HierLoc: Hyperbolic Entity Embeddings for Hierarchical Visual Geolocation
Authors: Hari Krishna Gadi
Daniel Matos
Hongyi Luo
Lu Liu
Yongliang Wang
Yanfeng Zhang
Liqiu Meng
Venue: ICLR 2026 Poster (2026)
Keywords: Representation learning
Multimodal learning
Contrastive learning
Manifold learning
Hierarchical modeling
Geospatial AI
Primary area: applications to computer vision, audio, language, and other modalities
TL;DR: HierLoc reformulates geolocation as image-to-entity alignment in hyperbolic space, with geo-weighted contrastive learning and cross-modal attention, enabling compact inference and achieving SOTA on OSV-5M with 19.5% lower error.

Abstract: Visual geolocalization, the task of predicting where an image was taken, remains challenging due to global scale, visual ambiguity, and the inherently hierarchical structure of geography. Existing paradigms rely on either large-scale retrieval, which requires storing a large number of image embeddings, grid-based classifiers that ignore geographic continuity, or generative models that diffuse over space but struggle with fine detail. We introduce an entity-centric formulation of geolocation that replaces image-to-image retrieval with a compact hierarchy of geographic entities embedded in Hyperbolic space. Images are aligned directly to country, region, subregion, and city entities through Geo-Weighted Hyperbolic contrastive learning by directly incorporating haversine distance into the contrastive objective. This hierarchical design enables interpretable predictions and efficient inference with 240k entity embeddings instead of over 5 million image embeddings on the OSV5M benchmark, on which our method establishes a new state-of-the-art performance. Compared to the current methods in the literature, it reduces mean geodesic error by 19.5\%, while improving the fine-grained subregion accuracy by 43\%. These results demonstrate that geometry-aware hierarchical embeddings provide a scalable and conceptually new alternative for global image geolocation.

Published as a conference paper at ICLR 2026
HIERLOC: HYPERBOLIC ENTITY EMBEDDINGS FOR HIERARCHICAL VISUAL GEOLOCATION
Hari Krishna Gadi Daniel Matos', Hongyi Luo Lu Liu', Yongliang Wang', Yanfeng Zhang.". Liqiu Meng² HHuawei Riemann Lab, Hilbert Research Centre "Chair of Cartography, Technical University of Munich
Shari.krishan gadil, daniel matos, hongyi. luliul Juliuu]@huawei.com (wangyongliang775 zhangyanfengJ (harikrishna gadii, hongyi. luo, liqiu. miglummeng)ee Stum..deeuudd
thangyanfeno//euuavii...m (awnnn/ehwwww..c.
ABSTRACT
Visual geolocalization, the task of predicting where an image was taken, remains challenging due to global scale, visual ambiguity, and the inherently hierarchi- cal structure of geography. Existing paradigms rely either large-scale retrieval, which requires storing a large number of image embeddings, grid-based classifiers that ignore geographic continuity, generative models that diffuse space but struggle with fine detail. We introduce an entity- formulation of geoloca- tion that replaces image-to-imaae retrieval with compact hierarchy of geographic entities embedded in Hyperbolic space. Images are aligned directly to country, re- gion, subregion, and city entities through Geo-Wer Weighted Hyperbolic contrastive learning by directly incorporating haversine distance into the contrastive objec- tive. This hierarchical design enables interpretable predictions and efficient infer- ence with 240k entity embeddings instead of over 5 million image embeddings on the OSV5M benchmark, on which our method establishes a new stateoof-the-an performance. Compared to the current methods in the literature, it reduces mean geodesic error by 19.5%, while improving the fine-gre grained subregion accuracy by 43%. These results demonstrate that geometry-aware hierarchical embeddings provide a scalable and conceptually new alternative for global image geolocation.
INTRODUCTION
Visual geolocalization, inferring where an image was taken from its content alone, is fundamental challenge with applications in biodiversity monitoring (Van Horn et al., 202T), cultural heritage preservation (Del et al. (2066), news verification (Tahmasebzadeh et al., 2023), and augmented reality (Mercier et al., 2023). However, many real-world images lack geotags in their metadata Flatoow et al. 2015), making automated solutions increasingly important. The task remains difficult due to its scale and ambiguity (Dufour et al. 2025). The search space spans the entire globe; visual patterns such beaches or skylines recur across continents; language similarities in the street view images span continents; and geographic space itself is structured hierarchically from continents down cities.
Most existing methods follow one of three paradigms: retrieval-based classification, and more re- cently, generative methods. Retrieval-based approaches index millions of image embeddings and return nearest neighbors (Haas et al.] 2023), which capture fine-grained similarity but do not scale gracefully and provide limited interpretabilityy Classification methods (Astruc et al., 2024 Haas et al. 2024) tackle this task by predicting a discrete cell, respecting geography but failing to cap- ture cross-continental visual relationships. Generative models, such as diffusion, can model spatial uncertainty, but underperform retrieval methods at fine scales (Dufour et al. 2025).
We present geolocation architecture that models the world as a hierarchy of entities such as coun- tries, regions, subregions, and cities, and learns embeddings for each entity instead of indexing
"Athhor whom correspondence should be addressed

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individual images. Images are aligned to entity embeddings via a contrastive loss weighted by the scaled haversine distance. Conventional retrieval methods scale linearly, requiring O(N) compar- isons against millions of images; approximate nearest neighbor methods reduce runtime but still incur large memory and indexing overheads. Our approach instead operates on a fixed, compact set of entity emheddings which scale sub-linearly, enabling faster inference through hierarchical traver- sal: predictions are resolved coarsely at higher levels and refined only where needed. This allows for beam search over the hierarchy, allowing efficient exploration of plausible paths. This yields scalable inference, interpretable outputs, and even potential for client-side deployment. By refram- ing geolocation as "image-to-entic" aligmment" rather than "image-to to-image retrieval," the method makes the structure of geography central to the task.
To encode the geographic hierarchy effectively, we represent entities in hyperbolic space. In Fu- clidean space, hierarchical structures become increasingly compressed as depth grows: the number of entities expands roughly exponentially from country - region - subregion - city, but Euclidean distances grow only linearly. This mismatch causes deeper-level entities to crowd together, reduc- ing discriminative power during inference. Hyperbolic geometry, by contrast, naturally provides exponential volume growth and therefore allocates proportionally more space to represent large branching factors in deep hierarchies (Nickel & Kiela [017] Chen et al. 2021). As a result, related entities can remain close, while fine-grained locations can still be well separated, making hyperbolic space a more faithful and expressive emhedding space for geographic hierarchies. This effect can be observed visually in the Figure in the Appendix AA22] To our knowledge, this is the first application of Hyperbolic embeddings to represent hierarchical geographic entities for geolocation explicitly. To couple HYperbolic geometry with geographic structure, we introduce a Geo- Geo-Weighe Weighted Hyper- bolic InfoNCE (GWH-InfoNCE) loss that weights negative logits using the haversine formula. This objective materially improves fine-scale discrimination while preserving global structure.
We evaluate our method on OSV5M (Astruc et al., 2024). comprising 4.8 million training and 200k test images, and on MediaEval' 16 (Larson et al. 2017) with 4.7 million training images. On OSV5M, our approach establishes a new state of the art, yielding consistent gains across all hier- archical levels: country (+8.8%), region (+20.1 1)), subregion (+43.2%), and city (+16.8%), while reducing mean geodesic error by 19.5% relative to the strongest baselines. We further confirm ro- bustness on IM2GPS (Hays & Efros 2008), IM2GPS3K (Vo et al. 2017). and YFCC4K (Vo et al,, 2017). Beyond these benchmarks, our findings highlight that Hyperbolic embedding spaces provide a principled advantage for multimodal representation learning wherever data exhibit inherent hier- archical structure, with geolocation serving particularly suitable testbed. The following are our contributions:
Reduce search complexity by reformulating geolocation as image-to-entity alignment in Hyperbolic space, cutting the search from millions of images 240k entities while im- proving accuracy.
Demonstrate that Hyperbolic geometry captures multi-scale geographic relationships for hierarchical representation.
Introduce Geo- WeigWeeg Hyperbolic InfoNCE (GWH-InfoNCE), which incorporates great-cirele distance to emphasize geographically proximal negatives.
Achieve state-of-the-art results on OSV5M across all levels (country +8.8%, subregion +43.2%), validating the effectiveness of geometry-aware learning.
2 RELATED WORKS
Global visual geolocation. Classical work framed geolocation as image retrieval against large gal- leries, e.g. IM2GPS (Hays Efros 2008), later revisited with stronger deep learning baselines (Vo) et al. 2017). pioneers like PlaNet (Weyand et al. 2016) and CPlaNet (Seo et al. 2018)) used S2 cells to discretize the globe into multi-seale classes. Recent iterations like Where We Are and What We're Looking at |lark et al. (2023) and PIGEON (Haas al. 2024) have refined this via massive- scale classification and semantic fusion. While recent methods emphasize scalability (SC retrieval (Haas et al.) 2023). 5. PIGEON (Haas al. 2024)) or generative modeling of geodesic uncertainty (Duour et al. 2025). This trend continues with the work of LocDiff (Wang et al.] 2025) with multi-
scale latent diffusion. Benchmarks such as MediaEyal 16 and OSV5M (Astruc al. 2024) further
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standardized evaluation. The emergence of foundational models also resulted in works such as Geo- Reasonser (Li et al. 2025) and Img2Loc (Zhou et al. 2024), which push the boundary forward. Several hybrid approaches combine retrieval and classifccatin, such Translocator (Pramanick) iet al. 2022) and GeoDecoder (Clark et al. 2023).
While existing geo-classification methods multi-scale cells for partitioning, they often collapse into a single-level output, losing critical hierarchical signals. Our method explicitly preserves and leverages this hierarchical structure during both representation and inference.
Hyperbolic deep learning and vision. Hyperbolic spaces such as the Poincaré disk and Lorentz model are well-suited tree-like structures due to exponential volume growth (Nickel & Kiela 2017 Ganea et al., 2018). Poincaré embeddings (Nickel & Kiela (017) and hyperbolic neural net- works (Ganea et al. 2018) established this line of work, with applications in vision showing advan- lages over Euclidean and spherical embeddings for hierarchical classification (Khrulkov et al. 2020). However, to our knowledge, no prior work has embedded a global geolocation hierarchy (continent + city) in hyperbolic space or evaluated such embeddings on standard geolocation benchmarks. Our approach adapts the Lorentz model for stable training and cross-modal alignment.
Location encoders. Compact embeddings of raw geographic coordinates support geo-aware per- ception, e.g. Space2 (Mai et al.] (020), Sphere2Vec (Mai et al.) 2023), and GeoCLIP (Cepeda jet al., 2023). These methods treat coordinates directly as prediction targets. In contrast, we embed geographic entities enriched with multimodal features (image, text, coordinates) into hyperbolic space, yielding interpretable prototypes that unify hierarchical structure with cross-modal signals.
METHODOLOGY
3.1 HYPERBOLIC GEOMETRY
We operate in the Lorentz (hyperboloid) model of Hyperbolic space THy, with constant curvature -1/K K (Ganea et al. 2018 Ratcliffe, (2tel) All neural operations are performed in the tangent
space at the canonical origin = (vK, ............ 0), using the exponential and logarithmic maps.
R arcosh R
expo(u) [R cosh );ll), Rsinn (tll) m
logo (z)
J
V28
122
da(x, v) arcosh (omy)e
with R= VK, and x (xo, J). This decomposition of is due to the Lorentz model's different treatment of the first component compared to the subsequent ones, see Appendix A.2 for more information. Also, da(æ, y) denotes the geodesic distance. More details about the general forms are presented in Appendix A.2 Since neural layers rely on vector-space operations (linear maps, bias additions), they not directly well-defined H (Ganea et al. 2018). Our model therefore performs all such operations in the flat tangent space at the origin: inputs H& are mapped to (z), transformed in Rd and lifted back via expo(x). Fixing the base point to provides (i) a unique, global reference shared across all entities, (ii) closed-form exp/log maps with efficient implementation, and (iii) stable training without introducing additional learnable base points. This choice is standard in Hyperbolic neural networks and ensures outputs remain valid points on Hy-- Some libraries (e.g. gecopt!) parametrize the hyperboloid as (I,, x) = kk Our K corresponds exactly to this k so curvature is -1/K K and radius R VK.
3.2 CONSTRUCTION OF HIERARCHY AND ENTITIES
We construct hierarchical tree of geographic entities directly from the training metadata (Algo- rithm I in Appendix A.3). The hierarchy spans four levels: Country, Region, Subregion, and City. At each level h, we define the entity set E as the collection of unique geographic units observed in
the metadata (c.g., ISO2 codes for countries, canonical region names within countries, etc.). Entities
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Images
Geographical Hierarchical Entities
fing
Jing
floc
ftext 2f
ginde
Mean Pool
ft
caPo
exPo
B
cæpo
Logo
logo
Ty
Country
f fnsion
Friden
Excliteur Space
Hypertale Space
R
R
7611
Tangert lpaace origin
Attention context per hierarchy level
Ouer
Eurch sise iages
enttike soven alvveva
Cross modal Attention modalAttention per hierarchy level
Figure 1: HierLoc. Overall architecture. Images are encoded and mapped with expo into the Lorentz model of Hyperbolic space, while entities (countries, regions, subregions, cities) combine image, text, and location features. In the tangent space at the origin, cross-modal attention aligns each image with entities per hierarchy level; the resulting attention outputs are fused and projected back via expo- Entity embeddings are not updated with cross-attention context, while image em- beddings are updated using the context of cross-modal attention. Training employs our proposed Geo- PriiWWegt Hyperbolic InfoNCE InfoNCn,,,,E), which reweights negatives with the haver- sine formula between image and negative entity coordinates.
are assigned stable identifiers by concatenating ISO2 codes with sanitized region, subregion, and city tokens. Each training image is then mapped tuple of four entities (Ccountry: Cregion Csubregion Ceity For OSV5M, we use the official aaadrree-aligned labels provided with the dataset. For Medi- aEval'16 16, where only coordinates
available, we obtain labels through deterministic reverse geocoding with Nominatim and apply canonicalization rules for consistent identifiers (details in Appendix|A A.3). Each entity e, E & is associated with three multimodal features: image embed- ding Img, E R.ding, a text embedding Text, E deteett and geographic coordinates Coords; E IR.. The image embedding Img, and coordinate features Coords, are computed averages over all training images linked to the entity, using a frozen image encoder fimg (DINOV3 (Siméoni et al.) 2025), unless otherwise specified) and their latiuudellongitude metadata. The text embedding is de- rived from the entity name via pretrained CLIP text encoder (Radford et al.) 2021) represented by fiett- While averaging may seem like crude choice, at the entity level produces stable and discriminative prototypes: the mean embedding captures the dominant visual signal of an entity and sufficient to distinguish it from other entities in a contrastive learning setup. The role of an entity representation is not distinguish among all the images assigned to but capture enough shared signal to reliably separate it from other entities at the same hierarchical level. This construction also yields dramatic compression of the training metadata. Across both datasets, roughly 9.6 million image records are distilled into about 240k entities: 233 countries, 4,946 regions, 29,214 subregions, and 209,894 cities. This reduces the search space from millions of raw images to a compact set of entity prototypes without sacrificing discriminative power. The result is a compact, interpretable,
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and computationally efficient representation of the geographic hierarchy. Low-level implementation details such as sanitization, key construction, and reverse-geocodiee policies are deferred to Ap- pendix A.3 Please note that train two different models seperately please see section 4 for more details.
3.3 ENTITY EMBEDDINGS
We fix the tangent space dimension d 128, all update vectors lie in 128, Each entity et is assigned an anchor embedding A, E H initialized by sampling ei ~ N(0,o²1, in the tangent space at the origin Ty = R and mapping with A; = expo This anchor serves the hyperboloid. Each entity is also associated with multimodal features from Section 3.2 an averaged image embedding Img,, a text embedding Text, and normalized coordinates Coords; E [0, The coordinates are passed into the SphereM+ location encoder (Mai et al. p023p, yielding de = See (Coordss) Together with dit = Tmg, and of Text,, these features are concatenated and mapped to the tangent space by a three-layer MLP with Dropout and GELU activations (except after the last layer):
a stable reference point for the entity
u; = MM "1"""
D, Wau; + bb ER..
Here A, is learnable tangent-space update vector, while Wa and ba are the weights and biases of a linear projection. The final entity embedding then obtained by updating the anchor in the tangent space:
H; = cxpollogu (A.) O,) E H
where Onode is a learnable scalar controlling update strength. Thus, A, defines stable initialization, while A; injects multimodal evidence to adapt the entity embedding. Entities therefore reside in the 128 dis-dimensional Hyperbolic manifold H represented in Lorentz coordinates in F 129 Distances are computed via the Lorentz inner product in this (d + 1)-dimensional ambient space.
3.4
IMAGE EMBEDDINGS
Each imput image is encoded by fing into Euclidean feature vector dimg R This represen- tation is mapped into the tangent space at the origin by a projection MIP with two linear layers (Dropout and GELU applied after the first layer):
u jig
MLP img (E) )
A img
Wing u + bimg E ERd.
We then prepend a zero to A img to respect the (d + 1)-dimensional Lorentz structure, and project to the hyperboloid using the mapping in Eq
Zime = = (Kimg A img) E H
where aimn is Icarnable scale. Unlike entities, image embeddings from frozen backbone projected to the tangent space at the origin the Lorentz model with an MLP layer, ft. They are then mapped onto the Lorentz model with cxpo and later refined through cross-modal attention module (Section 3.5) with entity embeddings. Both image embeddings Zimg and entity embeddings H, therefore reside HIJ28, 128-dimensional Hyperbolic manifold, and are represented in 129 for distance computations we use Eq. 2
3.5 CROSS-MODAL ATTENTION
As shown in Figure cross-modal attention operates in the tangent space at the origin, with images as queries, and entity features as keys/values. All cross-modal interactions are carried out in the tangent space the origin. For each hierarchy level l E (country, subregion, city), ), entity embeddings H E Hy& are mapped to h logo (H)) and each image Zung to 2img logo (Zmg). ). At level multihead attention is applied with the image queries. and the entities as keys and values, yielding 2img = Attny (he) ). We use multihead attention block with 8 heads for each level. The four level-wise contexts are concatenated, fused by a small MLP, and added back to the original feature.
Zimg = 2mmg + MLP Juse ( country |= ssubregion
||
which is then lifted back via Z expo (mmg)) E HHd- Only the image stream is updated with attention outputs; entity embeddings remain fixed, an asymmetry that prevents the overfitting of entity embeddings the training data while still providing hierarchical geographic context.
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3.6 GWH-INFONCE LOSS
We propose Geo- Weighted Hyperbollic InfoNCE (GWH-InfoNCE),, novel contrastive objective that incorporates geographic structure into Hyperbolic alignment. For image embedding Zing HH the entity at level & provides the positive H while all other entities in that level serve as negatives ( Distances are measured directly on the Lorentz manifold using Eq.
df du Zimg: 2²
= dg H(,))²
To emphasize geographical spatial proximity in the embedding space, we reweight each negative ac- cording to its great-circle distance ge.k from the image location, computed via the haversine formula (Appendix A.4) The per-level loss
exp(-d; /T)
Ce = -log
We,k = 1 X exp(-9tx/o).
(4)
exp(-d.//1 + Ex we,k expl- ddxx//)
We use Laplace decay for geo- weighting with (ep(-9e///))) which can also be ablated using other decaying functions such as Gaussian and Inverse kernels. We determine the optimal kernel for weight decay through experiments (see Appendix [A.7 for more details). Here T, X, a are learn- able hyperparameters, with representing the temperature scaling, À and control the strength of geographic weighting and geographic distance scaling, respectively. The total training objective aggregates across hierarchy levels to minimize,
Σ Be Li,
BEH
where 3g trades off supervision across levels, allowing for finer or coarser granularity. We optimize entity and image parameters in Euclidean and Hyperbolic space, respectively (details in Section
4 DATASETS AND EXPERIMENTS
4.1 DATASETS
We evaluate our method using two large-scale training datasets and several standard benchmarks. Specifically, we train two separate models the OSV5M and MediaEval" 16 datasets respectively. OSVSM (Astruc et al. 2024) contains 4.8 million street-view images for training and 210,000 im- ages for testing:
follow the official split and report results the test set for direct comparison with published baselines. MediaEval' (Larson et al.) 2017) provides 4.7 million geo-tagged im- ages, all of which we use for training since no official split is publicly available, and we evaluate on external benchmarks. Specifically, we test model trained on MediaEvvll 16 with YFCC4K (Vo) al. (2017), IM2GPS (Hays & Efros 2008), and IM2GPS3K (Vo al. 2017). which widely used standard datasets in visual geolocation.
4.1.1 METRICS
On OSVSM, we follow the official evaluation protocol and report five metrics: classification aceu- racy at the country, region, subregion, and city levels; the mean geodesic error (computed as the average great-cirele distance between predicted and ground-truth coordinates); and the GeoScore, inspired by the GeoGuessr game") B defined as 5000 X cxp( - 88/1492.7) (Dufour al. 2025). The possible range of values for GeoScore from 0 to 5000. For YFCC4K. IM2GPS, and IM2GPS3K. report the standard "% @ km" recall statistics used in prior geolocalization work (Haas al. 2024). This measures the percentage of predictions within fixed distance radii of the ground-truth: 1 km (street-level), 25 km (eity-level), 200 km (region-level), 750 km (country-level), and 2500 km (continent-level), We also report the median distance error for these datasets.
4.1.2 EXPERIMENTS
Given a query image and its embedding, we retrieve predictions using a beam search procedure over entity embeddings at each hierarchy level. At each step, candidates are ranked by the Hy- perbolic geodesic distance defined in Section 3.1 and the top-k candidates are retained, allowing
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Table 1: Geolocation performance comparison on OSVSM with official training and test splits with current basclines. Best results are reported in bold, second-bess results are underlined.
Method
GeoScore
Dist. (km)
Classification Accuracy (56
Country
Region
Subregion
City
SC O-shot
(Hans et al. 2023
2273
2854
38.4
20.8
9.9
14.8
Regression
(Astruc et 2024
3028
1481
56.5
16.3
1.5
0.7
ISNs
[Muller-Budack ct al.
3331
2308
66.8
39.4
4.2
Hybrid
(Astruc el al. 2024
3361
1814
68.0
39.4
10.3
SC Retrieval
[Haas et al 2023
3597
1386
73.4
45.8
28.4
19.9
RFM Sg
Duuouur et al. 2025
3767
1069
76.2
44.2
5.4
LocDiff
Wang ct al. 2025
77.0
46.3
11.0
HierLoc (VITL-14) (ours)
3850
1067
80.1
52.9
39.0
22.2
HierLoc (DINOV3) (ours)
3963
861
82.9
55.0
40.7
23.3
exploration of multiple plausible locations. The final prediction is selected from the best-scoring beam. This retrieval strategy leverages the hierarchical structure of entity embeddings, making beam search computationally feasible. We use a beam width of k = 10 throughout. The procedure yields classification accuracies at the country, region, subregion, and city levels on OSV5M. At the city level, the coordinates of the predicted entity serve as the image's 's location estimate, from which compute mean geodesic error and GeoScore on OSV5M, and distance-basee recall and median error on YFCC4K, IM2GPS, and IM2GPS3K. All nearest-neighhor lookups use FAISS FlatIP with tome-coordinate flip, ensuring Lorentz imner products can be ranked efficiently without explicit dis- tance computation (for more details see Appendix A.8). For training, we use AdamW for Euclidean parameters and AiemannianAdam (Bécigneul & Ganea (019)) for manifold parameters, with gra- dient clipping for stability. Models trained with batch size of B 16 images, a learning rate 10 and run on 6XNVIDIA L40S GPUs for epochs. Each full training run requires approximately 60 hours.
4.1.3 RESULTS
Table summarizes the results for the large-scale OSV5M benchmark. HierLoc trained on OSV5M dataset and tested on OSV5M test set. HierLoc achieves GeoScore of 3963 and re- duces the mean geodesic eтror to 861 km, significant improvement over retrieval- baselines such as SC Retrieval (1386 km) and even the generative RFM S2 model (1069 km). At the same time, HierLoc sets new state-of-the-ar classification accuracies across all hierarchy levels, reaching 82.93% at the country level and 23.26% at the city level. These gains highlight the effectiveness of combining Hyperbolic embeddings with beam search retrieval to exploit the hicrarchical structure of geographic entities. Since all of the current baselines use the VITL-14 backbone for fair compari- son, we also train HierLoc with the VITL-14 backbone and report the results, surpassing the current baselines all the metries. This proves results not only because of the DINOV3 backbone but also because of our framework. To ensure further fair comparisons with baselines since the model RFM S2 is trained on StreetCLIIP (Haas et al. 2023) backbone, we have ablated the choice of backbone and show HierLoc's 's performance boost does not depend on the choice of the Encoder. We have included these ablations in the tables 4
Table 2 extends the evaluation to the long-standing IM2GPS, IM2GPS3K, and YFCC4K bench- marks Tor the model trained on MediaEval'16.. On IM2GPS, HierLoc achieves a median error of 21.4 km while maintaining strong recall at large scales (92.4% @ 2500 km). On IM2GPS3K, Hi- erLoe balances fine-grained and coarse performance, cutting the median error nearly in half relative to PIGEON (72.7 km vs. 147.3 km) and yielding +7.1 points improvement at 25 km recall. On YFCC4K, our model lowers the median error to 341.9 km and improves recall at the city (30.2% @ 25 km) and regional (43.3% @ 200 km) levels, demonstrating robustness beyond landmark-centric datasets.
Finally, Table compares HierLoc against the generative RFM Sn models (Dufour et al. 2025 on YFCC4K. Despite being trained on only 4.7M images, HierLoc outperforms the IM-iteration RFM S2 variant and matches the mean geodesic enror of the much larger 10M-iteration model trained on 48M images (2058 km). Although slightly behind in GeoScore and continent-scale recall, HierLoc achieves competitive city and region level performance, highlighting the efficiency of our approach

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Table 2: Comparison of Hierlooc model with DinoV3 Bbackbone trained MediaFval' 16 data to baselines on benchmark datasets, Median distance error (km, lower is better) and recall (% within radius, higher is better) best results are in bold, and the second-best results are underlined.
IM2GPS (ayy Efros 2008
Method
Median (km)
kmt
km/
200 km
750 km/
2500 kmt
PlaNet
[Weyand et al. 2016
>> 200
8.4
24.5
37.6
71.3
CPlaNet
(Se0 2118
16.5
37.1
62.0
78.5
ISNs (M,1*,S3)
Muller-Budack Budack
2018
25
16.9
43.0
51.9
66.7
80.2
Translocator
Prumanck al. 2022
25
19.9
48.1
64.6
75.6
86.7
GeoDecoder
Clark ct 2025
~ 25
22.1
50.2
69.0
80.0
89.1
PIGEON
Haas et
70.5
14.8
40.9
63.3
82.3
21.1
GooRcasoner
2025
13.0
44.0
86.0
HierLoc (ours)
21.4
10.5
51.9
67.5
92.4
IM2GPS3K (Vo al
2017
PlaNet
Weyand al.
8.5
24.8
64.6
CPlaNet
et
750
10.2
26.5
34.6
48.6
64.6
ISNs (M.1 S33
Mutler-Budack al 2018
750
10.5
28.0
36.6
49.7
66.0
Translocator
Pramanick ct 2022
> 200
11.8
31.1
46.7
58.9
80.1
GcoCLIP
(Cepdda sl. 2125
14.1
34.5
50.6
69.7
83.8
GeoDecoder
[C.lak
12.8
33.5
76.1
PIGEON
|aaus
147.3
11.3
36.7
53.8
72.4
85.3
Img2Loc
Zhou el 2024
17.1
45.1
57.8
72.9
84.6
GeoReasoner
Li ct al 2025
10.0
38.0
83.0
HierLoe (ours)
73.4
11.3
43.8
58.4
74.1
85.1
YFCC4K (Vo et al.
2017
PlaNet
WWeyand et al. 2016
> 750
5.6
14.3
22.2
36.4
55.8
CPlaNet (S00 et al. 2018
> 750
7.9
14.8
21.9
36.4
55.5
ISNs (M.F"S3)
Balller-Budck al. 2018
> 750
6.7
16.5
24.2
37.5
54.9
Translocator
Pramanick ala
8.4
18.6
60.4
GeoDeedder
C.lark ef 2025
750
10.3
24.4
33.9
50.0
68.7
PIGBON
Haiis al.
4024
383.0
10.4
23.7
40.6
62.2
77.7
Img2Loc
Zhou cl al
2024
14.1
29.5
41.4
59.2
76.8
HierLoc (ours)
341.9
8.4
30.2
43.3
61.7
75.8
Table 3: Comparison of HierLoc with RFM S2, generative model YFCC4K. RFM S2 is trained on 48 million YFCC dataset; in contrast, HierLoc is trained on MediaEval' 16 with 4.7 million images (10x fewer images). Median distance error (km, lower is better) and recall (% within radius, higher hetter). Best results are in bold, second-best results are underlined.
YFCC4K Vo et al. 2017
Method
GeoScore f Mean Distance (km)
25 km
200 kmr
750 km/
2500 kmr
RFM Sa
Dufour et al. 2025
2889
2461
23.7
36.4
54.5
73.6
RFM1gxr Sa (Dufour et al. 2025
3210
2058
33.5
45.3
61.1
77.7
HierLoc (ours)
3189
2058
30.2
43.3
61.7
75.9
relative to generative models trained on 10 times more data. To further isolate the affect of DinoV backbone choice of HierLoe, we provide experiments in the Ablations section 4.2] In summary, across OSV5M and standard benchmarks, HierLoc consistently reduces geolocation error relative to previous baselines, setting new state-of-the-art results, especially on OSV5M. These results validate design choices of hyperbolic entity embeddings, multimodal fusion, and beam search retrieval as a scalable alternative to current geolocation models.
4.2 ABLATIONS
Table reports OSV5M results for three different visual backbones (DINOv3, StreetCLIP, ViT- L/14). All encoders produce highly consistent rankings across the hierarchical accuracy levels, and their absolute performance remains stable, with each backbone outperforming all non-HierLoe base- lines. This indicates that the gains do not originate from particular choice of vision model but from the hierarchical hyperbolic design itself. To also isolate the cross-datane hierarchy construction, we construct the hierarchies only using VSV5M dataset and train model OSV5M with StreetCI.IP
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Table 4: Encoder ablation of models trained and tested OSV5M. We compare the effect of dif- ferent vision backbones on the HierLoc framework. Backbone
GeoScore 1
Dist. (km) 4
Classification Accuracy (%) f
Country
Region
Subregion
City
HierLLo (DINOv3)
3963
861
82.9
55.0
40.7
23.3
HierLoc (StreetCLIP)
3862
1051
80.3
53.1
39.2
22.5
Hierl.oc (ViT-L/114)
3850
1067
80.1
52.9
39.0
22.2
Table 5: Encoder ablation of models trained MP16 and tested YFCC4K.
Method
GeoScore
Mean Distance (km) 25 kmt
200 km
750 km
2500 km
Hierl ne (DINOv2)
3106
2211 2058
28.2
42.2
59.8
74.0
HierLoc (DINOv3)
3189
30.2
43.3
61.7
75.9
Table 6: Ablation study the choice of embedding space in HierLoc, evaluated the OSV5M dataset. Results are reported in terms of GeoScore, mean localization error, and hierarchical classi- fication accuracy. Method
GeoScore Mean Dist (km)
Classification Accuracy (%) f
Country
Region
Subregion
City
HierLoc (Buclidean)
3865
968 1258
81.0
51.5
37.5
21.1
HierLoc (Spherical)
3364
75.2
31.3
15.9
4.3
HierL.oc (Hyperbolic)
3963
861
82.9
55.0
40.7
23.3
Table 7: Ablation study of HierLoc on OSV5M, demonstrating the importance of GWH-InfoNCE loss and cross attention for fine-grained localization.
Method
GeoScore 1
Mean Dist (km)
Classification Accuracy (%) ^
Country
Region
Subregion
City
DINOV3 zero shot
2962
1999
58.7
25.8
17.1
9.6
HierLoc w/ InfoNCE
3840
949
80.5
49,9
35.7
19.4
HierLoe w/o attention
2904
1366
71.5
35.6
23.5
11.4
HierLoe w/o squared distance
3752
1043
79.5
47.3
33.1
17.5
HierLoc w/o text location
3890
1029
81.8
52.1
37.9
21.1
HierLoc (full)
3963
861
82.9
55.0
40.7
23.3
Table 8: Comparison of inference strategies OSV5M (top-1 accuracy). Flat search ignores hi- erarchy, while beam search enforces path-consistency. Beam width 1=10 achieves the best aceu- racy-efficiency trade-off.
Method
Country
Region
Subregion
City
Flat per-level (no hierarchy)
79.6
50.8
39.4
22.1
Hicrarchical (bcam=1)
79.4
48.9
36.4
21.9
Hicrarchical (bcam=10)
82.9
55.0
40.7
23.3
backbone. The results in the table 4 for StreetCLII show that cross-dataset hierarchy construction does not have any influence with the performance of HierLoc. Table presents presents the corresponding analysis MP16, comparing HierLoc using DINOv2 and DINOv3. There is drop in perfor- mance with DinoV2 but not significant enough to outperform RFM S2 model, further reinforcing that HierLoc's improvements generalize across encoders and datasets.
on ablation studies in OSVSM, isolating the independent impact of the main compo- nents of HierLoc. Replacing the Lorentz model of HierLoc architecture with Euclidean embedding space increases the mean geodesic error to 968 km and lowers accuracy across all hierarchy levels, confirming the advantage of Hyperbolic space for the geolocation task. Moreover, the Spherical

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embedding space performs worse than both the Euclidean and Hyperbolic embedding spaces. This can be attributed to higher distance distortions in the Spherical manifold. We further validate this finding the YFCC4K, IM2GPS, and IM2GPS3K benchmarks (Appendix, Table D), where Hy- perbolic embeddings consistently reduce median error and improve recall compared to Euclidean space.
Table reports the performance of DINOV3 zero shot, without any training, by finding the nearest neighbors from its image embeddings entities that have been initialized with only mean image embeddings. Substituting our Geo- SeeeWWegt Hyperbolic InfoNCE with the standard InfoNCE ob- jective also degrades performance (949 km), particularly the region and subregion levels, showing that reweighting negatives by geographic distance provides more effective supervision. Removing cross-modal attention between images and entity prototypes leads the largest error (1366 km), highlighting that hierarchical context and cross-modal attention are critical for fine-grained localiza- tion. Finally, replacing the squared distance Eq. without the square of the distance also shows a worse performance at all levels.
The ablation of removing the text and location modalities shown in the table does reduce the per- formance a little across all levels. but it is not significant, and the image signal is the most important modality for this task. But the combination of all three modalities results in the best performance. Furthermore, other ablations such role of mean image embeddings, hyper parameter sensitivity, curvature choice for the Lorentz model and the choice of weight decaying function for the geo- weights in the loss reported in the Appendix AA.5 Further analysis of the computational effi- ciency of our framework against retrieval and generative methods is also reported in the Appendix A.8 which quantifies the improvements over existing retrieval methods. We perform an ablation study to evaluate the impact of the hierarchical structure by comparing our approach against flat retrieval baseline (Table 8). We further analyze the effect of beam search width on localization performance. Figure iillusttraees the beam search inference process on geographic map, demon- strating how candidate entities are identified and refined across different hierarchical levels using a beam width of 10.
DISCUSSION
Our experiments demonstrate that HierLoc provides a principled and scalable solution to visual ge- olocation. By reformulating the task from image-to-ime to-mmge retrieval into image-to-entity alignment in Hyperbolic space, Hierl.oc consistently outperforms prior methods across large-scale benchmarks. The improvements are most pronounced at fine-grained levels (subregion and city), where modeling hierarchical structure together with geographically weighted contrastive learning delivers signifi- cant gains. Moreover, HierLoc remains competitive with recent generative approaches trained on an order of magnitude more data (c.g.RRMMo0 S2 ), highlighting the efficiency of our formulation. Beyond accuracy, HierLoc offers several key advantages. First, predictions are interpretable: images aligned explicit geographic entities, enabling structured error analysis and clearer insights into model behavior. Second, inference is computationally efficient, as the number of entities is vastly smaller than the number of training images required for large-scale retrieval. Third, the framework naturally integrates multimodal signals such as text and coordinates improving performance. While Hyperbolic embeddings have been studied extensively, our contributions lie extending them to planet-scale geolocation, introducing a geo-aware loss in Hyperbolic space, and reformulating re- trieval as learnable entity representation learning.
Several limitations remain, 1 km localization performance of our method is inherently bounded by a discretization limit resulting from our selection of 240k fixed entities, which lacks dense street- level granularity. We acknowledge this as fundamental trade-off: our hierarchical representation prioritizes structural and regional interpretability over sub-kilometer accuracy. Our evaluation in Appendix A.9 further demonstrates difficulties in performance generalization between regions with less number of training samples.
Looking ahead, the broader promise of HierLoc lies in its generality. Any task with hierarchically structured data such as taxonomies in biodiversity, linguistic families, or knowledge graphs could benefit from the same principles of Hyperbolic entity embeddings, multimodal fusion, and structured retrieval. Visual geolocation thus serves as a challenging and high-impact testbed, but the underlying methodology extends beyond it.
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6 ETHICS STATEMENT
This work relies exclusively on publicly available datasets for visual geolocation, including OSV5M, MediaEval'16, 16, YFCCЧK, IM2GPS, and IM2GPS3K, which do not contain personally identifiable information beyond image content already released for research purposes. No additional human subjects were involved, and no private or sensitive data were collected. We acknowledge that geolo- cation technologies may pose privacy and security risks if misapplied, for example in surveillance, tracking individuals, or identifying sensitive locations. Our work is intended solely for scientific benchmarking and methodological advancement in large-scale representation learning. All datasets are cited from their original sources and used under their research licenses. We encourage future research consider fairness and bias issues, particularly regarding underrepresented geographic regions, and to assess societal impacts of deploying such models.
7 REPRODUCIBILITY STATEMENT
We have taken several steps to ensure reproducibility of our results. All datasets used are publicly available and are described in Section 4 and Appendix A.3 with preprocessing steps (c.g., entity construction, reverse geocoding) detailed in Algorithm and Appendix A.3 Model architecture, hyperparameters, and training schedules are described in Sections and [ with additional abla- tions (e.g., curvature sensitivity, kernel functions) reported in Appendix A.5 Evaluation protocols
strictly follow prior work and official benchmarks. We also detail how FATSS can be leveraged with Hyperbolic nearest neighbor search in the Appendix(A.8
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A
APPENDIX
A.1 LLM USAGE
During the preparation of this paper, large language models (LLMs) were used as assistive tools for writing and polishing text. Specifically, they were employed to improve the clarity, grammar, and style of certain sections, and to suggest alternative phrasings in accordance with the ICLR author guidelines. LLMs were not involved in research ideation, implementation, experimental design, or analysis of results. All technical content, including methodology, experiments, and conclusions, were designed, implemented, and validated by the authors. The authors take full responsibility for the correctness and originality of the content.
A.2 PRELIMINARIES ON HYPERBOLIC GEOMETRY
We use the Lorentz (hyperboloid) model of d-dimensional Hyperbolic space (Ratcliffe 2019). This a Riemannian manifold HIG- with constant negative sectional curvature (-1/K) (Ganea al. 2018
H { x 1d+11 (x,x)² -K, Za > 0)) K > 0,
with Minkowski bilinear form
d
(x. v/ = -00800 +
Σ
3r Fzyli-
im1
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H K
expo
logo
d R
Figure 2: Illustration of expo and logo projection functions projecting points from Tangent space to Hyperbolic space and vice versa.
The geodesic distance between x, y E H is dn(r, y) arcosh (2,a)2 K
(5)
It is often convenient to write the radius as R = VK, with curvature K -
For any base point p E Hy. the tangent space is TpH {u Rd+1 (p. v)c 0}. Let
||ul|c := (lu, v) denote the (spacelike) Lorentz norm on T. With Rt = VK, the exponential and logarithmic maps p are
expp(u) cosh( [[llc)) p + R sint( [Illle) Rx
ee T2
(6)
|
dz(p,x)
log, (2) (x)
sinh( dz(p.z)) x cost du du(pa)) )p)
E Hy.
with the continuous extensions (O) p and log, (p) O. Let the canonical origin be
(R, O......0 0) = (VK,0,... 0.,,0..... E H ToH = {(0, "I,..., va)) ~ Rd. Replacing = in
Eqs. 6 gives
expo(r) = (Rcosh) |1-11) Rsinh
[|=l]] R
E Rd
(8)
|Tl|
logo(z) It arcosh
#
E.
(zo. F
H K
(9)
R
where ||al]] is the Euclidean norm of v, and E E Rd are the "spacelike" coordinates of x. Note that logo (x) is not simply the Fuclidean projection of 7 the prefactor ensures exact agreement with the Riemannian logarithm. Figure illustratively shows the process of projecting points from Rd to H using expo function, conversely, the process of projecting points from Hy to Ed using loga function.
A.3 FURTHER DETAILS ON CONSTRUCTION OF ENTITIES
We construct the entity hierarchy directly from the metadata of the train splits of OSV5M and Me- diaEval' 16 datasets. For each dataset, we first resolve schema columns (country, region, subregion, city, latitude, longitude, image embedding) in a format-agnostic way. Each row is then normal- ized: the country field is mapped to ISO2 code, canonical name: missing labels country, region, subregion, and city labels are filled by reverse geocoding the coordinates with Nominatin in the
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case of MediaEval' 16; and all region, subregion, and city names sanitized to ensure consistent identifiers.
The hierarchy is built incrementally: for every row, traverse from country to region, subregion, and city, creating nodes as needed. Each node accumulates a count of images, the sum of coordi- nates, and the sum of image embeddings, which returned from frozen image encoder backbone such as DINOV3 or VITL-14. After all rows are processed, entity features are finalized by averaging accumulated values: the mean image embedding, the mean latitude/loniiudee coordinates, and text embedding computed from the entity name (via frozen pretrained text encoder such as CLIP Text Encoder).
Finally, the tree is serialized. The construction runs in linear time in the num- ber of rows and requires memory proportional to the number of unique entities.
Algorithm 1: BuildHHearrchyyFnnneettaaaaaaaa
Input: Training metadata of a datasct dataset
Output: Hierarchy tree T
Initialize: T <- 0 (hierarchy starts countries): foreach record (c, r, s, ci, o, X, v) in metadata do Map country + (ISO2, canonical name);
if dataset = Modi aEval 16 and labels missing then
sc + ReverseGioccdde(,, via Nominatim;
Sanitize (r, 8, ci) to canonical tokens;
foreach level E /country, region, subregion, city] do
CreateOrGeuNode(T level, identifiers):
Update counts and coordinate
10
Accumulate image embedding (from frozen encoder);
foreach node ''' do of image embeddings; Coords, +- mean of lat/lon;
Img,
13
14
Text, + feeaaaaann (Nee(Nam((n)) (n)) (frozen text encoder);
Serialize T to JSON;
16
Complexity: ((V) over records memory x number of unique entities;
A.4 HAVERSINE DISTANCE
We compute the geographic distances ge.k used in Eq. For two locations (111, A1) and (122, A2) in radians (latitude, longitude), define
sin
82
cos yo1 cos p2 sin )a
The haversine formula yields the central angle (great-cirele distance in radians)
2 arctan 2( Va, vI vI-a). In our implementation, we omit the constant factor of 2 and work with
Ifull 2 aresin( va)
arcsin( v
since both the factor 2 and the Earth's 's mean radius R = 6371 km simply rescale distances with- changing their relative ordering gradient directions. These constants absorbed into the bandwidth parameter of our loss. For reporting physical distances, we reintroduce them as
d 2Rg (in kilometers).
A.5 FURTHER ABLATIONS
Manifold sensitivity In addition to the OSV5M ablation (Table we also compare Euclidean and Hyperbolic variants of HierLoc on three widely used recall-at-km benchmarks: YFCC4K, IM2GPS. and IM2GPS3K (Table 9). The Hyperbolic manifold consistently outperforms Euclidean space across datasets, reducing median localization enror by 23 23-45% and improving recall city- and region-level thresholds (25-200 km). This confirms that the advantages of Hyperbolic embeddings robust and not specific to OSV5M.
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Table 9: Manifold sensitivity on recall-at-km benchmarks (YFCC4K, IM2GPS, IM2GPS3K). Same backbone, loss, and training schedule; only the embedding manifold differs. Hyperbolic space con- sistently reduces median localization error and improves recall across scales.
Dataset
Median (km) & km 1 25 km
200 km 1
750 km 1
2500 km 1
YFCC4K (Vo et al. 2017)
HierLoc (Euclidean) 445.3
7.0 25.9
39.7
58.2
73.4
Hierloo (Hyperbolic)
341.9
8.4
30.2
43.3
61.7
75.8
IM2GPS (Hays & Efros 2008
HierLoc (Euclidean)
47.3
8.4
45.9
64.9
81.8
91.1
HierLoc (Hyperbolic)
21.4
10.5
51.9
67.5
83.1
92.4
IM2GPS3K (Vo et al. 2017)
HierLoc (Euclidean)
121.6
10.2
41.2
55.1
71.6
83.3
HierLoc (Hyperbolic)
73.4
11.3
43.8
58.4
74.1
85.1
Table 10: Ablation study of removing mean image embeddings for each hierarchy level sequentially
Ablation (Removed Mean Embeddings)
Country (%)
Region (%)
Sub-region (%)
City (%)
None
82.93
55.03
40.68
23,26
Country
81.59
54.27
39.97
22.63
Country & Region
79.96
50.40
36.61
20.59
Country & Region & Sub-region
77.12
44.34
30.76
16.32
Country & Region & Sub-region & City
70.46
30.00
14.06
3.58
Table 11:
Ablation study of HierLoe on OSV5M subset of 100k training set and 10k test set for search of the best curvature, K for Lorentz model.
Curvature (K)
Mean Dist (km)
Classification Accuracy (%)² 1
Country
Region
Subregion
City
0.25
1719
64.7
28.8
17.7
8.36
0.50
1603
67.4
31.6
19.9
9.51
0.75
1534
69.1
33.5
21.1
10.0
0.80
1462
69.2
33.7
22.3
11.0
1.00
1687
67.4
30.2
19.3
9.1
Mean Image Embeddings Sensitivity To quantify the contribution of mean image embeddings across spatial scales, we progressively remove them coarse-to-fine order (country + region subregion + city). Table shows that removing country-level means yields only a minor accuracy drop, indicating that coarse aggregates provide limited discriminative signal. The impact grows as we remove means from finer levels, with the largest decline at the city level where local visual context most informative. Importantly, the model remains stable and does not collapse even when all mean embeddings are removed. This demonstrates that Hierl.e is not dependent any single level's mean representation; rather, its performance stems from the hierarchical architecture and the multi-level integration of visual cues.
Lorentz model on the OSV5M subset of 100k training images and 10k test images. Owing to the size of the dataset, perform this search on a smaller subset. Through the experiments, we find that curvature 0.8 best fits the OSV5M dataset, focusing on. We keep the same curvature for both models
Table II shows the search the best curvature, K,
given that it is the primary dataset on the OSV5M dataset and also the MediaEval" 16 dataset.
A.6 HYPERPARAMETER SENSITIVITY ANALYSES
We extend our analysis to two further hyperparameters of HierLoc's training objective: the tem- perature and the geographic weighting coefficient À used in the GWH-InfoNCE loss. All experi-
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Published as a conference paper at ICLR 2026
ments conducted 100k/10k OSV5M split. Table 12 reports the performance of HierLoc for T E {0.07. 0.10, 0.15, 0.30). The model exhibits stable behavior across broad range, with T = 0.1 yielding the best overall accuracy
Table 12: Temperature sensitivity of the GWH-InfoNCE loss on OSV5M (100k/10K split).
Country (%)
Region (%)
Sub-region (%)
City (%)
0.07
68. 72
32.76
20.62
10.31
0.10
69.20
33.70
22.30
11.00
0.15
69.00
32.50
20.50
9.80
0.30
67.80
32.30
20.00
9.67
Table varies the geographic weighting coefficient À in the GWH-InfoNCE loss. The model reaches peak performance at À = 1.0, but accuracy degrades smoothly as À moves away from this value, demonstrating that the method is not overly sensitive to the choice of weighting strength. Across both hyperparameters, HierLoc maintains stable performance and does not exhibit collapse within a wide range of settings. The smooth variation in accuracy further confirms that the method robust to moderate deviations from the default 0.1 and À 1.0, and does not rely finely tuned hyperparameter values.
Table 13: Sensitivity to the geographic weighting parameter À in GWH-InfoNCE.
Country (%)
Region (%)
Sub-region (%)
City (%)
0.0
63.90
27.80
16.20
7.30
0.5
67.80
32.00
20.20
9.60
1.0
69.20
33.70
22.30
11.00
2.0
65.00
29.50
17.70
8.20
A.7 GEOGRAPHIC WEIGHTING KERNELS.
Our loss defined in the Eq. 4 incorporate family of distance-dependent kernels k(d)) that transform geographic distance d (in kilometers) into a similarity weight. Let d denote the great- circle distance in kilometers between the image and negative entity, >> 0 scale parameter, > a weight strength, and > 0 an exponent. We support three kernel families:
Laplace kernel (default): Exponential decay in distance:
ka (d) exp(-
Gaussian kernel: Squared-distange decay, producing narrower band of influence:
KGauss (d) exp (xx))-())
Inverse kernel: Power-law decay, yielding long-range tails:
kim (d) (1 7)²²
The final geographic weight for negative sample, which upweights negatives that are geographi- cally close to the positive is
w(d) x
We observe in Table 14 that the choice of kernel has measurable effect on geolocation perfor- mance. The Gaussian kernel, which decays very rapidly with squared distance, yields reasonable accuracy at coarse levels (country and region) but underperforms at finer scales, since moderately close negatives receive almost no weight and thus provide little contrastive pressure. The Inverse kernel, with its heavy-tailed power-law form, performs slightly better at coarse levels but fails to emphasize ine-scale discrimination, as distant negatives retain substantial weight and dominate the denominator.
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Table 14: Ablation study of Hierl.oe OSVSM subset of 100k training set and 10k test set for search of the best geoweighting decay kernel for GWH-InfoNCE
kernel (k(d))
Mean Dist (km) 4
Classification Accuracy (%)
Country
Region
Subregion
City
Gauss Inverse
1525
69.7
33.7
21.1
10.1
1529
69.8
34.1
21.7
10.3
Laplace
1462
69.2
33.7
22.3
11.0
In contrast, the Laplace kernel achieves the best trade-off: it decays exponentially with distance, pre- serving emphasis on geographically nearby negatives without entirely discarding moderately distant ones. This balance leads to superior performance finer levels (subregion and city), where dis- tinguishing between visually similar but geographically close entities is most critical. Moreover, Laplace also reduces the mean geodesic error, showing that its weighting improves localization pre- cision overall.
We therefore adopt the Laplace kernel as the default geo-weighting strategy for GWH-InfoNCE, as it provides the most effective compromise between local discrimination and global robustness the hierarchical geolocation setting.
Reglon
Soarch Time 1o
03
1.5
1.6
30
64
128
256
1.0
76
32
136
256
Boam 02.
Boam 19
Figure 3: Comparison of accuracy and search time tradeoff with different beam widths.
A.8 COMPUTATIONAL AND STORAGE EFFICIENCY
Modern retrieval systems typically use libraries such as FAIS$] fast nearest-neighhor search, and this can be leveraged for Hyperbolic distances in the Lorentz model as well. Figure highlights efficiency advantages of HierLoc over standard image-based retrieval. While most research benchmarks rely datasets with millions of images, real-world platforms be orders of magni- tude larger: for example, Mapillary reports more than billion street-level images (Mapillary Team 2024]. At such scales, SC Retrieval, which grows linearly with database size, becomes compu- tationally and storage prohibitive. By contrast, HierLoc scales sublinearly because the number of geographic entities expands far more slowly than the number of raw images. This structural dif- ference translates into significant savings: HierLoc reduces wall-clock inference time by more than 10x, achieves over 20x lower storage requirements, and cuts FLOPs per query by two orders of magnitude, all while sustaining higher throughput. Although beam search introduces a slight over- head relative to flat entity search due sequential parent-chil expansion, it yields higher accuracy at all levels with negligible additional cost. Overall, Hierl oc achieves favorable trade-off between scalability and precision, enabling efficient billion-scale deployment that is infeasible with standard retrieval pipelines.
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$96.77
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600
15000
500
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10000
300
200
5000
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Sc. Recnevvll
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Hirrtor (Bean=10)
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Figure 4: Comparison of computational efficiency across methods. We report wall-clock search time, throughput (queries per second), storage footprint, and FLOPs per query. Arrows indicate whether lower or higher values are better.
FAISS for Hyperbolic (Lorentz) search and beam expansion. In the Lorentz model, geodesic distance and the Lorentz inner product are monotone-cqiivalent
d Σ 2.yi. = VK.
cosh(dx (x, = - (x, (Z, (I,8)L = -oolo +
Thus minimizing dn is equivalent to maximizing (..)). We convert Lorentz MIPS into stan- dard Fuclidean inner-product search supported by FAISS via a one-line linear map on the query only: for Z = (=o. z) define Ż (-20, z). Then HTH = (Z, H) so FAISS Flat (or IVF-Flat IP/NSWWW index over entity embeddings returns the same ranking as sorting by in- creasing Hyperbolic distance, without evaluating arcosh at search time. We do not nz-nomallize Lorentz vectors (normalization would distort the geometry). Beam-search integration. We build one FAISS index per hierarchy level (country~vcity in Lorentz coordinates and: (i) seed the beam the top level with the top-k entities from single FAISS query using the time-coordinate flip; (ii) for each deeper level, query the corresponding FAISS index and parent-filter candidates so only children of the previous-level beam are retained; (iii) accumulate path score (c.g.. IP or, for exact scoring of a small shortlist, the true dg) and prune to the fixed beam width. This hybrid "FAISS-guided parent-constrained" expansion amortizes calls while enforcing path consistency. On GPU, GpuIndex: aa IP provides the best throughput; approximate variants (IVE) /NSW) can be enabled at larger scales with no change the fign-flip trick. We batch queries, reuse indices across batches, and maintain per-level indices to avoid rebuilds during inference.
work into few high-throughput IP
To directly assess inference-time efficiency against other diffusion based methods, we compare Hi- erLoc against the strongest non-retrieval baseline, RFMS,, under identical hardware conditions. Ta- ble 15 reports the latency breakdown. HierLoc achieves substantially lower forward-pass time and adds only a negligible retrieval cost due to its compact hierarchical search, resulting in an overall 6.56x speedup relative to RFMS,. This demonstrates that the hierarchical entity-based formula- tion not only improves accuracy, but also yields a highly efficient inference pipeline suitable for large-scale deployment.
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Published as a conference paper at ICLR 2026
Table 15: Inference latency comparison the GPU. HierLoc provides 6.56x speedup RFMS2.
Model
Inference (ms)
Retrieval (ms)
Total (ms)
Speedup
RFM S2
14.17
14.17 2.16
1x
Hierl.o occ (ours)
2.09
0.075
6.56x
Country
Region
Sub-region
City
Query Image
(b)
a
Peru
Cusco
Provincia de Urub... Ollantaytambo
Bolivia, Plurinat...
Junin
Provincia de Caka
Cusco
Ecuaddr
Apurimac
Provincia de La C...
Pisa
Calombia
Paz
Cusco Subregion
Santa Teresa
Country
Region
Sub-region
(c)
(d)
(e)
(f)
Provincia de Urubamba
Ollantaytambo
Peru
11.0 km
Cusco
Lowe
Eigh
Low
High
Low
High
Producted
Candidate
Predicted location
Ground Inulh location
Candidak (pet
Figure 5: Hierarchical beam search visualization for visual geolocation. Given a query street-view image (a), HierLoc performs coarse-to-fine geographic search through four hierarchical levels (b). At each level, the model scores candidate regions and selects the highest-scoring entity (red path). Panels (c)-() show the candidate regions each level choropleth, where color intensity indicates the model's confidence score normalized within that level. Panel (f) shows the final city- level prediction on an OpenStreetMap basemap, with the predicted location (red cross) and the ground truth image coordinate (gold star).
A.9 QUALITATIVE ANALYSIS
To provide interpretable insight into the inference behavior of HicrLoc, we visualize the full hier- archical beam search trace alongside its geographic realization across the four entity levels in the figure Panel (b) displays the beam search tree, where each column corresponds to a hierarchy level (Country, Region, Sub-region, City) and each node represents candidate geographic entity scored by computing the squared hyperbolic distance between the query image embedding and the entity embedding in the Lorentz manifold. The predicted path, shown in red, traces the highest-scoring entity selected at each level. Pruned candidates appear as faint background nodes, illustrating the breadth of the search space that the beam width of k=10 efficiently narrows at each step. Panels (c) through (f) project this search onto geographic maps with progressively increasing zoom, mirroring the coarse-to- to-see-----neeeee structure of the hierarchy. At the country level (c), all 10 candidate countries are rendered on a world map with choropleth shading proportional to their normalized scores. At the re- gion level (d), the view restricts to regions within the selected country, and similarly for sub-regions (e) within the selected region. This geographic drill-down directly reflects the computational sav- ings of hierarchical beam search, which reduces the candidate space from 240k entities to a tractable subset at each level. The city-level panel (f) overlays the final predicted location and ground truth coordinate on an OpenStreetMap basemap, with a dotted line and distance annotation quantifying the localization error. In this example, HierLoc correctly identifies Peru, narrows the Cusco
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gion, localizes Provincia de Urubamba, and predicts Ollantaytambo within 11.0 km of the true coordinate, demonstrating the model's ability to perform structured geographic reasoning through the learned hyperbolic entity hierarchy.
Mean Geolocation Error by Grid Cell (1* x 19)
Moan crrar (km lig scol))
10"
Figure 6: Mean geographic error distribution HierLoc on the OSV5M dataset.
Figure shows the global distribution of localization errors OSV5M. Unlike smaller benchmarks such as YFCC4K, IM2GPS, or IM2GPS3K, OSV5M provides a geographically diverse test set with 200k images, enabling systematic analysis global scale. Urban regions in Europe and North America exhibit relatively low errors due to dense training coverage, while sparsely imaged regions such as inland Asia and central Africa show higher mean errors, reflecting persistent data imbalance. Because OSV5M is more geographically balanced and diverse than prior datasets (Astruc et al., 2024), performance this benchmark offers a stronger measure of robustness and generalization. Figure demonstrates that Hyperbolic embeddings, trained solely from image- location pairs, cap- ture meaningful geographic, cultural, and linguistic relationships. Clusters emerge without explicit supervision, reflecting both geographic proximity and cultural ties. Notably, island nations form distinct peripheral cluster, suggesting that their embedding geometry encodes the same structural differences reflected in their error statisties.
Taken together, these qualitative analyses reveal three systematic error modes: (i) data imbalance, where underrepresented regions (e.g., inland Asia, central Africa) yield higher error; (ii) cultural and linguistic clustering, where embeddings align geographically distant but historically linked nations; and (iii) recurring visual ambiguity in island environments, where beaches and coastlines lack dis- tinctive geographic context and drive long- tail errors. Understanding these modes highlights both the strengths and the remaining challenges for scalable global geolocation.
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Continents
SI
Africa
Europe
DE
Oceania
South America
Figure 7: UMAP projection of country embeddings learned in Hyperbolic space. Colors denote continents, with insets highlighting emergent clusters. Geographically distant but culturalyy linked nations (e.g., Australia, New Zealand, UK, US, Canada) cluster together, while regions with shared history (c.g.. the Mediterrancan basin) form coherent cross- coss--onntinenal groups. Island nations con- sistently appear the periphery of the embedding space.
Samphe Mean Eroe
Ener Clarroution tiaal
1850
Ontari Emer COPE
2004
33
MADMP
Figure 8: Comparison of geolocation performance across island and non-island territories. Left: Scatter plot of mean eπrо samples, but islands (blue) show higher variance and extreme outliers. Right: Error distributions by group. Although island territories achieve comparable median error non-islands (84.3 km vs. 91.9 km), their mean error is nearly twice as high (1368 km vs. 763 km), indicating a heavier tail. This reflects the difficulty of disambiguating visually repetitive environments such as coastlines and beaches, where recurring patterns provide weak geographic cues. These challenges consistent with the peripheral island clusters observed in Figure
training samples per country. Both groups benefit from more
22


Reviews:
[{"review_id": "gwDWqMNzyD", "reviewer": "Reviewer_k8zX", "summary": "This paper proposes to solve **geolocation as a hierarchical retrieval problem**. By leveraging different levels of administrative segmentation, they assign one embedding per entity and then perform **hierarchical retrieval to achieve efficient retrieval** while achieving **SOTA performance**.", "questions": "**Motivation for Hyperbolic Embeddings:** The paper **struggles to clearly explain the intuition for using hyperbolic embeddings**. I understand that it works better, but what is the **underlying motivation**?", "limitations": "", "rating": 6, "confidence": 5, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "1. The paper showcases **extensive experiments** to back up its claims.\n\n2. The method's inference structure allows for **very efficient inference**.\n\n3. The method is showcased on two datasets: **OSV-5M** (street view focused) and **MediaEval** (more generalist).\n\n4. The authors achieve **SOTA performances on OSV-5M**.", "weaknesses": "1. **Data Curation:** It is not clear, but **entities seem to be learned *across* datasets** (per Section 3.2). If true, this **makes the results not comparable**, as the model is trained on significantly more data. This also potentially **breaks the data decontamination** for OSV-5M (1km exclusion zone). I would like to see **results with entities computed separately for each dataset**.\n\n2. **Mean Embeddings for Large Regions:** Taking the mean embedding may be suitable for fine-grained regions, but it **likely doesn't make sense for wider regions** like countries. I would like to see an **ablation study sequentially removing these mean embeddings** for countries, regions, sub-regions, and cities.\n\n3. **Importance of the Encoder:** The paper **fails to ablate the importance of the feature extractor**. For all we know, it’s **DinoV3 that is responsible for the improvement**. **Networks used by other SOTA methods should be ablated** as well (e.g., StreetCLIP on OSV, DinoV2 on YFCC for RFM S2).\n\n4. **Lack of Qualitative Samples:** I would have loved to see some **visualisation of the inference process**. (Perhaps drawing the beam search trees on a map with colors for scores?) It would also beD; good to be able to visualise some final predictions.\n\n5. **Efficiency Comparison:** I would like to see the **inference efficiency compared to non-retrieval methods** as well.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "HfL1xKSFpp", "reviewer": "Reviewer_V4da", "summary": "This paper is an incremental work on traditional retrieval-based geolocalization methods. Instead of performing contrastive learning between a query image and a full gallery of candidate locations, the authors propose to aggregate the candidate locations into a hierarchy of entities (country, region, subregion, city) and perform hierarchical contrastive learning in the hyperbolic space. This is an intuitive approach since it mimics the human spatial reasoning patterns -- narrow down from large-scale to fine-grained guesses. It shows some competitive performance against other baselines, while suffers from generalizability problems.", "questions": "1. Have you ever tested with cross-dataset experiments? For example, in GeoCLIP, the model trained on MP16 is evaluated on Im2GPS3k and YFCC, and obviously YFCC has much weaker performance because its data distribution is different from MP16. In your experiments, all test data seem to be a left-out of the training data. This will cover your generalizability issue, since the test locations are likely to align with the entity hierarchy you build from the training data.", "limitations": "", "rating": 2, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "1. A hierarchical representation of locations and a beam search through hierarchical entities is a very natural and geographically sound alternative to traditional single-location-based retrieval geolocation methods.\n\n2. Using hyperbolic embedding to represent hierarchy is very efficient.\n\n3. Geo-Weighted InfoNCE introduces geo-awareness into the contrastive learning loss.", "weaknesses": "1. The key weakness, which severely restricts the generalizability of the method, is that the proposed entity hierarchy relies heavily on the **coverage** of the dataset. That is, if a location in the test set never appears in any neighborhoods of an entity in the training dataset, the model will never be able to predict its location. This is no rare case -- both MP16 and OSV5M are highly spatially biased, i.e. most data concentrate in North America and Western Europe. This is already a known problem in traditional retrieval based methods such as GeoCLIP (see a recent NeurIPS paper https://openreview.net/pdf/c2d943add9cd78700f9acc1101286c2082105a70.pdf, Section 5.2 and Appendix A.7), and the entity hierarchy which simplifies 4 million candidate locations into 240k entities only makes the problem worse. In other words, the proposed method, on its very basis, can not handle spatially out-of-distribution cases. This is a huge weak point compared to recently developed generative geolocation models (RFM, LocDiff) which naturally generalizes to arbitrary locations on Earth.\n\nThis problem is covered in the paper because the authors only performed testing on the same datasets the models are trained -- i.e., if a model is trained on the OSV5M training dataset, it is evaluated on the OSV5M test dataset. It \"hides\" the generalizability problem.\n\n2. Errors in citations. Too many citations are in wrong formats -- e.g. throughout the paper, most citations are not properly put into parentheses.\n\n3. From Appendix A.2, $\\exp_0$ and $\\log_0$ should be $\\exp_o$ and $\\log_o$, because here the $o$ represents the origin *point*, not the number $0$.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "RsGBnR3Mv4", "reviewer": "Reviewer_ZDzY", "summary": "The paper presents hierloc, a new framework for worldwide image geolocalization that reformulates the task as aligning images to a compact hierarchy of geographic entities, embedded in hyperbolic spaces. Rather than image-to-image retrieval, hierloc computes and aligns image embeddings to entity prototypes via contrastive learning, directly incorporating haversine distance to weight negatives (GWH-InfoNCE). This allows efficient hierarchical beam search inference, interpretability, and strong performance. Empirical results on the OSV5M benchmark and others demonstrate improved mean geodesic error and classificationn accuracies relative to prior methods, while reducing storage and computation requirements.", "questions": "please refer to the weakness part", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The paper is clearly presented, and the reader can smoothly follow the authors’ logic.\n2. The idea is relatively novel, and alignment itself is a challenging problem.", "weaknesses": "1. The related work section misses several relevant studies (e.g., GeoReasoner [1] , Img2Loc [2]). I recommend that the authors do a more thorough survey.\n2. In Table 2, which backbone is used for HierLoc? Is the comparison with other methods fair?\n3. The code and data will only be released after acceptance.\n4. Similar to the first point, the experimental section also lacks comparisons with strong baselines. The current results still show a gap from the state-of-the-art on some metrics.\n\nOverall, I think this paper is well-presented, and the experiments are generally self-consistent. However, the lack of strong and up-to-date baselines is quite noticeable. If the authors can include comparisons with more recent baselines in this field, I would consider increasing my score.\n\n[1] Li, Ling, et al. \"Georeasoner: Geo-localization with reasoning in street views using a large vision-language model.\" Forty-first International Conference on Machine Learning. 2024.\n[2] Zhou, Zhongliang, et al. \"Img2Loc: Revisiting image geolocalization using multi-modality foundation models and image-based retrieval-augmented generation.\" Proceedings of the 47th international acm sigir conference on research and development in information retrieval. 2024.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "7ipkmEnKEB", "reviewer": "Reviewer_7XjS", "summary": "The paper trains on two datasets (OSV5M and MediaEval’16) but does not include an ablation showing how each dataset affects performance.\nPrevious geolocation works (e.g., PIGEON, RFM S, GeoDecoder) trained and evaluated using only one dataset, ensuring fair comparison.\n\nBecause HierLoc uses multiple datasets—OSV5M for one benchmark and MediaEval’16 for others—the reported gains may partly come from additional training data diversity, not just from the proposed hyperbolic embedding method.\nWithout a controlled experiment (e.g., training only on OSV5M and testing cross-dataset), it is unclear whether improvements are architectural or data-driven.", "questions": "None", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "The paper is clearly written, with a logical flow.\nThe figures effectively illustrate the hierarchical process.\nEquations are well-defined and consistent with hyperbolic geometry notation.\nIntroduces the first explicit use of hyperbolic embeddings for visual geolocation, representing geographic hierarchies as hyperbolic manifolds.\nThe Geo-Weighted Hyperbolic InfoNCE (GWH-InfoNCE) loss incorporating haversine distance is novel and well-justified.\nReformulating geolocation as image-to-entity alignment instead of image-to-image retrieval is conceptually new.", "weaknesses": "1. Some hyperparameters are found empirically, more justification or sensitivity plots would be valuable.\n\n2. The paper employs two large-scale datasets (OSV5M and MediaEval’16) for training but does not provide ablations isolating their effects. Prior works (e.g., PIGEON, GeoDecoder, RFM) train and evaluate using a single dataset, ensuring fair comparison. In contrast, HierLoc benefits from additional data diversity, which may contribute to improved cross-dataset generalization. Without an ablation where HierLoc is trained solely on OSV5M or MediaEval’16 and evaluated on the same benchmarks, it is unclear how much of the reported gains are due to the proposed method versus the increased data volume.\n\nI recommend adding an ablation or at least clarifying which datasets were used for each benchmark evaluation, and ensuring fair comparison with prior work under identical training data conditions.\n\n3. The field of visual geolocation is niche within ICLR’s broader ML audience; the paper’s impact may depend on perceived relevance beyond geolocation (e.g., general multimodal hierarchy learning).", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)