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Since distribution shifts are common in real-world applications, there is a pressing need to develop prediction models that are robust against such shifts. Existing frameworks, such as empirical risk minimization or distributionally robust…
This paper presents an experience report on the development of Retrieval Augmented Generation (RAG) systems using PDF documents as the primary data source. The RAG architecture combines generative capabilities of Large Language Models…
We develop new techniques for rounding packing integer programs using iterative randomized rounding. It is based on a novel application of multidimensional Brownian motion in $\mathbb{R}^n$. Let $\overset{\sim}{x} \in {[0,1]}^n$ be a…
In this paper, we consider a class of finite-sum convex optimization problems whose objective function is given by the summation of $m$ ($\ge 1$) smooth components together with some other relatively simple terms. We first introduce a…
Recent advances in 3D Gaussian Splatting (3DGS) have enabled impressive real-time photorealistic rendering. However, conventional training pipelines inherently assume full multi-view consistency among input images, which makes them…
Multi-modal Retrieval-Augmented Generation (RAG) has become a critical method for empowering LLMs by leveraging candidate visual documents. However, current methods consider the entire document as the basic retrieval unit, introducing…
A central goal of modern magnetic resonance imaging (MRI) is to reduce the time required to produce high-quality images. Efforts have included hardware and software innovations such as parallel imaging, compressed sensing, and deep…
Angular data are commonly encountered in settings with a directional or orientational component. Regressing an angular response on real-valued features requires intrinsically capturing the circular or spherical manifold the data lie on, or…
We introduce the Hessian reweighting of parton distribution functions (PDFs). Similarly to the better-known Bayesian methods, its purpose is to address the compatibility of new data and the quantitative modifications they induce within an…
The retrieval augmented generation (RAG) framework addresses an ambiguity in user queries in QA systems by retrieving passages that cover all plausible interpretations and generating comprehensive responses based on the passages. However,…
We introduce an adaptive regularization approach. In contrast to conventional Tikhonov regularization, which specifies a fixed regularization operator, we estimate it simultaneously with parameters. From a Bayesian perspective we estimate…
How much visual information about the retinal images can be extracted from the different layers of the visual pathway?. Separate subsystems (e.g. opponent channels, spatial filters, nonlinearities of the texture sensors) have been suggested…
We consider an inertial primal-dual fixed point algorithm (IPDFP) to compute the minimizations of the following Problem (1.1). This is a full splitting approach, in the sense that the nonsmooth functions are processed individually via their…
The declining response rates in probability surveys along with the widespread availability of unstructured data has led to growing research into non-probability samples. Existing robust approaches are not well-developed for non-Gaussian…
A method providing optimal estimate of probability density functions (PDFs) from time series is proposed. It allows almost arbitrary resolution PDFs when applied to either, sampled analytic functions or digitized data from experiments. When…
The Random Variable Transformation (RVT) method is a fundamental tool for determining the probability distribution function associated with a Random Variable (RV) Y=g(X), where X is a RV and g is a suitable transformation. In the usual…
In this paper we explore the role of duality principles within the problem of rotation averaging, a fundamental task in a wide range of computer vision applications. In its conventional form, rotation averaging is stated as a minimization…
Diffusion models enable high-quality and diverse visual content synthesis. However, they struggle to generate rare or unseen concepts. To address this challenge, we explore the usage of Retrieval-Augmented Generation (RAG) with image…
We present a variational renormalization group (RG) approach using a deep generative model based on normalizing flows. The model performs hierarchical change-of-variables transformations from the physical space to a latent space with…
Over the last years, deep learning methods have become an increasingly popular choice to solve tasks from the field of inverse problems. Many of these new data-driven methods have produced impressive results, although most only give point…