Abstract: The ability to efficiently solve topology optimization problems is of great importance for many practical applications. Hence, there is a demand for efficient solution algorithms. In this paper, we propose novel quasi-Newton methods for solving PDE-constrained topology optimization problems. Our approach is based on and extends the popular solution algorithm of Amstutz and Andrä (A new algorithm for topology optimization using a level-set method, Journal of Computational Physics, 216, 2006). To do so, we introduce a new perspective on the commonly used evolution equation for the level-set method, which allows us to derive our quasi-Newton methods for topology optimization.

Abstract: In this letter, we focus on the problem of millimeter-Wave channels estimation in massive MIMO communication systems. Inspired by the sparsity of mmWave MIMO channel in the angular domain, we formulate the estimation problem as a sparse signal recovery problem. We propose a deep learning based trainable proximal gradient descent network (TPGD-Net) for mmWave channel estimation. Specifically, we unfold the iterative proximal gradient descent (PGD) algorithm into a layer-wise network. Different from the PGD algorithm, the gradient descent step size in TPGD-Net is set as a trainable parameter.

However, obtaining an HR image is not always possible due to the limitations of optical sensors and their costs. An alternative solution called Single Image Super-Resolution (SISR) is a software-driven approach that aims to take a Low-Resolution (LR) image and obtain the HR image. Most supervised SISR solutions use ground truth HR image as a target and do not include the information provided in the LR image, which could be valuable. In this work, we introduce Triplet Loss-based Generative Adversarial Network hereafter referred as SRTGAN for Image Super-Resolution problem on real-world degradation. We introduce a new triplet-based adversarial loss function that exploits the information provided in the LR image by using it as a negative sample. Allowing the patch-based discriminator with access to both HR and LR images optimizes to better differentiate between HR and LR images; hence, improving the adversary. Further, we propose to fuse the adversarial loss, content loss, perceptual loss, and quality loss to obtain Super-Resolution (SR) image with high perceptual fidelity. We validate the superior performance of the proposed method over the other existing methods on the RealSR dataset in terms of quantitative and qualitative metrics.

Abstract: The gradient descent-ascent (GDA) algorithm has been widely applied to solve minimax optimization problems. In order to achieve convergent policy parameters for minimax optimization, it is important that GDA generates convergent variable sequences rather than convergent sequences of function values or gradient norms. However, the variable convergence of GDA has been proved only under convexity geometries, and there lacks understanding for general nonconvex minimax optimization. This paper fills such a gap by studying the convergence of a more general proximal-GDA for regularized nonconvex-strongly-concave minimax optimization. Specifically, we show that proximal-GDA admits a novel Lyapunov function, which monotonically decreases in the minimax optimization process and drives the variable sequence to a critical point.

Abstract: Mirror descent is a gradient descent method that uses a dual space of parametric models. The great idea has been developed in convex optimization, but not yet widely applied in machine learning. In this study, we provide a possible way that the mirror descent can help data-driven parameter initialization of neural networks. Abstract: The stochastic mirror descent (SMD) algorithm is a general class of training algorithms, which includes the celebrated stochastic gradient descent (SGD), as a special case. It utilizes a mirror potential to influence the implicit bias of the training algorithm.

Abstract: The logarithmic divergence is an extension of the Bregman divergence motivated by optimal transport and a generalized convex duality, and satisfies many remarkable properties. Using the geometry induced by the logarithmic divergence, we introduce a generalization of continuous time mirror descent that we term the conformal mirror descent. We derive its dynamics under a generalized mirror map, and show that it is a time change of a corresponding Hessian gradient flow. We also prove convergence results in continuous time. We apply the conformal mirror descent to online estimation of a generalized exponential family, and construct a family of gradient flows on the unit simplex via the Dirichlet optimal transport problem.

Colleagues, coming in at #7 on our Top 10 Countdown is Data Structures, Algorithms, and Machine Learning Optimization. Learn to use "Big O" notation to characterize the time efficiency and space efficiency of a given algorithm, enabling you to select or devise the most sensible approach for tackling a particular machine learning problem with the hardware resources available to you, get acquainted with the entire range of the most widely-used Python data structures, including list-, dictionary-, tree-, and graph-based structures, develop a working understanding of all of the essential algorithms for working with data, including those for searching, sorting, hashing, and traversing, discover how the statistical and machine learning approaches to optimization differ, and why you would select one or the other for a given problem you're solving, understand exactly how the extremely versatile (stochastic) gradient descent optimization algorithm works and how to apply it and learn "fancy" optimizers that are available for advanced machine learning approaches (e.g., deep learning) and when you should consider using them. Training modules include: 1) Data Structures and Algorithms, 2) "Big O" Notation, 3) List-Based Data Structures, 4) Searching and Sorting, 5) Sets and Hashing, 6) Trees, 7) Graphs, 8) Machine Learning Optimization, and 9) Fancy Deep Learning Optimizers. Much career success, Lawrence E. Wilson -- Artificial Intelligence Academy (share & subscribe)

In this course, you will learn what hyperparameters are, what Genetic Algorithm is, and what hyperparameter optimization is. In this course, you will apply Genetic Algorithm to optimize the performance of Support Vector Machines and Multilayer Perceptron Neural Networks. Hyperparameter optimization will be done on two datasets, a regression dataset for the prediction of cooling and heating loads of buildings, and a classification dataset regarding the classification of emails into spam and non-spam. The SVM and MLP will be applied on the datasets without optimization and compare their results to after their optimization. By the end of this course, you will have learnt how to code Genetic Algorithm in Python and how to optimize your Machine Learning algorithms for maximal performance.

Instacart is an online delivery service for groceries under one hour. Customers order the items on the website or using the mobile app, and a group of Instacart's shoppers go to local stores, purchase the items and deliver them to the customer. InfoQ interviewed Mathieu Ripert, data scientist at Instacart, to find out how machine learning is leveraged to guarantee a better customer experience. InfoQ: What architecture are you using to process event data and what is the data volume/ throughput? Ripert: First, we have a distributed architecture. Our system is split on business domain (Catalog, Logistics, Shoppers, Partners, Customers, etc.), as this allows each domain to be developed and deployed independently, and ensures a clear primary owner for the code and models within.