Pseudo-Euclidean Attract-Repel Embeddings for Undirected Graphs, Léon Bottou. Joint work with Alex Peysakhovich
ABSTRACT: Dot product embeddings take a graph and construct vectors for nodes such that dot products between two vectors give the strength of the edge. Dot products make a strong transitivity assumption, however, many important forces generating graphs in the real world are specifically non-transitive. We remove the transitivity assumption by embedding nodes into a pseudo-Euclidean space - giving each node an attract and a repel vector. The inner product between two nodes is defined by taking the dot product in attract vectors and subtracting the dot product in repel vectors. Pseudo-Euclidean embeddings can compress networks efficiently, allow for multiple notions of nearest neighbors each with their own interpretation, and can be `slotted' into existing models such as exponential family embeddings or graph neural networks for better link prediction.
BIO: Léon Bottou received the Diplôme d’Ingénieur de l’École Polytechnique (X84) in 1987, the Magistère de Mathématiques Fondamentales et Appliquées et d’Informatique from École Normale Supérieure in 1988, and a Ph.D. in Computer Science from Université de Paris-Sud in 1991. His research career took him to AT&T Bell Laboratories, AT&T Labs Research, NEC Labs America and Microsoft. He joined Facebook AI Research in 2015. The long-term goal of Léon Bottou’s research is to understand and replicate intelligence. Because this goal requires conceptual advances that cannot be anticipated, Leon’s research has followed many practical and theoretical turns: neural networks applications in the late 1980s, stochastic gradient learning algorithms and statistical properties of learning systems in the early 1990s, computer vision applications with structured outputs in the late 1990s, theory of large scale learning in the 2000s. During the last few years, Léon Bottou’s research aims to clarify the relation between learning and reasoning, with more and more focus on the many aspects of causation (inference, invariance, reasoning, affordance, and intuition.)