Fast Graph Learning with Unique Optimal Solutions

Graph Representation Learning (GRL) has been advancing at an unprecedented rate. However, many results rely on careful design and tuning of architectures, objectives, and training schemes. We propose efficient GRL methods that optimize convexified objectives with known closed form solutions. Guaranteed convergence to a global optimum releases practitioners from hyper-parameter and architecture tuning. Nevertheless, our proposed method achieves competitive or state-of-the-art performance on popular GRL tasks while providing orders of magnitude speedup. Although the design matrix ($\mathbf{M}$) of our objective is expensive to compute, we exploit results from random matrix theory to approximate solutions in linear time while avoiding an explicit calculation of $\mathbf{M}$. Our code is online: http://github.com/samihaija/tf-fsvd