# Guided Manifold Alignment with Geometry-Regularized Twin Autoencoders

arXiv: https://arxiv.org/abs/2509.22913 · HTML: https://mlsanity.com/paper/2509.22913/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 51 references that are in the map.
- First posted on arXiv 26 Sep 2025.

## Builds on (most cited first, 13 of 13)

- [A Closer Look at Memorization in Deep Networks](https://mlsanity.com/paper/1706.05394/) (2017)
- [Parametric UMAP embeddings for representation and semi-supervised learning](https://mlsanity.com/paper/2009.12981/) (2020)
- [Extendable and invertible manifold learning with geometry regularized autoencoders](https://mlsanity.com/paper/2007.07142/) (2020)
- [MAGAN: Aligning Biological Manifolds](https://mlsanity.com/paper/1803.00385/) (2018)
- [Diffusion Transport Alignment](https://mlsanity.com/paper/2206.07305/) (2022)
- [Manifold Matching using Shortest-Path Distance and Joint Neighborhood Selection](https://mlsanity.com/paper/1412.4098/) (2014)
- [Manifold Alignment with Label Information](https://mlsanity.com/paper/2210.12774/) (2022)
- [Graph Integration for Diffusion-Based Manifold Alignment](https://mlsanity.com/paper/2410.22978/) (2024)
- [PCA-Based Out-of-Sample Extension for Dimensionality Reduction](https://mlsanity.com/paper/1511.00831/) (2015)
- [Supervised Manifold Learning via Random Forest Geometry-Preserving Proximities](https://mlsanity.com/paper/2307.01077/) (2023)
- [Forest Proximities for Time Series](https://mlsanity.com/paper/2410.03098/) (2024)
- [Random Forest-Supervised Manifold Alignment](https://mlsanity.com/paper/2411.15179/) (2024)
- [Compressed Diffusion](https://mlsanity.com/paper/1902.00033/) (2019)

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

- [Universal Latent Homeomorphic Manifolds: A Framework for Cross-Domain Representation Unification](https://mlsanity.com/paper/2601.09025/) (2026)

## Abstract (arXiv)

Manifold alignment (MA) involves a set of techniques for learning shared representations across domains, yet many traditional MA methods are incapable of performing out-of-sample extension, limiting their real-world applicability. We propose a guided representation learning framework leveraging a geometry-regularized twin autoencoder (AE) architecture to enhance MA while enabling generalization to unseen data. Our method enforces structured cross-modal mappings to maintain geometric fidelity in learned embeddings. By incorporating a pre-trained alignment model and a multitask learning formulation, we improve cross-domain generalization and representation robustness while maintaining alignment fidelity. We evaluate our approach using several MA methods, showing improvements in embedding consistency, information preservation, and cross-domain transfer. Additionally, we apply our framework to Alzheimer's disease diagnosis, demonstrating its ability to integrate multi-modal patient data and enhance predictive accuracy in cases limited to a single domain by leveraging insights from the multi-modal problem.