相关论文: A new class of $\alpha$-transformations for the sp…

Topography and gravity are geophysical fields whose joint statistical structure derives from interface-loading processes modulated by the underlying mechanics of isostatic and flexural compensation in the shallow lithosphere. Under this…

We present $\texttt{LAMINAR}$, a novel unsupervised machine learning pipeline designed to enhance the representation of structure within data via producing a more-informative distance metric. Analysis methods in the physical sciences often…

We consider statistical linear inverse problems in separable Hilbert spaces and filter-based reconstruction methods of the form $\hat f_\alpha = q_\alpha \left(T^*T\right)T^*Y$, where $Y$ is the available data, $T$ the forward operator,…

Large Language Models (LLMs) are increasingly being adopted as tools for learning; however, most tools remain text-only, limiting their usefulness for domains where visualizations are essential, such as mathematics. Recent work shows that…

We use the refined isogeometric analysis (rIGA) to solve generalized Hermitian eigenproblems $({Ku=\lambda Mu})$. The rIGA framework conserves the desirable properties of maximum-continuity isogeometric analysis (IGA) discretizations while…

Performative prediction is a recently proposed framework where predictions guide decision-making and hence influence future data distributions. Such performative phenomena are ubiquitous in various areas, such as transportation, finance,…

With the large models easing the labor-intensive manipulation process, image manipulations in today's real scenarios often entail a complex manipulation process, comprising a series of editing operations to create a deceptive image.…

Accurate and reliable probability predictions are essential for multi-class supervised learning tasks, where well-calibrated models enable rational decision-making. While isotonic regression has proven effective for binary calibration, its…

Finding the sparset solution of an underdetermined system of linear equations $y=Ax$ has attracted considerable attention in recent years. Among a large number of algorithms, iterative thresholding algorithms are recognized as one of the…

Many existing two-phase kernel-based hypothesis transfer learning algorithms employ the same kernel regularization across phases and rely on the known smoothness of functions to obtain optimality. Therefore, they fail to adapt to the…

In this work, we conceptualize the learning process as information compression. We seek to equip generative pre-trained models with human-like learning capabilities that enable data compression during inference. We present a novel approach…

Structural reliability methods aim at computing the probability of failure of systems with respect to some prescribed performance functions. In modern engineering such functions usually resort to running an expensive-to-evaluate…

This paper presents an information-theoretic approach for model reduction for finite time simulation. Although system models are typically used for simulation over a finite time, most of the metrics (and pseudo-metrics) used for model…

Geometric shape features have been widely used as strong predictors for image classification. Nevertheless, most existing classifiers such as deep neural networks (DNNs) directly leverage the statistical correlations between these shape…

Recent advances in large language models (LLMs) have been driven by pretraining, supervised fine tuning (SFT), and alignment tuning. Among these, SFT plays a crucial role in transforming a model 's general knowledge into structured…

Kernel methods, particularly kernel ridge regression (KRR), are time-proven, powerful nonparametric regression techniques known for their rich capacity, analytical simplicity, and computational tractability. The analysis of their predictive…

Targeted data selection has emerged as a crucial paradigm for efficient instruction tuning, aiming to identify a small yet influential subset of training examples for a specific target task. In practice, influence is often measured through…

In this paper, we propose a new optimization method for independent low-rank matrix analysis (ILRMA) based on a parametric majorization-equalization algorithm. ILRMA is an efficient blind source separation technique that simultaneously…

The transformer architecture, which processes sequences of input tokens to produce outputs for query tokens, has revolutionized numerous areas of machine learning. A defining feature of transformers is their ability to perform previously…

Knowledge Graphs (KG), composed of entities and relations, provide a structured representation of knowledge. For easy access to statistical approaches on relational data, multiple methods to embed a KG into f(KG) $\in$ R^d have been…