🏊 GeoPool: From Pixels to Patches

Accepted at the ICLR 2026 ML4RS Workshop in Rio de Janeiro, Brazil 🇧🇷

Benchmark for evaluating pixel-to-patch pooling methods on geospatial foundation model embeddings.

As geospatial foundation models shift from patch-level to pixel-level embeddings, practitioners must aggregate thousands of pixel vectors into patch representations. We benchmark 13 pooling methods across 3 GFMs (AlphaEarth, OlmoEarth, Tessera) on EuroSAT land-cover classification and release EuroSAT-Embed: 81,000 embedding GeoTIFFs for reproducible pooling research. Across the benchmark, simple distributional pooling methods improve spatial-split performance over mean pooling and substantially reduce the random-to-spatial generalization gap.

📊 Key Results

Stats pooling (min/max/mean/std) is the strongest default: for linear probes it improves average spatial accuracy from 87.3% to 93.0% and cuts the random-to-spatial gap from 8.8 pp to 3.8 pp. Covariance pooling reaches the best accuracy on two of three encoders when higher dimensionality is acceptable, while mean+max is another strong low-complexity option with a small spatial generalization gap.

Random vs. spatial split accuracy across encoders. Points near the diagonal generalize better under geographic shift.

💡 Recommendation: Mean Baseline, Stats Default

Use mean as a low-cost baseline. When a modest increase in dimensionality is acceptable, use stats pooling as the default. When maximum accuracy matters more than representation size, use covariance pooling. If you want a lighter-weight alternative to covariance, mean+max is a strong option.

NumPy implementations:

import numpy as np

def stats_pool(x: np.ndarray) -> np.ndarray:
    """Stats pooling over spatial dims. x: (H, W, D) -> (4D,)"""
    mins = x.min(axis=(0, 1))
    maxs = x.max(axis=(0, 1))
    means = x.mean(axis=(0, 1))
    stds = x.std(axis=(0, 1))
    return np.concatenate([mins, maxs, means, stds], axis=-1)


def mean_max_pool(x: np.ndarray) -> np.ndarray:
    """Mean+max pooling over spatial dims. x: (H, W, D) -> (2D,)"""
    means = x.mean(axis=(0, 1))
    maxs = x.max(axis=(0, 1))
    return np.concatenate([means, maxs], axis=-1)


def covariance_pool(x: np.ndarray) -> np.ndarray:
    """Upper-triangular covariance pooling. x: (H, W, D) -> (D(D+1)/2,)"""
    pixels = x.reshape(-1, x.shape[-1])
    centered = pixels - pixels.mean(axis=0, keepdims=True)
    denom = max(pixels.shape[0] - 1, 1)
    cov = centered.T @ centered / denom
    tri = np.triu_indices(cov.shape[0])
    return cov[tri]

🗂️ Pooling Methods

Training-Free

Method	Key	Dim	Description
Mean	mean	D	Global average pooling
Max	max	D	Global max pooling
Std	std	D	Global standard deviation
GeM	gem	D	Generalized mean pooling (p=3)
Center-Weighted	center_weighted_mean	D	Gaussian-weighted mean (center focus)
Mean+Std	mean_std	2D	Concatenation of mean and std
Mean+Max	mean_max	2D	Concatenation of mean and max
Median+IQR	median_iqr	2D	Median and interquartile range
Stats	stats	4D	min, max, mean, std concatenated
Percentiles	percentiles	5D	10th, 25th, 50th, 75th, 90th percentiles
Covariance	flattened_cov	D(D+1)/2	Upper triangle of covariance matrix

Parametric (require training data)

Method	Key	Dim	Description
PCA	pca_64	64	PCA on mean-pooled embeddings
BoVW	bovw_128	128	Bag of Visual Words (k-means clustering)

⚙️ Setup

make install

For the download/embed workflow, install the extra dependency group too:

uv sync --dev --group download

📦 Datasets

The dense pixel embedding variants of EuroSAT and pooled versions are on HuggingFace.

# pooled embeddings
wget https://hf.co/datasets/isaaccorley/eurosat-embed/resolve/main/embeddings-aef-pooled.tar.gz
wget https://hf.co/datasets/isaaccorley/eurosat-embed/resolve/main/embeddings-olmoearth-nano-pooled.tar.gz
wget https://hf.co/datasets/isaaccorley/eurosat-embed/resolve/main/embeddings-tessera-pooled.tar.gz

# pixel embeddings
wget https://hf.co/datasets/isaaccorley/eurosat-embed/resolve/main/eurosat-aef.tar.gz
wget https://hf.co/datasets/isaaccorley/eurosat-embed/resolve/main/eurosat-olmoearth-nano.tar.gz
wget https://hf.co/datasets/isaaccorley/eurosat-embed/resolve/main/eurosat-tessera.tar.gz

🧪 Evaluation

Once pooled embeddings are downloaded/created in embeddings/:

Run kNN and linear probes

uv run python scripts/knnprobe.py --dataset-name aef
uv run python scripts/linearprobe.py --dataset-name aef

Generate paper tables

uv run python scripts/knn_table.py --output paper/knn_table.tex
uv run python scripts/linear_table.py --output paper/linear_table.tex

Plot results

uv run python scripts/plot_results.py

🔧 (Optional) Generating Pixel Embeddings

All data is available on HuggingFace above. To regenerate from scratch:

Download EuroSAT and splits

uv run python data/download_eurosat.py

Create EuroSAT-AEF from Google Earth Engine (requires GEE auth)

uv run python data/download_eurosat_aef.py
uv run python data/convert_aef.py

Generate EuroSAT-OlmoEarth and EuroSAT-Tessera embeddings

Install the download/embed dependency group first:

uv sync --dev --group download

uv run python scripts/embed_olmoearth.py --model-size nano
uv run python scripts/embed_tessera.py

Cache pooled embeddings

uv run python scripts/pool.py --dataset-name aef
uv run python scripts/pool.py --dataset-name tessera
uv run python scripts/pool.py --dataset-name olmoearth-nano
uv run python scripts/pool.py --dataset-name olmoearth-tiny
uv run python scripts/pool.py --dataset-name olmoearth-base

If running OOM, use scripts/pool-stream.py which streams in batches (slower).

🛠️ Development

make install # install deps
make check  # lint + format + typecheck
make test   # run tests

📝 Citation

@article{corley2026pixels,
  title={From Pixels to Patches: Pooling Strategies for Earth Embeddings},
  author={Corley, Isaac and Robinson, Caleb and Becker-Reshef, Inbal and Ferres, Juan M Lavista},
  journal={arXiv preprint arXiv:2603.02080},
  year={2026}
}