Topological Deep Learning
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Related Articles from SNS
Geometric Analysis of Magnetic Labyrinthine Stripe Evolution via Deep Learning Segmentation
Announce Type: replace-cross Abstract: Labyrinthine stripe patterns are common in many physical systems, yet their lack of long-range order makes quantitative characterization challenging. We investigate the evolution of such patterns in bismuth-doped yttrium iron garnet (Bi:YIG) films subjected to a magnetic field annealing protocol. A U-Net deep learning model, trained with synthetic degradations including additive white Gaussian and Simplex noise, enables robust segmentation of...
A Lightweight Deep Learning-based Model for Ranking Influential Nodes in Complex Networks
Announce Type: cross Abstract: Identifying influential nodes in complex networks is a critical task with a wide range of applications across different domains. However, existing approaches often face trade-offs between accuracy and computational efficiency. To address these challenges, we propose 1D-CGS, a lightweight and effective hybrid model that integrates the speed of one-dimensional convolutional neural networks (1D-CNN) with the topological representation power of GraphSAGE for...
Learning Coherent Representations: A Topological Approach to Interpretability
arXiv:2606.02841v1 Announce Type: new Abstract: Deep neural networks learn representations where individual features often lack interpretable meaning; a single neuron may activate for scattered, unrelated inputs. We introduce coherence, a geometric property inspired by neural coding in the brain, where neurons like grid cells and head direction cells respond to contiguous regions of state space. A non-negative matrix is coherent if each row (sample) attends to geometrically clustered columns...
HOPSE: Scalable Higher-Order Positional and Structural Encoder for Combinatorial Representations
Announce Type: replace Abstract: While Graph Neural Networks (GNNs) have proven highly effective at modeling relational data, pairwise connections cannot fully capture multi-way relationships naturally present in complex real-world systems. In response to this, Topological Deep Learning (TDL) leverages more general combinatorial representations--such as simplicial or cellular complexes--to accommodate higher-order interactions. Existing TDL methods often extend GNNs through Higher-Order...
CytoGem-XAI:A Hypergraph Neural Network Framework for Genome-Scale Metabolic Modeling and Interpretable Analysis
Genome-scale metabolic models are essential for understanding cellular metabolism, yet existing deep learning approaches remain black boxes, and traditional flux balance analysis (FBA) cannot provide sample-specific predictions. To our knowledge, CytoGem-XAI is the first framework to combine hypergraph neural network representation with interpretable, FBA-parallel analysis and sample-specific metabolic characterization. Built upon hypergraph representations where reactions are encoded as...
Rethinking Neural Width for Alternating Current Optimal Power Flow Proxies
arXiv:2606.03125v1 Announce Type: new Abstract: Deep learning proxies for Alternating Current Optimal Power Flow (ACOPF) lack systematic methods for determining architectural size. This paper conducts a constructive thought experiment to answer a fundamental inquiry: how wide must a neural network be to almost accurately approximate the ACOPF manifold? We introduce a Loss-Guided Neural Densification (LG-ND) algorithm that incrementally discovers necessary capacity by expanding only when the...
GloResNet: A lightweight 3D CNN with global topological features for preterm brain injury prediction
arXiv:2606.02498v1 Announce Type: new Abstract: This study introduces an automated deep learning framework for predicting brain injury (BI) in preterm infants from T2-weighted MRI (dHCP dataset). We propose GloResNet, a lightweight 3D CNN based on ResNet-10, pretrained on MedicalNet to address data scarcity. A global manifold mapping strategy first resamples each 3D volume to 128x128x128 and then applies subject-wise z-score intensity normalization, thereby preserving global topology while...
Full-field prediction for engineering-scale three-dimensional aircraft with multigrid-hierarchical learning
arXiv:2605.30375v1 Announce Type: new Abstract: High-fidelity computational fluid dynamics is essential for aerospace design, but engineering-scale simulations of practical three-dimensional aircraft remain computationally expensive. Learning-based flow-field initialization can improve efficiency by reducing the numerical distance between the initial and converged solutions, yet existing deep learning approaches remain difficult to scale to large three-dimensional aircraft flows with...
Full-field prediction for engineering-scale three-dimensional aircraft with multigrid-hierarchical learning
arXiv:2605.30375v1 Announce Type: cross Abstract: High-fidelity computational fluid dynamics is essential for aerospace design, but engineering-scale simulations of practical three-dimensional aircraft remain computationally expensive. Learning-based flow-field initialization can improve efficiency by reducing the numerical distance between the initial and converged solutions, yet existing deep learning approaches remain difficult to scale to large three-dimensional aircraft flows with...
TetraFuse: A Synergistic Four-Dimensional Dynamic Fusion Framework for Efficient and Robust Medical Image Classification
Accurate and robust classification of medical pathology images is pivotal for computer-aided diagnosis. However, the deployment of deep learning models in high-throughput clinical screening faces a fundamental challenge: the trade-off between diagnostic accuracy and computational efficiency. Current lightweight architectures, while reducing parameter complexity through grouped convolutions, often lead to cross-channel information isolation and diminished representational capacity.