mlsanityData to 14 Oct 2026

One Operator for Many Densities: Amortized Approximation of Conditioning by Neural Operators

arXiv 2605.06873 ↗First posted 7 May 2026stat.ML cs.LG cs.NAcited by 4

Not on the map. Why?

Abstract (arXiv)

Probabilistic conditioning is concerned with the identification of a distribution of a random variable X given a random variable Y. It is a cornerstone of scientific and engineering applications where modeling uncertainty is key. This problem has traditionally been addressed in machine learning by directly learning the conditional distribution of a fixed joint distribution. This paper introduces a novel perspective: we propose to solve the conditioning problem by identifying a single operator that maps any joint density to its conditional, thus amortizing over joint-conditional pairs. We establish that the conditioning operator can be approximated to arbitrary accuracy by neural operators. Our proof relies on new results establishing continuity of the conditioning operator over suitable classes of densities. Finally, we learn the conditioning map for a class of Gaussian mixtures using neural operators, illustrating the promise of our framework. This work provides the theoretical underpinnings for general-purpose, amortized methods for probabilistic conditioning, such as foundation models for Bayesian inference.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 42 of its 62 references that are in the map. First posted on arXiv 7 May 2026.

Builds on

42 of 62 references.

References · 42

  1. 2022Flow Matching for Generative Modelingcited by 5,702
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30 more
  1. 2024All-in-one simulation-based inferencecited by 74
  2. 2025FourCastNet 3: A geometric approach to probabilistic machine-learning weather forecasting at scalecited by 62
  3. 2022Optimal Rates for Regularized Conditional Mean Embedding Learningcited by 50
  4. 2014Learning Theory for Distribution Regressioncited by 48
  5. 2024Optimal experimental design: Formulations and computationscited by 45
  6. 2023Nonlocality and Nonlinearity Implies Universality in Operator Learningcited by 43
  7. 2024Transformers are Universal In-context Learnerscited by 43
  8. 2024Continuum Attention for Neural Operatorscited by 40
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  10. 2020Linear Optimal Transport Embedding: Provable Wasserstein classification for certain rigid transformations and perturbationscited by 37
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  17. 2026In-Context Operator Learning on the Space of Probability Measurescited by 11
  18. 2024Universal Approximation of Mean-Field Models via Transformerscited by 7
  19. 2025Transformers through the lens of support-preserving maps between measurescited by 6
  20. 2025DiScoFormer: Plug-In Density and Score Estimation with Transformerscited by 6
  21. 2025Learning Memory and Material Dependent Constitutive Lawscited by 5
  22. 2025Fast filtering of non-Gaussian models using Amortized Optimal Transport Mapscited by 4
  23. 2026Transformers as Measure-Theoretic Associative Memory: A Statistical Perspective and Minimax Optimalitycited by 4
  24. 2026A short tour of operator learning theory: Convergence rates, statistical limits, and open questionscited by 4
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Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 4.

4 papers.

  1. 2026Learning Probabilistic Filters with Strictly Proper Scoring Rulescited by 6
  2. 2026Universal Approximation of Measure-to-Measure Operators by Pushforwardscited by 1
  3. 2026Attention Kernels for Learning Maps Between Heavy-Tailed Measurescited by 1
  4. 2026Stability of Measure-to-Measure Transformers on Sub-Gaussian Datacited by 0