Cambridge University（剑桥大学）；University of Florence（佛罗伦萨大学）；Politecnico di Torino（都灵理工大学）；University of Picardie Jules Verne（皮卡第儒勒-凡尔纳大学）；University of South Pacific（南太平洋大学）
Pietro Barbiero, Gabriele Ciravegna, Vincenzo Randazzo, Giansalvo Cirrincione
Topological learning is a wide research area aiming at uncovering the mutual spatial relationships between the elements of a set. Some of the most common and oldest approaches involve the use of unsupervised competitive neural networks. However, these methods are not based on gradient optimization which has been proven to provide striking results in feature extraction also in unsupervised learning. Unfortunately, by focusing mostly on algorithmic efficiency and accuracy, deep clustering techniques are composed of overly complex feature extractors, while using trivial algorithms in their top layer. The aim of this work is to present a novel comprehensive theory aspiring at bridging competitive learning with gradient-based learning, thus allowing the use of extremely powerful deep neural networks for feature extraction and projection combined with the remarkable flexibility and expressiveness of competitive learning. In this paper we fully demonstrate the theoretical equivalence of two novel gradient-based competitive layers. Preliminary experiments show how the dual approach, trained on the transpose of the input matrix i.e. $X^T$, lead to faster convergence rate and higher training accuracy both in low and high-dimensional scenarios.
University of Picardie Jules Verne（皮卡第儒勒-凡尔纳大学）；University of South Pacific（南太平洋大学）；Cambridge University（剑桥大学）；University of Florence（佛罗伦萨大学）；Politecnico di Torino（都灵理工大学）
Online Convex Optimization with Switching Cost with Only One Single Gradient Evaluation
Indian Institute of Technology Bombay (IITB)（印度理工学院班加罗尔分校）；Indian Institute of Technology Delhi (IITD)（印度理工学院德里分校）；Tata Institute of Fundamental Research (TIFR)（塔塔基础研究机构）
Gradient-free variational learning with conditional mixture networks
VERSES AI Research Lab（VERSES AI研究实验室）；Max Planck Institute of Animal Behavior（马克斯·普朗克动物行为研究所）；Technische Universität Dresden（德累斯顿工业大学）；University of Sussex（萨塞克斯大学）；Duke University（杜克大学）
