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Large-Momentum Effective Theory (LaMET) is a physics-guided systematic expansion to calculate light-cone parton distributions, including collinear (PDFs) and transverse-momentum-dependent ones, at any fixed momentum fraction $x$ within a…

One proposal to compute parton distributions from first principles is the large momentum effective theory (LaMET), which requires the Fourier transform of matrix elements computed non-perturbatively. Lattice quantum chromodynamics (QCD)…

Large-momentum effective theory (LaMET) provides an approach to directly calculate the $x$-dependence of generalized parton distributions (GPDs) on a Euclidean lattice through power expansion and a perturbative matching. When a parton's…

The development of LLMs has greatly enhanced the intelligence and fluency of question answering, while the emergence of retrieval enhancement has enabled models to better utilize external information. However, the presence of noise and…

In high-dimensional data, structured noise caused by observed and unobserved factors affecting multiple target variables simultaneously, imposes a serious challenge for modeling, by masking the often weak signal. Therefore, (1) explaining…

We systematically investigated the limited inverse discrete Fourier transform of the quasi distributions from the perspective of inverse problem theory. This transformation satisfies two of Hadamard's well-posedness criteria, existence and…

Model editing techniques are essential for efficiently updating knowledge in large language models (LLMs). However, the effectiveness of existing approaches degrades in massive editing scenarios, particularly when evaluated with practical…

We address the problem of inferring descriptions of system behavior using Linear Temporal Logic (LTL) from a finite set of positive and negative examples. Most of the existing approaches for solving such a task rely on predefined templates…

Noise in data appears to be inevitable in most real-world machine learning applications and would cause severe overfitting problems. Not only can data features contain noise, but labels are also prone to be noisy due to human input. In this…

A continuing mystery in understanding the empirical success of deep neural networks is their ability to achieve zero training error and generalize well, even when the training data is noisy and there are more parameters than data points. We…

In the present paper we consider Laplace deconvolution for discrete noisy data observed on the interval whose length may increase with a sample size. Although this problem arises in a variety of applications, to the best of our knowledge,…

In a paper by Willems and coauthors it was shown that persistently exciting data can be used to represent the input-output behavior of a linear system. Based on this fundamental result, we derive a parametrization of linear feedback systems…

Large-Momentum Effective Theory (or LaMET) advocated by the present authors provides a direct approach to simulate parton physics in Eulidean lattice QCD theory. Recently, there has been much interest in this theory in the literature, with…

Synthetic data has gained attention for training large language models, but poor-quality data can harm performance (see, e.g., Shumailov et al. (2023); Seddik et al. (2024)). A potential solution is data pruning, which retains only…

We consider inverse problems estimating distributed parameters from indirect noisy observations through discretization of continuum models described by partial differential or integral equations. It is well understood that the errors…

Assessing data informativity, determining whether the measured data contains sufficient information for a specific control objective, is a fundamental challenge in data-driven control. In noisy scenarios, existing studies deal with system…

We propose a general approach to construct weighted likelihood estimating equations with the aim of obtaining robust parameter estimates. We modify the standard likelihood equations by incorporating a weight that reflects the statistical…

Large Momentum Effective Theory (LaMET) provides a general framework for computing the multi-dimensional partonic structure of the proton from first principles using lattice quantum chromodynamics (QCD). In this effective field theory…

Mathematical models of real life phenomena are highly nonlinear involving multiple parameters and often exhibiting complex dynamics. Experimental data sets are typically small and noisy, rendering estimation of parameters from such data…

Modern technologies are producing datasets with complex intrinsic structures, and they can be naturally represented as matrices instead of vectors. To preserve the latent data structures during processing, modern regression approaches…