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Benchmark

Overview

The Scandium Benchmark defines a standard evaluation protocol for ML models trained on the Scandium Dataset. All models report results on the same frozen splits using the same metrics, enabling fair comparison.

Splits

Four split types, all formula-grouped (no same formula across splits), seed=42:

Split Train Val Test Tests
random_80_10_10 200,122 26,670 39,940 Basic generalization
composition_held_out 213,383 27,011 26,338 No formula overlap
family_held_out 260,984 5,165 583 Cross-family generalization
chemistry_held_out 227,384 26,673 12,675 OOD (all halides as test)

Metrics

Required

  • MAE, RMSE, R² for FE, EaH, BG
  • Report per split, per family, per source

Recommended

  • ECE (Expected Calibration Error)
  • Spearman ρ (ranking correlation)
  • F1 for stability classification (EaH < 25 meV)

Baseline Results

Composition-Only Baseline (RF + Ridge on bag-of-elements features)

Results on the random 80/10/10 split, comparing training on the full dataset vs Gold-tier only. See MODEL_LEADERBOARD.md for complete results.

Full Dataset

Split FE MAE FE RMSE FE R² EaH MAE EaH RMSE BG MAE BG RMSE
random_80_10_10 0.392 0.572 0.791 0.224 0.414 0.494 0.863
composition_held_out 0.390 0.547 0.801 0.223 0.376 0.497 0.861
family_held_out 0.739 0.832 −1.556 0.169 0.496 1.105 1.264
chemistry_held_out 1.657 1.829 −2.539 0.355 0.496 1.966 2.461

Gold Tier Only

Split FE MAE FE RMSE FE R² EaH MAE EaH RMSE BG MAE BG RMSE
random_80_10_10 0.298 0.424 0.854 0.024 0.028 0.762 1.077
composition_held_out 0.306 0.439 0.838 0.024 0.028 0.772 1.091
family_held_out 0.458 0.495 −3.481 0.019 0.024 0.943 1.110
chemistry_held_out 1.384 1.522 −1.873 0.027 0.032 2.129 2.724

Key Takeaway

Gold-tier training consistently beats full-dataset training. FE MAE drops from 0.392 → 0.298 on the random split and from 1.657 → 1.384 on the chemistry held-out split, despite having ~3× fewer training examples. This directly validates the tiering system: higher-quality data produces better models even with less data.

Evaluation Runner

# Evaluate predictions on all splits
python benchmark/evaluate.py \
    --splits random_80_10_10 composition_held_out \
    --predictions predictions.json \
    --model-name my_model

# Run baseline
python benchmark/evaluate.py --baseline mean
python benchmark/evaluate.py --baseline median

Leaderboard

See MODEL_LEADERBOARD.md for complete results.