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The regularity of images generated by convolutional neural networks, such as the U-net, generative networks, or the deep image prior, is analyzed. In a resolution-independent, infinite dimensional setting, it is shown that such images,…
Shift neural networks reduce computation complexity by removing expensive multiplication operations and quantizing continuous weights into low-bit discrete values, which are fast and energy efficient compared to conventional neural…
Modified gravity theories have received increased attention lately to understand the late time acceleration of the universe. This viewpoint essentially modifies the geometric components of the universe. Among numerous extension to…
Deep learning in the form of 1D convolutional neural networks have previously been shown to be capable of efficiently classifying the evolutionary state of oscillating red giants into red giant branch stars and helium-core burning stars by…
Recent work has highlighted a surprising alignment between gradients and the top eigenspace of the Hessian -- termed the Dominant subspace -- during neural network training. Concurrently, there has been growing interest in the distinct…
Artificial Recurrent Neural Networks (RNNs) are widely used in neuroscience to model the collective activity of neurons during behavioral tasks. The high dimensionality of their parameter and activity spaces, however, often make it…
The phase space of stellar streams is proposed to detect dark substructure in the Milky Way through the perturbations created by passing subhalos - and thus is a powerful test of the cold dark matter paradigm and its alternatives. Using…
Large-scale structures, observed today, are generally believed to have grown from random, small-amplitude inhomogeneities, present in the early Universe. We investigate how gravitational instability drives the distribution of these…
Convolutional neural networks have allowed remarkable advances in single image super-resolution (SISR) over the last decade. Among recent advances in SISR, attention mechanisms are crucial for high-performance SR models. However, the…
The idea that we live in a Universe undergoing a period of acceleration is a strongly held notion in cosmology. As this can, potentially, be explained with a modification to General Relativity we look at current cosmological data with the…
General relativity predicts that a rotating body produces a frame-dragging (or Lense-Thirring) effect: the orbital plane of a test particle in a non-equatorial orbit precesses about the body's symmetry axis. In this paper we compute the…
This work introduces the Nirenberg Neural Network: a numerical approach to the Nirenberg problem of prescribing Gaussian curvature on $S^2$ for metrics that are pointwise conformal to the round metric. Our mesh-free physics-informed neural…
Recent experiments have shown that training trajectories of multiple deep neural networks with different architectures, optimization algorithms, hyper-parameter settings, and regularization methods evolve on a remarkably low-dimensional…
The observed acceleration of the universe, explained through dark energy, could alternatively be explained through a modification of gravity that would also induce modifications in the evolution of cosmological perturbations. We use new…
In gradient descent dynamics of neural networks, the top eigenvalue of the loss Hessian (sharpness) displays a variety of robust phenomena throughout training. This includes early time regimes where the sharpness may decrease during early…
Efficient algorithms are being developed to search for strong gravitational lens systems owing to increasing large imaging surveys. Neural networks have been successfully used to discover galaxy-scale lens systems in imaging surveys such as…
We study the large-scale stellar and gaseous kinematics of the E4 galaxy NGC2974, based on panoramic integral-field data obtained with SAURON. We quantify the velocity fields with Fourier methods (kinemetry), and show that the large-scale…
The advent of the Hubble Space Telescope (HST) has provided images of galaxies at moderate and high redshifts and changed the scope of galaxy morphologies considerably. It is evident that the Hubble Sequence requires modifications in order…
Magnetic activity in stars manifests as dark spots on their surfaces that modulate the brightness observed by telescopes. These light curves contain important information on stellar rotation. However, the accurate estimation of rotation…
Neural networks have been successfully used for classification tasks in a rapidly growing number of practical applications. Despite their popularity and widespread use, there are still many aspects of training and classification that are…