# Mixture Manifold Networks: A Computationally Efficient Baseline for Inverse Modeling

arXiv: https://arxiv.org/abs/2211.14366 · HTML: https://mlsanity.com/paper/2211.14366/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 22 references that are in the map.
- First posted on arXiv 25 Nov 2022.

## Builds on (most cited first, 6 of 6)

- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Analyzing Inverse Problems with Invertible Neural Networks](https://mlsanity.com/paper/1808.04730/) (2018)
- [Accounting for Variance in Machine Learning Benchmarks](https://mlsanity.com/paper/2103.03098/) (2021)
- [Benchmarking deep inverse models over time, and the neural-adjoint method](https://mlsanity.com/paper/2009.12919/) (2020)
- [Benchmarking Invertible Architectures on Inverse Problems](https://mlsanity.com/paper/2101.10763/) (2021)
- [Inverse deep learning methods and benchmarks for artificial electromagnetic material design](https://mlsanity.com/paper/2112.10254/) (2021)

## Built on by (most cited first, 1 of 1)

- [Gaussian Linear Functional Manifold Method for Massive Point Cloud Data](https://mlsanity.com/paper/2609.05744/) (2026)

## Abstract (arXiv)

We propose and show the efficacy of a new method to address generic inverse problems. Inverse modeling is the task whereby one seeks to determine the control parameters of a natural system that produce a given set of observed measurements. Recent work has shown impressive results using deep learning, but we note that there is a trade-off between model performance and computational time. For some applications, the computational time at inference for the best performing inverse modeling method may be overly prohibitive to its use. We present a new method that leverages multiple manifolds as a mixture of backward (e.g., inverse) models in a forward-backward model architecture. These multiple backwards models all share a common forward model, and their training is mitigated by generating training examples from the forward model. The proposed method thus has two innovations: 1) the multiple Manifold Mixture Network (MMN) architecture, and 2) the training procedure involving augmenting backward model training data using the forward model. We demonstrate the advantages of our method by comparing to several baselines on four benchmark inverse problems, and we furthermore provide analysis to motivate its design.