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

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, with finite-sample recovery guarantees for a group-lasso estimator and empirical evaluation of MOSAIC's entropy regularizer. 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.

Accepted at NeurIPS 2026. 39 pages, including references and appendices

Machine Learning (cs.LG); Artificial Intelligence (cs.AI)

arXiv:2605.05524 [cs.LG]

(or arXiv:2605.05524v2 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2605.05524 Focus to learn more arXiv-issued DOI via DataCite

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