Topological and Geometric Data Analysis

Neueste Paper

• NervePool: A Simplicial Pooling Layer

  Sarah McGuire Scullen, Ernst R\"oell, Elizabeth Munch, Bastian Rieck, Matthew Hirn · 17. November 2025

  For deep learning problems on graph-structured data, pooling layers are important for down sampling, reducing computational cost, and to minimize overfitting. We define a pooling layer, nervePool, for data structured as simplicial complexes, which are generalizations of graphs that include higher-di…

• A Novel Sliced Fused Gromov-Wasserstein Distance

  Moritz Piening, Robert Beinert · 14. November 2025

  The Gromov--Wasserstein (GW) distance and its fused extension (FGW) are powerful tools for comparing heterogeneous data. Their computation is, however, challenging since both distances are based on non-convex, quadratic optimal transport (OT) problems. Leveraging 1D OT, a sliced version of GW has be…

• Incremental Generation is Necessity and Sufficient for Universality in Flow-Based Modelling

  Hossein Rouhvarzi, Anastasis Kratsios · 14. November 2025

  Incremental flow-based denoising models have reshaped generative modelling, but their empirical advantage still lacks a rigorous approximation-theoretic foundation. We show that incremental generation is necessary and sufficient for universal flow-based generation on the largest natural class of sel…

• Limits of Discrete Energy of Families of Increasing Sets

  Hari Sarang Nathan · 13. November 2025

  The Hausdorff dimension of a set can be detected using the Riesz energy. Here, we consider situations where a sequence of points, $\{x_n\}$, ``fills in'' a set $E \subset \mathbb{R}^d$ in an appropriate sense and investigate the degree to which the discrete analog to the Riesz energy of these sets c…

• On topological descriptors for graph products

  Mattie Ji, Amauri H. Souza, Vikas Garg · 13. November 2025

  Topological descriptors have been increasingly utilized for capturing multiscale structural information in relational data. In this work, we consider various filtrations on the (box) product of graphs and the effect on their outputs on the topological descriptors - the Euler characteristic (EC) and …

• Scalable Signature Kernel Computations for Long Time Series via Local Neumann Series Expansions

  Matthew Tamayo-Rios, Alexander Schell, Rima Alaifari · 12. November 2025

  The signature kernel is a recent state-of-the-art tool for analyzing high-dimensional sequential data, valued for its theoretical guarantees and strong empirical performance. In this paper, we present a novel method for efficiently computing the signature kernel of long, high-dimensional time series…

• Contact Wasserstein Geodesics for Non-Conservative Schr\"odinger Bridges

  Andrea Testa, S{\o}ren Hauberg, Tamim Asfour, Leonel Rozo · 12. November 2025

  The Schr\"odinger Bridge provides a principled framework for modeling stochastic processes between distributions; however, existing methods are limited by energy-conservation assumptions, which constrains the bridge's shape preventing it from model varying-energy phenomena. To overcome this, we intr…

• Contact Wasserstein Geodesics for Non-Conservative Schrodinger Bridges

  Andrea Testa, Soren Hauberg, Tamim Asfour, Leonel Rozo · 11. November 2025

  The Schr\"odinger Bridge provides a principled framework for modeling stochastic processes between distributions; however, existing methods are limited by energy-conservation assumptions, which constrains the bridge's shape preventing it from model varying-energy phenomena. To overcome this, we intr…

• Prototype Selection Using Topological Data Analysis

  Jordan Eckert, Elvan Ceyhan, Henry Schenck · 10. November 2025

  Recently, there has been an explosion in statistical learning literature to represent data using topological principles to capture structure and relationships. We propose a topological data analysis (TDA)-based framework, named Topological Prototype Selector (TPS), for selecting representative subse…

• Persistent reachability homology in machine learning applications

  Luigi Caputi, Nicholas Meadows, Henri Riihim\"aki · 10. November 2025

  We explore the recently introduced persistent reachability homology (PRH) of digraph data, i.e. data in the form of directed graphs. In particular, we study the effectiveness of PRH in network classification task in a key neuroscience problem: epilepsy detection. PRH is a variation of the persistent…

• Autoencoding Dynamics: Topological Limitations and Capabilities

  Matthew D. Kvalheim, Eduardo D. Sontag · 10. November 2025

  Given a "data manifold" $M\subset \mathbb{R}^n$ and "latent space" $\mathbb{R}^\ell$, an autoencoder is a pair of continuous maps consisting of an "encoder" $E\colon \mathbb{R}^n\to \mathbb{R}^\ell$ and "decoder" $D\colon \mathbb{R}^\ell\to \mathbb{R}^n$ such that the "round trip" map $D\circ E$ is …

• Vectorized Computation of Euler Characteristic Functions and Transforms

  Jessi Cisewski-Kehe, Brittany Terese Fasy, Alexander McCleary, Eli Quist, Jack Ruder · 7. November 2025

  The weighted Euler characteristic transform (WECT) and Euler characteristic function (ECF) have proven to be useful tools in a variety of applications. However, current methods for computing these functions are neither optimized for speed nor do they scale to higher-dimensional settings. In this wor…

• Composing Linear Layers from Irreducibles

  Travis Pence, Daisuke Yamada, Vikas Singh · 6. November 2025

  Contemporary large models often exhibit behaviors suggesting the presence of low-level primitives that compose into modules with richer functionality, but these fundamental building blocks remain poorly understood. We investigate this compositional structure in linear layers by asking: can we identi…

• Continuous-time Riemannian SGD and SVRG Flows on Wasserstein Probabilistic Space

  Mingyang Yi, Bohan Wang · 5. November 2025

  Recently, optimization on the Riemannian manifold have provided valuable insights to the optimization community. In this regard, extending these methods to to the Wasserstein space is of particular interest, since optimization on Wasserstein space is closely connected to practical sampling processes…

• Zero-knowledge LLM hallucination detection and mitigation through fine-grained cross-model consistency

  Aman Goel, Daniel Schwartz, Yanjun Qi · 4. November 2025

  Large language models (LLMs) have demonstrated impressive capabilities across diverse tasks, but they remain susceptible to hallucinations--generating content that appears plausible but contains factual inaccuracies. We present Finch-Zk, a black-box framework that leverages fine-grained cross-model …

• Solution Space Topology Guides CMTS Search

  Mirco A. Mannucci · 4. November 2025

  A fundamental question in search-guided AI: what topology should guide Monte Carlo Tree Search (MCTS) in puzzle solving? Prior work applied topological features to guide MCTS in ARC-style tasks using grid topology -- the Laplacian spectral properties of cell connectivity -- and found no benefit. We …

• Hypergraph clustering using Ricci curvature: an edge transport perspective

  Olympio Hacquard · 30. Oktober 2025

  In this paper, we introduce a novel method for extending Ricci flow to hypergraphs by defining probability measures on the edges and transporting them on the line expansion. This approach yields a new weighting on the edges, which proves particularly effective for community detection. We extensively…

• Unveiling m-Sharpness Through the Structure of Stochastic Gradient Noise

  Haocheng Luo, Mehrtash Harandi, Dinh Phung, Trung Le · 28. Oktober 2025

  Sharpness-aware minimization (SAM) has emerged as a highly effective technique for improving model generalization, but its underlying principles are not fully understood. We investigated the phenomenon known as m-sharpness, where the performance of SAM improves monotonically as the micro-batch size …

• Lorentz Local Canonicalization: How to Make Any Network Lorentz-Equivariant

  Jonas Spinner, Luigi Favaro, Peter Lippmann, Sebastian Pitz, Gerrit Gerhartz, Tilman Plehn, Fred A. Hamprecht · 27. Oktober 2025

• Relative Representations: Topological and Geometric Perspectives

  Alejandro Garc\'ia-Castellanos, Giovanni Luca Marchetti, Danica Kragic, Martina Scolamiero · 27. Oktober 2025