arXiv subjects

Eleanor Wiesler

Publications and source records attributed to Eleanor Wiesler.

3 recordsLinked to original sources

arXiv2026

Ollivier's Ricci Curvature on Complex-weighted Graphs

Understanding the geometry of complex networks is critical for effective modeling and analysis across domains. While discrete notions of Ricci curvature have emerged as powerful tools for characterizing both local and global network structure, existing formulations are largely confined to undirected networks with real-valued weights. This limits the use of curvature-based analysis of directional and complex-weighted relations that arise naturally in many applications, from social and biological systems to quantum and signal-processing networks. In this work, we introduce a principled extension of Ollivier's Ricci curvature to complex-weighted graphs, which encompasses directed graphs as a special case. We establish fundamental theoretical properties of this new notion, including relations to the magnetic Laplacian and combinatorial upper and lower bounds that relate curvature to cycle structure in local neighborhoods. We further develop computational methods for curvature estimation and demonstrate their utility in community detection on directed networks.

cs.SI↗

arXiv2026

Graph Neural Network-Informed Predictive Flows for Faster Ford-Fulkerson and PAC-Learnability

We propose a learning-augmented framework for accelerating max-flow computation and image segmentation by integrating Graph Neural Networks (GNNs) with the Ford-Fulkerson algorithm. Rather than predicting initial flows, our method learns edge importance probabilities to guide augmenting path selection. We introduce a Message Passing GNN (MPGNN) that jointly learns node and edge embeddings through coupled updates, capturing both global structure and local flow dynamics such as residual capacity and bottlenecks. Given an input image, we propose a method to construct a grid-based flow network with source and sink nodes, extract features, and perform a single GNN inference to assign edge probabilities reflecting their likelihood of belonging to high-capacity cuts. These probabilities are stored in a priority queue and used to guide a modified Ford-Fulkerson procedure, prioritizing augmenting paths via an Edmonds-Karp-style search with bottleneck-aware tie-breaking. This avoids repeated inference over residual graphs while leveraging learned structure throughout optimization. We further introduce a bidirectional path construction strategy centered on high-probability edges and provide a theoretical framework relating prediction quality to efficiency via a weighted permutation distance metric. Our method preserves max-flow/min-cut optimality while reducing the number of augmentations in practice. We also outline a hybrid extension combining flow warm-starting with edge-priority prediction, establishing a foundation for learning-guided combinatorial optimization in image segmentation.

cs.LG↗

arXiv2026

A Probabilistic Framework for Improving Dense Object Detection in Underwater Image Data via Annealing-Based Data Augmentation

Object detection models typically perform well on images captured in controlled environments with stable lighting, water clarity, and viewpoint, but their performance degrades substantially in real-world underwater settings characterized by high variability and frequent occlusions. In this work, we address these challenges by introducing a novel data augmentation framework designed to improve robustness in dense and unconstrained underwater scenes. Using the DeepFish dataset, which contains images of fish in natural environments, we first generate bounding box annotations from provided segmentation masks to construct a custom detection dataset. We then propose a pseudo-simulated annealing-based augmentation algorithm, inspired by the copy-paste strategy of Deng et al. [1], to synthesize realistic crowded fish scenarios. Our approach improves spatial diversity and object density during training, enabling better generalization to complex scenes. Experimental results show that our method significantly outperforms a baseline YOLOv10 model, particularly on a challenging test set of manually annotated images collected from live-stream footage in the Florida Keys. These results demonstrate the effectiveness of our augmentation strategy for improving detection performance in dense, real-world underwater environments.

cs.CV↗