# Semi-Modular Inference: enhanced learning in multi-modular models by tempering the influence of components

arXiv: https://arxiv.org/abs/2003.06804 · HTML: https://mlsanity.com/paper/2003.06804/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Mar 2020.

## Built on by (most cited first, 4 of 4)

- [Scalable Semi-Modular Inference with Variational Meta-Posteriors](https://mlsanity.com/paper/2204.00296/) (2022)
- [Adversarial Disentanglement by Backpropagation with Physics-Informed Variational Autoencoder](https://mlsanity.com/paper/2506.13658/) (2025)
- [Bayesian Surrogate Training on Multiple Data Sources: A Hybrid Modeling Strategy](https://mlsanity.com/paper/2412.11875/) (2024)
- [MOCA: A Transformer-based Modular Causal Inference Framework with One-way Cross-attention and Cutting Feedback](https://mlsanity.com/paper/2604.23107/) (2026)

## Abstract (arXiv)

Bayesian statistical inference loses predictive optimality when generative models are misspecified. Working within an existing coherent loss-based generalisation of Bayesian inference, we show existing Modular/Cut-model inference is coherent, and write down a new family of Semi-Modular Inference (SMI) schemes, indexed by an influence parameter, with Bayesian inference and Cut-models as special cases. We give a meta-learning criterion and estimation procedure to choose the inference scheme. This returns Bayesian inference when there is no misspecification. The framework applies naturally to Multi-modular models. Cut-model inference allows directed information flow from well-specified modules to misspecified modules, but not vice versa. An existing alternative power posterior method gives tunable but undirected control of information flow, improving prediction in some settings. In contrast, SMI allows tunable and directed information flow between modules. We illustrate our methods on two standard test cases from the literature and a motivating archaeological data set.