SearcharxivSearch

arXiv subjects

Javier Morales

Publications and source records attributed to Javier Morales.

15 recordsLinked to original sources

Improving Content Recommendation: Knowledge Graph-Based Semantic Contrastive Learning for Diversity and Cold-Start Users

Addressing the challenges related to data sparsity, cold-start problems, and diversity in recommendation systems is both crucial and demanding. Many current solutions leverage knowledge graphs to tackle these issues by combining both item-based and user-item collaborative signals. A common trend in these approaches focuses on improving ranking performance at the cost of escalating model complexity, reducing diversity, and complicating the task. It is essential to provide recommendations that are both personalized and diverse, rather than solely relying on achieving high rank-based performance, such as Click-through Rate, Recall, etc. In this paper, we propose a hybrid multi-task learning approach, training on user-item and item-item interactions. We apply item-based contrastive learning on descriptive text, sampling positive and negative pairs based on item metadata. Our approach allows the model to better understand the relationships between entities within the knowledge graph by utilizing semantic information from text. It leads to more accurate, relevant, and diverse user recommendations and a benefit that extends even to cold-start users who have few interactions with items. We perform extensive experiments on two widely used datasets to validate the effectiveness of our approach. Our findings demonstrate that jointly training user-item interactions and item-based signals using synopsis text is highly effective. Furthermore, our results provide evidence that item-based contrastive learning enhances the quality of entity embeddings, as indicated by metrics such as uniformity and alignment.

cs.IR

Leveraging Unlabeled Data for Sketch-based Understanding

Sketch-based understanding is a critical component of human cognitive learning and is a primitive communication means between humans. This topic has recently attracted the interest of the computer vision community as sketching represents a powerful tool to express static objects and dynamic scenes. Unfortunately, despite its broad application domains, the current sketch-based models strongly rely on labels for supervised training, ignoring knowledge from unlabeled data, thus limiting the underlying generalization and the applicability. Therefore, we present a study about the use of unlabeled data to improve a sketch-based model. To this end, we evaluate variations of VAE and semi-supervised VAE, and present an extension of BYOL to deal with sketches. Our results show the superiority of sketch-BYOL, which outperforms other self-supervised approaches increasing the retrieval performance for known and unknown categories. Furthermore, we show how other tasks can benefit from our proposal.

cs.CV

Semi-discrete optimization through semi-discrete optimal transport: a framework for neural architecture search

In this paper we introduce a theoretical framework for semi-discrete optimization using ideas from optimal transport. Our primary motivation is in the field of deep learning, and specifically in the task of neural architecture search. With this aim in mind, we discuss the geometric and theoretical motivation for new techniques for neural architecture search (in a companion paper we show that algorithms inspired by our framework are competitive with contemporaneous methods). We introduce a Riemannian-like metric on the space of probability measures over a semi-discrete space $\mathbb{R}^d \times \mathcal{G}$ where $\mathcal{G}$ is a finite weighted graph. With such Riemmanian structure in hand, we derive formal expressions for the gradient flow of a relative entropy functional, as well as second order dynamics for the optimization of said energy. Then, with the aim of providing a rigorous motivation for the gradient flow equations derived formally, we also consider an iterative procedure known as minimizing movement scheme (i.e., Implicit Euler scheme, or JKO scheme) and apply it to the relative entropy with respect to a suitable cost function. For some specific choices of metric and cost, we rigorously show that the minimizing movement scheme of the relative entropy functional converges to the gradient flow process provided by the formal Riemannian structure. This flow coincides with a system of reaction-diffusion equations on $\mathbb{R}^d$.

math.AP

Traditional and accelerated gradient descent for neural architecture search

In this paper we introduce two algorithms for neural architecture search (NASGD and NASAGD) following the theoretical work by two of the authors [5] which used the geometric structure of optimal transport to introduce the conceptual basis for new notions of traditional and accelerated gradient descent algorithms for the optimization of a function on a semi-discrete space. Our algorithms, which use the network morphism framework introduced in [2] as a baseline, can analyze forty times as many architectures as the hill climbing methods [2, 14] while using the same computational resources and time and achieving comparable levels of accuracy. For example, using NASGD on CIFAR-10, our method designs and trains networks with an error rate of 4.06 in only 12 hours on a single GPU.

cs.LG

On the trend to global equilibrium for Kuramoto Oscillators

In this paper, we study the convergence to the stable equilibrium for Kuramoto oscillators. Specifically, we derive estimates on the rate of convergence to the global equilibrium for solutions of the Kuramoto-Sakaguchi equation in a large coupling strength regime from generic initial data. As a by-product, using the stability of the equation in the Wasserstein distance, we quantify the rate at which discrete Kuramoto oscillators concentrate around the global equilibrium. In doing this, we achieve a quantitative estimate in which the probability that the oscillators will concentrate at the given rate tends to one as the number of oscillators increases. Among the essential steps in our proof are: 1) An entropy production estimate inspired by the formal Riemannian structure of the space of probability measures, first introduced by F. Otto in [35]; 2) A new quantitative estimate on the instability of equilibria with antipodal oscillators based on the dynamics of norms of the solution in sets evolving by the continuity equation; 3) The use of generalized local logarithmic Sobolev and Talagrand type inequalities, similar to the ones derived by F. Otto and C. Villani in [36]; 4) The study of a system of coupled differential inequalities, by a treatment inspired by the work of L. Desvillettes and C. Villani [13]. Since the Kuramoto-Sakaguchi equation is not a gradient flow with respect to the Wasserstein distance, we derive such inequalities under a suitable fibered transportation distance.

math.AP

Flocking with short-range interactions

We study the large-time behavior of continuum alignment dynamics based on Cucker-Smale (CS)-type interactions which involve short-range kernels, that is, communication kernels with support much smaller than the diameter of the crowd. We show that if the amplitude of the interactions is larger than a finite threshold, then unconditional hydrodynamic flocking follows. Since we do not impose any regularity nor do we require the kernels to be bounded, the result covers both regular and singular interaction kernels. Moreover, we treat initial densities in the general class of compactly supported measures which are required to have positive mass on average (over balls at small enough scale), but otherwise vacuum is allowed at smaller scales. Consequently, our arguments of hydrodynamic flocking apply, mutatis mutandis, to the agent-based CS model with finitely many Dirac masses. In particular, discrete flocking threshold is shown to depend on the number of dense clusters of communication but otherwise does not grow with the number of agents.

math.AP

Synthesising Evolutionarily Stable Normative Systems

Within the area of multi-agent systems, normative systems are a widely used framework for the coordination of interdependent activities. A crucial problem associated with normative systems is that of synthesising norms that effectively accomplish a coordination task and whose compliance forms a rational choice for the agents within the system. In this work, we introduce a framework for the synthesis of normative systems that effectively coordinate a multi-agent system and whose norms are likely to be adopted by rational agents. Our approach roots in evolutionary game theory. Our framework considers multi-agent systems in which evolutionary forces lead successful norms to prosper and spread within the agent population, while unsuccessful norms are discarded. The outputs of this evolutionary norm synthesis process are normative systems whose compliance forms a rational choice for the agents. We empirically show the effectiveness of our approach through empirical evaluation in a simulated traffic domain.

cs.MA

Emergent dynamics of the Kuramoto ensemble under the effect of inertia

We study the emergent collective behaviors for an ensemble of identical Kuramoto oscillators under the effect of inertia. In the absence of inertial effects, it is well known that the generic initial Kuramoto ensemble relaxes to the phase-locked states asymptotically (emergence of complete synchronization) in a large coupling regime. Similarly, even for the presence of inertial effects, similar collective behaviors are observed numerically for generic initial configurations in a large coupling strength regime. However, this phenomenon has not been verified analytically in full generality yet, although there are several partial results in some restricted set of initial configurations. In this paper, we present several improved complete synchronization estimates for the Kuramoto ensemble with inertia in two frameworks for a finite system. Our improved frameworks describe the emergence of phase-locked states and its structure. Additionally, we show that as the number of oscillators tends to infinity, the Kuramoto ensemble with infinite size can be approximated by the corresponding kinetic mean-field model uniformly in time. Moreover, we also establish the global existence of measure-valued solutions for the Kuramoto equation and its large-time asymptotics.

math.DS

Automating decision making to help establish norm-based regulations

Norms have been extensively proposed as coordination mechanisms for both agent and human societies. Nevertheless, choosing the norms to regulate a society is by no means straightforward. The reasons are twofold. First, the norms to choose from may not be independent (i.e, they can be related to each other). Second, different preference criteria may be applied when choosing the norms to enact. This paper advances the state of the art by modeling a series of decision-making problems that regulation authorities confront when choosing the policies to establish. In order to do so, we first identify three different norm relationships -namely, generalisation, exclusivity, and substitutability- and we then consider norm representation power, cost, and associated moral values as alternative preference criteria. Thereafter, we show that the decision-making problems faced by policy makers can be encoded as linear programs, and hence solved with the aid of state-of-the-art solvers.

cs.MA

Emergence of phase concentration for the Kuramoto-Sakaguchi equation

We study the asymptotic phase concentration phenomena for the Kuramoto-Sakaguchi(K-S) equation in a large coupling strength regime. For this, we analyze the detailed dynamics of the order parameters such as the amplitude and the average phase. For the infinite ensemble of oscillators with the identical natural frequency, we show that the total mass distribution concentrates on the average phase asymptotically, whereas the mass around the antipodal point of the average phase decays to zero exponentially fast in any positive coupling strength regime. Thus, generic initial kinetic densities evolve toward the Dirac measure concentrated on the average phase. In contrast, for the infinite ensemble with distributed natural frequencies, we find a certain time-dependent interval whose length can be explicitly quantified in terms of the coupling strength. Provided that the coupling strength is sufficiently large, the mass on such an interval is eventually non-decreasing over the time. We also show that the amplitude order parameter has a positive lower bound that depends on the size of support of the distribution function for the natural frequencies and the coupling strength. The proposed asymptotic lower bound on the order parameter tends to unity, as the coupling strength increases to infinity. This is reminiscent of practical synchronization for the Kuramoto model, in which the diameter for the phase configuration is inversely proportional to the coupling strength. Our results for the K-S equation generalize the results in [19] on the emergence of phase-locked states for the Kuramoto model in a large coupling strength regime.

math.AP

Dynamics of a spatially homogeneous Vicsek model for oriented particles on the plane

We consider a spatially homogeneous Kolmogorov-Vicsek model in two dimensions, which describes the alignment dynamics of self-driven stochastic particles that move on the plane at a constant speed, under space-homogeneity. In \cite{F-K-M}, Alessio Figalli and the authors have shown the existence of global weak solutions for this two-dimensional model. However, no time-asymptotic behavior has been obtained for the two-dimensional case, due to the failure of the celebrated Bakery and Emery condition for the logarithmic Sobolev inequality. We prove exponential convergence (with quantitative rate) of the weak solutions towards a Fisher-von Mises distribution, using a new condition for the logarithmic Sobolev inequality.

math.AP

A new family of transportation costs with applications to reaction-diffusion and parabolic equations with boundary conditions

This paper introduces a family of transportation costs between non-negative measures. This family is used to obtain parabolic and reaction-diffusion equations with drift, subject to Dirichlet boundary condition, as the gradient flow of the entropy functional $\int_Ωρ\logρ+Vρ+1\hspace{1mm}dx$. In 2010, Alessio Figalli and Nicola Gigli introduced a transportation cost that can be used to obtain parabolic equations with drift subject to Dirichlet boundary condition. However, the drift and the boundary condition are coupled in their work. The costs in this paper allow the drift and the boundary condition to be detached.

math.AP

Global well-posedness of the spatially homogeneous Kolmogorov-Vicsek model as a gradient flow

We consider the so-called spatially homogenous Kolmogorov-Vicsek model, a non-linear Fokker-Planck equation of self-driven stochastic particles with orientation interaction under the space-homogeneity. We prove the global existence and uniqueness of weak solutions to the equation. We also show that weak solutions exponentially converge to a steady state, which has the form of the Fisher-von Mises distribution.

math.AP

Trend and Fractality Assessment of Mexico's Stock Exchange

The total value of domestic market capitalization of the Mexican Stock Exchange was calculated at 520 billion of dollars by the end of November 2013. To manage this system and make optimum capital investments, its dynamics needs to be predicted. However, randomness within the stock indexes makes forecasting a difficult task. To address this issue, in this work, trends and fractality were studied using GNU-R over the opening and closing prices indexes over the past 23 years. Returns, Kernel density estimation, autocorrelation function and R/S analysis and the Hurst exponent were used in this research. As a result, it was found that the Kernel estimation density and the autocorrelation function shown the presence of long-range memory effects. In a first approximation, the returns of closing prices seems to behave according to a Markovian random walk with a length of step size given by an alpha-stable random process. For extreme values, returns decay asymptotically as a power law with a characteristic exponent approximately equal to 2.5.

q-fin.ST

Growth of Diamond Films from Tequila

Diamond thin films were growth using Tequila as precursor by Pulsed Liquid Injection Chemical Vapor Deposition (PLI-CVD) onto both silicon (100) and stainless steel 304 at 850 C. The diamond films were characterized by Scanning Electron Microscopy (SEM) and Raman spectroscopy. The spherical crystallites (100 to 400 nm) show the characteristic 1332 cm-1 Raman band of diamond.

cond-mat.mtrl-sci