Riemannian Generative Decoder Eval

riemannian-generative-decoder-eval

Riemannian generative decoder — Bjerregaard et al. (2025) (arXiv:2506.19133, 2025)

What this evaluates

Evaluates the ability of a decoder-only latent variable model to learn geometry-respecting latent spaces on Riemannian manifolds. It probes reconstruction fidelity, preservation of intrinsic data structures (cyclical, hierarchical, phylogenetic), and downstream predictive utility of the learned latents.

Datasets

• Cell cycle stages (scRNA-seq) — total ?; splits: train (-1), val (-1), test (-1)
• Branching diffusion process (synthetic tree) — total ?; splits: train (-1), test (-1)
• Human mitochondrial DNA (hmtDNA) — total ?; splits: train (-1), test (-1)

Metrics

• Pearson correlation (primary) — range: [-1, 1]
  • Linear correlation coefficient between ground-truth pairwise distances (e.g., cell cycle phase, tree path length, haplogroup distance) and latent geodesic distances on the chosen manifold.
• Spearman correlation — range: [-1, 1]
  • Rank-based correlation coefficient between ground-truth pairwise distances and latent geodesic distances, capturing monotonic but non-linear relationships.
• MAE — range: [0, ∞)
  • Mean Absolute Error measuring reconstruction fidelity via L1-norm between original data samples and decoder reconstructions.
• MSE — range: [0, ∞)
  • Mean Squared Error measuring reconstruction fidelity via L2-norm between original data samples and decoder reconstructions.
• Accuracy — range: [0, 1]
  • Classification accuracy of downstream models (logistic regression or XGBoost) trained on learned latents to predict categorical metadata (e.g., geographical region, haplogroup).

Input / output format

Input: Raw biological or synthetic data samples (scRNA-seq gene counts, synthetic tree node features, hmtDNA sequences) fed into a decoder-only network to produce manifold-valued latents and reconstructions.

Output: Manifold-valued latent vectors and reconstructed data samples. Downstream classifiers are trained on the latents to predict categorical labels or continuous phases.

Scoring recipe

def evaluate(latents, data, targets, manifold):
    reconstructions = decoder(latents)
    mae = mean(abs(data - reconstructions))
    mse = mean((data - reconstructions)**2)
    true_dists = pairwise_distance(targets)
    latent_dists = manifold.geodesic_distance(latents)
    pearson = pearsonr(true_dists, latent_dists)
    spearman = spearmanr(true_dists, latent_dists)
    acc = train_classifier(latents, targets).score(test_latents, test_targets)
    return pearson, spearman, mae, mse, acc

Common pitfalls

• Generalization performance is noted as generally of little significance for dimensionality reduction, so test set metrics may not reflect practical utility.
• Hyperbolic models rescale absolute path lengths by curvature, causing Spearman (rank) to improve while Pearson (linear) may not, requiring careful interpretation of correlation metrics.
• Noise scale σ heavily trades off local reconstruction accuracy against global geometric correlation; optimal σ varies by manifold and dataset.

Evidence (verbatim from paper)

Pearson/Spearman correlate phase distances to latent distances while MAE/MSE measure reconstruction by L1/L2-norm.

Citation

@misc{bjerregaard2025riemannian,
  title={Riemannian generative decoder},
  author={Bjerregaard et al. (2025)},
  year={2025},
  note={arXiv:2506.19133}
}

• arXiv: 2506.19133