CoPHo: Classifier-guided Conditional Topology Generation with Persistent Homology

• URL: http://arxiv.org/abs/2512.19736v1
• Date: Wed, 17 Dec 2025 13:10:22 GMT
• Title: CoPHo: Classifier-guided Conditional Topology Generation with Persistent Homology
• Authors: Gongli Xi, Ye Tian, Mengyu Yang, Zhenyu Zhao, Yuchao Zhang, Xiangyang Gong, Xirong Que, Wendong Wang,
• Abstract summary: Topology structure underpins research on performance and robustness.<n>Generation of synthetic graphs with desired properties for testing or release.<n>We propose Persistent Topology Generation with Conditional Homology (CoPHo)<n>Experiments on four generic/network datasets demonstrate that CoPHo outperforms existing methods at matching target metrics.
• Score: 14.522233245543687
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The structure of topology underpins much of the research on performance and robustness, yet available topology data are typically scarce, necessitating the generation of synthetic graphs with desired properties for testing or release. Prior diffusion-based approaches either embed conditions into the diffusion model, requiring retraining for each attribute and hindering real-time applicability, or use classifier-based guidance post-training, which does not account for topology scale and practical constraints. In this paper, we show from a discrete perspective that gradients from a pre-trained graph-level classifier can be incorporated into the discrete reverse diffusion posterior to steer generation toward specified structural properties. Based on this insight, we propose Classifier-guided Conditional Topology Generation with Persistent Homology (CoPHo), which builds a persistent homology filtration over intermediate graphs and interprets features as guidance signals that steer generation toward the desired properties at each denoising step. Experiments on four generic/network datasets demonstrate that CoPHo outperforms existing methods at matching target metrics, and we further validate its transferability on the QM9 molecular dataset.

Related papers

• SIGMA: Scalable Spectral Insights for LLM Collapse [51.863164847253366]
  We introduce SIGMA (Spectral Inequalities for Gram Matrix Analysis), a unified framework for model collapse.<n>By utilizing benchmarks that deriving and deterministic bounds on the matrix's spectrum, SIGMA provides a mathematically grounded metric to track the contraction of the representation space.<n>We demonstrate that SIGMA effectively captures the transition towards states, offering both theoretical insights into the mechanics of collapse.
  arXiv  Detail & Related papers  (2026-01-06T19:47:11Z)
• ReDiSC: A Reparameterized Masked Diffusion Model for Scalable Node Classification with Structured Predictions [64.17845687013434]
  We propose ReDiSC, a structured diffusion model for structured node classification.<n>We show that ReDiSC achieves superior or highly competitive performance compared to state-of-the-art GNN, label propagation, and diffusion-based baselines.<n> Notably, ReDiSC scales effectively to large-scale datasets on which previous structured diffusion methods fail due to computational constraints.
  arXiv  Detail & Related papers  (2025-07-19T04:46:53Z)
• Classification of Histopathology Slides with Persistence Homology Convolutions [0.0]
  We present a novel method that generates local persistent homology-based data using a modified version of the convolution operator called Persistent Homology Convolutions.<n>These results indicate that persistent homology convolutions extract meaningful geometric information from the histopathology slides.
  arXiv  Detail & Related papers  (2025-07-18T21:56:53Z)
• Diffeomorphic interpolation for efficient persistence-based topological optimization [3.7550827441501844]
  Topological Data Analysis (TDA) provides a pipeline to extract quantitative topological descriptors from structured objects. We show that our approach combines efficiently with subsampling techniques, as the diffeomorphism derived from the gradient computed on a subsample can be used to update the coordinates of the full input object. We also showcase the relevance of our approach for black-box autoencoder (AE) regularization, where we aim at enforcing topological priors on the latent spaces associated to fixed, pre-trained, blackbox AE models.
  arXiv  Detail & Related papers  (2024-05-29T07:00:28Z)
• Variational Classification [51.2541371924591]
  We derive a variational objective to train the model, analogous to the evidence lower bound (ELBO) used to train variational auto-encoders. Treating inputs to the softmax layer as samples of a latent variable, our abstracted perspective reveals a potential inconsistency. We induce a chosen latent distribution, instead of the implicit assumption found in a standard softmax layer.
  arXiv  Detail & Related papers  (2023-05-17T17:47:19Z)
• On the Expressivity of Persistent Homology in Graph Learning [13.608942872770855]
  Persistent homology, a technique from computational topology, has recently shown strong empirical performance in the context of graph classification.<n>This paper provides a brief introduction to persistent homology in the context of graphs, as well as a theoretical discussion and empirical analysis of its expressivity for graph learning tasks.
  arXiv  Detail & Related papers  (2023-02-20T08:19:19Z)
• Alleviating neighbor bias: augmenting graph self-supervise learning with structural equivalent positive samples [1.0507062889290775]
  We propose a signal-driven self-supervised method for graph representation learning. It uses a topological information-guided structural equivalence sampling strategy. The results show that the model performance can be effectively improved.
  arXiv  Detail & Related papers  (2022-12-08T16:04:06Z)
• GSMFlow: Generation Shifts Mitigating Flow for Generalized Zero-Shot Learning [55.79997930181418]
  Generalized Zero-Shot Learning aims to recognize images from both the seen and unseen classes by transferring semantic knowledge from seen to unseen classes. It is a promising solution to take the advantage of generative models to hallucinate realistic unseen samples based on the knowledge learned from the seen classes. We propose a novel flow-based generative framework that consists of multiple conditional affine coupling layers for learning unseen data generation.
  arXiv  Detail & Related papers  (2022-07-05T04:04:37Z)
• The Manifold Hypothesis for Gradient-Based Explanations [55.01671263121624]
  gradient-based explanation algorithms provide perceptually-aligned explanations. We show that the more a feature attribution is aligned with the tangent space of the data, the more perceptually-aligned it tends to be. We suggest that explanation algorithms should actively strive to align their explanations with the data manifold.
  arXiv  Detail & Related papers  (2022-06-15T08:49:24Z)
• Generating Topological Structure of Floorplans from Room Attributes [4.1715767752637145]
  We propose to extract topological information from room attributes using Iterative and adaptive graph Topology Learning (ITL) ITL progressively predicts multiple relations between rooms; at each iteration, it improves node embeddings, which in turn facilitates generation of a better topological graph structure.
  arXiv  Detail & Related papers  (2022-04-26T14:24:58Z)
• Structure-Aware Feature Generation for Zero-Shot Learning [108.76968151682621]
  We introduce a novel structure-aware feature generation scheme, termed as SA-GAN, to account for the topological structure in learning both the latent space and the generative networks. Our method significantly enhances the generalization capability on unseen-classes and consequently improve the classification performance.
  arXiv  Detail & Related papers  (2021-08-16T11:52:08Z)
• Mitigating Generation Shifts for Generalized Zero-Shot Learning [52.98182124310114]
  Generalized Zero-Shot Learning (GZSL) is the task of leveraging semantic information (e.g., attributes) to recognize the seen and unseen samples, where unseen classes are not observable during training. We propose a novel Generation Shifts Mitigating Flow framework for learning unseen data synthesis efficiently and effectively. Experimental results demonstrate that GSMFlow achieves state-of-the-art recognition performance in both conventional and generalized zero-shot settings.
  arXiv  Detail & Related papers  (2021-07-07T11:43:59Z)
• Goal-directed Generation of Discrete Structures with Conditional Generative Models [85.51463588099556]
  We introduce a novel approach to directly optimize a reinforcement learning objective, maximizing an expected reward. We test our methodology on two tasks: generating molecules with user-defined properties and identifying short python expressions which evaluate to a given target value.
  arXiv  Detail & Related papers  (2020-10-05T20:03:13Z)

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.