MOSAIC: Module Discovery via Sparse Additive Identifiable Causal Learning for Scientific Time Series

TL;DR

MOSAIC is a novel sparse temporal VAE that enhances causal representation learning by enabling the discovery of interpretable, domain-specific modules in scientific time series data.

Contribution

It introduces a method combining temporal CRL with support recovery to achieve module-level interpretability in latent variables.

Findings

MOSAIC recovers domain-consistent variable groups across multiple scientific datasets.

Finite-sample guarantees are provided for sparse-additive support recovery.

Empirical results demonstrate interpretable discovery of latent mechanisms.

Abstract

Causal representation learning (CRL) seeks to recover latent variables with identifiability guarantees, typically up to permutation and component-wise reparameterization under appropriate assumptions. However, identifiability does not imply interpretability: latent semantics are typically assigned post hoc by alignment with known ground-truth factors. This limitation is particularly acute in scientific time series, where underlying mechanisms are unknown and discovering interpretable structure is a primary goal. In contrast, scientific observations (such as residue-pair distances, climate indices, or process sensors) are inherently semantic, as they correspond to named physical quantities. This raises a key question: can the interpretability of observations be transferred to the identifiable latent space? We propose MOSAIC (Module discovery via Sparse Additive Identifiable Causal learning), a sparse temporal VAE that integrates temporal CRL identifiability with support recovery over observed variables. MOSAIC identifies latent variables via regime-conditioned temporal variation, and recovers for each latent a sparse set of associated observations through an additive decoder, yielding module-level interpretability. We show that ANOVA main-effect supports are identifiable under general smooth mixing functions, and provide finite-sample recovery guarantees for a tractable sparse-additive variant. Empirically, MOSAIC recovers domain-consistent variable groups across RNA molecular dynamics, solar wind, ENSO climate, the Tennessee Eastman process, and a synthetic tokamak benchmark, enabling interpretable discovery of latent mechanisms in scientific time series.