6 papers
Restricted Strong Convexity of Deep Learning Models with Smooth Activations
Arindam Banerjee, Pedro Cisneros-Velarde, Libin Zhu +1
We consider the problem of optimization of deep learning models with smooth activation functions. While there exist influential results on the problem from the ``near initializatio…
Weak and Semi-Contraction for Network Systems and Diffusively-Coupled Oscillators
Saber Jafarpour, Pedro Cisneros-Velarde, Francesco Bullo
We develop two generalizations of contraction theory, namely, semi-contraction and weak-contraction theory. First, using the notion of semi-norm, we propose a geometric framework f…
Structural Balance via Gradient Flows over Signed Graphs
Pedro Cisneros-Velarde, Noah E. Friedkin, Anton V. Proskurnikov +1
Structural balance is a classic property of signed graphs satisfying Heider's seminal axioms. Mathematical sociologists have studied balance theory since its inception in the 1040s…
Distributionally Robust Formulation and Model Selection for the Graphical Lasso
Pedro Cisneros-Velarde, Sang-Yun Oh, Alexander Petersen
Building on a recent framework for distributionally robust optimization, we consider estimation of the inverse covariance matrix for multivariate data. We provide a novel notion of…
Signed Network Formation Games and Clustering Balance
Pedro Cisneros-Velarde, Francesco Bullo
We propose a signed network formation game, in which pairs of individuals strategically change the signs of the edges in a complete network. These individuals are members of a soci…
Polarization and Fluctuations in Signed Social Networks
Pedro Cisneros-Velarde, Kevin S. Chan, Francesco Bullo
Much recent research on social networks has focused on the modeling and analysis of how opinions evolve as a function of interpersonal relationships. It is also of great interest t…