Physics and Chemistry from Parsimonious Representations: Image Analysis via Invariant Variational Autoencoders

Electron, optical, and scanning probe microscopy methods are generating ever increasing volume of image data containing information on atomic and mesoscale structures and functionalities. This necessitates the development of the machine learning methods for discovery of physical and chemical phenomena from the data, such as manifestations of symmetry breaking in electron and scanning tunneling microscopy images, variability of the nanoparticles. Variational autoencoders (VAEs) are emerging as a powerful paradigm for the unsupervised data analysis, allowing to disentangle the factors of variability and discover optimal parsimonious representation. Here, we summarize recent developments in VAEs, covering the basic principles and intuition behind the VAEs. The invariant VAEs are introduced as an approach to accommodate scale and translation invariances present in imaging data and separate known factors of variations from the ones to be discovered. We further describe the opportunities enabled by the control over VAE architecture, including conditional, semi-supervised, and joint VAEs. Several case studies of VAE applications for toy models and experimental data sets in Scanning Transmission Electron Microscopy are discussed, emphasizing the deep connection between VAE and basic physical principles. All the codes used here are available at https://github.com/saimani5/VAE-tutorials and this article can be used as an application guide when applying these to own data sets.Comment: 55 pages, 16 figure

A Simple and Generic Framework for Feature Distillation via Channel-wise Transformation

Knowledge distillation is a popular technique for transferring the knowledge from a large teacher model to a smaller student model by mimicking. However, distillation by directly aligning the feature maps between teacher and student may enforce overly strict constraints on the student thus degrade the performance of the student model. To alleviate the above feature misalignment issue, existing works mainly focus on spatially aligning the feature maps of the teacher and the student, with pixel-wise transformation. In this paper, we newly find that aligning the feature maps between teacher and student along the channel-wise dimension is also effective for addressing the feature misalignment issue. Specifically, we propose a learnable nonlinear channel-wise transformation to align the features of the student and the teacher model. Based on it, we further propose a simple and generic framework for feature distillation, with only one hyper-parameter to balance the distillation loss and the task specific loss. Extensive experimental results show that our method achieves significant performance improvements in various computer vision tasks including image classification (+3.28% top-1 accuracy for MobileNetV1 on ImageNet-1K), object detection (+3.9% bbox mAP for ResNet50-based Faster-RCNN on MS COCO), instance segmentation (+2.8% Mask mAP for ResNet50-based Mask-RCNN), and semantic segmentation (+4.66% mIoU for ResNet18-based PSPNet in semantic segmentation on Cityscapes), which demonstrates the effectiveness and the versatility of the proposed method. The code will be made publicly available.Comment: 13 page

Inequalities for generalized matrix function and inner product

We present inequalities related to generalized matrix function for positive semidefinite block matrices. We introduce partial generalized matrix functions corresponding to partial traces and then provide an unified extension of the recent inequalities due to Choi [6], Lin [14] and Zhang et al. [5,19]. We demonstrate the applications of a positive semidefinite $3\times 3$ block matrix, which motivates us to give a simple alternative proof of Dragomir's inequality and Krein's inequality.Comment: 12 pages. This paper was originally written on Nov. 02, 2019; Recently, we make a new revision. Any commennts are wellcom