# Geodesic Semantic Search: Cartographic Navigation of Citation Graphs with Learned Local Riemannian Maps

arXiv: https://arxiv.org/abs/2602.23665 · HTML: https://mlsanity.com/paper/2602.23665/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 29 references that are in the map.
- First posted on arXiv 27 Feb 2026.

## Builds on (most cited first, 21 of 21)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Dense Passage Retrieval for Open-Domain Question Answering](https://mlsanity.com/paper/2004.04906/) (2020)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Unsupervised Dense Information Retrieval with Contrastive Learning](https://mlsanity.com/paper/2112.09118/) (2021)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Graph Convolutional Neural Networks for Web-Scale Recommender Systems](https://mlsanity.com/paper/1806.01973/) (2018)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [C-Pack: Packed Resources For General Chinese Embeddings](https://mlsanity.com/paper/2309.07597/) (2023)
- [SPECTER: Document-level Representation Learning using Citation-informed Transformers](https://mlsanity.com/paper/2004.07180/) (2020)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [Constant Curvature Graph Convolutional Networks](https://mlsanity.com/paper/1911.05076/) (2019)

## Abstract (arXiv)

We present Geodesic Semantic Search (GSS), a retrieval system that learns node-specific Riemannian metrics on citation graphs to enable geometry-aware semantic search. Unlike standard embedding-based retrieval that relies on fixed Euclidean distances, gss learns a low-rank metric tensor mLi ∈ Rd × r at each node, inducing a local positive semi-definite metric mGi = mLi mLi^top + eps mI. This parameterization guarantees valid metrics while keeping the model tractable. Retrieval proceeds via multi-source Dijkstra on the learned geodesic distances, followed by Maximal Marginal Relevance reranking and path coherence filtering. On citation prediction benchmarks with 169K arXiv papers, GSS achieves 23% relative improvement in Recall@20 over SPECTER+FAISS baselines. We provide a Bridge Recovery Guarantee characterizing when geodesic retrieval qualitatively outperforms direct similarity, a margin separation result connecting training loss to retrieval quality, and characterize the expressiveness of low-rank metric parameterization. Our hierarchical coarse-to-fine search with k-means pooling reduces computational cost by 4× while maintaining 97% retrieval quality.