Michael Scherbela, Rafael Reisenhofer, Leon Gerard et al.
Accurate numerical solutions for the Schrödinger equation are of utmost importance in quantum chemistry. However, the computational cost of current high-accuracy methods scales poorly with the number of interacting particles. Combining Monte Carlo methods with unsupervised training of neural networks has recently been proposed as a promising approach to overcome the curse of dimensionality in this setting and to obtain accurate wavefunctions for individual molecules at a moderately scaling computational cost. These methods currently do not exploit the regularity exhibited by wavefunctions with respect to their molecular geometries. Inspired by recent successful applications of deep transfer learning in machine translation and computer vision tasks, we attempt to leverage this regularity by introducing a weight-sharing constraint when optimizing neural network-based models for different molecular geometries. That is, we restrict the optimization process such that up to 95 percent of weights in a neural network model are in fact equal across varying molecular geometries. We find that this technique can accelerate optimization when considering sets of nuclear geometries of the same molecule by an order of magnitude and that it opens a promising route towards pre-trained neural network wavefunctions that yield high accuracy even across different molecules.
We present a novel approach to the detection and characterization of edges, ridges, and blobs in two-dimensional images which exploits the symmetry properties of directionally sensitive analyzing functions in multiscale systems that are constructed in the framework of alpha-molecules. The proposed feature detectors are inspired by the notion of phase congruency, stable in the presence of noise, and by definition invariant to changes in contrast. We also show how the behavior of coefficients corresponding to differently scaled and oriented analyzing functions can be used to obtain a comprehensive characterization of the geometry of features in terms of local tangent directions, widths, and heights. The accuracy and robustness of the proposed measures are validated and compared to various state-of-the-art algorithms in extensive numerical experiments in which we consider sets of clean and distorted synthetic images that are associated with reliable ground truths. To further demonstrate the applicability, we show how the proposed ridge measure can be used to detect and characterize blood vessels in digital retinal images and how the proposed blob measure can be applied to automatically count the number of cell colonies in a Petri dish.
Dominik Alfke, Weston Baines, Jan Blechschmidt et al.
We present a novel technique based on deep learning and set theory which yields exceptional classification and prediction results. Having access to a sufficiently large amount of labelled training data, our methodology is capable of predicting the labels of the test data almost always even if the training data is entirely unrelated to the test data. In other words, we prove in a specific setting that as long as one has access to enough data points, the quality of the data is irrelevant.
Rafael Reisenhofer, Sebastian Bosse, Gitta Kutyniok et al.
In most practical situations, the compression or transmission of images and videos creates distortions that will eventually be perceived by a human observer. Vice versa, image and video restoration techniques, such as inpainting or denoising, aim to enhance the quality of experience of human viewers. Correctly assessing the similarity between an image and an undistorted reference image as subjectively experienced by a human viewer can thus lead to significant improvements in any transmission, compression, or restoration system. This paper introduces the Haar wavelet-based perceptual similarity index (HaarPSI), a novel and computationally inexpensive similarity measure for full reference image quality assessment. The HaarPSI utilizes the coefficients obtained from a Haar wavelet decomposition to assess local similarities between two images, as well as the relative importance of image areas. The consistency of the HaarPSI with the human quality of experience was validated on four large benchmark databases containing thousands of differently distorted images. On these databases, the HaarPSI achieves higher correlations with human opinion scores than state-of-the-art full reference similarity measures like the structural similarity index (SSIM), the feature similarity index (FSIM), and the visual saliency-based index (VSI). Along with the simple computational structure and the short execution time, these experimental results suggest a high applicability of the HaarPSI in real world tasks.