One Operator for Many Densities: Amortized Approximation of Conditioning by Neural Operators
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913113211666432 |
|---|---|
| author | Tsimpos, Panos Calvello, Edoardo Belhadji, Ayoub Nelsen, Nicholas H. |
| author_facet | Tsimpos, Panos Calvello, Edoardo Belhadji, Ayoub Nelsen, Nicholas H. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_06873 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | One Operator for Many Densities: Amortized Approximation of Conditioning by Neural Operators Tsimpos, Panos Calvello, Edoardo Belhadji, Ayoub Nelsen, Nicholas H. Machine Learning Numerical Analysis 68T07 (Primary), 62E17, 65J15 (Secondary) 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. |
| title | One Operator for Many Densities: Amortized Approximation of Conditioning by Neural Operators |
| topic | Machine Learning Numerical Analysis 68T07 (Primary), 62E17, 65J15 (Secondary) |
| url | https://arxiv.org/abs/2605.06873 |