arXiv subjects

David Mendez

Publications and source records attributed to David Mendez.

5 recordsLinked to original sources

arXiv2026

Algebraic Machine Learning for Small-to-Medium Datasets Is Competitive against Strong Standard Baselines

Symbolic methods are generally not considered competitive with strong modern learners on realistic supervised tasks. We evaluate Algebraic Machine Learning (AML), a framework that learns through subdirect decomposition of algebraic structure rather than numerical optimization, against standard baselines on image and tabular classification across varying training-set sizes. We find that AML trained only on training data without using validation or cross-validation outperforms a family of cross-validated baseline methods including CNNs on small to medium image datasets (50--2000 training examples). On tabular datasets in the same size range, XGBoost is overall the best performing method, but AML is nonetheless comparable to methods incorporating task-specific biases such as LightGBM and random forests. AML achieves this competitive performance across two very different types of datasets using a generic algebraic inductive bias, rather than the modality-specific biases built into standard baselines like CNNs for images or XGBoost for tabular data, and requires no cross validation because it has no task-dependent hyperparameters to tune.

cs.LG↗

arXiv2025

Trials and Tribulations of Chemodynamical Tagging: Investigating the Recovery of Open Clusters in the Gaia DR3-GALAH DR4 Catalog

Chemodynamical tagging has been suggested as a powerful tool to trace stars back to their birth clusters. However, the efficacy of chemodynamical tagging as a means to recover individual stellar clusters is still under debate. In this study, we present a detailed investigation of chemodynamical tagging of open clusters using both dynamical and chemical data from the \textit{Gaia} DR3 and GALAH DR4 surveys, respectively. Using a sample of open clusters and mock field stars, we conduct a bootstrap analysis to evaluate every unique combination of orbital components ($E, J_R, J_\phi, J_Z$) and chemical abundances ([X/Fe] for O, Na, Mg, Al, Si, K, Ca, Sc, Ti, Cr, Mn, Ni, Cu, Y, and Ba) on how well they recover open clusters when used as parameters in the clustering algorithm, HBDSCAN. We find that using primarily dynamical orbital parameters leads to the highest recovery rate of open cluster stars. Nevertheless, even employing the best performing parameter combinations leads to low open cluster recovery rates. We find that, in most cases, chemodynamical tagging of open clusters using blind clustering algorithms is not efficient, which is in line with previous theoretical and observational work. However, we show that the addition of cuts based on metallicity, age, and birth radii in order to reduce the size of the clustering catalog can marginally improve the recovery rate of open clusters.

astro-ph.GA↗

arXiv2025

Algebraic Machine Learning: Learning as computing an algebraic decomposition of a task

Statistics and Optimization are foundational to modern Machine Learning. Here, we propose an alternative foundation based on Abstract Algebra, with mathematics that facilitates the analysis of learning. In this approach, the goal of the task and the data are encoded as axioms of an algebra, and a model is obtained where only these axioms and their logical consequences hold. Although this is not a generalizing model, we show that selecting specific subsets of its breakdown into algebraic atoms obtained via subdirect decomposition gives a model that generalizes. We validate this new learning principle on standard datasets such as MNIST, FashionMNIST, CIFAR-10, and medical images, achieving performance comparable to optimized multilayer perceptrons. Beyond data-driven tasks, the new learning principle extends to formal problems, such as finding Hamiltonian cycles from their specifications and without relying on search. This algebraic foundation offers a fresh perspective on machine intelligence, featuring direct learning from training data without the need for validation dataset, scaling through model additivity, and asymptotic convergence to the underlying rule in the data.

cs.LG↗

arXiv2023

Infinite Atomized Semilattices

We extend the theory of atomized semilattices to the infinite setting. We show that it is well-defined and that every semilattice is atomizable. We also study atom redundancy, focusing on complete and finitely generated semilattices and show that for finitely generated semilattices, atomizations consisting exclusively of non-redundant atoms always exist.

math.AC↗

arXiv2015

Optimizing CMS build infrastructure via Apache Mesos

The Offline Software of the CMS Experiment at the Large Hadron Collider (LHC) at CERN consists of 6M lines of in-house code, developed over a decade by nearly 1000 physicists, as well as a comparable amount of general use open-source code. A critical ingredient to the success of the construction and early operation of the WLCG was the convergence, around the year 2000, on the use of a homogeneous environment of commodity x86-64 processors and Linux. Apache Mesos is a cluster manager that provides efficient resource isolation and sharing across distributed applications, or frameworks. It can run Hadoop, Jenkins, Spark, Aurora, and other applications on a dynamically shared pool of nodes. We present how we migrated our continuos integration system to schedule jobs on a relatively small Apache Mesos enabled cluster and how this resulted in better resource usage, higher peak performance and lower latency thanks to the dynamic scheduling capabilities of Mesos.

cs.DC↗