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Integral functionals based on convex normal integrands are minimized subject to finitely many moment constraints. The integrands are finite on the positive and infinite on the negative numbers, strictly convex but not necessarily…

The usual approach to developing and analyzing first-order methods for smooth convex optimization assumes that the gradient of the objective function is uniformly smooth with some Lipschitz constant $L$. However, in many settings the…

We discuss non-Euclidean deterministic and stochastic algorithms for optimization problems with strongly and uniformly convex objectives. We provide accuracy bounds for the performance of these algorithms and design methods which are…

Dual averaging-type methods are widely used in industrial machine learning applications due to their ability to promoting solution structure (e.g., sparsity) efficiently. In this paper, we propose a novel accelerated dual-averaging…

Few-shot semantic segmentation (FSS) is a crucial challenge in computer vision, driving extensive research into a diverse range of methods, from advanced meta-learning techniques to simple transfer learning baselines. With the emergence of…

This paper provides convergence analysis for the approximation of a class of path-dependent functionals underlying a continuous stochastic process. In the first part, given a sequence of weak convergent processes, we provide a sufficient…

Many weak instrumental variables (IVs) are routinely used in the health and social sciences to improve identification and inference of the treatment effect of interest, along with a broad collection of data on potential confounding factors…

Though image-level weakly supervised semantic segmentation (WSSS) has achieved great progress with Class Activation Maps (CAMs) as the cornerstone, the large supervision gap between classification and segmentation still hampers the model to…

We present a novel and effective binary representation for convex shapes. We show the equivalence between the shape convexity and some properties of the associated indicator function. The proposed method has two advantages. Firstly, the…

The Weak Gravity Conjecture (WGC) was proposed to constrain Effective Field Theories (EFTs) with Abelian gauge symmetry coupled to gravity. In this article, I study the WGC from low energy observers' perspective, and revisit the issue of to…

We analyze two recently proposed methods to establish a priori lower bounds on the minimum of general integral variational problems. The methods, which involve either `occupation measures' or a `pointwise dual relaxation' procedure, are…

The Weak Gravity Conjecture imposes stringent constraints on effective field theories to allow for an ultraviolet completion within quantum gravity. While substantial evidence supports the conjecture across broad classes of string…

Submodularity is a discrete domain functional property that can be interpreted as mimicking the role of the well-known convexity/concavity properties in the continuous domain. Submodular functions exhibit strong structure that lead to…

Weakly Supervised Semantic Segmentation (WSSS) addresses the challenge of training segmentation models using only image-level annotations. Existing WSSS methods struggle with precise object boundary localization and focus only on the most…

In this paper, we address a manifold constrained nonsmooth optimization problem involving the composition of a weakly convex function and a smooth mapping under the availability of a parametrization of the manifold. To find a stationary…

Semantic segmentation is an important and prevalent task, but severely suffers from the high cost of pixel-level annotations when extending to more classes in wider applications. To this end, we focus on the problem named weak-shot semantic…

Stochastic approximation techniques have been used in various contexts in data science. We propose a stochastic version of the forward-backward algorithm for minimizing the sum of two convex functions, one of which is not necessarily…

The paper studies primal and dual characterizations of a class of sign-symmetric norms on product vector spaces. Correspondences between these norms and a class of convex functions are established. Explicit formulas for the dual norm and…

Minimax optimization has been central in addressing various applications in machine learning, game theory, and control theory. Prior literature has thus far mainly focused on studying such problems in the continuous domain, e.g.,…

We propose and experimentally realize a general scheme of differential imaging employing the idea of weak measurement. We show that the weak coupling between the system of interest and a two-level ancilla can introduce a two-beam circuit…