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No Location Left Behind: Measuring and Improving the Fairness of Implicit Representations for Earth Data
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Introduces FAIR-Earth, a multi-modal Earth dataset with subgroup metadata for auditing fairness of implicit neural representations, and proposes spherical wavelet location encodings that reduce local-vs-global performance disparities versus spherical harmonics.
Problem
Implicit neural representations for Earth data optimize global average performance and show large disparities across subgroups such as islands and coastlines, and no systematic fairness benchmark exists for them.
Approach
Provide a high-resolution Earth benchmark with subgroup metadata (islands, coastlines, landmass size, population density, countries) and replace global spherical harmonic location encodings with spherical Morlet wavelet encodings that have localized support across scales.
Key results
- Spherical Harmonic encodings show strong negative land-island loss correlations (e.g., R = -0.88 at 10000 samples), while Spherical Wavelet shows positive or weaker negative correlations (R = 0.51 at 5000 samples).
- Spherical Wavelet achieves land-sea cross-entropy of 0.1404 best / 0.1473 average at 5000 samples versus SH at 0.1392 / 0.1524, i.e. competitive rather than uniformly superior.
- Spherical Wavelet has higher surface temperature errors on coast (0.101) than SH (0.083), but its subgroup profile is more uniform than Theory (0.249 coast).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use spherical wavelet rather than spherical harmonic encoding | Earth INR · FAIR-Earth land-sea classification | cross-entropy loss: 0.1462 $\pm$ 0.0013 -> 0.1419 $\pm$ 0.0009; 0.0933 $\pm$ 0.0010 -> 0.0890 $\pm$ 0.0003; 0.1057 $\pm$ 0.0010 -> 0.1017 $\ | Helped |
| Use spherical wavelet rather than spherical harmonic encoding | Earth INR · FAIR-Earth carbon emissions | mean-squared error: 0.0158 $\pm$ 0.0005 -> 0.0177 $\pm$ 0.0005; 0.0104 $\pm$ 0.0005 -> 0.0108 $\pm$ 0.0002; 0.0089 $\pm$ 0.0002 -> 0.0095 $\ | Hurt |
| Use spherical wavelet rather than spherical harmonic encoding | Earth INR · FAIR-Earth surface temperature | mean-squared error: 0.0269 $\pm$ 0.0004 -> 0.0306 $\pm$ 0.0008; 0.0203 $\pm$ 0.0004 -> 0.0237 $\pm$ 0.0001; 0.0158 $\pm$ 0.0003 -> 0.0169 $\ | Hurt |
| Use spherical wavelet rather than spherical harmonic encoding | Earth INR · External land-sea classification | cross-entropy loss: 0.0984 $\pm$ 0.0004 -> 0.0993 $\pm$ 0.0004; 0.0984 $\pm$ 0.0006 -> 0.0980 $\pm$ 0.0007; 0.0982 $\pm$ 0.0004 -> 0.0986 $\ | Mixed |
| Use spherical wavelet rather than spherical harmonic encoding | Earth INR · Checkerboard classification | cross-entropy loss: 0.1631 $\pm$ 0.0011 -> 0.1622 $\pm$ 0.0011; 0.1080 $\pm$ 0.0010 -> 0.1116 $\pm$ 0.0007; 0.0773 $\pm$ 0.0007 -> 0.0848 $\ | Mixed |
| Increase spherical harmonic encoding size (ablation) | Spherical Harmonic · FAIR-Earth land-sea classification | island cross-entropy loss | Hurt |
| Increase spherical harmonic encoding size (ablation) | Spherical Harmonic · FAIR-Earth land-sea classification | land cross-entropy loss | No clear effect |
| Replace the Morlet mother wavelet with spherical Butterfly or Mexican Hat wavelets (ablation) | Spherical Wavelet · FAIR-Earth land-sea classification | classification loss | Hurt |
| Use spherical wavelet rather than spherical harmonic encoding | Earth INR · Land-island performance across training resolutions | Pearson correlation: 0.51 vs -0.73; 0.42 vs -0.88; 0.04 vs -0.88; 0.31 vs -0.68 | Helped |
| Use spherical wavelet rather than spherical harmonic encoding | Earth INR · Encoding generation at size 625 | generation time: 220.13 $\pm$ 9.05 ms -> 129.58 $\pm$ 18.43 ms | Helped |
| Use spherical wavelet rather than spherical harmonic encoding | Earth INR · Encoding generation at size 900 | generation time: 368.73 $\pm$ 17.93 ms -> 204.25 $\pm$ 27.05 ms | Helped |
Surprising findings
- Spherical Harmonic's island loss worsens as encoding size increases, despite larger capacity.
- Spherical Wavelet performance degrades near the poles, limiting its advantage on the land-sea task.
Limitations
- Spherical Wavelet underperforms Spherical Harmonic on the simple checkerboard task and at higher resolutions in the land-sea task.
- Spherical Wavelet degrades near the poles due to inverse stereographic projection being ill-defined at the poles.
- Subgroup thresholds (e.g., island size) are ad hoc and the gridded format may induce temporal and polar biases.
Experimental setup
Datasets: IMERG OCO-2 CO2 emissions CHELSA temperature and precipitation GPWv4 population density NaturalEarth country boundaries checkerboard classification task land-sea classification dataset
Benchmarks: FAIR-Earth land-sea classification FAIR-Earth carbon emissions FAIR-Earth surface temperature FAIR-Earth precipitation checkerboard classification land-sea classification (external)
Metrics: cross-entropy loss mean-squared error Pearson correlation between subgroup losses
Baselines: Spherical Harmonic Theory Grid and Sphere (SphereC+) SphereM+ Cartesian3D
Builds on: SirenNet spherical harmonic location encoding (Rußwurm et al.) Theory location encoding Grid and Sphere encodings Gabor wavelets via inverse stereographic projection
Closest papers by meaning
- GeoCore-9B: Towards Geo-Aware Generative Foundation Models in Earth Observation (NeurIPS 2026 · similarity 0.87)
- Terra: A Multimodal Spatio-Temporal Dataset Spanning the Earth (NeurIPS 2024 · similarity 0.86)
- Earthfarsser: Versatile Spatio-Temporal Dynamical Systems Modeling in One Model (AAAI 2024 · similarity 0.85)
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- AnySat: One Earth Observation Model for Many Resolutions, Scales, and Modalities (CVPR 2025 · similarity 0.85)
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