
In recent studies, several asymptotic upper bounds on generalization errors on deep neural networks (DNNs) are theoretically derived. These bounds are functions of several norms of weights of the DNNs, such as the Frobenius and spectral…
We study the existence of normalized ground states for the 3D dipolar Bose-Einstein condensate equation with attractive three-body interactions: \begin{align}\label{1} -\Delta u+\beta u+\lambda_1|u|^2 u+\lambda_2…
Bayesian neural networks (BNN) and deep ensembles are principled approaches to estimate the predictive uncertainty of a deep learning model. However their practicality in real-time, industrial-scale applications are limited due to their…
Memory-augmented neural networks (MANNs) can perform algorithmic tasks such as sorting. However, they often fail to generalise to input sequence lengths not encountered during training. We introduce two approaches that constrain the state…
Batch Normalization (BN) has become an out-of-box technique to improve deep network training. However, its effectiveness is limited for micro-batch training, i.e., each GPU typically has only 1-2 images for training, which is inevitable for…
In this work we present In-Place Activated Batch Normalization (InPlace-ABN) - a novel approach to drastically reduce the training memory footprint of modern deep neural networks in a computationally efficient way. Our solution substitutes…
Deep neural networks (DNNs) are typically optimized using various forms of mini-batch gradient descent algorithm. A major motivation for mini-batch gradient descent is that with a suitably chosen batch size, available computing resources…