# Forest-Guided Semantic Transport for Label-Supervised Manifold Alignment

arXiv: https://arxiv.org/abs/2602.00974 · HTML: https://mlsanity.com/paper/2602.00974/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 81 references that are in the map.
- First posted on arXiv 1 Feb 2026.

## Builds on (most cited first, 20 of 20)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Unpaired Image-to-Image Translation using Cycle-Consistent Adversarial Networks](https://mlsanity.com/paper/1703.10593/) (2017)
- [Unsupervised Alignment of Embeddings with Wasserstein Procrustes](https://mlsanity.com/paper/1805.11222/) (2018)
- [Low-Rank Sinkhorn Factorization](https://mlsanity.com/paper/2103.04737/) (2021)
- [Understanding Random Forests: From Theory to Practice](https://mlsanity.com/paper/1407.7502/) (2014)
- [Geometry- and Accuracy-Preserving Random Forest Proximities](https://mlsanity.com/paper/2201.12682/) (2022)
- [MAGAN: Aligning Biological Manifolds](https://mlsanity.com/paper/1803.00385/) (2018)
- [Kernel Manifold Alignment](https://mlsanity.com/paper/1504.02338/) (2015)
- [Geometry-Based Data Generation](https://mlsanity.com/paper/1802.04927/) (2018)
- [Hierarchical Refinement: Optimal Transport to Infinity and Beyond](https://mlsanity.com/paper/2503.03025/) (2025)
- [Multidimensional Scaling: Approximation and Complexity](https://mlsanity.com/paper/2109.11505/) (2021)
- [Diffusion Transport Alignment](https://mlsanity.com/paper/2206.07305/) (2022)
- [Unsupervised Manifold Alignment with Joint Multidimensional Scaling](https://mlsanity.com/paper/2207.02968/) (2022)
- [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)
- [Random Forest Autoencoders for Guided Representation Learning](https://mlsanity.com/paper/2502.13257/) (2025)
- [Random Forest-Supervised Manifold Alignment](https://mlsanity.com/paper/2411.15179/) (2024)
- [Revisiting Forest Proximities via Sparse Leaf-Incidence Kernels](https://mlsanity.com/paper/2601.02735/) (2026)

## Abstract (arXiv)

Label-supervised manifold alignment bridges the gap between unsupervised and correspondence-based paradigms by leveraging shared label information to align multimodal datasets. However, existing methods either rely on label-independent intra-domain geometry or incorporate supervision primarily through the alignment objective, rather than directly constructing task-aware intra-domain affinities. To address this limitation, we introduce FoSTA (Forest-guided Semantic Transport Alignment), which learns supervised forest geometries independently within each domain and uses their shared class-semantic structure to infer cross-domain correspondences without predefined anchors. FoSTA extends RF-GAP affinities to partially labeled data and aligns the resulting semantic representations through scalable hierarchical transport. Extensive comparisons with established baselines demonstrate strong correspondence recovery and semantic structure preservation on synthetic and real-world benchmarks, including multimodal data integration and single-cell batch correction.