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Mapping the Multiverse of Latent Representations

ICML 2024 · Probabilistic and scientific modeling › Molecules and proteins · approach: Probabilistic embeddings and relational inference · 0 citations (OpenAlex)

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Introduces PRESTO, a topological multiverse framework that uses persistent homology and persistence landscapes to compare, measure sensitivity of, and compress collections of latent representations from VAEs and transformers.

Problem

Representational variability of latent-space models across architectures, hyperparameters, implementation choices and datasets is poorly understood, threatening interpretability, robustness and reliable model selection.

Approach

Map each model's latent embedding (after optional normalization and low-dimensional random or deterministic projection) to a persistence landscape via alpha-complexes, then define a landscape-based distance (PRESTO distance) and variance (PRESTO variance) over a multiverse of models, enabling sensitivity scores, outlier detection, and search-space compression, with projection-stability theorems.

Key results

• PRESTO sensitivity analysis shows InfoVAE has the largest variability in hyperparameter sensitivities and is less representationally stable than beta-VAE and WAE.
• Compressing the VAE hyperparameter search space with PRESTO set-cover representatives can halve the search space while keeping low topological distortion.
• Theoretical bounds show pairwise distance perturbation under projection of at most 2 times the topological loss, and a bounded change in PRESTO variance under projection.

Measured effects reported in the paper

Surprising findings

• Landscape norms are approximately normally distributed, and models with similar performance can show substantial variability in landscape norms, suggesting representational variability is orthogonal to performance variability.
• Among the VAE models, only beta-VAE shows the cross-dataset latent-space consistency needed to justify reusing hyperparameter knowledge across datasets.

Limitations

• No suitable baselines exist for sensitivity analysis and outlier detection since existing methods are performance-based.
• Several design choices in the pipeline (normalization, deterministic vs random projection) are not systematically analyzed and their interpretation is left open.
• Pairwise comparisons with competitor methods are limited to aligned embeddings.

Experimental setup

Datasets: celebA CIFAR-10 dsprites FashionMNIST MNIST arXiv bbc cnn patents XYC

Benchmarks: VAE hyperparameter multiverse transformer multiverse over summarization abstracts

Metrics: PRESTO distance PRESTO variance PRESTO sensitivity Mantel correlation Pearson correlation with geometric distances landscape norm

Baselines: representation topology divergence linear CKA RBF CKA Mantel correlation

Builds on: multiverse analysis persistent homology alpha-complexes beta-VAE representation topology divergence

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