Geometric Embedding Alignment via Curvature Matching in Transfer Learning

• URL: http://arxiv.org/abs/2506.13015v1
• Date: Mon, 16 Jun 2025 00:54:22 GMT
• Title: Geometric Embedding Alignment via Curvature Matching in Transfer Learning
• Authors: Sung Moon Ko, Jaewan Lee, Sumin Lee, Soorin Yim, Kyunghoon Bae, Sehui Han,
• Abstract summary: We introduce a novel approach to integrate multiple models into a unified transfer learning framework.<n>By aligning the Ricci curvature of latent space of individual models, we construct an interrelated architecture.<n>This framework enables the effective aggregation of knowledge from diverse sources, thereby improving performance on target tasks.
• Score: 4.739852004969771
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: 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.

Related papers

• The Geometry of Machine Learning Models [0.0]
  This paper presents a framework for analyzing machine learning models through the geometry of their induced partitions.<n>For neural networks, we introduce a differential forms approach that tracks geometric structure through layers via pullback operations.<n>While focused on mathematical foundations, this geometric perspective offers new approaches to model interpretation, regularization, and diagnostic tools for understanding learning dynamics.
  arXiv  Detail & Related papers  (2025-08-04T05:45:52Z)
• Geometric Operator Learning with Optimal Transport [77.16909146519227]
  We propose integrating optimal transport (OT) into operator learning for partial differential equations (PDEs) on complex geometries.<n>For 3D simulations focused on surfaces, our OT-based neural operator embeds the surface geometry into a 2D parameterized latent space.<n> Experiments with Reynolds-averaged Navier-Stokes equations (RANS) on the ShapeNet-Car and DrivAerNet-Car datasets show that our method achieves better accuracy and also reduces computational expenses.
  arXiv  Detail & Related papers  (2025-07-26T21:28:25Z)
• Connecting Neural Models Latent Geometries with Relative Geodesic Representations [21.71782603770616]
  We show that when a latent structure is shared between distinct latent spaces, relative distances between representations can be preserved, up to distortions.<n>We assume that distinct neural models parametrize approximately the same underlying manifold, and introduce a representation based on the pullback metric.<n>We validate our method on model stitching and retrieval tasks, covering autoencoders and vision foundation discriminative models.
  arXiv  Detail & Related papers  (2025-06-02T12:34:55Z)
• PRISM: Probabilistic Representation for Integrated Shape Modeling and Generation [79.46526296655776]
  PRISM is a novel approach for 3D shape generation that integrates categorical diffusion models with Statistical Shape Models (SSM) and Gaussian Mixture Models (GMM)<n>Our method employs compositional SSMs to capture part-level geometric variations and uses GMM to represent part semantics in a continuous space.<n>Our approach significantly outperforms previous methods in both quality and controllability of part-level operations.
  arXiv  Detail & Related papers  (2025-04-06T11:48:08Z)
• Geometry Distributions [51.4061133324376]
  We propose a novel geometric data representation that models geometry as distributions. Our approach uses diffusion models with a novel network architecture to learn surface point distributions. We evaluate our representation qualitatively and quantitatively across various object types, demonstrating its effectiveness in achieving high geometric fidelity.
  arXiv  Detail & Related papers  (2024-11-25T04:06:48Z)
• (Deep) Generative Geodesics [57.635187092922976]
  We introduce a newian metric to assess the similarity between any two data points. Our metric leads to the conceptual definition of generative distances and generative geodesics. Their approximations are proven to converge to their true values under mild conditions.
  arXiv  Detail & Related papers  (2024-07-15T21:14:02Z)
• Automatic Parameterization for Aerodynamic Shape Optimization via Deep Geometric Learning [60.69217130006758]
  We propose two deep learning models that fully automate shape parameterization for aerodynamic shape optimization. Both models are optimized to parameterize via deep geometric learning to embed human prior knowledge into learned geometric patterns. We perform shape optimization experiments on 2D airfoils and discuss the applicable scenarios for the two models.
  arXiv  Detail & Related papers  (2023-05-03T13:45:40Z)
• GNPM: Geometric-Aware Neural Parametric Models [6.620111952225635]
  We propose a learned parametric model that takes into account the local structure of data to learn disentangled shape and pose latent spaces of 4D dynamics. We evaluate GNPMs on various datasets of humans, and show that it achieves comparable performance to state-of-the-art methods that require dense correspondences during training.
  arXiv  Detail & Related papers  (2022-09-21T19:23:31Z)
• The Geometry of Self-supervised Learning Models and its Impact on Transfer Learning [62.601681746034956]
  Self-supervised learning (SSL) has emerged as a desirable paradigm in computer vision. We propose a data-driven geometric strategy to analyze different SSL models using local neighborhoods in the feature space induced by each.
  arXiv  Detail & Related papers  (2022-09-18T18:15:38Z)
• A Class of Geometric Structures in Transfer Learning: Minimax Bounds and Optimality [5.2172436904905535]
  We exploit the geometric structure of the source and target domains for transfer learning. Our proposed estimator outperforms state-of-the-art transfer learning methods in both moderate- and high-dimensional settings.
  arXiv  Detail & Related papers  (2022-02-23T18:47:53Z)
• Hermitian Symmetric Spaces for Graph Embeddings [0.0]
  We learn continuous representations of graphs in spaces of symmetric matrices over C. These spaces offer a rich geometry that simultaneously admits hyperbolic and Euclidean subspaces. The proposed models are able to automatically adapt to very dissimilar arrangements without any apriori estimates of graph features.
  arXiv  Detail & Related papers  (2021-05-11T18:14:52Z)
• GELATO: Geometrically Enriched Latent Model for Offline Reinforcement Learning [54.291331971813364]
  offline reinforcement learning approaches can be divided into proximal and uncertainty-aware methods. In this work, we demonstrate the benefit of combining the two in a latent variational model. Our proposed metrics measure both the quality of out of distribution samples as well as the discrepancy of examples in the data.
  arXiv  Detail & Related papers  (2021-02-22T19:42:40Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.