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We use geometric invariant theory (GIT) to construct a large class of compactifications of the moduli space M_{0,n}. These compactifications include many previously known examples, as well as many new ones. As a consequence of our GIT…

Galaxy morphology offers significant insights into the evolutionary pathways and underlying physics of galaxies. As astronomical data grows with surveys such as Euclid and Vera C. Rubin , there is a need for tools to classify and analyze…

Despite the recent success of graph neural networks (GNN), common architectures often exhibit significant limitations, including sensitivity to oversmoothing, long-range dependencies, and spurious edges, e.g., as can occur as a result of…

Robust correlation estimation is essential in high-dimensional settings, particularly when data are contaminated by outliers or exhibit heavy-tailed behavior. Many robust loss functions of practical interest-such as those involving…

With the exponential growth of time series data across diverse domains, there is a pressing need for effective analysis tools. Time series clustering is important for identifying patterns in these datasets. However, prevailing methods often…

Decision tree (DT) attracts persistent research attention due to its impressive empirical performance and interpretability in numerous applications. However, the growth of traditional yet widely-used univariate decision trees (UDTs) is…

In this paper, we propose a unified convergence analysis for a class of generic shuffling-type gradient methods for solving finite-sum optimization problems. Our analysis works with any sampling without replacement strategy and covers many…

In lattice quantum field theory studies, parameters defining the lattice theory must be tuned toward criticality to access continuum physics. Commonly used Markov chain Monte Carlo (MCMC) methods suffer from critical slowing down in this…

In this paper, we study the form over the minimum spanning tree problem (MST) from which we will derive an intuitively generalized model and new methods with the upper bound of runtimes of logarithm. The new pattern we made has taken…

Obtaining a single-vector representation from a Large Language Model's (LLM) token-level outputs is a critical step for nearly all sentence-level tasks. However, standard pooling methods like mean or max aggregation treat tokens as an…

We present a new algorithm to explore or count the numerical semigroups of a given genus which uses the unleaved version of the tree of numerical semigroups. In the unleaved tree there are no leaves rather than the ones at depth equal to…

The algebraic properties of flattenings and subflattenings provide direct methods for identifying edges in the true phylogeny -- and by extension the complete tree -- using pattern counts from a sequence alignment. The relatively small…

The majority of finite mixture models suffer from not allowing asymmetric tail dependencies within components and not capturing non-elliptical clusters in clustering applications. Since vine copulas are very flexible in capturing these…

A general framework for dealing with both linear regression and clustering problems is described. It includes Gaussian clusterwise linear regression analysis with random covariates and cluster analysis via Gaussian mixture models with…

Recently, parallel text generation has received widespread attention due to its success in generation efficiency. Although many advanced techniques are proposed to improve its generation quality, they still need the help of an…

Finite-temperature magnetism gives rise to many phenomena in alloy materials, such as magnetic phase transformations, short or medium range order in magnetic alloys, spin waves, critical phenomena, and the magnetocaloric effect. Lattice…

Generalization techniques have many applications, including template construction, argument generalization, and indexing. Modern interactive provers can exploit advancement in generalization methods over expressive type theories to further…

Despite the success of deep learning for text and image data, tree-based ensemble models are still state-of-the-art for machine learning with heterogeneous tabular data. However, there is a significant need for tabular-specific…

Realizing when a model is right for a wrong reason is not trivial and requires a significant effort by model developers. In some cases an input salience method, which highlights the most important parts of the input, may reveal problematic…

To increase the interpretability and prediction accuracy of the Machine Learning (ML) models, visualization of ML models is a key part of the ML process. Decision Trees (DTs) are essential in machine learning (ML) because they are used to…