# GeoMM: On Geodesic Perspective for Multi-modal Learning

arXiv: https://arxiv.org/abs/2505.11216 · HTML: https://mlsanity.com/paper/2505.11216/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 69 of its 108 references that are in the map.
- First posted on arXiv 16 May 2025.

## Builds on (most cited first, 30 of 69)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [End-to-End Object Detection with Transformers](https://mlsanity.com/paper/2005.12872/) (2020)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [BLIP: Bootstrapping Language-Image Pre-training for Unified Vision-Language Understanding and Generation](https://mlsanity.com/paper/2201.12086/) (2022)
- [Scaling Up Visual and Vision-Language Representation Learning With Noisy Text Supervision](https://mlsanity.com/paper/2102.05918/) (2021)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [Unsupervised Learning of Visual Features by Contrasting Cluster Assignments](https://mlsanity.com/paper/2006.09882/) (2020)
- [Visual Genome: Connecting Language and Vision Using Crowdsourced Dense Image Annotations](https://mlsanity.com/paper/1602.07332/) (2016)
- [VQA: Visual Question Answering](https://mlsanity.com/paper/1505.00468/) (2015)
- [Improved Baselines with Momentum Contrastive Learning](https://mlsanity.com/paper/2003.04297/) (2020)
- [ViLBERT: Pretraining Task-Agnostic Visiolinguistic Representations for Vision-and-Language Tasks](https://mlsanity.com/paper/1908.02265/) (2019)
- [Align before Fuse: Vision and Language Representation Learning with Momentum Distillation](https://mlsanity.com/paper/2107.07651/) (2021)
- [LXMERT: Learning Cross-Modality Encoder Representations from Transformers](https://mlsanity.com/paper/1908.07490/) (2019)
- [Flickr30k Entities: Collecting Region-to-Phrase Correspondences for Richer Image-to-Sentence Models](https://mlsanity.com/paper/1505.04870/) (2015)
- [VisualBERT: A Simple and Performant Baseline for Vision and Language](https://mlsanity.com/paper/1908.03557/) (2019)
- [CoCa: Contrastive Captioners are Image-Text Foundation Models](https://mlsanity.com/paper/2205.01917/) (2022)
- [ViLT: Vision-and-Language Transformer Without Convolution or Region Supervision](https://mlsanity.com/paper/2102.03334/) (2021)
- [Conceptual 12M: Pushing Web-Scale Image-Text Pre-Training To Recognize Long-Tail Visual Concepts](https://mlsanity.com/paper/2102.08981/) (2021)
- [Oscar: Object-Semantics Aligned Pre-training for Vision-Language Tasks](https://mlsanity.com/paper/2004.06165/) (2020)
- [ImageBind: One Embedding Space To Bind Them All](https://mlsanity.com/paper/2305.05665/) (2023)

## Built on by (most cited first, 2 of 2)

- [Multimodal Distribution Matching for Vision-Language Dataset Distillation](https://mlsanity.com/paper/2605.23482/) (2026)
- [TASSO: TAsk-Specific Subspace Optimization for Continual Learning of Vision-Language Models](https://mlsanity.com/paper/2608.21487/) (2026)

## Abstract (arXiv)

Geodesic distance serves as a reliable means of measuring distance in nonlinear spaces, and such nonlinear manifolds are prevalent in the current multimodal learning. In these scenarios, some samples may exhibit high similarity, yet they convey different semantics, making traditional distance metrics inadequate for distinguishing between positive and negative samples. This paper introduces geodesic distance as a novel distance metric in multi-modal learning for the first time, to mine correlations between samples, aiming to address the limitations of common distance metric. Our approach incorporates a comprehensive series of strategies to adapt geodesic distance for the current multimodal learning. Specifically, we construct a graph structure to represent the adjacency relationships among samples by thresholding distances between them and then apply the shortest-path algorithm to obtain geodesic distance within this graph. To facilitate efficient computation, we further propose a hierarchical graph structure through clustering and combined with incremental update strategies for dynamic status updates. Extensive experiments across various downstream tasks validate the effectiveness of our proposed method, demonstrating its capability to capture complex relationships between samples and improve the performance of multimodal learning models.