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

2026-05-06

AI Summary

This work addresses the challenge that the underlying causal mechanisms of scientific time series are often unknown, and while existing causal representation learning methods offer identifiability, they typically lack semantic interpretability. To bridge this gap, the authors propose MOSAIC, a novel approach that uniquely transfers semantic interpretability from observed variables to an identifiable latent space. MOSAIC employs an additive decoder to associate each latent variable with a sparse subset of observations, providing theoretical guarantees for support recovery under finite samples. The method integrates a sparse temporal variational autoencoder, additive mixing functions, ANOVA-based main effect analysis, and mechanism-switching-driven latent variable identification. Evaluated on diverse datasets—including RNA dynamics, solar wind, ENSO climate phenomena, the Tennessee Eastman process, and tokamak plasma data—MOSAIC successfully recovers domain-consistent variable modules, enabling interpretable discovery of latent causal 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.

Problem

• causal representation learning
• interpretability
• scientific time series
• identifiability
• latent variables

Innovation

• identifiable causal representation learning
• sparse additive decoder
• module discovery
• scientific time series
• temporal VAE