The paper presents TopoGPU, a GPU streaming pipeline that computes persistence diagrams of cubical complexes from 2D and 3D images. It processes image chunks with massively parallel GPU kernels, accumulates boundary relations in host memory, and performs boundary matrix reduction on the CPU. TopoGPU introduces a stratification‑aware discrete Morse matching, parallel topological sorting, and a parallel V‑path parity algorithm, achieving up to 198× speedup over Cubical Ripser and reducing persistent homology computation costs in a topology‑preserving deep network.
arXiv:2609.37177v1 Announce Type: cross Abstract: Persistent homology (PH) is a frequently used tool for extracting and preserving topological information from image data, particularly in image segme...
arXiv:2507. 07156v2 Announce Type: replace-cross Abstract: Supervised machine learning pipelines trained on features derived from persistent homology have been experimentally observed to ignore much of the information contained in a persistence diagram.
arXiv:2606. 29763v1 Announce Type: cross Abstract: Topological data analysis (TDA), particularly persistent homology (PH), captures geometric structural properties in medical images (e.
Batch Before You Lift: Scalable Topological Deep Learning on Large Graphs introduces Cluster‑TNN, a framework that lifts graph data locally instead of globally, enabling efficient mini‑batch construction for higher‑order domains such as hypergraphs and simplicial complexes. By partitioning the input graph and dynamically sampling node clusters at runtime, Cluster‑TNN reduces peak GPU memory usage by an average of 83.2% across 21 comparisons while preserving connectivity needed for topological structures. This approach allows the first training of multiple higher‑order Topological Neural Networks on large datasets like Reddit and OGBN Products, demonstrating a general strategy for scaling Topological Deep Learning beyond global domain construction.
H3DNAS is a hardware‑aware compression framework that operates directly on ONNX computational graphs, eliminating the need for original source code or gradient access. It introduces a Channel Dependency Graph to classify operators and compute a provable compression ceiling, and employs a two‑stage hierarchical search that prunes architectures via L1‑importance channel selection and applies GhostConv mutations to Pareto‑optimal candidates. Applied to 3D point‑cloud models on the ModelNet40 dataset, H3DNAS reduces parameters by up to 65.5% and achieves significant inference speedups with negligible accuracy loss.
arXiv:2611.06191v1 Announce Type: new Abstract: Dimensionality reduction (DR) techniques are fundamental to the analysis of high-dimensional data, yet their substantial computational cost limits thei...
arXiv:2601. 07048v5 Announce Type: replace-cross Abstract: Approximate nearest neighbor search (ANNS) is a core problem in machine learning and information retrieval applications.
Batch Before You Lift: Scalable Topological Deep Learning on Large Graphs introduces Cluster‑TNN, a framework that lifts graph data locally instead of constructing a full lifted representation. By partitioning the input graph, sampling node clusters, and reconstructing induced subgraphs at runtime, Cluster‑TNN creates topological mini‑batches that preserve necessary connectivity for higher‑order structures. Across 21 matched comparisons, it reduces peak GPU memory by an average of 83.2% while maintaining competitive predictive performance, enabling the first training of multiple higher‑order Topological Neural Networks on large datasets such as Reddit and OGBN Products.
The paper introduces SNTO, a simultaneous neural topology optimization framework that represents state, adjoint, and design variables with custom neural networks optimized in a single loop. It employs a hardware‑aware training scheme that partitions the design domain across multiple GPUs and slices subdomains to manage memory, enabling stress‑constrained topology optimization at millions of degrees of freedom. Experiments on 2D benchmarks show sharper boundaries and reduced gray areas compared to finite element methods, while 3D problems with up to eight million points are solved efficiently on eight GPUs.
arXiv:2610.05441v2 Announce Type: replace-cross Abstract: Multiparameter persistent homology is a rapidly developing branch of topological data analysis that improves the robustness of single-paramet...
arXiv:2506. 20686v2 Announce Type: replace-cross Abstract: Recent advances in biomolecular modeling have been catalyzed by models such as AlphaFold3 (AF3), which introduce science-informed changes to the transformer architecture.
arXiv:2608.20725v1 Announce Type: cross Abstract: Convolution is a principal computational bottleneck in deep neural networks, and its efficiency depends on tight integration between algorithms and G...