Related papers: A Tutorial on Dual Decomposition and Lagrangian Re…
Local Fourier analysis is a strong and well-established tool for analyzing the convergence of numerical methods for partial differential equations. The key idea of local Fourier analysis is to represent the occurring functions in terms of a…
The continuous nonlinear resource allocation problem (CONRAP) has broad applications in economics, engineering, production and inventory management, and often serves as a subproblem in complex programming. Without relying on monotonicity…
Bilevel optimization has been widely used in decision-making process. However, there still lacks an efficient algorithm to determine an optimal solution of a bilevel optimization problem, especially for a large-size problem. To bridge the…
Analogy has been shown to be important in many key cognitive abilities, including learning, problem solving, creativity and language change. For cognitive models of analogy, the fundamental computational question is how its inherent…
In this paper we provide a detailed analysis of the iteration complexity of dual first order methods for solving conic convex problems. When it is difficult to project on the primal feasible set described by convex constraints, we use the…
The widespread application of pre-trained language models (PLMs) in natural language processing (NLP) has led to increasing concerns about their explainability. Selective rationalization is a self-explanatory framework that selects…
A novel augmented Lagrangian method for solving non-convex programs with nonlinear cost and constraint couplings in a distributed framework is presented. The proposed decomposition algorithm is made of two layers: The outer level is a…
Large language models (LLMs) have achieved strong empirical performance in various fields, benefiting from their huge amount of parameters that store knowledge. However, LLMs still suffer from several key issues, such as hallucination…
This thesis provides methods and analysis of models which make progress on this goal. The techniques outlined are task agnostic, and should provide benefit when used with nearly any transformer LM. We introduce two new finetuning methods…
We introduce a general method for relaxing decision diagrams that allows one to bound job sequencing problems by solving a Lagrangian dual problem on a relaxed diagram. We also provide guidelines for identifying problems for which this…
Efficient representations of the Hamiltonian such as double factorization drastically reduce circuit depth or number of repetitions in error corrected and noisy intermediate scale quantum (NISQ) algorithms for chemistry. We report a…
Motivated by applications in large-scale knowledge base construction, we study the problem of scaling up a sophisticated statistical inference framework called Markov Logic Networks (MLNs). Our approach, Felix, uses the idea of Lagrangian…
Simulation and modeling are essential in product development, integrated into the design and manufacturing process to enhance efficiency and quality. They are typically represented as complex nonlinear differential algebraic equations. The…
Dual decomposition provides a tractable framework for designing algorithms for finding the most probable (MAP) configuration in graphical models. However, for many real-world inference problems, the typical decomposition has a large…
Our goal is to create an interactive natural language interface that efficiently and reliably learns from users to complete tasks in simulated robotics settings. We introduce a neural semantic parsing system that learns new high-level…
This research introduces a Positive Reconstruction Framework based on positive psychology theory. Overcoming negative thoughts can be challenging, our objective is to address and reframe them through a positive reinterpretation. To tackle…
Compressed sensing is a new methodology for constructing sensors which allow sparse signals to be efficiently recovered using only a small number of observations. The recovery problem can often be stated as the one of finding the solution…
Domain reduction techniques are at the core of any global optimization solver for NLP or MINLP problems. In this paper, we delve into several of these techniques and assess the impact they may have in the performance of an RLT-based…
This article emphasizes that NLP as a science seeks to make inferences about the performance effects that result from applying one method (compared to another method) in the processing of natural language. Yet NLP research in practice…
We associate with each convex optimization problem posed on some locally convex space with an infinite index set T, and a given non-empty family H formed by finite subsets of T, a suitable Lagrangian-Haar dual problem. We provide reverse…