TopoPrune: Robust Data Pruning via Unified Latent Space Topology

• URL: http://arxiv.org/abs/2602.02739v1
• Date: Mon, 02 Feb 2026 19:53:59 GMT
• Title: TopoPrune: Robust Data Pruning via Unified Latent Space Topology
• Abstract summary: We introduce TopoPrune, a framework which resolves this challenge by leveraging topology to capture the stable, intrinsic structure of data.<n>TopoPrune operates at two scales, (1) utilizing a topology-aware manifold approximation to establish a global low-dimensional embedding of the dataset.<n>We demonstrate that our unified dual-scale topological approach ensures high accuracy and precision, particularly at significant dataset pruning rates.
• Score: 9.204659134755792
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Geometric data pruning methods, while practical for leveraging pretrained models, are fundamentally unstable. Their reliance on extrinsic geometry renders them highly sensitive to latent space perturbations, causing performance to degrade during cross-architecture transfer or in the presence of feature noise. We introduce TopoPrune, a framework which resolves this challenge by leveraging topology to capture the stable, intrinsic structure of data. TopoPrune operates at two scales, (1) utilizing a topology-aware manifold approximation to establish a global low-dimensional embedding of the dataset. Subsequently, (2) it employs differentiable persistent homology to perform a local topological optimization on the manifold embeddings, ranking samples by their structural complexity. We demonstrate that our unified dual-scale topological approach ensures high accuracy and precision, particularly at significant dataset pruning rates (e.g., 90%). Furthermore, through the inherent stability properties of topology, TopoPrune is (a) exceptionally robust to noise perturbations of latent feature embeddings and (b) demonstrates superior transferability across diverse network architectures. This study demonstrates a promising avenue towards stable and principled topology-based frameworks for robust data-efficient learning.

Related papers

• Learning Spatio-Temporal Foundation Models from Pure Synthetic Data [85.23980441738811]
  NeoST is a scalable synthetic-training corpus to real-world bias, a latent-space reasoning architecture that generates and iteratively refines multiple future trajectories, and latent-space objectives that emphasize structural dynamics and enable inference-time correction under distribution shifts.<n>Extensive experiments across diverse real-world benchmarks show that NeoST consistently outperforms existing STFMs in diverse real-worldtemporal systems.
  arXiv  Detail & Related papers  (2026-06-27T02:56:46Z)
• Topological Flow Matching [56.16372813551555]
  Flow matching is a powerful generative modeling framework, valued for its simplicity and strong empirical performance.<n>We introduce topological flow matching, a topology-aware generalization of flow matching.<n>We demonstrate its effectiveness on diverse structured datasets, including brain fMRIs, ocean currents, seismic events, and traffic flows.
  arXiv  Detail & Related papers  (2026-06-14T16:29:33Z)
• Robust Subspace-Constrained Quadratic Models for Low-Dimensional Structure Learning [6.624243167811649]
  We develop a robust subspace-constrained quadratic model (SCQM) for learning low-constrained radial structure from high-dimensional data.<n>We show that the proposed approach consistently outperforms existing methods in terms of robustness and accuracy.
  arXiv  Detail & Related papers  (2026-05-19T12:35:13Z)
• SEED: Targeted Data Selection by Weighted Independent Set [76.68391670109433]
  We develop a robust and scalable data selection pipeline dubbed SEED.<n>SEED consistently outperforms state-of-the-art methods on instruction tuning, visual instruction tuning, and semantic segmentation.
  arXiv  Detail & Related papers  (2026-05-15T07:26:54Z)
• A Mean Curvature Approach to Boundary Detection: Geometric Insights for Unsupervised Learning [52.452902154360565]
  We introduce Mean Curvature Boundary Points (MCBP), a novel geometric framework grounded in Geometric Machine Learning.<n>MCBP explicitly models the intrinsic curvature of the data manifold and computes pointwise mean curvature without requiring principled manifold parametrization.<n>Experiments on synthetic and real-world datasets demonstrate that MCBP consistently improves clustering performance.
  arXiv  Detail & Related papers  (2026-05-05T20:19:09Z)
• Attention-Guided Flow-Matching for Sparse 3D Geological Generation [7.734651455015875]
  3D-GeoFlow is the first Attention-Guided Continuous Flow Matching framework tailored for sparse multimodal geological modeling.<n>By reformulating discrete categorical generation as a simulation-free, continuous vector field regression, our model establishes stable, deterministic optimal transport paths.<n>To validate our framework, we curated a large-scale multimodal dataset comprising 2,200 procedurally generated 3D geological cases.
  arXiv  Detail & Related papers  (2026-04-07T07:02:53Z)
• Function-Space Decoupled Diffusion for Forward and Inverse Modeling in Carbon Capture and Storage [65.51149575007149]
  We present Fun-DDPS, a generative framework that combines function-space diffusion models with differentiable neural operator surrogates for both forward and inverse modeling.<n>Fun-DDPS produces physically consistent realizations free from the high-frequency artifacts observed in joint-state baselines.
  arXiv  Detail & Related papers  (2026-02-12T18:58:12Z)
• Binary Flow Matching: Prediction-Loss Space Alignment for Robust Learning [23.616336786063552]
  Flow matching has emerged as a powerful framework for generative modeling.<n>We identify a latent structural mismatch that arises when it is coupled with velocity-based objectives.<n>We prove that re-aligning the objective to the signal space eliminates the singular weighting.
  arXiv  Detail & Related papers  (2026-02-11T02:02:30Z)
• Leveraging generative adversarial networks with spatially adaptive denormalization for multivariate stochastic seismic data inversion [0.0]
  We propose an iterative geostatistical inversion algorithm, SPADE-GANInv, for the prediction of facies and multiple correlated continuous properties from seismic data.<n>The SPADE-GAN is trained to reproduce realistic geometries, while sequential co-simulation predicts the spatial variability of the facies-dependent continuous properties.<n>The method is demonstrated on both 2-D synthetic scenarios and field data, targeting the prediction of facies, porosity, and acoustic impedance from full-stack seismic data.
  arXiv  Detail & Related papers  (2025-12-02T15:25:22Z)
• VIKING: Deep variational inference with stochastic projections [48.946143517489496]
  Variational mean field approximations tend to struggle with contemporary overparametrized deep neural networks.<n>We propose a simple variational family that considers two independent linear subspaces of the parameter space.<n>This allows us to build a fully-correlated approximate posterior reflecting the overparametrization.
  arXiv  Detail & Related papers  (2025-10-27T15:38:35Z)
• From Imperfect Signals to Trustworthy Structure: Confidence-Aware Inference from Heterogeneous and Reliability-Varying Utility Data [8.390328146420211]
  We propose a scalable framework that reconstructs a trustworthy grid topology by systematically integrating heterogeneous data.<n>The proposed framework is validated using data from over 8000 meters across 3 feeders in Oncor's service territory.
  arXiv  Detail & Related papers  (2025-08-07T19:05:19Z)
• Topology-Aware Modeling for Unsupervised Simulation-to-Reality Point Cloud Recognition [63.55828203989405]
  We introduce a novel Topology-Aware Modeling (TAM) framework for Sim2Real UDA on object point clouds.<n>Our approach mitigates the domain gap by leveraging global spatial topology, characterized by low-level, high-frequency 3D structures.<n>We propose an advanced self-training strategy that combines cross-domain contrastive learning with self-training.
  arXiv  Detail & Related papers  (2025-06-26T11:53:59Z)
• Latent Manifold Reconstruction and Representation with Topological and Geometrical Regularization [1.8335627278682702]
  We present an AutoEncoder-based method that integrates a manifold reconstruction layer, which uncovers latent manifold structures from noisy point clouds.<n>Experiments on point cloud datasets demonstrate that our method outperforms baselines like t-SNE, UMAP, and Topological AutoEncoders.
  arXiv  Detail & Related papers  (2025-05-07T13:47:22Z)
• SDF-TopoNet: A Two-Stage Framework for Tubular Structure Segmentation via SDF Pre-training and Topology-Aware Fine-Tuning [2.3436632098950456]
  Key challenge is ensuring topological correctness while maintaining computational efficiency.<n>We propose textbfSDF-TopoNet, an improved topology-aware segmentation framework.<n>We show that SDF-TopoNet outperforms existing methods in both topological accuracy and quantitative segmentation metrics.
  arXiv  Detail & Related papers  (2025-03-14T23:54:38Z)
• TopoFR: A Closer Look at Topology Alignment on Face Recognition [58.45515807380505]
  We propose TopoFR, a novel FR model that leverages a topological structure alignment strategy called PTSA and a hard sample mining strategy named SDE.<n> PTSA uses persistent homology to align the topological structures of the input and latent spaces, effectively preserving the structure information and improving the generalization performance of FR model.<n> Experimental results on popular face benchmarks demonstrate the superiority of our TopoFR over the state-of-the-art methods.
  arXiv  Detail & Related papers  (2024-10-14T14:58:30Z)
• The Risk of Federated Learning to Skew Fine-Tuning Features and Underperform Out-of-Distribution Robustness [50.52507648690234]
  Federated learning has the risk of skewing fine-tuning features and compromising the robustness of the model. We introduce three robustness indicators and conduct experiments across diverse robust datasets. Our approach markedly enhances the robustness across diverse scenarios, encompassing various parameter-efficient fine-tuning methods.
  arXiv  Detail & Related papers  (2024-01-25T09:18:51Z)
• Robust Model-Based Optimization for Challenging Fitness Landscapes [96.63655543085258]
  Protein design involves optimization on a fitness landscape. Leading methods are challenged by sparsity of high-fitness samples in the training set. We show that this problem of "separation" in the design space is a significant bottleneck in existing model-based optimization tools. We propose a new approach that uses a novel VAE as its search model to overcome the problem.
  arXiv  Detail & Related papers  (2023-05-23T03:47:32Z)
• ROME: Robustifying Memory-Efficient NAS via Topology Disentanglement and Gradient Accumulation [106.04777600352743]
  Differentiable architecture search (DARTS) is largely hindered by its substantial memory cost since the entire supernet resides in the memory. The single-path DARTS comes in, which only chooses a single-path submodel at each step. While being memory-friendly, it also comes with low computational costs. We propose a new algorithm called RObustifying Memory-Efficient NAS (ROME) to give a cure.
  arXiv  Detail & Related papers  (2020-11-23T06:34:07Z)
• A Fast and Robust Method for Global Topological Functional Optimization [70.11080854486953]
  We introduce a novel backpropagation scheme that is significantly faster, more stable, and produces more robust optima. This scheme can also be used to produce a stable visualization of dots in a persistence diagram as a distribution over critical, and near-critical, simplices in the data structure.
  arXiv  Detail & Related papers  (2020-09-17T18:46:16Z)
• Stable and consistent density-based clustering via multiparameter persistence [49.1574468325115]
  We consider the degree-Rips construction from topological data analysis.<n>We analyze its stability to perturbations of the input data using the correspondence-interleaving distance.<n>We integrate these methods into a pipeline for density-based clustering, which we call Persistable.
  arXiv  Detail & Related papers  (2020-05-18T19:45:04Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.