The code is available on GitHub.

Graph Neural Networks (GNNs) have shown impressive performance in graph representation learning, but they face challenges in capturing long-range dependencies due to their limited expressive power. To address this, Graph Transformers (GTs) were introduced, utilizing self-attention mechanism to effectively model pairwise node relationships. Despite their advantages, GTs suffer from quadratic complexity w.r.t. the number of nodes in the graph, hindering their applicability to large graphs. In this work, we present Graph-Enhanced Contextual Operator (GECO), a scalable and effective alternative to GTs that leverages neighborhood propagation and global convolutions to effectively capture local and global dependencies in quasilinear time. Our study on synthetic datasets reveals that GECO reaches 169x speedup on a graph with 2M nodes w.r.t. optimized attention. Further evaluations on diverse range of benchmarks showcase that GECO scales to large graphs where traditional GTs often face memory and time limitations. Notably, GECO consistently achieves comparable or superior quality compared to baselines, improving the SOTA up to 4.5%, and offering a scalable and effective solution for large-scale graph learning.

In spite of remarkable progress in deep latent variable generative modeling, training still remains a challenge due to a combination of optimization and generalization issues. In practice, a combination of heuristic algorithms (such as hand-crafted annealing of KL-terms) is often used in order to achieve the desired results, but such solutions are not robust to changes in model architecture or dataset. The best settings can often vary dramatically from one problem to another, which requires doing expensive parameter sweeps for each new case. Here we develop on the idea of training VAEs with additional constraints as a way to control their behaviour. We first present a detailed theoretical analysis of constrained VAEs, expanding our understanding of how these models work. We then introduce and analyze a practical algorithm termed Generalized ELBO with Constrained Optimization, GECO. The main advantage of GECO for the machine learning practitioner is a more intuitive, yet principled, process of tuning the loss. This involves defining of a set of constraints, which typically have an explicit relation to the desired model performance, in contrast to tweaking abstract hyper-parameters which implicitly affect the model behavior. Encouraging experimental results in several standard datasets indicate that GECO is a very robust and effective tool to balance reconstruction and compression constraints.

We address the problem of minimizing a convex function over the space of large matrices with low rank. While this optimization problem is hard in general, we propose an efficient greedy algorithm and derive its formal approximation guarantees. Each iteration of the algorithm involves (approximately) finding the left and right singular vectors corresponding to the largest singular value of a certain matrix, which can be calculated in linear time. This leads to an algorithm which can scale to large matrices arising in several applications such as matrix completion for collaborative filtering and robust low rank matrix approximation.