Related papers: When does third order efficiency imply fourth orde…

We consider a one-dimensional singularly perturbed 4th order problem with the additional feature of a shift term. An expansion into a smooth term, boundary layers and an inner layer yields a formal solution decomposition, and together with…

An important challenge in machine translation (MT) is to generate high-quality and diverse translations. Prior work has shown that the estimated likelihood from the MT model correlates poorly with translation quality. In contrast, quality…

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…

Distributed learning of probabilistic models from multiple data repositories with minimum communication is increasingly important. We study a simple communication-efficient learning framework that first calculates the local maximum…

We prove concentration inequalities for $f\left( X\right) $ about its median, where $X$ is a random vector in $\mathbb{R}^n$ with independent heavy tailed coordinates of Weibull or power type, and $f:\mathbb{R}^n\rightarrow\mathbb{R}$ is a…

In this paper, we re-examine the Markov property in the context of neural machine translation. We design a Markov Autoregressive Transformer~(MAT) and undertake a comprehensive assessment of its performance across four WMT benchmarks. Our…

The scaling trend in Large Language Models (LLMs) has prioritized increasing the maximum context window to facilitate complex, long-form reasoning and document analysis. However, managing this expanded context introduces severe…

Parameter-efficient transfer learning (PETL) aims to adapt pre-trained models to new downstream tasks while minimizing the number of fine-tuned parameters. Adapters, a popular approach in PETL, inject additional capacity into existing…

In fair division of indivisible goods, using sequences of sincere choices (or picking sequences) is a natural way to allocate the objects. The idea is the following: at each stage, a designated agent picks one object among those that…

The distribution of the spacing, or the difference between consecutive order statistics, is known only for uniform and exponential random variates. We add here logistic and Gumbel variates, and present an estimator for distributions with a…

This paper proves an impossibility result for stochastic network utility maximization for multi-user wireless systems, including multiple access and broadcast systems. Every time slot an access point observes the current channel states for…

In this paper the Gaussian quasi maximum likelihood estimator (GQMLE) is generalized by applying a transform to the probability distribution of the data. The proposed estimator, called measure-transformed GQMLE (MT-GQMLE), minimizes the…

We prove maximum and comparison principles for fractional discrete derivatives in the integers. Regularity results when the space is a mesh of length $h$, and approximation theorems to the continuous fractional derivatives are shown. When…

Suppose we are given observations, where each observation is drawn independently from one of $k$ known distributions. The goal is to match each observation to the distribution from which it was drawn. We observe that the maximum likelihood…

Throughout this article we develop and change the definitions and the ideas in "arXiv:1006.4939", in order to consider the efficiency of functions and complexity time problems. The central idea here is effective enumeration and listing, and…

Correlated outcomes are common in many practical problems. In some settings, one outcome is of particular interest, and others are auxiliary. To leverage information shared by all the outcomes, traditional multi-task learning (MTL)…

In supervised machine learning, the choice of loss function implicitly assumes a particular noise distribution over the data. For example, the frequently used mean squared error (MSE) loss assumes a Gaussian noise distribution. The choice…

Multimodal Large Language Models (MLLMs) utilize multimodal contexts consisting of text, images, or videos to solve various multimodal tasks. However, we find that changing the order of multimodal input can cause the model's performance to…

In this paper, by treating in-context learning (ICL) as a meta-optimization process, we explain why LLMs are sensitive to the order of ICL examples. This understanding leads us to the development of Batch-ICL, an effective, efficient, and…

An optimized Rayleigh-Schr\"{o}dinger expansion scheme of solving the functional Schr\"odinger equation with an external source is proposed to calculate the effective potential beyond the Gaussian approximation. For a scalar field theory…