# DIVIDE: A Framework for Learning from Independent Multi-Mechanism Data Using Deep Encoders and Gaussian Processes

arXiv: https://arxiv.org/abs/2511.12745 · HTML: https://mlsanity.com/paper/2511.12745/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 40 references that are in the map.
- First posted on arXiv 16 Nov 2025.

## Builds on (most cited first, 15 of 15)

- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets](https://mlsanity.com/paper/1606.03657/) (2016)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [Multimodal Generative Models for Scalable Weakly-Supervised Learning](https://mlsanity.com/paper/1802.05335/) (2018)
- [Multi-Level Variational Autoencoder: Learning Disentangled Representations from Grouped Observations](https://mlsanity.com/paper/1705.08841/) (2017)
- [Weakly Supervised Disentanglement with Guarantees](https://mlsanity.com/paper/1910.09772/) (2019)
- [Gaussian Process Prior Variational Autoencoders](https://mlsanity.com/paper/1810.11738/) (2018)
- [Bayesian Active Learning for Scanning Probe Microscopy: from Gaussian Processes to Hypothesis Learning](https://mlsanity.com/paper/2205.15458/) (2022)
- [Deep Kernel Methods Learn Better: From Cards to Process Optimization](https://mlsanity.com/paper/2303.14554/) (2023)
- [Active learning in open experimental environments: selecting the right information channel(s) based on predictability in deep kernel learning](https://mlsanity.com/paper/2203.10181/) (2022)
- [Building Workflows for Interactive Human in the Loop Automated Experiment (hAE) in STEM-EELS](https://mlsanity.com/paper/2404.07381/) (2024)
- [Deep Gaussian Processes with Decoupled Inducing Inputs](https://mlsanity.com/paper/1801.02939/) (2018)
- [Integrating Predictive and Generative Capabilities by Latent Space Design via the DKL-VAE Model](https://mlsanity.com/paper/2503.02978/) (2025)

## Abstract (arXiv)

Scientific datasets often arise from multiple independent mechanisms such as spatial, categorical or structural effects, whose combined influence obscures their individual contributions. We introduce DIVIDE, a framework that disentangles these influences by integrating mechanism-specific deep encoders with a structured Gaussian Process in a joint latent space. Disentanglement here refers to separating independently acting generative factors. The encoders isolate distinct mechanisms while the Gaussian Process captures their combined effect with calibrated uncertainty. The architecture supports structured priors, enabling interpretable and mechanism-aware prediction as well as efficient active learning. DIVIDE is demonstrated on synthetic datasets combining categorical image patches with nonlinear spatial fields, on FerroSIM spin lattice simulations of ferroelectric patterns, and on experimental PFM hysteresis loops from PbTiO3 films. Across benchmarks, DIVIDE separates mechanisms, reproduces additive and scaled interactions, and remains robust under noise. The framework extends naturally to multifunctional datasets where mechanical, electromagnetic or optical responses coexist.