Reproducing the figures and tables¶

Each figure and table of the paper has one section below with the cells to train, the inference and evaluation stages, the plotting command, and the command that draws it from the paper's figure data instead. The commands assume the setup of Reproducing: data, checkpoints and training: S=scripts/neurips2026, the train function, GEOSAE_STORE, and PD pointing at the figure-data folder of the Zenodo record.

Main figures¶

Fig. 1: overview and two regional features¶

Train: train alphaearth matryoshka 1024 16 0
Predict: part of geosae run.
Evaluate: nothing further.

Plot:

python $S/fig1_overview.py runs/alphaearth/matryoshka_M1024_k16_s0/* --out figures

From the paper data (regional_features.npz):

python $S/fig1_overview.py --paper-data $PD --out figures

Fig. 2: reconstruction against sparsity¶

Train: the full sweep, both embeddings.
Predict: not needed; the panel runs every model on its own pixel sample.

Evaluate: one panel per embedding, scoring every run and the dense baselines:

for emb in alphaearth tessera; do
  geosae panel -c configs/neurips2026/$emb.yaml -c configs/neurips2026/panel.yaml \
    -o run.dir=eval/$emb/panel -o "panel.runs=[runs/$emb/*/*]"
done

Plot:

python $S/fig2_pareto.py --panel-alphaearth eval/alphaearth/panel --panel-tessera eval/tessera/panel --out figures

From the paper data (real_products.json, dense_topk.json):

python $S/fig2_pareto.py --paper-data $PD --out figures

Fig. 3: correlation lengths¶

One call draws Fig. 3 (fig3_correlation_length) and Figs. S3 and S4 (figS_variogram_<embedding>).

Train: the M = 1024, k = 16 cells of every variant with seed 0, and the frozen decoder with seeds 1 and 2, on both embeddings:

for emb in alphaearth tessera; do
  for v in batchtopk matryoshka relu_l1 frozen; do train $emb $v 1024 16 0; done
  train $emb frozen 1024 16 1; train $emb frozen 1024 16 2
done

Predict: not needed.

Evaluate:

for emb in alphaearth tessera; do
  geosae variogram -c configs/neurips2026/$emb.yaml -c configs/neurips2026/variogram.yaml \
    -o run.dir=eval/$emb/variogram \
    -o "variogram.runs=[runs/$emb/*_M1024_k16_s0/*,runs/$emb/frozen_M1024_k16_s[12]/*]"
done

Plot:

python $S/fig3_variogram.py --variogram-alphaearth eval/alphaearth/variogram \
  --variogram-tessera eval/tessera/variogram --out figures

From the paper data (variogram_ae.npz, variogram_te.npz):

python $S/fig3_variogram.py --paper-data $PD --out figures

Fig. 4: concept alignment¶

Train: train alphaearth matryoshka 1024 16 0 and train alphaearth frozen 1024 16 0.
Predict: not needed.

Evaluate: concept alignment on the evaluation pool:

for run in runs/alphaearth/{matryoshka,frozen}_M1024_k16_s0/*; do
  geosae coverage --run $run -c configs/neurips2026/coverage.yaml
done

Plot:

python $S/fig4_monosemanticity.py --runs runs/alphaearth --variant matryoshka --out figures

From the paper data (monosemanticity_matryoshka_ae.json):

python $S/fig4_monosemanticity.py --paper-data $PD --out figures

Fig. 5: aligned features and sub-concepts¶

Train: train alphaearth matryoshka 1024 16 0
Predict: part of geosae run.
Evaluate: geosae coverage --run runs/alphaearth/matryoshka_M1024_k16_s0/* -c configs/neurips2026/coverage.yaml. The random-partition p-values the text quotes come from geosae subconcepts --run <run> -c configs/neurips2026/subconcepts.yaml.

Plot (also writes Table S8 into its JSON):

python $S/fig5_aligned_features.py runs/alphaearth/matryoshka_M1024_k16_s0/* --esri --out figures

From the paper data (qualitative_ae.npz, subconcepts.npz, subconcepts.json, subconcepts_frozen.json):
```
python $S/fig5_aligned_features.py --paper-data $PD --out figures
```

Fig. 6: area-of-applicability gain¶

Train: BatchTopK at M = 1024, k = 16, seeds 0, 1, 2, on both embeddings:

for emb in alphaearth tessera; do for seed in 0 1 2; do train $emb batchtopk 1024 16 $seed; done; done

Predict: not needed.

Evaluate: the graded hold-outs, with the random sparse code:

for run in runs/{alphaearth,tessera}/batchtopk_M1024_k16_s*/*; do
  geosae aoa --run $run -c configs/neurips2026/aoa.yaml -c configs/neurips2026/aoa_graded.yaml
done

Plot:

python $S/fig6_aoa_gain.py --alphaearth runs/alphaearth/batchtopk_M1024_k16_s*/* \
  --tessera runs/tessera/batchtopk_M1024_k16_s*/* --out figures

From the paper data (applicability.json):

python $S/fig6_aoa_gain.py --paper-data $PD --out figures

Appendix figures¶

Fig. S1: dataset overview¶

Train, predict, evaluate: nothing; the figure reads only the store.
Plot: python $S/figS_dataset_overview.py $GEOSAE_STORE --out figures
From the paper data: not available; the figure needs the store.

Fig. S2: per-dimension reconstruction¶

Train: train alphaearth $v 1024 16 0 for v in matryoshka, batchtopk, relu_l1.
Predict, evaluate: nothing; the script runs each SAE forward on three patches of the store.
Plot: python $S/figS_recon_quality.py runs/alphaearth --esri --out figures
From the paper data: not available; the figure needs the store and the three checkpoints, which the Zenodo record has (see Checkpoints).

Figs. S3, S4: spatial scales on AlphaEarth and Tessera¶

Written by the Fig. 3 command; see Fig. 3.

Fig. S5: patch-mean Moran's I¶

Train: the M = 1024, k = 16 cells of every variant with seed 0, and the frozen decoder with seeds 1 and 2, on both embeddings, as for Fig. 3.
Predict: part of geosae run.
Evaluate: nothing further; the script computes Moran's I from the predictions.

Plot:

python $S/figS_moran.py --runs-alphaearth runs/alphaearth --runs-tessera runs/tessera --out figures

From the paper data (spatial_coherence.npz):

python $S/figS_moran.py --paper-data $PD --out figures

Fig. S6: principal components against SAE atoms¶

Train: train alphaearth matryoshka 1024 16 0
Predict, evaluate: nothing; the script reads the fitting table of geosae fit-table.
Plot: python $S/figS_pcs_vs_atoms.py --runs runs/alphaearth --device cpu --out figures

From the paper data (pcs_vs_atoms.npz):

python $S/figS_pcs_vs_atoms.py --paper-data $PD --out figures

Fig. S7: concept alignment on Tessera¶

Train: train tessera matryoshka 1024 16 0 and train tessera frozen 1024 16 0.
Evaluate: geosae coverage --run <run> -c configs/neurips2026/coverage.yaml on both runs.

Plot:

python $S/fig4_monosemanticity.py --runs runs/tessera --name figS_mono_tessera --out figures

From the paper data (monosemanticity_matryoshka_te.json):

python $S/fig4_monosemanticity.py --paper-data $PD --embedding tessera --name figS_mono_tessera --out figures

Fig. S8: concept alignment of BatchTopK¶

Train: train alphaearth batchtopk 1024 16 0 and train alphaearth frozen 1024 16 0.
Evaluate: geosae coverage --run <run> -c configs/neurips2026/coverage.yaml on both runs.

Plot:

python $S/fig4_monosemanticity.py --runs runs/alphaearth --variant batchtopk --name figS_mono_batchtopk --out figures

From the paper data (monosemanticity_batchtopk_ae.json):

python $S/fig4_monosemanticity.py --paper-data $PD --variant batchtopk --name figS_mono_batchtopk --out figures

Fig. S9: woody features of the frozen decoder¶

Train: train alphaearth frozen 1024 16 0
Predict: part of geosae run.
Evaluate: geosae coverage --run runs/alphaearth/frozen_M1024_k16_s0/* -c configs/neurips2026/coverage.yaml

Plot:

python $S/figS_subconcepts_frozen.py runs/alphaearth/frozen_M1024_k16_s0/* --esri --out figures

From the paper data (subconcepts_frozen.npz, subconcepts_frozen.json):

python $S/figS_subconcepts_frozen.py --paper-data $PD --out figures

Figs. S10, S11: galleries on AlphaEarth and Tessera¶

Train: train $emb matryoshka 1024 16 0 for both embeddings.
Evaluate: geosae coverage --run <run> -c configs/neurips2026/coverage.yaml on both runs.

Plot:

python $S/figS_galleries.py runs/alphaearth/matryoshka_M1024_k16_s0/* --esri --out figures   # figS_qual_only
python $S/figS_galleries.py runs/tessera/matryoshka_M1024_k16_s0/* --esri --out figures      # figS_qual_only_tessera

Add --device cpu on a machine without a GPU.

From the paper data (qualitative_ae.npz, qualitative_te.npz):

python $S/figS_galleries.py --paper-data $PD --out figures
python $S/figS_galleries.py --paper-data $PD --embedding tessera --out figures

Figs. S12, S13: area of applicability with Europe held out¶

Train: as for Fig. 6, plus train alphaearth matryoshka 1024 16 0.

Evaluate: the continent and plant-functional-type folds, then the leave-Europe-out maps of Table S9, which write figures/aoa_europe.npz:

for run in runs/alphaearth/batchtopk_M1024_k16_s*/* runs/alphaearth/matryoshka_M1024_k16_s0/*; do
  geosae aoa --run $run -c configs/neurips2026/aoa.yaml
done
python $S/table_aoa_europe.py runs/alphaearth/batchtopk_M1024_k16_s*/* \
  --map-run runs/alphaearth/matryoshka_M1024_k16_s0/* --out figures

Plot:

python $S/figS_aoa_gain.py figures/aoa_europe.npz --alphaearth runs/alphaearth/batchtopk_M1024_k16_s*/* \
  --tessera runs/tessera/batchtopk_M1024_k16_s*/* --out figures                  # Fig. S12
python $S/figS_aoa.py figures/aoa_europe.npz --out figures                        # Fig. S13

From the paper data (aoa_europe.npz, applicability.json):

python $S/figS_aoa_gain.py --paper-data $PD --out figures
python $S/figS_aoa.py --paper-data $PD --out figures

Appendix tables¶

Tables S1 (data sources) and S2 (concept groups) describe the setup and report no results.

Table S3: reconstruction at L0 = 16¶

Train, evaluate: as for Fig. 2.

Plot:

python $S/table_reconstruction.py --panel-alphaearth eval/alphaearth/panel \
  --panel-tessera eval/tessera/panel --out figures

From the paper data (recon_table.json):

python $S/table_reconstruction.py --paper-data $PD --out figures

Note

The paper's table is scored on the cleaned test pixels of recon_table.json, Fig. 2 on the panel's sample, so the two differ in the third digit (PCA with 16 components: 0.696 in the table, 0.697 in the figure). Fresh panels reproduce Fig. 2's sample.

Tables S4, S5: further embeddings¶

Data: the Sentinel-2 subset with the OlmoEarth and MMEarth tokens, and the 0.25° Copernicus-FM store (see Building a dataset):

geosae subset -c configs/download.yaml -o subset.stage=fetch     # CPU and network
geosae subset -c configs/download.yaml -o subset.stage=embed     # one GPU; the embed extra
geosae subset -c configs/download.yaml -o subset.stage=stats
geosae gridded -c configs/download.yaml

Train: BatchTopK SAEs and frozen-decoder baselines, seeds 42, 43, 44: OlmoEarth (M = 4096, k ∈ {16, 192}) and MMEarth (M = 4096, k ∈ {16, 80}) on the tokens, Copernicus-FM (M = 1024, k ∈ {16, 192}) on its grid:

E=configs/neurips2026/embeddings
for seed in 42 43 44; do for v in batchtopk frozen; do
  for k in 16 192; do
    geosae run -c $E/patch_tokens.yaml -c $E/olmoearth.yaml -c configs/neurips2026/variants/$v.yaml \
      -o model.latent_dim=4096 -o model.k=$k -o seed=$seed -o name=olmoearth/${v}_M4096_k${k}_s${seed}
    geosae run -c $E/gridded.yaml -c $E/copernicusfm.yaml -c configs/neurips2026/variants/$v.yaml \
      -o model.latent_dim=1024 -o model.k=$k -o seed=$seed -o name=copernicusfm/${v}_M1024_k${k}_s${seed}
  done
  for k in 16 80; do
    geosae run -c $E/patch_tokens.yaml -c $E/mmearth.yaml -c configs/neurips2026/variants/$v.yaml \
      -o model.latent_dim=4096 -o model.k=$k -o seed=$seed -o name=mmearth/${v}_M4096_k${k}_s${seed}
  done
done; done

Evaluate: a panel per embedding with baselines at the SAEs' L0, and concept alignment of the token runs:

for emb in olmoearth mmearth; do
  ks=$([ $emb = mmearth ] && echo 16,80 || echo 16,192)
  geosae panel -c configs/neurips2026/panel.yaml -c $E/patch_tokens.yaml -c $E/$emb.yaml \
    -o run.dir=eval/$emb/panel -o "panel.runs=[runs/$emb/*/*]" -o "panel.baselines.widths=[$ks]"
  for run in runs/$emb/*/*; do geosae coverage --run $run; done
done
geosae panel -c configs/neurips2026/panel.yaml -c $E/gridded.yaml -c $E/copernicusfm.yaml \
  -o run.dir=eval/copernicusfm/panel -o "panel.runs=[runs/copernicusfm/*/*]" -o "panel.baselines.widths=[16,192]"

Plot:

python $S/table_further_embeddings.py --panel-copernicusfm eval/copernicusfm/panel \
  --panel-olmoearth eval/olmoearth/panel --panel-mmearth eval/mmearth/panel \
  --runs-olmoearth runs/olmoearth --runs-mmearth runs/mmearth --out figures

From the paper data (products/{copernicusfm,olmoearth,mmearth}.json):

python $S/table_further_embeddings.py --paper-data $PD --out figures

Table S6: UCov¶

Train: the M = 1024, k = 16 cells of every variant on both embeddings.

Evaluate: concept alignment of every M = 1024, k = 16 run, and the untrained random dictionary on one BatchTopK run:

for run in runs/{alphaearth,tessera}/*_M1024_k16_s*/*; do
  geosae coverage --run $run -c configs/neurips2026/coverage.yaml
done
geosae coverage --run runs/alphaearth/batchtopk_M1024_k16_s0/* -c configs/neurips2026/coverage.yaml \
  -o "coverage.random_widths=[1024]"

Plot: python $S/table_ucov.py --runs runs/alphaearth runs/tessera --out figures

From the paper data (tables.json, null_coverage.json):

python $S/table_ucov.py --paper-data $PD --out figures

Table S7: monosemanticity scores of Betti et al.¶

Train: the M = 1024, k = 16 cells of every variant, seeds 0, 1, 2, on both embeddings.
Predict: part of geosae run.
Evaluate: nothing further; the script scores the predictions.
Plot: python $S/table_betti.py --runs runs/alphaearth runs/tessera --out figures. MS also needs image embeddings of the test patches (--image-embeddings, see -h); without them the script reports GeoMS only.
From the paper data (betti_scores_ae.json, betti_scores_te.json, betti_relu_fixed.json):
```
python $S/table_betti.py --paper-data $PD --out figures
```

Table S8: sub-concept agreement¶

Train, evaluate: as for Fig. 5 and Fig. S9.

Plot:

python $S/table_subconcepts.py runs/alphaearth/matryoshka_M1024_k16_s0/* \
  runs/alphaearth/frozen_M1024_k16_s0/* --out figures

From the paper data (subconcepts.json, subconcepts_frozen.json):

python $S/table_subconcepts.py --paper-data $PD --out figures

Table S9: area of applicability with Europe held out¶

Train, evaluate, plot: the table_aoa_europe.py command of Figs. S12, S13; it writes table_aoa_europe.tex and .json.
From the paper data: not available. The table re-scores the held-out sites each geosae aoa run caches (eval/aoa/sites.npz), which the record does not hold; aoa_europe.npz carries the leave-Europe-out numbers of the mapped Matryoshka model only.