The main idea of spectral approaches such as Graph neural networks is to generalize the Fourier transform theorem for graph and manifold data and doing the convolution on the spectral domain. The generalization of the Fourier transform consists on using the already defined eigenfunctions of graph laplacian as bases for the Fourier transform. The process to apply a convolution using this generalization is as follows. This approach has presented very good results on data presented as a graph, but has an important weakness: Laplacian eigenfunctions are inconsistent across different domains.

Optimizing the execution time of tensor program, e.g., a convolution, involves finding its optimal configuration. Searching the configuration space exhaustively is typically infeasible in practice. In line with recent research using TVM, we propose to learn a surrogate model to overcome this issue. The model is trained on an acyclic graph called an abstract syntax tree, and utilizes a graph convolutional network to exploit structure in the graph. We claim that a learnable graph-based data processing is a strong competitor to heuristic-based feature extraction. We present a new dataset of graphs corresponding to configurations and their execution time for various tensor programs. We provide baselines for a runtime prediction task.

Continuous vector representations of words and objects appear to carry surprisingly rich semantic content. In this paper, we advance both the conceptual and theoretical understanding of word embeddings in three ways. First, we ground embeddings in semantic spaces studied in cognitive-psychometric literature and introduce new evaluation tasks. Second, in contrast to prior work, we take metric recovery as the key object of study, unify existing algorithms as consistent metric recovery methods based on co-occurrence counts from simple Markov random walks, and propose a new recovery algorithm. Third, we generalize metric recovery to graphs and manifolds, relating co-occurence counts on random walks in graphs and random processes on manifolds to the underlying metric to be recovered, thereby reconciling manifold estimation and embedding algorithms. We compare embedding algorithms across a range of tasks, from nonlinear dimensionality reduction to three semantic language tasks, including analogies, sequence completion, and classification.