Javier Morales

Javier Morales, Nils Murrugarra-Llerena, Jose M. Saavedra

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.

Nicolas Garcia Trillos, Javier Morales

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 $\mathbb{R}^d$.

Nicolas Garcia Trillos, Felix Morales, Javier Morales

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.