Research map / Probabilistic and scientific modeling / Uncertainty and Gaussian processes

TopoFisher: Learning Topological Summary Statistics by Maximizing Fisher Information

NeurIPS 2026 · Probabilistic and scientific modeling › Uncertainty and Gaussian processes · approach: Nonparametric and PAC-Bayes Bayesian learning · 0 citations (OpenAlex)

Read the paperCheck your idea against 108,967 papers

AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.

Proposes TopoFisher, a differentiable persistent-homology pipeline whose trainable filtrations, vectorizations and compressors are optimized to maximize local Gaussian Fisher information, with a Lipschitz stability result and experiments on spirals, GRFs and weak lensing.

Problem

Persistence-based summaries for simulation-based inference require hand-chosen filtrations, vectorizations and compressors without an objective tied to parameter uncertainty.

Approach

Train the full persistence pipeline (filtration, vectorization, compressor) by minimizing the negative log-determinant of a local Gaussian Fisher matrix estimated from simulations at a fiducial parameter, and prove local Lipschitz continuity of this loss under regularity assumptions.

Key results

• On weak lensing, TF-Cubical-PersLay reaches log|F|=21.51 vs 13.78 for power spectrum, 17.14 peak counts, 19.27 wavelet scattering, and 22.35 for IMNN in-distribution.
• Under lognormal-to-LPT shift, TF-Cubical-PersLay retains log|F|=19.24 while IMNN drops to 8.92.
• On GRFs, TF-Cubical-PersLay recovers 90.9% of the total log-determinant Fisher score (12.63 of 13.89), vs 88.4% for IMNN.

Surprising findings

• The unconstrained IMNN has the highest in-distribution Fisher information but transfers poorly (8.92) and gives the weakest NPE posterior (14.32).
• Learning the CNN filtration jointly with PersLay was less robust under simulator shift (12.72) than learning only the vectorization on a fixed cubical filtration (19.24).

Limitations

• Local summary design around one fiducial point under a Gaussian approximation; no global injectivity or calibrated posteriors over wide priors.
• Theoretical Lipschitz result does not formally transfer to the finite-sample estimator used in training.
• Lensing evaluations use additive auto-bin approximation rather than full joint tomographic Fisher.

Experimental setup

Datasets: noisy spiral point clouds (simulated) Gaussian random fields (simulated) sbi_lens lognormal and LPT convergence maps

Benchmarks: noisy spirals Gaussian random fields weak lensing local Fisher weak lensing transfer Fisher weak lensing NPE posterior

Metrics: log|F| marginal constraints sigma efficiency eta_log

Baselines: IMNN power spectrum peak counts wavelet scattering transform DTM Cubical-PI Cubical-Silhouette Cubical-Curves MLP-only GNN-only

Builds on: PersLay IMNN MOPED persistence images differentiable persistent homology

Closest papers by meaning

• Diffeomorphic interpolation for efficient persistence-based topological optimization (NeurIPS 2024 · similarity 0.87)
• Topological Periodicity Test (TopPT) via Confidence Bound of Time-Delay Embeddings (NeurIPS 2026 · similarity 0.86)
• Point-Level Topological Representation Learning on Point Clouds (ICML 2025 · similarity 0.85)
• TopoDiffusionNet: A Topology-aware Diffusion Model (ICLR 2025 · similarity 0.85)
• Topological Neural Networks go Persistent, Equivariant, and Continuous (ICML 2024 · similarity 0.85)
• Topological Blindspots: Understanding and Extending Topological Deep Learning Through the Lens of Expressivity (ICLR 2025 · similarity 0.85)