The global trends of urbanization and increased personal mobility force us to rethink the way we live and use urban space. The Traffic4cast competition series tackles this problem in a data-driven way, advancing the latest methods in machine learning for modeling complex spatial systems over time. In this edition, our dynamic road graph data combine information from road maps, $10^{12}$ probe data points, and stationary vehicle detectors in three cities over the span of two years. While stationary vehicle detectors are the most accurate way to capture traffic volume, they are only available in few locations. Traffic4cast 2022 explores models that have the ability to generalize loosely related temporal vertex data on just a few nodes to predict dynamic future traffic states on the edges of the entire road graph. In the core challenge, participants are invited to predict the likelihoods of three congestion classes derived from the speed levels in the GPS data for the entire road graph in three cities 15 min into the future. We only provide vehicle count data from spatially sparse stationary vehicle detectors in these three cities as model input for this task. The data are aggregated in 15 min time bins for one hour prior to the prediction time. For the extended challenge, participants are tasked to predict the average travel times on super-segments 15 min into the future - super-segments are longer sequences of road segments in the graph. The competition results provide an important advance in the prediction of complex city-wide traffic states just from publicly available sparse vehicle data and without the need for large amounts of real-time floating vehicle data.

We show that the transformer attention mechanism is the update rule of a modern Hopfield network with continuous states. This new Hopfield network can store exponentially (with the dimension) many patterns, converges with one update, and has exponentially small retrieval errors. The number of stored patterns is traded off against convergence speed and retrieval error. The new Hopfield network has three types of energy minima (fixed points of the update): (1) global fixed point averaging over all patterns, (2) metastable states averaging over a subset of patterns, and (3) fixed points which store a single pattern. Transformer and BERT models operate in their first layers preferably in the global averaging regime, while they operate in higher layers in metastable states. The gradient in transformers is maximal for metastable states, is uniformly distributed for global averaging, and vanishes for a fixed point near a stored pattern. Using the Hopfield network interpretation, we analyzed learning of transformer and BERT models. Learning starts with attention heads that average and then most of them switch to metastable states. However, the majority of heads in the first layers still averages and can be replaced by averaging, e.g. our proposed Gaussian weighting. In contrast, heads in the last layers steadily learn and seem to use metastable states to collect information created in lower layers. These heads seem to be a promising target for improving transformers. Neural networks with Hopfield networks outperform other methods on immune repertoire classification, where the Hopfield net stores several hundreds of thousands of patterns. We provide a new PyTorch layer called "Hopfield", which allows to equip deep learning architectures with modern Hopfield networks as a new powerful concept comprising pooling, memory, and attention. GitHub: https://github.com/ml-jku/hopfield-layers