Geo2Vec: Geospatial Vector Embeddings

• Geo2Vec is a family of methods that encode geographic entities into dense vectors, preserving spatial semantics, distances, and topology.
• It includes approaches like coordinate encoders (e.g., Sphere2Vec) and patch-based models that leverage weak supervision from geographic context.
• Models employ techniques such as adaptive sampling and signed distance functions to boost performance in distance estimation and topological classification.

Searching arXiv for the cited Geo2Vec-related papers to ground the article. Geo2Vec denotes a family of geospatial representation-learning approaches that map a geographic entity to a dense vector, typically through a function $f:\text{GeoEntity}\rightarrow\mathbb{R}^d$. In the literature, the term is used both generically—by analogy with Word2Vec for language—and specifically for the method "Geo2Vec: Shape- and Distance-Aware Neural Representation of Geospatial Entities." Across these usages, the common objective is to encode locations, image patches, pixels, vector geometries, or spatially grounded entities so that semantics, distance, topology, and context become directly usable in downstream GeoAI systems (Jean et al., 2018, Chu et al., 26 Aug 2025).

1. Definition, scope, and historical framing

Geo2Vec is not a single architecture. In one formulation, it is the general idea of turning “geo” into vectors: locations, coordinates, image patches, pixels, time series, or regions are embedded into $\mathbb{R}^d$ so that spatial information can be processed like text in Word2Vec or images in CLIP (Fang et al., 19 Jan 2026). In another formulation, it is a region-level or object-level encoder with a specific inductive bias, such as spatial context, spherical geometry, signed distance fields, or geospatial knowledge-graph structure.

A foundational formulation appears in "Tile2Vec" (Jean et al., 2018), which extends the distributional hypothesis from language to space: image tiles that are geographic neighbors should have similar semantics and therefore similar representations, while distant tiles should be dissimilar. The resulting embedding function $f_\theta:\mathcal{X}\rightarrow\mathbb{R}^d$ is learned with triplets $(t_a,t_n,t_d)$ consisting of anchor, neighbor, and distant tiles. This established a canonical Geo2Vec pattern: use weak supervision from geography itself to structure latent space.

An urban and symbolic variant appears in "Hex2vec" (Woźniak et al., 2021). There, H3 resolution-9 hexagons are the atomic units, OSM tags are aggregated into count vectors, and Skip-gram with negative sampling is applied at the region level: neighboring hexagons define context, distant hexagons define negatives. This reinterprets Tobler’s first law of geography as a context-learning signal and shows that Geo2Vec can be built from vector semantics rather than imagery alone.

2. Coordinate and location encoders

A major branch of Geo2Vec treats the input as a coordinate pair or coordinate-time tuple. In this setting, the central question is how to encode the Earth’s geometry without introducing distortions from planar projections or arbitrary bases.

"Sphere2Vec" (Mai et al., 2023) directly encodes points on a spherical surface and proves that its base encoding preserves spherical surface distance. Its single-scale core is

$$PE_{\text{sphereC},1}(x)=\left[\sin\phi,\;\cos\phi\cos\lambda,\;\cos\phi\sin\lambda\right],$$

so the inner product between two encoded points is a monotone function of great-circle distance. This was developed precisely because 2D Euclidean encoders and 3D Euclidean positional encoders fail to model global GPS data without projection distortion or spherical-to-Euclidean approximation error.

"Tessellating The Earth" introduces a different coordinate-to-vector mechanism (Cher et al., 25 Jun 2026). It maps latitude and longitude to the unit sphere,

$$\mathbf{x}(\phi,\lambda)= \begin{bmatrix} \cos\phi\cos\lambda\ \cos\phi\sin\lambda\ \sin\phi \end{bmatrix}\in S^2,$$

then applies learnable Spherical Voronoi partitions with $K=4096$ sites and $R=64$ global semantic tokens. Each site carries its own embedding, and the encoder produces a 512-dimensional final representation by combining local Voronoi mixtures with globally shared semantic tokens distilled from satellite imagery. The explicit goal is to allocate representational capacity non-uniformly, concentrating it where geography is semantically dense rather than uniformly over the globe.

"Geotokens and Geotransformers" adapts Rotary Position Embedding to spherical coordinates (Unlu, 2024). Here, a geotoken is a semantic feature vector linked to latitude and longitude, and transformer queries and keys are rotated by a block-diagonal spherical rotation matrix rather than by sequence index. The consequence is that transformer attention becomes sensitive to relative position on the Earth rather than to arbitrary token order.

A training-free alternative is "Geolocation Representation from LLMs are Generic Enhancers for Spatio-Temporal Learning" (He et al., 2024). LLMGeovec constructs an OSM-based prompt for each coordinate, feeds it into a LLM, and averages final-layer hidden states to obtain a geolocation embedding. The method is explicitly presented as a modern, LLM-based Geo2Vec: a coordinate-to-vector encoder that can be concatenated into geographic prediction, long-term time series forecasting, and graph-based spatio-temporal forecasting.

3. Patch-, pixel-, and cell-based Earth embeddings

A second major branch of Geo2Vec encodes Earth observation data rather than coordinates alone. In this branch, the input may be a location, a patch, or a pixel, and the output is a learned representation of the Earth’s surface.

"Earth Embeddings as Products: Taxonomy, Ecosystem, and Standardized Access" formalizes this landscape with a three-layer taxonomy—Data, Tools, and Value (Fang et al., 19 Jan 2026). At the Data layer, it distinguishes location embeddings $f_{\text{loc}}:(x,y,t)\mapsto\mathbb{R}^d$, patch-level embeddings $f_{\text{patch}}:I\mapsto\mathbb{R}^d$, and pixel-level embeddings $\mathbb{R}^d$0. The paper’s central operational distinction is between Geospatial Foundation Models, which generate embeddings dynamically, and embedding products, which are pre-computed datasets—“frozen snapshots” of those models.

"Global and Dense Embeddings of Earth: Major TOM Floating in the Latent Space" makes this idea concrete at global scale (Czerkawski et al., 2024). It releases four global and dense embedding datasets derived from Major TOM Core data, with over 169 million embeddings from 3.5M images and 62 TB of raw source imagery. Each $\mathbb{R}^d$1 grid cell is fragmented into overlapping patches and encoded by pretrained models such as SSL4EO, SigLIP, and DINOv2, producing a ready-made Geo2Vec resource for retrieval and downstream modeling.

"Topo2vec" specializes Geo2Vec to digital elevation data (Kavitzky et al., 2021). It treats topography as semi-fractal and learns a 128-dimensional embedding by predicting a DEM tile at scale $\mathbb{R}^d$2 from the same location at scale $\mathbb{R}^d$3. This is a topography-specific Geo2Vec in which cross-scale reconstruction rather than neighborhood similarity supplies the self-supervision signal.

"S2Vec" moves from imagery to built-environment feature tensors on an S2 grid (Choudhury et al., 10 Apr 2025). It partitions the Earth with the S2 Geometry library, rasterizes 116-dimensional feature vectors for level-12 cells into 16×16 images at level 8, and applies masked autoencoding to produce 256-dimensional cell embeddings. This shows that Geo2Vec can be learned not only from pixels but also from spatially structured semantic count data.

4. Shape-aware encoders and the specific method titled Geo2Vec

The paper that explicitly bears the name "Geo2Vec" defines a unified neural representation for points, polylines, polygons, multipolygons, and polygons with holes (Chu et al., 26 Aug 2025). Its central idea is to represent each geo-entity by its signed distance field (SDF) in the original coordinate space rather than by decomposition in Fourier space. For a query point $\mathbb{R}^d$4,

$\mathbb{R}^d$5

where $\mathbb{R}^d$6 outside the spatial extent of $\mathbb{R}^d$7, $\mathbb{R}^d$8 inside, and $\mathbb{R}^d$9 is the shortest Euclidean distance to the boundary.

Geo2Vec then learns a neural approximation

$f_\theta:\mathcal{X}\rightarrow\mathbb{R}^d$0

and optimizes latent codes $f_\theta:\mathcal{X}\rightarrow\mathbb{R}^d$1 jointly with the network. The training objective is

$f_\theta:\mathcal{X}\rightarrow\mathbb{R}^d$2

The method separates location and shape embeddings, uses adaptive sampling around vertices, along edge-perpendicular directions, and over global space, and adds a rotation-invariant positional encoding by augmenting $f_\theta:\mathcal{X}\rightarrow\mathbb{R}^d$3 with $f_\theta:\mathcal{X}\rightarrow\mathbb{R}^d$4. This design is intended to preserve shape, location, topology, and distance simultaneously.

The immediate precursor in this line is "Poly2Vec" (Siampou et al., 2024), which uses continuous 2D Fourier transforms to encode points, polylines, and polygons in a polymorphic way. Poly2Vec preserves topology, direction, and distance, but it relies on decomposition and Fourier transformation. Geo2Vec explicitly targets these limitations by working directly in the original space, using signed distances and adaptive sampling. In the reported evaluations, it yields improvements of up to $f_\theta:\mathcal{X}\rightarrow\mathbb{R}^d$5 over prior methods in distance estimation and consistently improves topological relationship classification and downstream GeoAI tasks (Chu et al., 26 Aug 2025).

5. Cross-view, relational, and multimodal generalizations

Geo2Vec has also been extended beyond isolated locations or shapes into cross-view, graph-structured, and multimodal settings.

"Geo$f_\theta:\mathcal{X}\rightarrow\mathbb{R}^d$6: Geometry-Guided Cross-view Geo-Localization and Image Synthesis" learns a shared 3D-aware latent space for ground panoramas and aerial imagery (Zhang et al., 26 Mar 2026). GeoMap combines VGGT geometry features and ConvNeXt semantic features through cross-attention to produce aligned embeddings $f_\theta:\mathcal{X}\rightarrow\mathbb{R}^d$7. These embeddings support cross-view geo-localization via nearest-neighbor retrieval, and the same latent variables condition GeoFlow, a flow-matching model for bidirectional cross-view image synthesis. In this usage, Geo2Vec is a geometry-aware embedding space jointly usable for matching and generation.

"GeoRDF2Vec" transfers the same idea into RDF knowledge graphs with spatial entities (Boeckling et al., 23 Apr 2025). It first floods geometry from explicitly geographic nodes to reachable non-geographic nodes, then biases RDF2Vec walks with spatial weights derived from geodesic distance and an exponential kernel. The resulting embeddings are location-aware not only for cities, buildings, and landmarks, but also for entities that inherit geography through graph relations.

"VLM2GeoVec" pushes the concept toward universal multimodal remote-sensing embeddings (Aimar et al., 12 Dec 2025). It is a single-encoder vision-LLM that interleaves images, text, bounding boxes, and geographic coordinates into one token stream and trains a shared embedding space contrastively. On RSMEB it reports $f_\theta:\mathcal{X}\rightarrow\mathbb{R}^d$8 P@1 on region-caption retrieval, $f_\theta:\mathcal{X}\rightarrow\mathbb{R}^d$9 P@1 on referring-expression retrieval, and $(t_a,t_n,t_d)$0 P@1 on semantic geo-localization retrieval. The paper also states a key limitation: coordinates are encoded as textual tuples, which captures coarse geographic context but lacks continuous spatial embeddings for fine-grained topography or proximity relations.

6. Applications, ecosystem, limitations, and recurring misconceptions

The application space of Geo2Vec is broad but not uniform. Reported uses include land use / land cover classification, cropland mapping, poverty mapping, environmental monitoring, similarity search, retrieval, biodiversity priors, geographic prediction, long-term time series forecasting, and graph-based spatio-temporal forecasting (Fang et al., 19 Jan 2026, Cher et al., 25 Jun 2026, He et al., 2024). In practice, Geo2Vec often functions as a feature generator: a downstream model receives vectors instead of raw coordinates, raw imagery, or raw geometries.

A recurring misconception is to treat Geo2Vec as one model. The literature instead uses the term for a family of representations: coordinate encoders, tile encoders, pixel encoders, region encoders, geometry encoders, knowledge-graph embeddings, and multimodal retrieval systems all fall under the label in different subfields. Another recurrent confusion is to equate a precomputed embedding product with the underlying Geospatial Foundation Model. The Earth-embeddings literature explicitly warns against this: an embedding product is a frozen dataset bound to a specific model, input stack, coverage, and temporal snapshot, not the full generalization behavior of the model that produced it (Fang et al., 19 Jan 2026).

The ecosystem is also fragmented. The Earth-embedding survey identifies incompatible distribution formats, grid resolutions, tiling schemes, coordinate reference systems, metadata standards, hosting platforms, and reproducibility practices as major interoperability barriers (Fang et al., 19 Jan 2026). Patch embeddings are often distributed in vector formats such as GeoParquet; pixel embeddings are often in GeoTIFF, .npy, or .pt; CRS and geotransform inconsistencies complicate alignment; and missing provenance obscures what an embedding actually represents. To address this, the paper extends TorchGeo with standardized dataset loaders and spatiotemporal dataset algebra so that embedding products can be treated as first-class geospatial datasets (Fang et al., 19 Jan 2026).

The limitations are correspondingly diverse. Coordinate-only encoders may fail on phenomena not encoded in location alone; imagery-derived encoders inherit sensor and training-data biases; LLM-derived geolocation vectors depend on OSM coverage and prompt quality; and multimodal encoders with textual coordinate representations may not capture continuous geodesic structure (He et al., 2024, Aimar et al., 12 Dec 2025). TTE also notes that its Earth model is static and does not encode time-varying processes (Cher et al., 25 Jun 2026). A plausible implication is that future Geo2Vec systems will continue to move toward richer provenance, cloud-native formats, stronger benchmarks, explicit uncertainty, and tighter integration of space, time, geometry, and multimodality.