Related papers: Generalized Inverse Based Decoding

Speculative decoding has emerged as a promising technique to accelerate the inference of Large Language Models (LLMs) by employing a small language model to draft a hypothesis sequence, which is then validated by the LLM. The effectiveness…

Iterative methods are widely used for solving partial differential equations (PDEs). However, the difficulty in eliminating global low-frequency errors significantly limits their convergence speed. In recent years, neural networks have…

While mixed-integer linear programming and convex programming solvers have advanced significantly over the past several decades, solution technologies for general mixed-integer nonlinear programs (MINLPs) have yet to reach the same level of…

A parameter-free method, namely the generalization of the Gauss-Seidel (GGS) method, is developed to solve generalized absolute value equations. Convergence of the proposed method is analyzed. Numerical results are given to demonstrate the…

We propose a novel Linear Program (LP) based formula- tion for solving jigsaw puzzles. We formulate jigsaw solving as a set of successive global convex relaxations of the stan- dard NP-hard formulation, that can describe both jigsaws with…

Our world is full of physics-driven data where effective mappings between data manifolds are desired. There is an increasing demand for understanding combined model-based and data-driven methods. We propose a nonlinear, learned singular…

This paper presents an approach to generalize the concept of isogeometric analysis (IGA) by allowing different spaces for parameterization of the computational domain and for approximation of the solution field. The method inherits the main…

We study the Out-of-Distribution (OOD) generalization in machine learning and propose a general framework that establishes information-theoretic generalization bounds. Our framework interpolates freely between Integral Probability Metric…

Stochastic gradient descent (SGD) and its variants have established themselves as the go-to algorithms for large-scale machine learning problems with independent samples due to their generalization performance and intrinsic computational…

Stochastic gradient descent (SGD) is a popular stochastic optimization method in machine learning. Traditional parallel SGD algorithms, e.g., SimuParallel SGD, often require all nodes to have the same performance or to consume equal…

Generalized semi-infinite programs (GSIP) are a class of mathematical optimization problems that generalize semi-infinite programs, which have a finite number of decision variables and infinite constraints. Mitsos et al. (Mitsos and…

Anomaly detection, finding patterns that substantially deviate from those seen previously, is one of the fundamental problems of artificial intelligence. Recently, classification-based methods were shown to achieve superior results on this…

In this article, we propose a general nonlinear sufficient dimension reduction (SDR) framework when both the predictor and response lie in some general metric spaces. We construct reproducing kernel Hilbert spaces whose kernels are fully…

Despite being highly over-parametrized, and having the ability to fully interpolate the training data, deep networks are known to generalize well to unseen data. It is now understood that part of the reason for this is that the training…

Transversal logical gates offer the opportunity for fast and low-noise logic, particularly when interspersed by a single round of parity check measurements of the underlying code. Using such circuits for the surface code requires decoding…

In recent years, deep learning methods have been extensively developed for inverse imaging problems (IIPs), encompassing supervised, self-supervised, and generative approaches. Most of these methods require large amounts of labeled or…

In this work we propose a theoretical and computational framework for solving the three dimensional inverse medium scattering problem, based on a set of data-driven basis arising from the linearized problem. This set of data-driven basis…

Neural operators on irregular meshes face a fundamental tension. Spectral positional encodings, the natural choice for capturing geometry, require cubic-complexity eigendecomposition and inadvertently break gauge invariance through…

The traditional approach of hand-crafting priors (such as sparsity) for solving inverse problems is slowly being replaced by the use of richer learned priors (such as those modeled by generative adversarial networks, or GANs). In this work,…

In this paper we introduce new types of square-piece jigsaw puzzles, where in addition to the unknown location and orientation of each piece, a piece might also need to be flipped. These puzzles, which are associated with a number of real…