ICLR 2026 论文列表

Cross-modal representation learning is fundamental for extracting structured information from multimodal data to enable semantic understanding and reasoning. However, current methods optimize statistical objectives without explicit causal constraints, where nonlinear mappings can introduce spurious dependencies or eliminate critical mediators, leading to representation-induced structural drift that undermines the reliability of causal inference. Therefore, establishing theoretical guarantees for causal invariance in cross-modal representation learning remains a foundational challenge. To this end, we propose Causal Alignment and Representation Learning (CARL), which explicitly embeds causal structure preservation constraints into cross-modal alignment objectives. Specifically, CARL introduces a multi-consistency loss architecture that jointly optimizes conditional independence preservation and information bottleneck regularization to balance cross-modal compression with critical variable retention, ensuring low-density modalities are not masked by high-density reconstruction demands. We further incorporate monotonic alignment consistency loss to establish correspondence between semantic similarity and representation distance through Spearman correlation, and Markov boundary preservation loss to maintain identifiability conditions including backdoor, frontdoor, and instrumental variable criteria in the shared representation space. In synthetic experiments with known causal ground truth, CARL achieves state-of-the-art performance in preserving conditional independence patterns and maintaining causal query identifiability under structural uncertainty. Real-world validation on Human Phenotype Project data reveals that CARL successfully preserves causal structures between fundus vascular representations and cardiovascular events, demonstrating its capacity for reliable cross-modal causal inference in complex biomedical applications.

Identifying the structure of a partially observed causal system is essential to various scientific fields. Recent advances have focused on constraint-based causal discovery to solve this problem, and yet in practice these methods often face challenges related to multiple testing and error propagation. These issues could be mitigated by a score-based method and thus it has raised great attention whether there exists a score-based greedy search method that can handle the partially observed scenario. In this work, we propose the first score-based greedy search method for the identification of structure involving latent variables with identifiability guarantees. Specifically, we propose Generalized N Factor Model and establish the global consistency: the true structure including latent variables can be identified up to the Markov equivalence class by using score. We then design Latent variable Greedy Equivalence Search (LGES), a greedy search algorithm for this class of model with well-defined operators, which search very efficiently over the graph space to find the optimal structure. Our experiments on both synthetic and real-life data validate the effectiveness of our method.

Quantile Partial Effect (QPE) is a statistic associated with conditional quantile regression, measuring the effect of covariates at different levels. Our theory demonstrates that when the QPE of cause on effect is assumed to lie in a finite linear span, cause and effect are identifiable from their observational distribution. This generalizes previous identifiability results based on Functional Causal Models (FCMs) with additive, heteroscedastic noise, etc. Meanwhile, since QPE resides entirely at the observational level, this parametric assumption does not require considering mechanisms, noise, or even the Markov assumption, but rather directly utilizes the asymmetry of shape characteristics in the observational distribution. By performing basis function tests on the estimated QPE, causal directions can be distinguished, which is empirically shown to be effective in experiments on a large number of bivariate causal discovery datasets. For multivariate causal discovery, leveraging the close connection between QPE and score functions, we find that Fisher Information is sufficient as a statistical measure to determine causal order when assumptions are made about the second moment of QPE. We validate the feasibility of using Fisher Information to identify causal order on multiple synthetic and real-world multivariate causal discovery datasets.

Existing causal discovery methods are fundamentally limited by the assumption of a static causal graph, a constraint that fails in real-world systems where causal relationships dynamically vary with underlying system parameters. This discrepancy prevents the application of causal discovery in critical domains such as industrial process control, where understanding how causal effects change is essential. We address this gap by proposing a new paradigm that moves beyond static graphs to learn functional causal representations. We introduce a framework that models each causal link not as a static weight but as a function of measurable system parameters. By representing these functions using Polynomial Chaos Expansions (PCE), we develop a tractable method to learn the complete parametric causal structure from observational data. We provide theoretical proofs for the identifiability of these functional models and introduce a novel, provably convergent learning algorithm. On a large-scale chemical reactor dataset, our method learns the dynamic causal structure with a 90.9% F1-score, nearly doubling the performance of state-of-the-art baselines and providing an interpretable model of how causal mechanisms evolve.