Despite incredible progress, many neural architectures fail to properly generalize beyond their training distribution. As such, learning to reason in a correct and generalizable way is one of the current fundamental challenges in machine learning. In this respect, logic puzzles provide a great testbed, as we can fully understand and control the learning environment. Thus, they allow to evaluate performance on previously unseen, larger and more difficult puzzles that follow the same underlying rules. Since traditional approaches often struggle to represent such scalable logical structures, we propose to model these puzzles using a graph-based approach. Then, we investigate the key factors enabling the proposed models to learn generalizable solutions in a reinforcement learning setting. Our study focuses on the impact of the inductive bias of the architecture, different reward systems and the role of recurrent modeling in enabling sequential reasoning. Through extensive experiments, we demonstrate how these elements contribute to successful extrapolation on increasingly complex puzzles.These insights and frameworks offer a systematic way to design learning-based systems capable of generalizable reasoning beyond interpolation.

Graph Visualization, also known as Graph Drawing, aims to find geometric embeddings of graphs that optimize certain criteria. Stress is a widely used metric; stress is minimized when every pair of nodes is positioned at their shortest path distance. However, stress optimization presents computational challenges due to its inherent complexity and is usually solved using heuristics in practice. We introduce a scalable Graph Neural Network (GNN) based Graph Drawing framework with sub-quadratic runtime that can learn to optimize stress. Inspired by classical stress optimization techniques and force-directed layout algorithms, we create a coarsening hierarchy for the input graph. Beginning at the coarsest level, we iteratively refine and un-coarsen the layout, until we generate an embedding for the original graph. To enhance information propagation within the network, we propose a novel positional rewiring technique based on intermediate node positions. Our empirical evaluation demonstrates that the framework achieves state-of-the-art performance while remaining scalable.

We introduce an extension to the CLRS algorithmic learning benchmark, prioritizing scalability and the utilization of sparse representations. Many algorithms in CLRS require global memory or information exchange, mirrored in its execution model, which constructs fully connected (not sparse) graphs based on the underlying problem. Despite CLRS's aim of assessing how effectively learned algorithms can generalize to larger instances, the existing execution model becomes a significant constraint due to its demanding memory requirements and runtime (hard to scale). However, many important algorithms do not demand a fully connected graph; these algorithms, primarily distributed in nature, align closely with the message-passing paradigm employed by Graph Neural Networks. Hence, we propose SALSA-CLRS, an extension of the current CLRS benchmark specifically with scalability and sparseness in mind. Our approach includes adapted algorithms from the original CLRS benchmark and introduces new problems from distributed and randomized algorithms. Moreover, we perform a thorough empirical evaluation of our benchmark.

Simulating fluid dynamics is crucial for the design and development process, ranging from simple valves to complex turbomachinery. Accurately solving the underlying physical equations is computationally expensive. Therefore, learning-based solvers that model interactions on meshes have gained interest due to their promising speed-ups. However, it is unknown to what extent these models truly understand the underlying physical principles and can generalize rather than interpolate. Generalization is a key requirement for a general-purpose fluid simulator, which should adapt to different topologies, resolutions, or thermodynamic ranges. We propose SURF, a benchmark designed to test the $\textit{generalization}$ of learned graph-based fluid simulators. SURF comprises individual datasets and provides specific performance and generalization metrics for evaluating and comparing different models. We empirically demonstrate the applicability of SURF by thoroughly investigating the two state-of-the-art graph-based models, yielding new insights into their generalization.

Graph Neural Networks are a natural fit for learning algorithms. They can directly represent tasks through an abstract but versatile graph structure and handle inputs of different sizes. This opens up the possibility for scaling and extrapolation to larger graphs, one of the most important advantages of an algorithm. However, this raises two core questions i) How can we enable nodes to gather the required information in a given graph (information exchange), even if is far away and ii) How can we design an execution framework which enables this information exchange for extrapolation to larger graph sizes (algorithmic alignment for extrapolation). Through its sparse but parallel activations it is provably more efficient in terms of message complexity. We study the proposed model and provide both empirical evidence and theoretical insights in terms of its expressiveness, efficiency, information exchange and ability to extrapolate. We study the problem of algorithm learning using Graph Neural Networks. The concept of an algorithm is best understood as a sequence of instructions which can be applied to compute a desired output given the respective input. Algorithms have the advantage, that they work correctly for their entire domain. If we want to multiply two numbers, we can easily illustrate and explain the multiplication algorithm using small numbers. However, the same procedure generalizes, i.e. the algorithm can be used to extrapolate and multiply together much larger numbers using the same algorithmic steps. Algorithm learning aims to grasp these underlying algorithmic principles and incorporate them into machine learning architectures. Therefore, the ability to process different input sizes and extrapolate are at the core of our study. Graphs and as an extension GNNs naturally present themselves to study algorithms as many algorithmic problems can be represented as graphs. Moreover, they can inherently capture instances of different sizes, which allows us to study extrapolation. GNNs follow the message passing paradigm, which closely corresponds to computation models studied in distributed computing.

While artificial intelligence (AI) models have achieved human or even superhuman performance in many well-defined applications, they still struggle to show signs of broad and flexible intelligence. The Abstraction and Reasoning Corpus (ARC), a visual intelligence benchmark introduced by Fran\c{c}ois Chollet, aims to assess how close AI systems are to human-like cognitive abilities. Most current approaches rely on carefully handcrafted domain-specific program searches to brute-force solutions for the tasks present in ARC. In this work, we propose a general learning-based framework for solving ARC. It is centered on transforming tasks from the vision to the language domain. This composition of language and vision allows for pre-trained models to be leveraged at each stage, enabling a shift from handcrafted priors towards the learned priors of the models. While not yet beating state-of-the-art models on ARC, we demonstrate the potential of our approach, for instance, by solving some ARC tasks that have not been solved previously.

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.

Classical graph algorithms work well for combinatorial problems that can be thoroughly formalized and abstracted. Once the algorithm is derived, it generalizes to instances of any size. However, developing an algorithm that handles complex structures and interactions in the real world can be challenging. Rather than specifying the algorithm, we can try to learn it from the graph-structured data. Graph Neural Networks (GNNs) are inherently capable of working on graph structures; however, they struggle to generalize well, and learning on larger instances is challenging. In order to scale, we focus on a recurrent architecture design that can learn simple graph problems end to end on smaller graphs and then extrapolate to larger instances. As our main contribution, we identify three essential techniques for recurrent GNNs to scale. By using (i) skip connections, (ii) state regularization, and (iii) edge convolutions, we can guide GNNs toward extrapolation. This allows us to train on small graphs and apply the same model to much larger graphs during inference. Moreover, we empirically validate the extrapolation capabilities of our GNNs on algorithmic datasets.

Traffic4cast is an annual competition to predict spatio temporal traffic based on real world data. We propose an approach using Graph Neural Networks that directly works on the road graph topology which was extracted from OpenStreetMap data. Our architecture can incorporate a hierarchical graph representation to improve the information flow between key intersections of the graph and the shortest paths connecting them. Furthermore, we investigate how the road graph can be compacted to ease the flow of information and make use of a multi-task approach to predict congestion classes and ETA simultaneously. Our code and models are released on Github.