Search

This thesis investigates critical phenomena and equilibrium states in various stochastic models through three interconnected studies. In the first chapter, we analyze the Activated Random Walk model on a one-dimensional ring in the high-density regime. We introduce a toppling procedure that incrementally constructs an environment demonstrating the sustained activity over extended periods. This approach provides a concise and self-contained proof of the existence of a slow phase for arbitrarily large sleep rates. The second chapter focuses on a modified unidimensional contact process with varying infection rates. Specifically, infection spreads at rate $\lambda_e$ at the boundaries of the infected region and at rate $\lambda_i$ elsewhere. We establish the existence of an invariant measure for this process when $\lambda_i=\lambda_c$, $\lambda_e=\lambda_c+\varepsilon$ where $\lambda_c$ denotes the critical parameter for the standard contact process. Furthermore, we demonstrate that the process, when observed from the right edge, converges weakly to this invariant measure. We also show that infection dies almost surely along the critical curve within the attractive region of the phase space. In the final chapter, we explore quasi-stationary distributions (QSDs) for two subcritical population processes in continuous time: branching random walks and branching processes with genealogy. We prove the existence and uniqueness of QSDs for these processes by leveraging spatial aspects of their dynamics., Comment: PhD thesis

This work explores the implications of the Exclusivity Principle (EP) in the context of quantum and post-quantum correlations. We first establish a key technical result demonstrating that given the set of correlations for a complementary experiment, the EP restricts the maximum set of correlations for the original experiment to the anti-blocking set. Based on it, we can prove our central result: if all quantum behaviors are accessible in Nature, the EP guarantees that no post-quantum behaviors can be realized. This can be seen as a generalization of the result of [Phys. Rev. A 89, 030101(R)], to a wider range of scenarios. It also provides novel insights into the structure of quantum correlations and their limitations., Comment: 5 pages

We present a characterization of the Hamiltonians that generate optimal-speed unitary time evolution and the associated dynamical trajectory, where the initial states are either pure states or quasi-pure quantum states. We construct the manifold of pure states as an orbit under the conjugation action of the Lie group $\SU(n)$ on the manifold of one-dimensional orthogonal projectors, obtaining an isometry with the flag manifold $\SU(n)/\textnormal{S}(\textnormal{U}(1)\times \textnormal{U}(n-1 ))$. From this construction, we show that Hamiltonians generating optimal-speed time evolution are fully characterized by equigeodesic vectors of $\SU(n)/\textnormal{S}(\textnormal{U}(1)\times \textnormal{U}(n-1))$. We later extend that result to quasi-pure quantum states., Comment: 14 pages

We study the Activated Random Walk model on the one-dimensional ring, in the high density regime. We develop a toppling procedure that gradually builds an environment that can be used to show that activity will be sustained for a long time. This yields a self-contained and relatively short proof of existence of a slow phase for arbitrarily large sleep rates.

Despite their wide adoption, the biases and unintended behaviors of language models remain poorly understood. In this paper, we identify and characterize a phenomenon never discussed before, which we call semantic leakage, where models leak irrelevant information from the prompt into the generation in unexpected ways. We propose an evaluation setting to detect semantic leakage both by humans and automatically, curate a diverse test suite for diagnosing this behavior, and measure significant semantic leakage in 13 flagship models. We also show that models exhibit semantic leakage in languages besides English and across different settings and generation scenarios. This discovery highlights yet another type of bias in language models that affects their generation patterns and behavior.

Swept laser interferometry is an extremely powerful solution embedded in several recent technologies such as absolute distance measurement, light detection and ranging, optical frequency domain reflectometry, optical coherence tomography, microresonator characterization, and gas spectroscopy. Nonlinearity in the optical frequency sweeping of tunable lasers is a fatal drawback in gaining the expected outcome from these technologies. Here, we introduce an onchip, millimeter scale, 7 m spiral resonator that is made of ultralow loss silicon nitride to act as a frequency ruler for correction of the tunable lasers sweeping nonlinearities. The sharp 2 MHz frequency lines of the 85 M high-quality resonator and the narrow spaced 25.57 MHz frequency ticks of the 7 m spiral allow unprecedented precise nonlinearity correction on an integrated photonics platform. Accurate measurements of the rulers frequency spacing, linewidth, and temperature and wavelength sensitivities of the frequency ticks are performed here to demonstrate the quality of the frequency ruler. In addition, the spiral resonator is implemented in an FMCW LiDAR experiment to demonstrate a potential application of the proposed onchip frequency ruler., Comment: 12 pages

A locally recoverable code of locality $r$ over $\mathbb{F}_{q}$ is a code where every coordinate of a codeword can be recovered using the values of at most $r$ other coordinates of that codeword. Locally recoverable codes are efficient at restoring corrupted messages and data which make them highly applicable to distributed storage systems. Quasi-cyclic codes of length $n=m\ell$ and index $\ell$ are linear codes that are invariant under cyclic shifts by $\ell$ places. %Quasi-cyclic codes are generalizations of cyclic codes and are isomorphic to $\mathbb{F}_{q} [x]/ \langle x^m-1 \rangle$-submodules of $\mathbb{F}_{q^\ell} [x] / \langle x^m-1 \rangle$. In this paper, we decompose quasi-cyclic locally recoverable codes into a sum of constituent codes where each constituent code is a linear code over a field extension of $\mathbb{F}_q$. Using these constituent codes with set parameters, we propose conditions which ensure the existence of almost optimal and optimal quasi-cyclic locally recoverable codes with increased dimension and code length., Comment: 12 pages

The "massively-multilingual" training of multilingual models is known to limit their utility in any one language, and they perform particularly poorly on low-resource languages. However, there is evidence that low-resource languages can benefit from targeted multilinguality, where the model is trained on closely related languages. To test this approach more rigorously, we systematically study best practices for adapting a pre-trained model to a language family. Focusing on the Uralic family as a test case, we adapt XLM-R under various configurations to model 15 languages; we then evaluate the performance of each experimental setting on two downstream tasks and 11 evaluation languages. Our adapted models significantly outperform mono- and multilingual baselines. Furthermore, a regression analysis of hyperparameter effects reveals that adapted vocabulary size is relatively unimportant for low-resource languages, and that low-resource languages can be aggressively up-sampled during training at little detriment to performance in high-resource languages. These results introduce new best practices for performing language adaptation in a targeted setting.

The relations between Bell nonlocality and Kochen-Specker contextuality have been subject of research from many different perspectives in the last decades. Recently, some interesting results on these relations have been explored in the so-called generalized Bell scenarios, that is, scenarios where Bell spatial separation (or agency independence) coexist with (at least one of the) parties' ability to perform compatible measurements at each round of the experiment. When this party has an $n$-cycle compatiblity setup, it was first claimed that Bell nonlocality could not be concomitantly observed with contextuality at this party's local experiment. However, by a more natural reading of the definition of locality, it turns out that both Bell nonlocality and local contextuality can, in fact, be jointly present. In spite of it, in this work we prove that there cannot be arbitrary amounts of both of these two resources together. That is, we show the existence of a trade-off relation between Bell nonlocality and local contextuality in such scenarios. We explore this trade-off both in terms of inequalities and quantifiers, and we discuss how it can be understood in terms of a `global' notion of contextuality. Furthermore, we show that such notion does not only encompass local contextuality and Bell nonlocality, but also other forms of nonclassical correlations.

In this work we study the effects of the proton and $Pb$ internal structure on charmonium production at high multiplicities. To do this, we assume that the nucleon has an Y shape, which means that the effective quarks (quarks + antiquarks + gluons) are in the extremities of the Y, connected by gluon lines. Since the quarks are in the periphery and the gluons are in the center, as $pp$ collisions go from peripheral to more central and then to ultra-central collisions, the interactions change from quark-quark to gluon-gluon. The enhanced growth of $J/\psi$ occurs because $\sigma( g + g \to c + \bar{c}) \gg \sigma( q + \bar{q} \to c + \bar{c})$. In the $p-Pb$ collisions the enhancement is caused by the high concentration of partons in the center of the nuclei. These effects can explain the growth seen in the data and give support to the Y picture of the proton., Comment: 50 pages

A major consideration in multilingual language modeling is how to best represent languages with diverse vocabularies and scripts. Although contemporary text encoding methods cover most of the world's writing systems, they exhibit bias towards the high-resource languages of the Global West. As a result, texts of underrepresented languages tend to be segmented into long sequences of linguistically meaningless units. To address the disparities, we introduce a new paradigm that encodes the same information with segments of consistent size across diverse languages. Our encoding convention (MYTE) is based on morphemes, as their inventories are more balanced across languages than characters, which are used in previous methods. We show that MYTE produces shorter encodings for all 99 analyzed languages, with the most notable improvements for non-European languages and non-Latin scripts. This, in turn, improves multilingual LM performance and diminishes the perplexity gap throughout diverse languages., Comment: Published at ACL 2024

While many hallucination detection techniques have been evaluated on English text, their effectiveness in multilingual contexts remains unknown. This paper assesses how well various factual hallucination detection metrics (lexical metrics like ROUGE and Named Entity Overlap, and Natural Language Inference (NLI)-based metrics) identify hallucinations in generated biographical summaries across languages. We compare how well automatic metrics correlate to each other and whether they agree with human judgments of factuality. Our analysis reveals that while the lexical metrics are ineffective, NLI-based metrics perform well, correlating with human annotations in many settings and often outperforming supervised models. However, NLI metrics are still limited, as they do not detect single-fact hallucinations well and fail for lower-resource languages. Therefore, our findings highlight the gaps in exisiting hallucination detection methods for non-English languages and motivate future research to develop more robust multilingual detection methods for LLM hallucinations.

Unmanned Aerial Vehicles need an online path planning capability to move in high-risk missions in unknown and complex environments to complete them safely. However, many algorithms reported in the literature may not return reliable trajectories to solve online problems in these scenarios. The Q-Learning algorithm, a Reinforcement Learning Technique, can generate trajectories in real-time and has demonstrated fast and reliable results. This technique, however, has the disadvantage of defining the iteration number. If this value is not well defined, it will take a long time or not return an optimal trajectory. Therefore, we propose a method to dynamically choose the number of iterations to obtain the best performance of Q-Learning. The proposed method is compared to the Q-Learning algorithm with a fixed number of iterations, A*, Rapid-Exploring Random Tree, and Particle Swarm Optimization. As a result, the proposed Q-learning algorithm demonstrates the efficacy and reliability of online path planning with a dynamic number of iterations to carry out online missions in unknown and complex environments.

Despite their popularity in non-English NLP, multilingual language models often underperform monolingual ones due to inter-language competition for model parameters. We propose Cross-lingual Expert Language Models (X-ELM), which mitigate this competition by independently training language models on subsets of the multilingual corpus. This process specializes X-ELMs to different languages while remaining effective as a multilingual ensemble. Our experiments show that when given the same compute budget, X-ELM outperforms jointly trained multilingual models across all considered languages and that these gains transfer to downstream tasks. X-ELM provides additional benefits over performance improvements: new experts can be iteratively added, adapting X-ELM to new languages without catastrophic forgetting. Furthermore, training is asynchronous, reducing the hardware requirements for multilingual training and democratizing multilingual modeling., Comment: EMNLP 2024

Graph matching is a fundamental problem in pattern recognition, with many applications such as software analysis and computational biology. One well-known type of graph matching problem is graph isomorphism, which consists of deciding if two graphs are identical. Despite its usefulness, the properties that one may check using graph isomorphism are rather limited, since it only allows strict equality checks between two graphs. For example, it does not allow one to check complex structural properties such as if the target graph is an arbitrary length sequence followed by an arbitrary size loop. We propose a generalization of graph isomorphism that allows one to check such properties through a declarative specification. This specification is given in the form of a Regular Graph Pattern (ReGaP), a special type of graph, inspired by regular expressions, that may contain wildcard nodes that represent arbitrary structures such as variable-sized sequences or subgraphs. We propose a SAT-based algorithm for checking if a target graph matches a given ReGaP. We also propose a preprocessing technique for improving the performance of the algorithm and evaluate it through an extensive experimental evaluation on benchmarks from the CodeSearchNet dataset., Comment: Shorter version accepted for publication at AAAI 2024

We introduce Universal NER (UNER), an open, community-driven project to develop gold-standard NER benchmarks in many languages. The overarching goal of UNER is to provide high-quality, cross-lingually consistent annotations to facilitate and standardize multilingual NER research. UNER v1 contains 18 datasets annotated with named entities in a cross-lingual consistent schema across 12 diverse languages. In this paper, we detail the dataset creation and composition of UNER; we also provide initial modeling baselines on both in-language and cross-lingual learning settings. We release the data, code, and fitted models to the public., Comment: NAACL 2024 Camera-ready