From Persistence to Survival: Hypothesis Testing, Effect Sizes and Vectorisation for Topological Features

Persistence diagrams are common representations in topological data analysis, but they do not naturally live in a vector space, and the statistical tools developed for comparing them have largely evolved separately from those used for downstream prediction. We introduce STRAND (Survival Topological Representation ANalysis of Diagrams), which treats (collections of) PDs as survival data: each topological feature with persistence value $p = d - b$ is a fully observed time-to-event, and the persistence survival function $S(t) = \mathbb{P}(p > t)$ is the central object for comparing diagrams. From this single representation we derive (i) a non-parametric two-sample test with calibrated Type I error and high power from a small number of diagrams; (ii) interpretable effect sizes; and (iii) a 1-Wasserstein-stable feature vector for downstream machine learning. We validate calibration and power on synthetic manifolds with controlled topology, demonstrate competitive vectorisation across 14 graph and 3D point cloud benchmarks, and apply the method to study functional brain connectivity in fMRI/neuroscience data. To our knowledge, STRAND is the first method to provide hypothesis testing and vectorisation for persistence diagrams from a single coherent and interpretable representation.

End-to-End Subgraph Detection with GraphDETR

Subgraph detection seeks to identify whether and where instances of query patterns occur within a larger graph. This problem is fundamental across scientific domains and is closely related to subgraph isomorphism, which is NP-complete, limiting combinatorial approaches to small patterns or moderately sized graphs. We introduce GraphDETR, a deep learning framework that formulates subgraph detection as a set prediction problem, analogous to DETR in object detection. GraphDETR encodes the target graph with a graph neural network, and employs a fixed set of learnable query vectors, decoded via a transformer decoder, to predict all pattern occurrences jointly in a single forward pass. This is enabled by training the model end-to-end with bipartite matching. Unlike traditional combinatorial methods that only solve exact structural matching, GraphDETR naturally extends to approximate matching, enabling detection beyond exact pattern correspondence. Empirically, we show that GraphDETR can detect diverse patterns, such as molecular structures, cycles, cliques, and fuzzy patterns of up to 50 nodes, in target graphs with up to 1000 nodes. We further evaluate on molecular functional group detection over the ChEMBL dataset, where GraphDETR predicts the complete set of functional groups per molecule, achieving a strong performance of $\text{AP}_{100} = 91.2$.

Protein Fold Classification at Scale: Benchmarking and Pretraining

Classifying protein topology is essential for deciphering biological function, but progress is held back by the lack of large-scale benchmarks that avoid duplicates and by models that do not scale well. We introduce TEDBench, a large-scale, non-redundant benchmark for protein fold classification constructed from the Encyclopedia of Domains (TED) and Foldseek-clustered AlphaFold structures. We show that on TEDBench, current protein representation learning methods either require very large models or fail to deliver strong performance. To address this challenge, we propose Masked Invariant Autoencoders (MiAE), a self-supervised framework for protein structure representation learning. MiAE uses an extremely high masking ratio of up to 90% with an $\mathrm{SE(3)}$-invariant encoder and a lightweight decoder that reconstructs backbone coordinates from the latent representation and mask tokens. MiAE scales well and outperforms supervised counterparts and state-of-the-art baselines on TEDBench, establishing a strong recipe for protein fold classification. To test transfer beyond AlphaFold structures, we further benchmark on a curated dataset from experimental structures of CATH v4.4. TEDBench is available at https://github.com/BorgwardtLab/TEDBench.

A Comprehensive Benchmark for RNA 3D Structure-Function Modeling

The RNA structure-function relationship has recently garnered significant attention within the deep learning community, promising to grow in importance as nucleic acid structure models advance. However, the absence of standardized and accessible benchmarks for deep learning on RNA 3D structures has impeded the development of models for RNA functional characteristics. In this work, we introduce a set of seven benchmarking datasets for RNA structure-function prediction, designed to address this gap. Our library builds on the established Python library rnaglib, and offers easy data distribution and encoding, splitters and evaluation methods, providing a convenient all-in-one framework for comparing models. Datasets are implemented in a fully modular and reproducible manner, facilitating for community contributions and customization. Finally, we provide initial baseline results for all tasks using a graph neural network. Source code: https://github.com/cgoliver/rnaglib Documentation: https://rnaglib.org

Towards Fast Graph Generation via Autoregressive Noisy Filtration Modeling

Graph generative models often face a critical trade-off between learning complex distributions and achieving fast generation speed. We introduce Autoregressive Noisy Filtration Modeling (ANFM), a novel approach that addresses both challenges. ANFM leverages filtration, a concept from topological data analysis, to transform graphs into short sequences of monotonically increasing subgraphs. This formulation extends the sequence families used in previous autoregressive models. To learn from these sequences, we propose a novel autoregressive graph mixer model. Our experiments suggest that exposure bias might represent a substantial hurdle in autoregressive graph generation and we introduce two mitigation strategies to address it: noise augmentation and a reinforcement learning approach. Incorporating these techniques leads to substantial performance gains, making ANFM competitive with state-of-the-art diffusion models across diverse synthetic and real-world datasets. Notably, ANFM produces remarkably short sequences, achieving a 100-fold speedup in generation time compared to diffusion models. This work marks a significant step toward high-throughput graph generation.

Flatten Graphs as Sequences: Transformers are Scalable Graph Generators

We introduce AutoGraph, a novel autoregressive framework for generating large attributed graphs using decoder-only transformers. At the core of our approach is a reversible "flattening" process that transforms graphs into random sequences. By sampling and learning from these sequences, AutoGraph enables transformers to model and generate complex graph structures in a manner akin to natural language. In contrast to diffusion models that rely on computationally intensive node features, our approach operates exclusively on these sequences. The sampling complexity and sequence length scale linearly with the number of edges, making AutoGraph highly scalable for generating large sparse graphs. Empirically, AutoGraph achieves state-of-the-art performance across diverse synthetic and molecular graph generation benchmarks, while delivering a 100-fold generation and a 3-fold training speedup compared to leading diffusion models. Additionally, it demonstrates promising transfer capabilities and supports substructure-conditioned generation without additional fine-tuning. By extending language modeling techniques to graph generation, this work paves the way for developing graph foundation models.

Learning Long Range Dependencies on Graphs via Random Walks

Message-passing graph neural networks (GNNs), while excelling at capturing local relationships, often struggle with long-range dependencies on graphs. Conversely, graph transformers (GTs) enable information exchange between all nodes but oversimplify the graph structure by treating them as a set of fixed-length vectors. This work proposes a novel architecture, NeuralWalker, that overcomes the limitations of both methods by combining random walks with message passing. NeuralWalker achieves this by treating random walks as sequences, allowing for the application of recent advances in sequence models in order to capture long-range dependencies within these walks. Based on this concept, we propose a framework that offers (1) more expressive graph representations through random walk sequences, (2) the ability to utilize any sequence model for capturing long-range dependencies, and (3) the flexibility by integrating various GNN and GT architectures. Our experimental evaluations demonstrate that NeuralWalker achieves significant performance improvements on 19 graph and node benchmark datasets, notably outperforming existing methods by up to 13% on the PascalVoc-SP and COCO-SP datasets. Code is available at https://github.com/BorgwardtLab/NeuralWalker.

Endowing Protein Language Models with Structural Knowledge

Understanding the relationships between protein sequence, structure and function is a long-standing biological challenge with manifold implications from drug design to our understanding of evolution. Recently, protein language models have emerged as the preferred method for this challenge, thanks to their ability to harness large sequence databases. Yet, their reliance on expansive sequence data and parameter sets limits their flexibility and practicality in real-world scenarios. Concurrently, the recent surge in computationally predicted protein structures unlocks new opportunities in protein representation learning. While promising, the computational burden carried by such complex data still hinders widely-adopted practical applications. To address these limitations, we introduce a novel framework that enhances protein language models by integrating protein structural data. Drawing from recent advances in graph transformers, our approach refines the self-attention mechanisms of pretrained language transformers by integrating structural information with structure extractor modules. This refined model, termed Protein Structure Transformer (PST), is further pretrained on a small protein structure database, using the same masked language modeling objective as traditional protein language models. Empirical evaluations of PST demonstrate its superior parameter efficiency relative to protein language models, despite being pretrained on a dataset comprising only 542K structures. Notably, PST consistently outperforms the state-of-the-art foundation model for protein sequences, ESM-2, setting a new benchmark in protein function prediction. Our findings underscore the potential of integrating structural information into protein language models, paving the way for more effective and efficient protein modeling Code and pretrained models are available at https://github.com/BorgwardtLab/PST.

Fisher Information Embedding for Node and Graph Learning

Attention-based graph neural networks (GNNs), such as graph attention networks (GATs), have become popular neural architectures for processing graph-structured data and learning node embeddings. Despite their empirical success, these models rely on labeled data and the theoretical properties of these models have yet to be fully understood. In this work, we propose a novel attention-based node embedding framework for graphs. Our framework builds upon a hierarchical kernel for multisets of subgraphs around nodes (e.g. neighborhoods) and each kernel leverages the geometry of a smooth statistical manifold to compare pairs of multisets, by "projecting" the multisets onto the manifold. By explicitly computing node embeddings with a manifold of Gaussian mixtures, our method leads to a new attention mechanism for neighborhood aggregation. We provide theoretical insights into genralizability and expressivity of our embeddings, contributing to a deeper understanding of attention-based GNNs. We propose efficient unsupervised and supervised methods for learning the embeddings, with the unsupervised method not requiring any labeled data. Through experiments on several node classification benchmarks, we demonstrate that our proposed method outperforms existing attention-based graph models like GATs. Our code is available at https://github.com/BorgwardtLab/fisher_information_embedding.

Unsupervised Manifold Alignment with Joint Multidimensional Scaling

We introduce Joint Multidimensional Scaling, a novel approach for unsupervised manifold alignment, which maps datasets from two different domains, without any known correspondences between data instances across the datasets, to a common low-dimensional Euclidean space. Our approach integrates Multidimensional Scaling (MDS) and Wasserstein Procrustes analysis into a joint optimization problem to simultaneously generate isometric embeddings of data and learn correspondences between instances from two different datasets, while only requiring intra-dataset pairwise dissimilarities as input. This unique characteristic makes our approach applicable to datasets without access to the input features, such as solving the inexact graph matching problem. We propose an alternating optimization scheme to solve the problem that can fully benefit from the optimization techniques for MDS and Wasserstein Procrustes. We demonstrate the effectiveness of our approach in several applications, including joint visualization of two datasets, unsupervised heterogeneous domain adaptation, graph matching, and protein structure alignment.