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A fundamental challenge in Bayesian inference is efficient representation of a target distribution. Many non-parametric approaches do so by sampling a large number of points using variants of Markov Chain Monte Carlo (MCMC). We propose an…
Fine-tuning a pre-trained language model (PLM) emerges as the predominant strategy in many natural language processing applications. However, this process is known to be expensive, especially on edge devices with low computing power. While…
Feature-preserving mesh denoising has received noticeable attention in visual media, with the aim of recovering high-fidelity, clean mesh shapes from the ones that are contaminated by noise. Existing denoising methods often design smaller…
Due to diverse architectures in deep neural networks (DNNs) with severe overparameterization, regularization techniques are critical for finding optimal solutions in the huge hypothesis space. In this paper, we propose an effective…
Multigrid methods are one of the most efficient techniques for solving linear systems arising from Partial Differential Equations (PDEs) and graph Laplacians from machine learning applications. One of the key components of multigrid is…
Recent advances in deep learning have been pushing image denoising techniques to a new level. In self-supervised image denoising, blind-spot network (BSN) is one of the most common methods. However, most of the existing BSN algorithms use a…
Many imaging science tasks can be modeled as a discrete linear inverse problem. Solving linear inverse problems is often challenging, with ill-conditioned operators and potentially non-unique solutions. Embedding prior knowledge, such as…
In this paper we propose an augmented smoothing function for nonlinear L1 -norm minimization problem and consider a global stability of a gradient-based neural network model to minimize the smoothing function. The numerical simulations show…
Quasi-Newton (QN) methods provide an efficient alternative to second-order methods for minimizing smooth unconstrained problems. While QN methods generally compose a Hessian estimate based on one secant interpolation per iteration,…
The advancement of imaging devices and countless images generated everyday pose an increasingly high demand on image denoising, which still remains a challenging task in terms of both effectiveness and efficiency. To improve denoising…
In this technical report, we investigate efficient representations of articulated objects (e.g. human bodies), which is an important problem in computer vision and graphics. To deform articulated geometry, existing approaches represent…
The Muon optimizer has recently demonstrated remarkable empirical success in training large language models. However, the theoretical understanding of its mechanisms remains limited. Current convergence guarantees for Muon rely heavily on…
Image denoising is a fundamental operation in image processing and holds considerable practical importance for various real-world applications. Arguably several thousands of papers are dedicated to image denoising. In the past decade,…
We propose a neural regularization method that refines the noisy 3D semantic field produced by lifting multi-view inconsistent 2D features, in order to obtain an accurate and robust 3D semantic Gaussian Splatting. The 2D features extracted…
We present a novel method for 3D surface reconstruction from multiple images where only a part of the object of interest is captured. Our approach builds on two recent developments: surface reconstruction using neural radiance fields for…
Smoothing is one technique to overcome data sparsity in statistical language model. Although in its mathematical definition there is no explicit dependency upon specific natural language, different natures of natural languages result in…
Neural network ensembles, such as Bayesian neural networks (BNNs), have shown success in the areas of uncertainty estimation and robustness. However, a crucial challenge prohibits their use in practice. BNNs require a large number of…
Several results on constrained spline smoothing are obtained. In particular, we establish a general result, showing how one can constructively smooth any monotone or convex piecewise polynomial function (ppf) (or any $q$-monotone ppf,…
Recent advances in 3D Gaussian Splatting (3DGS) have achieved remarkable success in high-fidelity Novel View Synthesis (NVS), yet the optimization process inevitably introduces noisy Gaussian primitives due to the sparse and incomplete…
The Modified Direct Method (MDM) is an iterative mesh smoothing method for smoothing planar and surface meshes, which is developed from the non-iterative smoothing method originated by Balendran [1]. When smooth planar meshes, the…