Graphs are a representation of structured data that captures the relationships between sets of objects. With the ubiquity of available network data, there is increasing industrial and academic need to quickly analyze graphs with billions of nodes and trillions of edges. A common first step for network understanding is Graph Embedding, the process of creating a continuous representation of nodes in a graph. A continuous representation is often more amenable, especially at scale, for solving downstream machine learning tasks such as classification, link prediction, and clustering. A high-performance graph embedding architecture leveraging Tensor Processing Units (TPUs) with configurable amounts of high-bandwidth memory is presented that simplifies the graph embedding problem and can scale to graphs with billions of nodes and trillions of edges. We verify the embedding space quality on real and synthetic large-scale datasets.

Despite advances in the field of Graph Neural Networks (GNNs), only a small number (~5) of datasets are currently used to evaluate new models. This continued reliance on a handful of datasets provides minimal insight into the performance differences between models, and is especially challenging for industrial practitioners who are likely to have datasets which are very different from academic benchmarks. In the course of our work on GNN infrastructure and open-source software at Google, we have sought to develop benchmarks that are robust, tunable, scalable, and generalizable.

Current autonomous bidding strategies for complex auctions typically employ a two phased architecture: first, the agent predicts a distribution over good prices, and then the agent generates bids given those predictions, usually using a heuristic. For computational reasons, previous state-of-the-art methods assumed prices were independent across goods, and then bid based on marginal price distributions. However, prices for goods are typically dependent, especially for complements and substitutes. We examine and bound the potential error from bidding with respect to marginal price distributions when good prices are in fact correlated. Then, to mitigate this error, we develop computationally feasible methods for predicting joint price distributions, and employing such predictions in bidding strategies. We also demonstrate experimentally that the state-of-the-art heuristic for bidding in simultaneous second-price sealed-bid auctions is outdone by the analog of this same heuristic bidding with respect to joint instead of marginal price predictions.