# Geometric Embedding Alignment via Curvature Matching in Transfer Learning

arXiv: https://arxiv.org/abs/2506.13015 · HTML: https://mlsanity.com/paper/2506.13015/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 44 references that are in the map.
- First posted on arXiv 16 Jun 2025.

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

- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [Analyzing Learned Molecular Representations for Property Prediction](https://mlsanity.com/paper/1904.01561/) (2019)
- [Understanding the Latent Space of Diffusion Models through the Lens of Riemannian Geometry](https://mlsanity.com/paper/2307.12868/) (2023)
- [Learning Multimodal Graph-to-Graph Translation for Molecular Optimization](https://mlsanity.com/paper/1812.01070/) (2018)
- [On Representation Knowledge Distillation for Graph Neural Networks](https://mlsanity.com/paper/2111.04964/) (2021)
- [Geodesic Clustering in Deep Generative Models](https://mlsanity.com/paper/1809.04747/) (2018)
- [Geometry-Aware Generative Autoencoders for Warped Riemannian Metric Learning and Generative Modeling on Data Manifolds](https://mlsanity.com/paper/2410.12779/) (2024)
- [Adversarial Autoencoders with Constant-Curvature Latent Manifolds](https://mlsanity.com/paper/1812.04314/) (2018)
- [Efficient Equivariant Transfer Learning from Pretrained Models](https://mlsanity.com/paper/2305.09900/) (2023)
- [Counterfactual Explanations via Riemannian Latent Space Traversal](https://mlsanity.com/paper/2411.02259/) (2024)
- [Geometrically Aligned Transfer Encoder for Inductive Transfer in Regression Tasks](https://mlsanity.com/paper/2310.06369/) (2023)
- [Grouping-matrix based Graph Pooling with Adaptive Number of Clusters](https://mlsanity.com/paper/2209.02939/) (2022)
- [Transfer Learning with Kernel Methods](https://mlsanity.com/paper/2211.00227/) (2022)
- [Transfer learning for atomistic simulations using GNNs and kernel mean embeddings](https://mlsanity.com/paper/2306.01589/) (2023)
- [Multitask Extension of Geometrically Aligned Transfer Encoder](https://mlsanity.com/paper/2405.01974/) (2024)
- [Task Addition in Multi-Task Learning by Geometrical Alignment](https://mlsanity.com/paper/2409.16645/) (2024)
- [Scalable Multi-Task Transfer Learning for Molecular Property Prediction](https://mlsanity.com/paper/2410.00432/) (2024)

## Abstract (arXiv)

Geometrical interpretations of deep learning models offer insightful perspectives into their underlying mathematical structures. In this work, we introduce a novel approach that leverages differential geometry, particularly concepts from Riemannian geometry, to integrate multiple models into a unified transfer learning framework. By aligning the Ricci curvature of latent space of individual models, we construct an interrelated architecture, namely Geometric Embedding Alignment via cuRvature matching in transfer learning (GEAR), which ensures comprehensive geometric representation across datapoints. This framework enables the effective aggregation of knowledge from diverse sources, thereby improving performance on target tasks. We evaluate our model on 23 molecular task pairs sourced from various domains and demonstrate significant performance gains over existing benchmark model under both random (14.4%) and scaffold (8.3%) data splits.