2019/05/03 by Jean‐Marc Andreoli, Jean-Marc Andreoli, Andreoli, Jean-Marc · 1 voice · 19 citations
Computer Science · Mathematics · #A priori and a posteriori #Advanced Graph Neural Networks #Algorithm #Artificial intelligence #Artificial neural network #Computer science #Convolution (computer science) #Embedding #FOS: Computer and information sciences #Linear model #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine learning #Mathematics #Matrix multiplication #Neural Networks and Applications #Perceptron #Simple (philosophy) #Stochastic Gradient Optimization Techniques #Theoretical computer science #Topology (electrical circuits) #cs.LG #stat.ML
paper · pdf · doi:10.48550/arxiv.1905.01289
published in arXiv (Cornell University) (Cornell University) · Published in NeurIPS 2019 workshop on Graph Representation Learning, Dec 13, 2019, Vancouver, BC, Canada
openalex publication_date 2019/05/03 · arxiv published 2019/05/03 · arxiv created 2020/03/05 · arxiv updated 2020/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Deep neural networks are composed of layers of parametrised linear operations intertwined with non linear activations. In basic models, such as the multi-layer perceptron, a linear layer operates on a simple input vector embedding of the instance being processed, and produces an output vector embedding by straight multiplication by a matrix parameter. In more complex models, the input and output are structured and their embeddings are higher order tensors. The parameter of each linear operation must then be controlled so as not to explode with the complexity of the structures involved. This is essentially the role of convolution models, which exist in many flavours dependent on the type of structure they deal with (grids, networks, time series etc.). We present here a unified framework which aims at capturing the essence of these diverse models, allowing a systematic analysis of their properties and their mutual enrichment. We also show that attention models naturally fit in the same framework: attention is convolution in which the structure itself is adaptive, and learnt, instead of being given a priori.