Causal representation learning (CRL) aims to recover latent causal variables and their structural relations from high-dimensional observations. Existing CRL methods typically assume that all environments are defined over the same latent variables, or at least share a common latent representation space. We study a fragmented multi-client setting, where multiple clients interact with the same global latent causal system but each client only accesses and intervenes on a subset of the latent variables. In this regime, marginalizing unused latent variables induces bidirected edges, so a single client no longer admits a node-wise latent causal graph, and the global latent causal order must be recovered by assembling client-specific structural fragments. We propose \textbf{Jigsaw-CRL}, a framework for recovering global latent causal order from such fragmented interventions. Under soft interventions, differences between precision matrices across environments exhibit a low-rank structure governed by latent ancestor relations. This enables recovery, for each client, of a block partition, the corresponding block-level ancestral order, and latent subspaces, and then assembly of these fragments into the global node-level latent causal order. We establish identifiability guarantees, develop practical algorithms, and validate the framework on synthetic data. Our codes are available on https://anonymous.4open.science/r/code-for-Jigsaw-CRL-7B26
World Models (WM) are increasingly seen as a foundation for intelligent agents that can predict, plan, and act beyond their training distribution. In this paper, we study WMs from a causal perspective across multiple levels of abstraction, ranging from perceptual observations to building a conceptual representation of the structure governing the environment dynamics. We argue that useful WMs must go beyond generative capabilities alone: they should also capture entity properties, entity-to-entity interactions, and entity-to-environment interactions that determine and explain the dynamics of a system. We provide a formal definition of Causal WMs (CWMs) grounded in the tasks they are intended to support, connecting world modelling with existing work in causal representation learning, object-centric learning, causal discovery, structural causal models, and model-based decision-making. Finally, we relate CWMs to the literature on identifiability, clarifying when the components of a WM can be recovered from data and up to which equivalence. With this, we ground WMs in representations and structures that support causal reasoning and informed decision-making.
Domain generalization (DG) aims to learn from multiple source domains and generalize to unseen target domains. Most DG methods pursue invariance: they seek a causal representation whose prediction rule is invariant across domains. This principle is effective when the causal mechanism is stable, but becomes restrictive when the domain itself modulates how causal content maps to the response. In this case, directly feeding domain style into the predictor can create misleading shortcuts, since style does not by itself cause the response. Yet the apparent chaos of multiple styles can become a ladder: style can locate the unseen target domain among source domains and guide which domain-dependent prediction rules should be trusted. We propose \emph{Latent Adaptive Domain Disentanglement and Environment Reweighting} (LADDER), a fixed-model DG pipeline that learns causal/style representations, freezes the encoders, fits source-specific classifiers, and uses an unlabeled target-domain covariate set only at inference to compute weights over these fixed classifiers, with no target labels or model-state updates. We establish theoretical guarantees for source reweighting and validate LADDER on simulations, FMoW, and a location-grouped iWildCam protocol, with gains in overall and group-averaged accuracy.
Recent advances in foundation models have transformed AI for Science, enabling remarkably accurate predictive performance across domains ranging from protein folding to weather forecasting. Yet prediction alone does not constitute scientific discovery. Scientific understanding depends on uncovering the reusable explanatory mechanisms that generate observations, whereas contemporary machine learning remains fundamentally organised around predictive mappings rather than explanatory structure. In this paper, we argue that scientific discovery is fundamentally a problem of knowledge organisation. To this end, we introduce Mechanistic World Models, a new design paradigm that places reusable mechanisms at the centre of representation, computation and learning. Drawing on insights from the philosophy of science, we derive the computational capabilities required for discovery, identify the design principles and inductive pressures that encourage explanatory knowledge to emerge, and formalise the anatomy of a mechanism-centric world model. Finally, we show how diverse research directions including mechanistic interpretability, causal representation learning, equation discovery and modular architectures capture complementary ingredients of this paradigm while lacking a unified framework. We propose Mechanistic World Models as a conceptual foundation and computational blueprint for moving AI beyond predictive forecasting towards autonomous scientific discovery.
In multi-source image fusion scenarios, heterogeneous inputs are typically driven by distinct generative mechanisms and can be viewed as a composition of multiple causal systems. However, cross-system discrepancy (CSD) and cross-system entanglement (CSE) commonly arise during the fusion process, often leading to significant performance degradation under out-of-distribution (OOD) predictions. To address the CSD and CSE issues, we propose the additive causal construction (ACC) framework, which characterizes information fusion at two levels: firstly, it establishes causal "anchors" shared among multiple systems through intervention consistency to enable causal graph transferability (CGT); and secondly, it formalizes the fusion process as causal construction and models the reliability of constructed paths through uncertainty quantification to ensure causal graph reconfigurability (CGR). Building upon this, we revisit the traditional causal representation learning (CRL) with ACC and propose ACC-CRL as a learnable instantiation of the framework. The method explores joint causal content representations across systems via content-mechanism decoupling, and performs response alignment under shared anchors to mitigate CSD. Furthermore, it incorporates structural uncertainty to adaptively regulate the fusion process, thereby suppressing unstable CSE. We conduct systematic experiments on synthetic data (ColorMNIST) and real-world multi-center medical imaging tasks (microvascular invasion (MVI) prediction). The results demonstrate that the proposed method significantly improves OOD generalization while maintaining in-distribution (ID) performance, validating the effectiveness and robustness of the ACC-CRL strategy based on mechanism alignment and uncertainty modeling in open environments.
Yuanyuan Wang, Wenjie Wang, Haoxuan Li +2cs.LG stat.ML
Causal representation learning for time series has developed strong identifiability results in discrete-time latent causal models, but identifiability in continuous-time latent stochastic differential equation (SDE) models remains largely open. We address this gap using environment-induced shifts in diffusion covariance. We study additive-noise latent SDEs observed through an unknown nonlinear diffeomorphism, with shared drift but environment-specific diffusion covariance. We show that two diagonal diffusion regimes with pairwise distinct coordinate-wise variance ratios identify the latent coordinates up to permutation and scaling, without any sparsity assumption on the drift. We first prove this result for linear Ornstein--Uhlenbeck systems and then extend it to general additive-noise latent SDEs. Under mild smoothness, the instantaneous drift-Jacobian causal graph is identifiable up to the same permutation. We propose a two-stage estimator for latent disentanglement and optional graph recovery; experiments on synthetic systems confirm the predicted identifiability boundary, and an application to Hardanger Bridge monitoring data illustrates the approach on real sensor trajectories.
Reliable generalization in conditional latent variable models requires understanding both identifiability and extrapolation: how observed variation across attributes determines latent structure, and how that structure determines distributions at unseen attributes. However, existing identifiability and extrapolation guarantees are largely model-specific, with separate analyses in nonlinear ICA, causal representation learning, perturbation modeling, and related conditional latent variable models. We introduce concept modulation models (CMMs), an attribute-indexed class of conditional generative models with structure $A\to Λ\to C\to X$, where attributes select modulators, modulators induce latent concept laws, and concepts generate observed features. CMMs lift transition-based identifiability to conditional settings by showing that feature agreement on observed attributes induces a latent concept transition constrained by the CMM class. We express these constraints through attribute potentials, log-density ratios between attribute-conditioned concept laws, separating the generic lifting step from model-specific rigidity arguments. The same potentials control extrapolation: agreement at unseen attributes holds exactly when the transported attribute-potential identities extend to those attributes. This yields algebraic extrapolation criteria, identifies the common potential-based proof objects behind several existing identifiability and extrapolation results, and, when combined with the model-specific rigidity arguments in those works, recovers their stated conclusions.
Ankur Garg, Michael Stettler, Aaron Schein +1stat.ML cs.LG
Causal representation learning aims to infer the high-level latent causal concepts that give rise to observed low-level measurements. This is particularly relevant for heterogeneous data from different environments or domains since distribution shifts often arise through sparse, localized changes in some of the underlying causal mechanisms, while other parts of the generative process remain unchanged. Whereas identifiability of causal representations has been studied extensively, practical uncertainty-aware methods and real-world use cases remain less explored. In this work, we propose a Bayesian approach to learning causal representations from multi-environment data, focusing on the case of discrete causal concepts and unknown multi-node soft interventions. To this end, we translate causal assumptions and interpretability desiderata into suitable priors and parametric choices within a hierarchical model. We then devise an inference scheme based on sequential Monte Carlo sampling to approximate the resulting multimodal posterior. We showcase our approach through case studies on social survey data, where latent causal concepts correspond to cultural values or political opinions, measurements to survey responses, and environments to different countries or states. Our model infers meaningful high-level concepts and plausible causal relations among them, demonstrating its utility for learning causal representations of complex real-world data.