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Geometric Embedding Alignment via Curvature Matching in Transfer Learning

arXiv 2506.13015 ↗First posted 16 Jun 2025cs.LG cs.AIcited by 0

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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.

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References · 20

  1. 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,089
  2. 2013Spectral Networks and Locally Connected Networks on Graphscited by 1,102
  3. 2016Geometric deep learning: going beyond Euclidean datacited by 1,048
  4. 2015Convolutional Networks on Graphs for Learning Molecular Fingerprintscited by 754
  5. 2019Analyzing Learned Molecular Representations for Property Predictioncited by 375
  6. 2023Understanding the Latent Space of Diffusion Models through the Lens of Riemannian Geometrycited by 125
  7. 2018Learning Multimodal Graph-to-Graph Translation for Molecular Optimizationcited by 88
  8. 2021On Representation Knowledge Distillation for Graph Neural Networkscited by 38
  9. 2018Geodesic Clustering in Deep Generative Modelscited by 14
  10. 2024Geometry-Aware Generative Autoencoders for Warped Riemannian Metric Learning and Generative Modeling on Data Manifoldscited by 13
  11. 2018Adversarial Autoencoders with Constant-Curvature Latent Manifoldscited by 12
  12. 2023Efficient Equivariant Transfer Learning from Pretrained Modelscited by 11
8 more
  1. 2024Counterfactual Explanations via Riemannian Latent Space Traversalcited by 9
  2. 2023Geometrically Aligned Transfer Encoder for Inductive Transfer in Regression Taskscited by 6
  3. 2022Grouping-matrix based Graph Pooling with Adaptive Number of Clusterscited by 5
  4. 2022Transfer Learning with Kernel Methodscited by 5
  5. 2023Transfer learning for atomistic simulations using GNNs and kernel mean embeddingscited by 4
  6. 2024Multitask Extension of Geometrically Aligned Transfer Encodercited by 3
  7. 2024Task Addition in Multi-Task Learning by Geometrical Alignmentcited by 2
  8. 2024Scalable Multi-Task Transfer Learning for Molecular Property Predictioncited by 2

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