CuMPerLay: Learning Cubical Multiparameter Persistence Vectorizations

We present CuMPerLay, a novel differentiable vectorization layer that enables the integration of Cubical Multiparameter Persistence (CMP) into deep learning pipelines. While CMP presents a natural and powerful way to topologically work with images, its use is hindered by the complexity of multifiltration structures as well as the vectorization of CMP. In face of these challenges, we introduce a new algorithm for vectorizing MP homologies of cubical complexes. Our CuMPerLay decomposes the CMP into a combination of individual, learnable single-parameter persistence, where the bifiltration functions are jointly learned. Thanks to the differentiability, its robust topological feature vectors can be seamlessly used within state-of-the-art architectures such as Swin Transformers. We establish theoretical guarantees for the stability of our vectorization under generalized Wasserstein metrics. Our experiments on benchmark medical imaging and computer vision datasets show the benefit CuMPerLay on classification and segmentation performance, particularly in limited-data scenarios. Overall, CuMPerLay offers a promising direction for integrating global structural information into deep networks for structured image analysis.

Unveiling the Power of Multiple Gossip Steps: A Stability-Based Generalization Analysis in Decentralized Training

Decentralized training removes the centralized server, making it a communication-efficient approach that can significantly improve training efficiency, but it often suffers from degraded performance compared to centralized training. Multi-Gossip Steps (MGS) serve as a simple yet effective bridge between decentralized and centralized training, significantly reducing experiment performance gaps. However, the theoretical reasons for its effectiveness and whether this gap can be fully eliminated by MGS remain open questions. In this paper, we derive upper bounds on the generalization error and excess error of MGS using stability analysis, systematically answering these two key questions. 1). Optimization Error Reduction: MGS reduces the optimization error bound at an exponential rate, thereby exponentially tightening the generalization error bound and enabling convergence to better solutions. 2). Gap to Centralization: Even as MGS approaches infinity, a non-negligible gap in generalization error remains compared to centralized mini-batch SGD ($\mathcal{O}(T^{\frac{c\beta}{c\beta +1}}/{n m})$ in centralized and $\mathcal{O}(T^{\frac{2c\beta}{2c\beta +2}}/{n m^{\frac{1}{2c\beta +2}}})$ in decentralized). Furthermore, we provide the first unified analysis of how factors like learning rate, data heterogeneity, node count, per-node sample size, and communication topology impact the generalization of MGS under non-convex settings without the bounded gradients assumption, filling a critical theoretical gap in decentralized training. Finally, promising experiments on CIFAR datasets support our theoretical findings.

MATCH: Multi-faceted Adaptive Topo-Consistency for Semi-Supervised Histopathology Segmentation

In semi-supervised segmentation, capturing meaningful semantic structures from unlabeled data is essential. This is particularly challenging in histopathology image analysis, where objects are densely distributed. To address this issue, we propose a semi-supervised segmentation framework designed to robustly identify and preserve relevant topological features. Our method leverages multiple perturbed predictions obtained through stochastic dropouts and temporal training snapshots, enforcing topological consistency across these varied outputs. This consistency mechanism helps distinguish biologically meaningful structures from transient and noisy artifacts. A key challenge in this process is to accurately match the corresponding topological features across the predictions in the absence of ground truth. To overcome this, we introduce a novel matching strategy that integrates spatial overlap with global structural alignment, minimizing discrepancies among predictions. Extensive experiments demonstrate that our approach effectively reduces topological errors, resulting in more robust and accurate segmentations essential for reliable downstream analysis. Code is available at \href{https://github.com/Melon-Xu/MATCH}{https://github.com/Melon-Xu/MATCH}.

Discovering Communities in Continuous-Time Temporal Networks by Optimizing L-Modularity

Community detection is a fundamental problem in network analysis, with many applications in various fields. Extending community detection to the temporal setting with exact temporal accuracy, as required by real-world dynamic data, necessitates methods specifically adapted to the temporal nature of interactions. We introduce LAGO, a novel method for uncovering dynamic communities by greedy optimization of Longitudinal Modularity, a specific adaptation of Modularity for continuous-time networks. Unlike prior approaches that rely on time discretization or assume rigid community evolution, LAGO captures the precise moments when nodes enter and exit communities. We evaluate LAGO on synthetic benchmarks and real-world datasets, demonstrating its ability to efficiently uncover temporally and topologically coherent communities.

Linear Causal Representation Learning by Topological Ordering, Pruning, and Disentanglement

Causal representation learning (CRL) has garnered increasing interests from the causal inference and artificial intelligence community, due to its capability of disentangling potentially complex data-generating mechanism into causally interpretable latent features, by leveraging the heterogeneity of modern datasets. In this paper, we further contribute to the CRL literature, by focusing on the stylized linear structural causal model over the latent features and assuming a linear mixing function that maps latent features to the observed data or measurements. Existing linear CRL methods often rely on stringent assumptions, such as accessibility to single-node interventional data or restrictive distributional constraints on latent features and exogenous measurement noise. However, these prerequisites can be challenging to satisfy in certain scenarios. In this work, we propose a novel linear CRL algorithm that, unlike most existing linear CRL methods, operates under weaker assumptions about environment heterogeneity and data-generating distributions while still recovering latent causal features up to an equivalence class. We further validate our new algorithm via synthetic experiments and an interpretability analysis of large language models (LLMs), demonstrating both its superiority over competing methods in finite samples and its potential in integrating causality into AI.

Self-Supervised and Topological Signal-Quality Assessment for Any PPG Device

Wearable photoplethysmography (PPG) is embedded in billions of devices, yet its optical waveform is easily corrupted by motion, perfusion loss, and ambient light, jeopardizing downstream cardiometric analytics. Existing signal-quality assessment (SQA) methods rely either on brittle heuristics or on data-hungry supervised models. We introduce the first fully unsupervised SQA pipeline for wrist PPG. Stage 1 trains a contrastive 1-D ResNet-18 on 276 h of raw, unlabeled data from heterogeneous sources (varying in device and sampling frequency), yielding optical-emitter- and motion-invariant embeddings (i.e., the learned representation is stable across differences in LED wavelength, drive intensity, and device optics, as well as wrist motion). Stage 2 converts each 512-D encoder embedding into a 4-D topological signature via persistent homology (PH) and clusters these signatures with HDBSCAN. To produce a binary signal-quality index (SQI), the acceptable PPG signals are represented by the densest cluster while the remaining clusters are assumed to mainly contain poor-quality PPG signals. Without re-tuning, the SQI attains Silhouette, Davies-Bouldin, and Calinski-Harabasz scores of 0.72, 0.34, and 6173, respectively, on a stratified sample of 10,000 windows. In this study, we propose a hybrid self-supervised-learning--topological-data-analysis (SSL--TDA) framework that offers a drop-in, scalable, cross-device quality gate for PPG signals.

Chordless cycle filtrations for dimensionality detection in complex networks via topological data analysis

Many complex networks, ranging from social to biological systems, exhibit structural patterns consistent with an underlying hyperbolic geometry. Revealing the dimensionality of this latent space can disentangle the structural complexity of communities, impact efficient network navigation, and fundamentally shape connectivity and system behavior. We introduce a novel topological data analysis weighting scheme for graphs, based on chordless cycles, aimed at estimating the dimensionality of networks in a data-driven way. We further show that the resulting descriptors can effectively estimate network dimensionality using a neural network architecture trained in a synthetic graph database constructed for this purpose, which does not need retraining to transfer effectively to real-world networks. Thus, by combining cycle-aware filtrations, algebraic topology, and machine learning, our approach provides a robust and effective method for uncovering the hidden geometry of complex networks and guiding accurate modeling and low-dimensional embedding.

FloorSAM: SAM-Guided Floorplan Reconstruction with Semantic-Geometric Fusion

Reconstructing building floor plans from point cloud data is key for indoor navigation, BIM, and precise measurements. Traditional methods like geometric algorithms and Mask R-CNN-based deep learning often face issues with noise, limited generalization, and loss of geometric details. We propose FloorSAM, a framework that integrates point cloud density maps with the Segment Anything Model (SAM) for accurate floor plan reconstruction from LiDAR data. Using grid-based filtering, adaptive resolution projection, and image enhancement, we create robust top-down density maps. FloorSAM uses SAM's zero-shot learning for precise room segmentation, improving reconstruction across diverse layouts. Room masks are generated via adaptive prompt points and multistage filtering, followed by joint mask and point cloud analysis for contour extraction and regularization. This produces accurate floor plans and recovers room topological relationships. Tests on Giblayout and ISPRS datasets show better accuracy, recall, and robustness than traditional methods, especially in noisy and complex settings. Code and materials: github.com/Silentbarber/FloorSAM.

A Graph Machine Learning Approach for Detecting Topological Patterns in Transactional Graphs

The rise of digital ecosystems has exposed the financial sector to evolving abuse and criminal tactics that share operational knowledge and techniques both within and across different environments (fiat-based, crypto-assets, etc.). Traditional rule-based systems lack the adaptability needed to detect sophisticated or coordinated criminal behaviors (patterns), highlighting the need for strategies that analyze actors' interactions to uncover suspicious activities and extract their modus operandi. For this reason, in this work, we propose an approach that integrates graph machine learning and network analysis to improve the detection of well-known topological patterns within transactional graphs. However, a key challenge lies in the limitations of traditional financial datasets, which often provide sparse, unlabeled information that is difficult to use for graph-based pattern analysis. Therefore, we firstly propose a four-step preprocessing framework that involves (i) extracting graph structures, (ii) considering data temporality to manage large node sets, (iii) detecting communities within, and (iv) applying automatic labeling strategies to generate weak ground-truth labels. Then, once the data is processed, Graph Autoencoders are implemented to distinguish among the well-known topological patterns. Specifically, three different GAE variants are implemented and compared in this analysis. Preliminary results show that this pattern-focused, topology-driven method is effective for detecting complex financial crime schemes, offering a promising alternative to conventional rule-based detection systems.

Learning Graph from Smooth Signals under Partial Observation: A Robustness Analysis

Learning the graph underlying a networked system from nodal signals is crucial to downstream tasks in graph signal processing and machine learning. The presence of hidden nodes whose signals are not observable might corrupt the estimated graph. While existing works proposed various robustifications of vanilla graph learning objectives by explicitly accounting for the presence of these hidden nodes, a robustness analysis of "naive", hidden-node agnostic approaches is still underexplored. This work demonstrates that vanilla graph topology learning methods are implicitly robust to partial observations of low-pass filtered graph signals. We achieve this theoretical result through extending the restricted isometry property (RIP) to the Dirichlet energy function used in graph learning objectives. We show that smoothness-based graph learning formulation (e.g., the GL-SigRep method) on partial observations can recover the ground truth graph topology corresponding to the observed nodes. Synthetic and real data experiments corroborate our findings.