Héctor Allende

Juan Pavez, Héctor Allende, Héctor Allende-Cid

During the last years, there has been a lot of interest in achieving some kind of complex reasoning using deep neural networks. To do that, models like Memory Networks (MemNNs) have combined external memory storages and attention mechanisms. These architectures, however, lack of more complex reasoning mechanisms that could allow, for instance, relational reasoning. Relation Networks (RNs), on the other hand, have shown outstanding results in relational reasoning tasks. Unfortunately, their computational cost grows quadratically with the number of memories, something prohibitive for larger problems. To solve these issues, we introduce the Working Memory Network, a MemNN architecture with a novel working memory storage and reasoning module. Our model retains the relational reasoning abilities of the RN while reducing its computational complexity from quadratic to linear. We tested our model on the text QA dataset bAbI and the visual QA dataset NLVR. In the jointly trained bAbI-10k, we set a new state-of-the-art, achieving a mean error of less than 0.5%. Moreover, a simple ensemble of two of our models solves all 20 tasks in the joint version of the benchmark.

Hector Allende, Emanuele Frandi, Ricardo Nanculef et al.

Recently, there has been a renewed interest in the machine learning community for variants of a sparse greedy approximation procedure for concave optimization known as {the Frank-Wolfe (FW) method}. In particular, this procedure has been successfully applied to train large-scale instances of non-linear Support Vector Machines (SVMs). Specializing FW to SVM training has allowed to obtain efficient algorithms but also important theoretical results, including convergence analysis of training algorithms and new characterizations of model sparsity. In this paper, we present and analyze a novel variant of the FW method based on a new way to perform away steps, a classic strategy used to accelerate the convergence of the basic FW procedure. Our formulation and analysis is focused on a general concave maximization problem on the simplex. However, the specialization of our algorithm to quadratic forms is strongly related to some classic methods in computational geometry, namely the Gilbert and MDM algorithms. On the theoretical side, we demonstrate that the method matches the guarantees in terms of convergence rate and number of iterations obtained by using classic away steps. In particular, the method enjoys a linear rate of convergence, a result that has been recently proved for MDM on quadratic forms. On the practical side, we provide experiments on several classification datasets, and evaluate the results using statistical tests. Experiments show that our method is faster than the FW method with classic away steps, and works well even in the cases in which classic away steps slow down the algorithm. Furthermore, these improvements are obtained without sacrificing the predictive accuracy of the obtained SVM model.