# BRUNO: A Deep Recurrent Model for Exchangeable Data

arXiv: https://arxiv.org/abs/1802.07535 · HTML: https://mlsanity.com/paper/1802.07535/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Feb 2018.

## Built on by (most cited first, 11 of 11)

- [Incoherent Probability Judgments in Large Language Models](https://mlsanity.com/paper/2401.16646/) (2024)
- [Do Finetti: On Causal Effects for Exchangeable Data](https://mlsanity.com/paper/2405.18836/) (2024)
- [What Should Embeddings Embed? Autoregressive Models Represent Latent Generating Distributions](https://mlsanity.com/paper/2406.03707/) (2024)
- [Deep Stochastic Processes via Functional Markov Transition Operators](https://mlsanity.com/paper/2305.15574/) (2023)
- [Deep de Finetti: Recovering Topic Distributions from Large Language Models](https://mlsanity.com/paper/2312.14226/) (2023)
- [Partially Observed Exchangeable Modeling](https://mlsanity.com/paper/2102.06083/) (2021)
- [DuMLP-Pin: A Dual-MLP-dot-product Permutation-invariant Network for Set Feature Extraction](https://mlsanity.com/paper/2203.04007/) (2022)
- [Beyond Intuition, a Framework for Applying GPs to Real-World Data](https://mlsanity.com/paper/2307.03093/) (2023)
- [Set2Seq Transformer: Temporal and Position-Aware Set Representations for Sequential Multiple-Instance Learning](https://mlsanity.com/paper/2408.03404/) (2024)
- [Exchangeability in Neural Network and its Application to Dynamic Pruning](https://mlsanity.com/paper/2506.02210/) (2025)
- [Revisiting Neural Processes via Fourier Transform and Volterra Series](https://mlsanity.com/paper/2606.01172/) (2026)

## Abstract (arXiv)

We present a novel model architecture which leverages deep learning tools to perform exact Bayesian inference on sets of high dimensional, complex observations. Our model is provably exchangeable, meaning that the joint distribution over observations is invariant under permutation: this property lies at the heart of Bayesian inference. The model does not require variational approximations to train, and new samples can be generated conditional on previous samples, with cost linear in the size of the conditioning set. The advantages of our architecture are demonstrated on learning tasks that require generalisation from short observed sequences while modelling sequence variability, such as conditional image generation, few-shot learning, and anomaly detection.