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Discovering and categorizing quantum orders in mixed many-body systems are currently one of the most important problems. Target model in this study is an extended version of the cluster model in one dimension with $Z_2\otimes Z_2$ symmetry,…

Graph Convolutional Neural Network (GCN), a widely adopted method for analyzing relational data, enhances node discriminability through the aggregation of neighboring information. Usually, stacking multiple layers can improve the…

Supervised dimensionality reduction strategies have been of great interest. However, current supervised dimensionality reduction approaches are difficult to scale for situations characterized by large datasets given the high computational…

Shape constraints, such as non-negativity, monotonicity, convexity or supermodularity, play a key role in various applications of machine learning and statistics. However, incorporating this side information into predictive models in a hard…

This paper presents a density-based topology optimization approach considering additive manufacturing limitations. The presented method considers the minimum size of parts, the minimum size of cavities, the inability of printing overhanging…

In this work, we explore the use of operator splitting algorithms for solving regularized structural topology optimization problems. The context is the classical structural design problems (e.g., compliance minimization and compliant…

We consider a wide range of regularized stochastic minimization problems with two regularization terms, one of which is composed with a linear function. This optimization model abstracts a number of important applications in artificial…

A very popular approach for solving stochastic optimization problems is the stochastic gradient descent method (SGD). Although the SGD iteration is computationally cheap and the practical performance of this method may be satisfactory under…

Topology optimization of microstructures plays a critical role in optimizing functional performance across diverse engineering applications. While metamaterials with enhanced mechanical properties -- such as hyperelasticity, energy…

We present a general learning-based solution for restoring images suffering from spatially-varying degradations. Prior approaches are typically degradation-specific and employ the same processing across different images and different pixels…

In this work, we study a novel class of projection-based algorithms for linearly constrained problems (LCPs) which have a lot of applications in statistics, optimization, and machine learning. Conventional primal gradient-based methods for…

This paper proposes a neural stochastic optimization method for efficiently solving the two-stage stochastic unit commitment (2S-SUC) problem under high-dimensional uncertainty scenarios. The proposed method approximates the second-stage…

This paper studies the complexity of finding an $\epsilon$-stationary point for stochastic bilevel optimization when the upper-level problem is nonconvex and the lower-level problem is strongly convex. Recent work proposed the first-order…

Solid-state Spatial Light Modulators (SLMs) are fundamentally limited in their ability to achieve high spatial complexity and high temporal bandwidth simultaneously. High-speed, low-energy modulation requires sub-wavelength active mode…

Many applications using large datasets require efficient methods for minimizing a proximable convex function subject to satisfying a set of linear constraints within a specified tolerance. For this task, we present a proximal projection…

Two-stage Stochastic Programming (2SP) is a standard framework for modeling decision-making problems under uncertainty. While numerous methods exist, solving such problems with many scenarios remains challenging. Selecting representative…

Cardinality constrained submodular function maximization, which aims to select a subset of size at most $k$ to maximize a monotone submodular utility function, is the key in many data mining and machine learning applications such as data…

We consider (stochastic) subgradient methods for strongly convex but potentially nonsmooth non-Lipschitz optimization. We provide new equivalent dual descriptions (in the style of dual averaging) for the classic subgradient method, the…

Recently, there has been a panoptic segmentation task combining semantic and instance segmentation, in which the goal is to classify each pixel with the corresponding instance ID. In this work, we propose a solution to tackle the panoptic…

Spike sorting is a fundamental preprocessing step for many neuroscience studies which rely on the analysis of spike trains. In this paper, we present two unsupervised spike sorting algorithms based on discriminative subspace learning. The…