Benchmarking Positional Encodings for GNNs and Graph Transformers

Recent advances in Graph Neural Networks (GNNs) and Graph Transformers (GTs) have been driven by innovations in architectures and Positional Encodings (PEs), which are critical for augmenting node features and capturing graph topology. PEs are essential for GTs, where topological information would otherwise be lost without message-passing. However, PEs are often tested alongside novel architectures, making it difficult to isolate their effect on established models. To address this, we present a comprehensive benchmark of PEs in a unified framework that includes both message-passing GNNs and GTs. We also establish theoretical connections between MPNNs and GTs and introduce a sparsified GRIT attention mechanism to examine the influence of global connectivity. Our findings demonstrate that previously untested combinations of GNN architectures and PEs can outperform existing methods and offer a more comprehensive picture of the state-of-the-art. To support future research and experimentation in our framework, we make the code publicly available.

SNAC: Multi-Scale Neural Audio Codec

Neural audio codecs have recently gained popularity because they can represent audio signals with high fidelity at very low bitrates, making it feasible to use language modeling approaches for audio generation and understanding. Residual Vector Quantization (RVQ) has become the standard technique for neural audio compression using a cascade of VQ codebooks. This paper proposes the Multi-Scale Neural Audio Codec, a simple extension of RVQ where the quantizers can operate at different temporal resolutions. By applying a hierarchy of quantizers at variable frame rates, the codec adapts to the audio structure across multiple timescales. This leads to more efficient compression, as demonstrated by extensive objective and subjective evaluations. The code and model weights are open-sourced at https://github.com/hubertsiuzdak/snac.

Towards Leveraging Contrastively Pretrained Neural Audio Embeddings for Recommender Tasks

Music recommender systems frequently utilize network-based models to capture relationships between music pieces, artists, and users. Although these relationships provide valuable insights for predictions, new music pieces or artists often face the cold-start problem due to insufficient initial information. To address this, one can extract content-based information directly from the music to enhance collaborative-filtering-based methods. While previous approaches have relied on hand-crafted audio features for this purpose, we explore the use of contrastively pretrained neural audio embedding models, which offer a richer and more nuanced representation of music. Our experiments demonstrate that neural embeddings, particularly those generated with the Contrastive Language-Audio Pretraining (CLAP) model, present a promising approach to enhancing music recommendation tasks within graph-based frameworks.

GraphFSA: A Finite State Automaton Framework for Algorithmic Learning on Graphs

Many graph algorithms can be viewed as sets of rules that are iteratively applied, with the number of iterations dependent on the size and complexity of the input graph. Existing machine learning architectures often struggle to represent these algorithmic decisions as discrete state transitions. Therefore, we propose a novel framework: GraphFSA (Graph Finite State Automaton). GraphFSA is designed to learn a finite state automaton that runs on each node of a given graph. We test GraphFSA on cellular automata problems, showcasing its abilities in a straightforward algorithmic setting. For a comprehensive empirical evaluation of our framework, we create a diverse range of synthetic problems. As our main application, we then focus on learning more elaborate graph algorithms. Our findings suggest that GraphFSA exhibits strong generalization and extrapolation abilities, presenting an alternative approach to represent these algorithms.

AEye: A Visualization Tool for Image Datasets

Image datasets serve as the foundation for machine learning models in computer vision, significantly influencing model capabilities, performance, and biases alongside architectural considerations. Therefore, understanding the composition and distribution of these datasets has become increasingly crucial. To address the need for intuitive exploration of these datasets, we propose AEye, an extensible and scalable visualization tool tailored to image datasets. AEye utilizes a contrastively trained model to embed images into semantically meaningful high-dimensional representations, facilitating data clustering and organization. To visualize the high-dimensional representations, we project them onto a two-dimensional plane and arrange images in layers so users can seamlessly navigate and explore them interactively. AEye facilitates semantic search functionalities for both text and image queries, enabling users to search for content. We open-source the codebase for AEye, and provide a simple configuration to add datasets.

Benchmarking GNNs Using Lightning Network Data

The Bitcoin Lightning Network is a layer 2 protocol designed to facilitate fast and inexpensive Bitcoin transactions. It operates by establishing channels between users, where Bitcoin is locked and transactions are conducted off-chain until the channels are closed, with only the initial and final transactions recorded on the blockchain. Routing transactions through intermediary nodes is crucial for users without direct channels, allowing these routing nodes to collect fees for their services. Nodes announce their channels to the network, forming a graph with channels as edges. In this paper, we analyze the graph structure of the Lightning Network and investigate the statistical relationships between node properties using machine learning, particularly Graph Neural Networks (GNNs). We formulate a series of tasks to explore these relationships and provide benchmarks for GNN architectures, demonstrating how topological and neighbor information enhances performance. Our evaluation of several models reveals the effectiveness of GNNs in these tasks and highlights the insights gained from their application.

Next Level Message-Passing with Hierarchical Support Graphs

Message-Passing Neural Networks (MPNNs) are extensively employed in graph learning tasks but suffer from limitations such as the restricted scope of information exchange, by being confined to neighboring nodes during each round of message passing. Various strategies have been proposed to address these limitations, including incorporating virtual nodes to facilitate global information exchange. In this study, we introduce the Hierarchical Support Graph (HSG), an extension of the virtual node concept created through recursive coarsening of the original graph. This approach provides a flexible framework for enhancing information flow in graphs, independent of the specific MPNN layers utilized. We present a theoretical analysis of HSGs, investigate their empirical performance, and demonstrate that HSGs can surpass other methods augmented with virtual nodes, achieving state-of-the-art results across multiple datasets.

CoRe-GD: A Hierarchical Framework for Scalable Graph Visualization with GNNs

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.

Decentralized Federated Policy Gradient with Byzantine Fault-Tolerance and Provably Fast Convergence

In Federated Reinforcement Learning (FRL), agents aim to collaboratively learn a common task, while each agent is acting in its local environment without exchanging raw trajectories. Existing approaches for FRL either (a) do not provide any fault-tolerance guarantees (against misbehaving agents), or (b) rely on a trusted central agent (a single point of failure) for aggregating updates. We provide the first decentralized Byzantine fault-tolerant FRL method. Towards this end, we first propose a new centralized Byzantine fault-tolerant policy gradient (PG) algorithm that improves over existing methods by relying only on assumptions standard for non-fault-tolerant PG. Then, as our main contribution, we show how a combination of robust aggregation and Byzantine-resilient agreement methods can be leveraged in order to eliminate the need for a trusted central entity. Since our results represent the first sample complexity analysis for Byzantine fault-tolerant decentralized federated non-convex optimization, our technical contributions may be of independent interest. Finally, we corroborate our theoretical results experimentally for common RL environments, demonstrating the speed-up of decentralized federations w.r.t. the number of participating agents and resilience against various Byzantine attacks.

SURF: A Generalization Benchmark for GNNs Predicting Fluid Dynamics

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.