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We present a novel adaptive machine-learning based approach for reconstructing three-dimensional (3D) crystals from coherent diffraction imaging (CDI). We represent the crystals using spherical harmonics (SH) and generate corresponding…
In this work, we focus on using convolution neural networks (CNN) to perform object recognition on the event data. In object recognition, it is important for a neural network to be robust to the variations of the data during testing. For…
In this paper we review the mathematical foundations of convolutional neural nets (CNNs) with the goals of: i) highlighting connections with techniques from statistics, signal processing, linear algebra, differential equations, and…
Understanding how convolutional neural networks (CNNs) can efficiently learn high-dimensional functions remains a fundamental challenge. A popular belief is that these models harness the local and hierarchical structure of natural data such…
Modeling the energy and forces of atomic systems is a fundamental problem in computational chemistry with the potential to help address many of the world's most pressing problems, including those related to energy scarcity and climate…
Deep convolutional neural networks accuracy is heavily impacted by rotations of the input data. In this paper, we propose a convolutional predictor that is invariant to rotations in the input. This architecture is capable of predicting the…
Convolutional Neural Networks (CNNs) have recently emerged as the dominant model in computer vision. If provided with enough training data, they predict almost any visual quantity. In a discrete setting, such as classification, CNNs are not…
Convolutional neural networks (CNNs) have achieved great success in natural image saliency prediction. The primary goal of this study is to investigate the performance of saliency prediction in CNN and classic models with psychophysical…
Convolutional kernels are basic and vital components of deep Convolutional Neural Networks (CNN). In this paper, we equip convolutional kernels with shape attributes to generate the deep Irregular Convolutional Neural Networks (ICNN).…
Despite the importance of image representations such as histograms of oriented gradients and deep Convolutional Neural Networks (CNN), our theoretical understanding of them remains limited. Aiming at filling this gap, we investigate three…
Convolutional neural networks (CNNs) can model complicated non-linear relations between images. However, they are notoriously sensitive to small changes in the input. Most CNNs trained to describe image-to-image mappings generate temporally…
Several recent works have empirically observed that Convolutional Neural Nets (CNNs) are (approximately) invertible. To understand this approximate invertibility phenomenon and how to leverage it more effectively, we focus on a theoretical…
Convolutional Neural Networks (CNN) offer state of the art performance in various computer vision tasks. Many of those tasks require different subtypes of affine invariances (scale, rotational, translational) to image transformations.…
Convolutional neural networks (CNNs) have been employed along with Variational Monte Carlo methods for finding the ground state of quantum many-body spin systems with great success. In order to do so, however, a CNN with only linearly many…
Convolutional Neural Networks (CNNs) have been providing the state-of-the-art performance for learning-related problems involving 2D/3D images in Euclidean space. However, unlike in the Euclidean space, the shapes of many structures in…
This paper investigates the super-resolution (SR) of velocity fields in two-dimensional fluids from the viewpoint of rotational equivariance. SR refers to techniques that estimate high-resolution images from those in low resolution and has…
The topic of achieving rotational invariance in convolutional neural networks (CNNs) has gained considerable attention recently, as this invariance is crucial for many computer vision tasks such as image classification and matching. In this…
Convolutional Neural Networks (CNNs) define an exceptionally powerful class of models for image classification, but the theoretical background and the understanding of how invariances to certain transformations are learned is limited. In a…
Regular group convolutional neural networks (G-CNNs) have been shown to increase model performance and improve equivariance to different geometrical symmetries. This work addresses the problem of SE(3), i.e., roto-translation equivariance,…
In the last two years, convolutional neural networks (CNNs) have achieved an impressive suite of results on standard recognition datasets and tasks. CNN-based features seem poised to quickly replace engineered representations, such as SIFT…