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We study the log-alignment ratio (LAR), a measure of parameter-activation alignment, introduced in parameterization theory. We reformulate it as the overlap between a weight spectrum $p$ of the normalized squared singular values of a matrix…

In-context learning (ICL) is a key building block of modern large language models, yet its theoretical mechanisms remain poorly understood. It is particularly mysterious how ICL operates in real-world applications where tasks have a common…

This article introduces a new nonparametric method for estimating a univariate regression function of bounded variation. The method exploits the Jordan decomposition which states that a function of bounded variation can be decomposed as the…

Many medical datasets have recently been created for medical image segmentation tasks, and it is natural to question whether we can use them to sequentially train a single model that (1) performs better on all these datasets, and (2)…

We consider four main goals when fitting spatial linear models: 1) estimating covariance parameters, 2) estimating fixed effects, 3) kriging (making point predictions), and 4) block-kriging (predicting the average value over a region). Each…

This paper introduces a novel decision-making framework that promotes consistency among decisions made by diverse models while utilizing external knowledge. Leveraging the Integer Linear Programming (ILP) framework, we map predictions from…

Item Response Theory (IRT) models aim to assess latent abilities of $n$ examinees along with latent difficulty characteristics of $m$ test items from categorical data that indicates the quality of their corresponding answers. Classical…

In Imitation Learning (IL), utilizing suboptimal and heterogeneous demonstrations presents a substantial challenge due to the varied nature of real-world data. However, standard IL algorithms consider these datasets as homogeneous, thereby…

In many sequential decision-making problems (e.g., robotics control, game playing, sequential prediction), human or expert data is available containing useful information about the task. However, imitation learning (IL) from a small amount…

Analysis of indoor spaces requires topological information. In this paper, we propose to extract topological information from room attributes using what we call Iterative and adaptive graph Topology Learning (ITL). ITL progressively…

The problem of data-driven recursive computation of receding horizon LQR control through a randomized combination of online/current and historical/recorded data is considered. It is assumed that large amounts of historical input-output data…

Compositional generalization in sequential decision-making requires identifying which parts of prior rollouts remain useful for new tasks. Existing methods reuse skills or predictive models, but often overlook rich local transition geometry…

Intelligent reflecting surfaces (IRSs) can be beneficial to both information and energy transfer, due to the gains achieved by their multiple elements. In this work, we deal with the impact of spatial correlation between the IRS elements,…

Integer Linear Programming (ILP) has a broad range of applications in various areas of artificial intelligence. Yet in spite of recent advances, we still lack a thorough understanding of which structural restrictions make ILP tractable.…

The paper introduces the application of information geometry to describe the ground states of Ising models by utilizing parity-check matrices of cyclic and quasi-cyclic codes on toric and spherical topologies. The approach establishes a…

Domain adaptation is an important problem and often needed for real-world applications. In this problem, instead of i.i.d. training and testing datapoints, we assume that the source (training) data and the target (testing) data have…

Compositional data, such as human gut microbiomes, consist of non-negative variables whose only the relative values to other variables are available. Analyzing compositional data such as human gut microbiomes needs a careful treatment of…

High-dimensional compositional data are frequently encountered in many fields of modern scientific research. In regression analysis of compositional data, the presence of covariate measurement errors poses grand challenges for existing…

In the paper, we propose an effective and efficient Compositional Federated Learning (ComFedL) algorithm for solving a new compositional Federated Learning (FL) framework, which frequently appears in many data mining and machine learning…

Transformer models have established new benchmarks in natural language processing; however, their increasing depth results in substantial growth in parameter counts. While existing recurrent transformer methods address this issue by…