Technical Summary: Tessellating The Earth (TTE)

Problem Statement

Geolocation encoders aim to map latitude-longitude coordinates to high-dimensional representations that capture latent geographic properties (climate, ecology, land cover) for downstream tasks like species distribution modeling and air quality forecasting. Existing approaches typically project raw coordinates onto fixed bases, such as spherical harmonics, multi-scale Fourier features, or random Fourier features.

The fundamental limitation of these fixed bases is their uniform allocation of representational capacity. They devote equal resources to the open ocean (which covers ~71% of the Earth's surface) as they do to complex, information-dense areas like metropolitan cities or coastlines. Furthermore, these bases are determined a priori and cannot adapt to the underlying data distribution. As demonstrated in the paper, replacing a learned spatial decomposition with a fixed one significantly degrades performance, confirming that the inability to adapt spatial support is a practical bottleneck for location encoders.

Methodology

The authors propose Tessellating The Earth (TTE), a location encoder that replaces fixed bases with a learnable Spherical Voronoi partition augmented by global semantic tokens. The architecture consists of three main components:

1. Learnable Spherical Voronoi Partitions

Instead of fixed basis functions, TTE utilizes a set of $K$ learnable sites $\{s_1, \dots, s_K\}$ on the unit sphere $S^2$.

• Soft Assignment: A query point $\mathbf{x}$ is assigned to sites based on proximity. The soft assignment weight $w_k(\mathbf{x})$ is computed using a softmax over the dot product of the site and query vectors, scaled by a learnable temperature $\tau_k$:
  $$w_k(\mathbf{x}) = \frac{\exp(\tau_k \cdot (\mathbf{s}_k \cdot \mathbf{x}))}{\sum_{j=1}^{K} \exp(\tau_j \cdot (\mathbf{s}_j \cdot \mathbf{x}))}$$
• Embedding Generation: Each site $k$ carries a learnable embedding vector $\mathbf{e}_k$. The location embedding is a soft combination of these site embeddings:
  $$\mathbf{f}(\mathbf{x}) = \sum_{k=1}^{K} w_k(\mathbf{x}) \cdot \mathbf{e}_k$$
• Adaptive Migration: Both site positions $\mathbf{s}_k$ and embeddings $\mathbf{e}_k$ are optimized end-to-end via contrastive pretraining with satellite imagery. During training, sites migrate toward discriminative areas (e.g., coastlines, ecological boundaries), concentrating capacity where geographic complexity is high, while leaving homogeneous areas (like the open ocean) sparsely covered.

2. Global Semantic Tokens

To bridge the gap between local spatial structure and global semantic understanding, TTE introduces a set of $R$ shared, learnable concept tokens $\{r_1, \dots, r_R\}$.

• Mechanism: Both the location encoder and a frozen image encoder (trained on co-located satellite imagery) attend to these tokens.
• Asymmetric Alignment: The image path uses a fixed, low temperature ($T_{img} = 0.05$) to produce peaked, nearly one-hot attention distributions, forcing images to activate specific semantic concepts. The location path uses a learnable temperature to predict this distribution based solely on coordinates.
• Fusion: The final location embedding combines the Voronoi embedding with the token-attended representation, allowing geographically distant sites covering similar environments (e.g., tropical forests on different continents) to share semantic knowledge through common tokens.

3. Training Objectives

The model is trained using three joint losses:

1. Contrastive Loss: Aligns location embeddings with image embeddings from co-located satellite imagery (Symmetric InfoNCE).
2. Reconstruction Loss: Ensures the tokens can reconstruct image features, preventing token collapse and ensuring they form a useful basis for the image feature space.
3. Alignment Loss: Minimizes the KL divergence between the location path's token attention distribution and the image path's distribution (with stop-gradient on the image side), forcing the location encoder to predict semantic concepts from coordinates alone.

Key Contributions

1. Learnable Spherical Voronoi Partitions: TTE introduces a location encoder where spatial decomposition is learned end-to-end from visual supervision. This replaces fixed bases with data-driven site placement, allowing the model to concentrate representational capacity in discriminative areas.
2. Global Semantic Tokens: The authors propose shared learnable concept tokens that distill semantic knowledge from a pretrained image encoder into a compact vocabulary. This enables cross-modal alignment and allows distant sites to share capacity via common concepts, addressing the isolation of local Voronoi sites.
3. State-of-the-Art Performance: TTE sets a new state of the art among parametric location encoders across a suite of geospatial classification and regression benchmarks.

Experimental Results

The authors evaluated TTE on a comprehensive geospatial benchmark suite and fine-grained species classification:

• Geospatial Benchmarks: TTE achieved the highest average classification accuracy (80.0%) and regression $R^2$ (0.777) among all parametric methods, outperforming the previous best (TaxaBind and SatCLIP) by 2.8% in classification and 0.045 in regression.
  • Notable gains were observed in Biome classification (+5.5 over TaxaBind), Country classification (+6.5 over SINR), and Elevation regression (+0.173 over SatCLIP).
  • Qualitative analysis showed TTE produces more spatially coherent biome predictions with smoother boundaries compared to other methods.
• Fine-Grained Species Classification (iNaturalist-2018): When used as a geographic prior for species classification, TTE achieved the best Top-1 accuracy (76.2%), improving upon the image-only baseline (66.1%) and outperforming other location encoders like SatCLIP (75.1%) and GeoCLIP (72.9%). It notably surpassed TaxaBind, which is specifically aligned with species data.
• Ablation Studies:
  • Site Migration: Fixing sites at their initial locations caused a significant performance drop (-12.9% classification), confirming that adaptive site placement is critical.
  • Semantic Tokens: Removing the semantic branch resulted in a -3.7% drop in classification, highlighting the importance of global semantic alignment.
  • Token Count: Performance peaked at 64 tokens; too few under-specified the vocabulary, while too many diluted the alignment signal.

Significance and Claims

The paper claims that TTE demonstrates that adaptive spatial partitioning combined with shared semantic anchors provides a rich inductive bias for geographic representation learning.

• Emergent Behavior: The model learns intuitive strategies without explicit supervision. Sites naturally migrate to concentrate on land masses, cluster along coastlines and ecological boundaries, and leave oceans sparsely covered.
• Semantic Specialization: The learned global tokens spontaneously specialize in coherent environmental concepts (e.g., snow/ice, arid desert, rocky terrain) and enable geographically distant sites to share meaning.
• Generalizability: While focused on Earth, the authors suggest the Voronoi-plus-tokens architecture is applicable to any domain where a function on a sphere exhibits non-uniform complexity, such as planetary science or molecular surface modeling.

The work establishes that moving away from fixed, uniform bases toward learnable, data-adaptive decompositions is essential for capturing the heterogeneous nature of the Earth's surface.