arXiv subjects

Luis Ortiz

Publications and source records attributed to Luis Ortiz.

3 recordsLinked to original sources

arXiv2026

Benchmarking a machine-learning differential equations solver on a neutral-atom logical processor

We report on a performance comparison between physical and logical computations on a prototypical machine-learning application: solving differential equations using quantum kernel methods. The algorithm is implemented on an atom-based logical quantum processor, both at the physical and logical levels. We show that the kernel estimated from the logical implementation performs better than its physical counterpart on relevant metrics. We observe how such performance improvement can be traced back to specific noise-induced errors detected by the chosen encoding. We apply the computed quantum kernel to the task of solving differential equations, confirming how the superior performance of a logical quantum kernel is retained also at an end-to-end applicative level. Our findings show that experimental validation of end-to-end protocols can already highlight the positive impact of fault-tolerant implementations despite their higher quantum resource count, and guide application-informed architectural choices.

quant-ph↗

arXiv2018

The hyperspace of non blockers of $F_1(X)$

A continuum is a compact connected metric space. A non-empty closed subset $B$ of a continuum $X$ does not block $x\in X\setminus B$ provided that the union of all subcontinua of $X$ containing $x$ and contained in $X\setminus B$ is dense in $X$. We denote the collection of all non-empty closed subset $B$ of $X$ such that $B$ does not block each element of $X\setminus B$ by $NB(F_1(X))$. In this paper we show some properties of the hyperspace $NB(F_1(X))$. Particularly, we prove that the simple closed curve is the unique continuum $X$ such that $NB(F_1(X))=F_1(X)$, given a positive answer to a question posed by Escobedo, Estrada-Obregón and Villanueva in 2012.

math.GN↗

arXiv2015

Learning the Structure and Parameters of Large-Population Graphical Games from Behavioral Data

We consider learning, from strictly behavioral data, the structure and parameters of linear influence games (LIGs), a class of parametric graphical games introduced by Irfan and Ortiz (2014). LIGs facilitate causal strategic inference (CSI): Making inferences from causal interventions on stable behavior in strategic settings. Applications include the identification of the most influential individuals in large (social) networks. Such tasks can also support policy-making analysis. Motivated by the computational work on LIGs, we cast the learning problem as maximum-likelihood estimation (MLE) of a generative model defined by pure-strategy Nash equilibria (PSNE). Our simple formulation uncovers the fundamental interplay between goodness-of-fit and model complexity: good models capture equilibrium behavior within the data while controlling the true number of equilibria, including those unobserved. We provide a generalization bound establishing the sample complexity for MLE in our framework. We propose several algorithms including convex loss minimization (CLM) and sigmoidal approximations. We prove that the number of exact PSNE in LIGs is small, with high probability; thus, CLM is sound. We illustrate our approach on synthetic data and real-world U.S. congressional voting records. We briefly discuss our learning framework's generality and potential applicability to general graphical games.

cs.LG↗