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arxiv: 2604.16220 · v1 · submitted 2026-04-17 · 💻 cs.LG

OT on the Map: Quantifying Domain Shifts in Geographic Space

Haoran Zhang , Livia Betti , Konstantin Klemmer , Esther Rolf , David Alvarez-Melis This is my paper

Pith reviewed 2026-05-10 08:25 UTC · model grok-4.3

classification 💻 cs.LG
keywords datageographicdistancesgeospotmodeldomaindomainsembeddings
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The pith

GeoSpOT applies optimal transport to longitude-latitude data to quantify geospatial domain shifts and predict cross-region model transfer performance.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Machine learning models for maps or satellite images often fail when moved to new places because the data looks different across regions. The authors create GeoSpOT, which treats locations as points and uses optimal transport to calculate a distance between two regions' distributions. They test this and find the distance correlates with how much a model's accuracy drops when applied elsewhere. They also show that simple models using only coordinates can create useful summaries of places, nearly as good as complex models that see actual images or text.

Core claim

In our experiments, GeoSpOT distances emerge as effective predictors of cross-domain transfer difficulty. We further demonstrate that embeddings from pretrained location encoders provide information comparable to image/text embeddings, despite relying solely on longitude-latitude pairs as input.

Load-bearing premise

That the optimal transport distance computed from geographic coordinates (or location embeddings) captures the aspects of domain shift that actually drive model performance degradation, rather than other unmeasured factors like task-specific semantics or data collection biases.

Figures

Figures reproduced from arXiv: 2604.16220 by David Alvarez-Melis, Esther Rolf, Haoran Zhang, Konstantin Klemmer, Livia Betti.

Figure 1
Figure 1. Figure 1: Overview of GEOSPOT domain distances: (Left) Pointwise cross-domain computation according to feature (image) embedding distance, raw geographic distance, or location embedding distance, highlighting the difference between the approaches. (Right) Distribution-level domain distance between the United States and Brazil. Red arrows represent transported mass under the coupling resulting from solving the optima… view at source ↗
Figure 2
Figure 2. Figure 2: GEOSPOT distances correlate with transfer performance (i.e., performance difference) between train and test domains, measured in a zero-shot transfer setting. GEOSPOT distances are computed with a single modality (λ = 1 for ResNet50/BERT, and λ = 0 for the location embeddings). Results are consistent across different embedding spaces (columns) and different datasets (rows). In the scatterplots, each point … view at source ↗
Figure 3
Figure 3. Figure 3: GEOSPOT distances can guide design of training datasets that transfer well to a given target domain. We show zero-shot performance in the target domain, with models pretrained on subsets of size N = 2, 000, sampling train locations most similar to the target domain based on different GEOSPOT distances. Results are shown for the Geo-YFCC-Image dataset. number of source domains), and (2) random subset traini… view at source ↗
Figure 4
Figure 4. Figure 4: Complementary—not nearest—domains form opti￾mal pools that jointly minimize the combined GEOSPOT dis￾tance. Source domains selected by Algorithm 1 using GeoCLIP￾based GEOSPOT distances for target domain Brazil in Geo-YFCC￾Image dataset. Points represent the combined GEOSPOT distances if that country were to be added to the source domains chosen at previous K values. Values below each selected domain show t… view at source ↗
Figure 5
Figure 5. Figure 5: Visualizing GEOSPOT distances can identify rele￾vant domains for data-sourcing or deployment. Applicability maps for the United States (black, dotted) for different types of GEOSPOT distances on the Geo-YFCC Dataset. Color scales are normalized within each panel. 8. Discussion In this work, we introduced GeoSpatial Optimal Transport (GEOSPOT), a geographically aware distance measure that combines feature a… view at source ↗
Figure 6
Figure 6. Figure 6: Correlation between GEOSPOT distances and zero-shot transfer performance with ViT-Small models on Geo-YFCC￾Image and FMoW-Wilds. (a) Geo-YFCC-Image (b) Geo-YFCC-Text (c) FMoW (d) GeoDE [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Rank Correlation (|ρ|) across datasets as a function of the weighting parameter λ. Each panel shows how |ρ| changes as the image/text and location-based information are combined, weighted by λ. 5, 000 and 10, 000 in [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Constrained dataset selection for Geo-YFCC-Image: Zero-shot performance on the target domain with models pretrained on subsets selected via different GEOSPOT distances. tances frequently outperforms other dataset selection meth￾ods, although for the United States at K = 2, GEOSPOT￾GeoCLIP and GEOSPOT-SatCLIP achieve higher accu￾racy. C.4. Applicability Maps As mentioned in Section B.1, the Geo-YFCC-Image a… view at source ↗
Figure 9
Figure 9. Figure 9: Constrained dataset selection for Geo-YFCC-Text: Zero-shot performance on the target domain with models pretrained on subsets selected via different GEOSPOT distances. 16 [PITH_FULL_IMAGE:figures/full_fig_p016_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Applicability maps for the United States (left) and Brazil (right). 17 [PITH_FULL_IMAGE:figures/full_fig_p017_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Applicability maps for China (left) and France (right). 18 [PITH_FULL_IMAGE:figures/full_fig_p018_11.png] view at source ↗
read the original abstract

In computer vision and machine learning for geographic data, out-of-domain generalization is a pervasive challenge, arising from uneven global data coverage and distribution shifts across geographic regions. Though models are frequently trained in one region and deployed in another, there is no principled method for determining when this cross-region adaptation will be successful. A well-defined notion of distance between distributions can effectively quantify how different a new target domain is compared to the domains used for model training, which in turn could support model training and deployment decisions. In this paper, we propose a strategy for computing distances between geospatial domains that leverages geographic information with Optimal Transport methods (GeoSpOT). In our experiments, GeoSpOT distances emerge as effective predictors of cross-domain transfer difficulty. We further demonstrate that embeddings from pretrained location encoders provide information comparable to image/text embeddings, despite relying solely on longitude-latitude pairs as input. This allows users to get an approximation of out-of-domain performance for geospatial models, even when the exact downstream task is unknown, or no task-specific data is available. Building on these findings, we show that GeoSpOT distances can preemptively guide data selection and enable predictive tools to analyze regions where a model is likely to underperform.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

Review performed on abstract only; no explicit free parameters, axioms, or invented entities are stated in the provided text. The method implicitly relies on standard optimal transport assumptions and the premise that geographic coordinates suffice to represent domain distributions.

axioms (1)
  • standard math Optimal transport defines a meaningful distance between probability distributions over geographic space
    Core of the proposed GeoSpOT distance computation.
invented entities (1)
  • GeoSpOT no independent evidence
    purpose: Strategy for computing distances between geospatial domains using optimal transport and geographic information
    New named method introduced in the paper.

pith-pipeline@v0.9.0 · 5521 in / 1234 out tokens · 42748 ms · 2026-05-10T08:25:34.776484+00:00 · methodology

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Works this paper leans on

4 extracted references · 4 canonical work pages

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