“Unpaired Image-to-Image Translation using Cycle-Consistent Adversarial Networks”の学習報告

Recently deep learning (DL), as a new data-driven technique compared to conventional approaches, has attracted increasing attention in geophysical community, resulting in many opportunities and challenges. DL was proven to have the potential to predict complex system states accurately and relieve the “curse of dimensionality” in large temporal and spatial geophysical applications. We address the basic concepts, state-of-the-art literature, and future trends by reviewing DL approaches in various geosciences scenarios. Exploration geophysics, earthquakes, and remote sensing are the main focuses. More applications, including Earth structure, water resources, atmospheric science, and space science, are also reviewed. Additionally, the difficulties of applying DL in the geophysical community are discussed. The trends of DL in geophysics in recent years are analyzed. Several promising directions are provided for future research involving DL in geophysics, such as unsupervised learning, transfer learning, multimodal DL, federated learning, uncertainty estimation, and active learning. A coding tutorial and a summary of tips for rapidly exploring DL are presented for beginners and interested readers of geophysics.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2021RG000742

Deep learning for geophysics: Current and future trends

In this paper, we present a novel and principled approach to learn the optimal transport between two distributions, from samples. Guided by the optimal transport theory, we learn the optimal Kantorovich potential which induces the optimal transport map. This involves learning two convex functions, by solving a novel minimax optimization. Building upon recent advances in the field of input convex neural networks, we propose a new framework where the gradient of one convex function represents the optimal transport mapping. Numerical experiments confirm that we learn the optimal transport mapping. This approach ensures that the transport mapping we find is optimal independent of how we initialize the neural networks. Further, target distributions from a discontinuous support can be easily captured, as gradient of a convex function naturally models a {\em discontinuous} transport mapping.

/pdf/optimal-transport-mapping-via-input-convex-neural-networks-11p8jy5dwq.pdf

Optimal transport mapping via input convex neural networks

This study reviews the technique of convolutional neural network (CNN) applied in a specific field of mammographic breast cancer diagnosis (MBCD). It aims to provide several clues on how to use CNN for related tasks. MBCD is a long-standing problem, and massive computer-aided diagnosis models have been proposed. The models of CNN-based MBCD can be broadly categorized into three groups. One is to design shallow or to modify existing models to decrease the time cost as well as the number of instances for training; another is to make the best use of a pretrained CNN by transfer learning and fine-tuning; the third is to take advantage of CNN models for feature extraction, and the differentiation of malignant lesions from benign ones is fulfilled by using machine learning classifiers. This study enrolls peer-reviewed journal publications and presents technical details and pros and cons of each model. Furthermore, the findings, challenges and limitations are summarized and some clues on the future work are also given. Conclusively, CNN-based MBCD is at its early stage, and there is still a long way ahead in achieving the ultimate goal of using deep learning tools to facilitate clinical practice. This review benefits scientific researchers, industrial engineers, and those who are devoted to intelligent cancer diagnosis.

/pdf/a-technical-review-of-convolutional-neural-network-based-1ux26auasy.pdf

A Technical Review of Convolutional Neural Network-Based Mammographic Breast Cancer Diagnosis.

The invariant line element |φ(z)|1/2|dz| was introduced in Section 5.3 and the local properties of the corresponding metric were investigated in Sections 5.4 and 8. In this chapter, we study its global properties.

The Metric Associated with a Quadratic Differential

https://par.nsf.gov/servlets/purl/10185254

A Geometric Understanding of Deep Learning

Generative adversarial networks (GANs) have attracted huge attention due to its capability to generate visual realistic images. However, most of the existing models suffer from the mode collapse or mode mixture problems. In this work, we give a theoretic explanation of the both problems by Figalli’s regularity theory of optimal transportation maps. Basically, the generator compute the transportation maps between the white noise distributions and the data distributions, which are in general discontinuous. However, DNNs can only represent continuous maps. This intrinsic conflict induces mode collapse and mode mixture. In order to tackle the both problems, we explicitly separate the manifold embedding and the optimal transportation; the first part is carried out using an autoencoder to map the images onto the latent space; the second part is accomplished using a GPU-based convex optimization to find the discontinuous transportation maps. Composing the extended OT map and the decoder, we can finally generate new images from the white noise. This AE-OT model avoids representing discontinuous maps by DNNs, therefore effectively prevents mode collapse and mode mixture.

/pdf/ae-ot-a-new-generative-model-based-on-extended-semi-discrete-2rpsxq5i25.pdf

Ae-ot: a new generative model based on extended semi-discrete optimal transport

This work builds the connection between the regularity theory of optimal transportation map, Monge-Ampere equation and GANs, which gives a theoretic understanding of the major drawbacks of GANs: convergence difficulty and mode collapse. 
According to the regularity theory of Monge-Ampere equation, if the support of the target measure is disconnected or just non-convex, the optimal transportation mapping is discontinuous. General DNNs can only approximate continuous mappings. This intrinsic conflict leads to the convergence difficulty and mode collapse in GANs. 
We test our hypothesis that the supports of real data distribution are in general non-convex, therefore the discontinuity is unavoidable using an Autoencoder combined with discrete optimal transportation map (AE-OT framework) on the CelebA data set. The testing result is positive. Furthermore, we propose to approximate the continuous Brenier potential directly based on discrete Brenier theory to tackle mode collapse. Comparing with existing method, this method is more accurate and effective.

Mode Collapse and Regularity of Optimal Transportation Maps.

https://par.nsf.gov/servlets/purl/10108793

Zhongxuan Luo

Papers

A Geometric Understanding of Deep Learning

Ae-ot: a new generative model based on extended semi-discrete optimal transport

Mode Collapse and Regularity of Optimal Transportation Maps.

Quadrilateral mesh generation I : Metric based method

Quadrilateral mesh generation II: Meromorphic quartic differentials and Abel-Jacobi condition