Structure-agnostic Causal Representation Learning

arXiv:2610.00968v1 Announce Type: cross Abstract: Causal representation learning aims to discover robust features by exploiting the causal structure underlying data generation. Existing methods require specifying the causal structure a priori, yet different structures demand fundamentally incompatible invariance constraints, and misspecification leads to representations that discard predictive information. We introduce SaCRL, a framework that jointly identifies the causal structure and learns the corresponding invariant representation without prior structural knowledge. Our approach formulates structure selection as a soft optimization over candidate invariances using HSIC-based violation metrics, with adaptive weights that automatically concentrate on the achievable structure. We provide theoretical guarantees for structure identification, including under random-feature approximation, invariance satisfaction, and out-of-distribution generalization. Empirically, SaCRL recovers the true structure on synthetic and semi-synthetic Bayesian-network benchmarks, outperforms fixed-invariance baselines on Colored MNIST, achieves state-of-the-art accuracy on three DomainBed benchmarks (PACS, VLCS, OfficeHome), and degrades gracefully under structural misspecification and limited environment diversity. Code is available at: https://github.com/ArmanBehnam/sacrl.

Abstract:Causal representation learning aims to discover robust features by exploiting the causal structure underlying data generation. Existing methods require specifying the causal structure a priori, yet different structures demand fundamentally incompatible invariance constraints, and misspecification leads to representations that discard predictive information. We introduce SaCRL, a framework that jointly identifies the causal structure and learns the corresponding invariant representation without prior structural knowledge. Our approach formulates structure selection as a soft optimization over candidate invariances using HSIC-based violation metrics, with adaptive weights that automatically concentrate on the achievable structure. We provide theoretical guarantees for structure identification, including under random-feature approximation, invariance satisfaction, and out-of-distribution generalization. Empirically, SaCRL recovers the true structure on synthetic and semi-synthetic Bayesian-network benchmarks, outperforms fixed-invariance baselines on Colored MNIST, achieves state-of-the-art accuracy on three DomainBed benchmarks (PACS, VLCS, OfficeHome), and degrades gracefully under structural misspecification and limited environment diversity. Code is available at: this https URL.

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

arXiv:2610.00968 [cs.LG]

(or arXiv:2610.00968v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.00968 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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Structure-agnostic Causal Representation Learning

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