It has become a de-facto standard to represent words as elements of a vector space (word2vec, GloVe).While this approach is convenient, it is unnatural for language: words form a graph with a latent hierarchical structure, and this structure has to be revealed and encoded by word embeddings.We introduce Graph-Glove: unsupervised graph word representations which are learned end-to-end.In our setting, each word is a node in a weighted graph and the distance between words is the shortest path distance between the corresponding nodes.We adopt a recent method learning a representation of data in the form of a differentiable weighted graph and use it to modify the GloVe training algorithm.We show that our graph-based representations substantially outperform vector-based methods on word similarity and analogy tasks.Our analysis reveals that the structure of the learned graphs is hierarchical and similar to that of WordNet, the geometry is highly non-trivial and contains subgraphs with different local topology.1

Nonlinearity is one of the key issues that hinder the development of high-capacity optical short reach systems. This paper proposes three variants of kernel affine projection (KAP) algorithms, all of which combine kernel mapping and affine projection in a reproducing kernel Hilbert space for compensating nonlinear impairments in optical short reach systems. An intensity modulation/direct detection system with a single digital-to-analogue converter, a packaged externally modulated laser and a packaged InP photo-detector is used for experimental demonstration, achieving 238-Gbps (net rate 222-Gbps). Experimental results show that the KAP algorithms can mitigate nonlinear impairments in short-reach communications while maintaining low complexity in reproducing kernel Hilbert space.