Causal Representation Learning

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.

Estimating heterogeneous treatment effects is central to targeted interventions, such as personalized promotions and precision medicine. We focus on the conditional average treatment effect (CATE), a standard estimand for characterizing such heterogeneity. Even under standard identification conditions, finite-sample CATE estimation requires learning the nuisance structure for covariate adjustment and treatment-effect heterogeneity, often together with an effective representation of X. Raw numerical and categorical encodings can leave semantic relations and higher-order interactions implicit, making this joint task locally unstable. A motivating study further shows that this instability appears through partially separable assignment- and heterogeneity-side channels. Building on this observation, we propose CURL (Causal Uncertainty-guided Representation Learning), a plug-in adapter that uses estimator uncertainty to allocate pretrained semantic capacity to locally unstable units. CURL queries a frozen LLM through two role-conditioned prompts, constructs assignment- and heterogeneity-oriented representations from the observed covariates, and routes them through separated pathways. On four benchmarks, CURL improves ten host learners in most settings, while ablation, refinement-dynamics, route-reassignment, and probe analyses support the intended design and roles of the two channels.

Consider a model trained at a single hospital to predict patient recovery, where the measured feature $X$ bundles the patient's true health signal ($C$) with a systematic artefact from that hospital's equipment ($S$). Within that hospital, the artefact correlates with outcomes through unmeasured confounders such as patient demographics; an in-context learner rationally routes predictions through $S$, not $C$, and fails silently when deployed at a new hospital with different equipment. We formalise this as \emph{spurious routing in composite representations}: when a feature $X = [C;\,αS;\,η]$ encodes a causal signal $C$ and a spurious signal $S$ in distinct subspaces, the ICL cannot determine which drives predictions. We prove that under ridge ICL, a linear in-context learner, this routing is unavoidable regardless of context size; TabPFN, a state-of-the-art pretrained tabular ICL model, shows qualitatively consistent behaviour empirically. We derive a closed-form characterisation, $\mathrm{CSR} \propto ρ_S/ρ_C$, confirmed at $r = 0.997$ for linear ICL and $r = 0.979$ for TabPFN. Contrary to intuition, larger context sharpens commitment to the dominant in-context signal, amplifying spurious routing by up to $1.74\times$; in the high-spurious corner, more expressive models show greater vulnerability empirically ($+2.22$ CSR gap at high entanglement). We introduce two lightweight mitigations: environment-stratified context construction and S-swap augmentation, that require only weak environment labels and no knowledge of the causal partition. S-swap reduces spurious routing by $74\%$ for linear ICL and $98.8\%$ for TabPFN, with TabPFN's causal sensitivity increasing $8.4\times$ simultaneously: the model does not become agnostic, it reroutes through the causal signal.

Deep Metric Learning (DML) often struggles with zero-shot generalization because standard objectives inherently capture what co-occurs rather than what causes similarity. Consequently, DML models are vulnerable to shortcut learning driven by two structurally distinct confounders: background spurious correlations (which create backdoor paths via scene context) and foreground nuisance perturbations (which inject non-semantic variations like pose or illumination). Although existing methods have proposed targeted solutions for each pathway individually, none can simultaneously address both due to their fundamentally distinct causal roles. To bridge this gap, we propose the Counterfactual Causal Embedding (CouCE), a unified causal framework that explicitly models and neutralizes both confounders. Specifically, we introduce Orthogonal Dictionary-Based Backdoor Adjustment (ODBA), which isolates spurious background patterns into a variance-gated dictionary and stably disentangles them from the learned embeddings via soft orthogonal regularization. Simultaneously, we propose Multi-Scale Randomized Causal Intervention (MSRCI) to enforce causal invariance against foreground nuisances through multi-scale Fourier amplitude randomization and a symmetric KL invariance constraint. Notably, CouCE seamlessly integrates with any proxy-based loss, incurring modest training overhead without requiring architectural modifications during inference. Extensive experiments on CUB-200-2011, Cars-196, and Stanford Online Products demonstrate that CouCE consistently achieves state-of-the-art performance, providing a principled and robust solution for debiased DML.

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.

Vertical federated learning (VFL) is a distributed learning paradigm that leverages vertically partitioned features across isolated parties without sharing raw samples; however, it remains vulnerable to active sample reconstruction attacks. Existing defenses fail to achieve a satisfactory trade-off between model utility and privacy protection, due to either suppressing task-relevant information alongside privacy-sensitive features or relying on end-to-end supervised training to converge the defense module, which exposes the model to early-epoch vulnerability. To address this challenge, we adopt a structural causal model (SCM) insight and construct CausShield. From a task-learning standpoint, causal features within a raw sample are those that are directly relevant and contributory to the learning objective, whereas non-causal features are task-irrelevant but often encode sample-specific private information, thereby facilitating reconstruction. Importantly, we lay a theoretical foundation to prove this insight. CausShield thus decomposes the shared representations between the client and the coordinating server in VFL into task-relevant and task-irrelevant components to ensure full-cycle privacy protection. Nonetheless, the decomposition is inherently challenging due to the dual objectives of preserving model utility while mitigating privacy leakage. We address this via a carefully formulated optimization problem, which is solved through unsupervised representation learning. We further theoretically prove that CausShield preserves the convergence behavior of standard VFL. Extensive experiments compare CausShield against seven SOTAs, including InvL (USENIX Security'25), and evaluate robustness against advanced reconstruction attacks such as URVFL (NDSS'25). Results demonstrate that CausShield consistently outperforms in privacy protection, model utility, and computational efficiency.

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.

Multi-task learning (MTL) aims to construct a joint model for multiple tasks by sharing a common representation across domains. To achieve this goal, existing optimization-centric methods either balance task gradients or modify the shared architecture. However, as these approaches remain agnostic to the content of the shared representation, they fail to disentangle task-relevant structure from spurious context, leading to negative transfer and poor generalization. To overcome this limitation, we propose Causal Orthogonal Representations for Multi-Task Learning (CORE-MTL), a causally motivated representation-centric framework that encourages a structured semantic-residual factorization of the shared representation, concentrating task-relevant structure in the semantic stream while relegating nuisance variation to the residual stream. We instantiate this framework in the visual domain by leveraging physical priors for structured scenes and statistical constraints for attributes. Theoretically, our method enjoys a tighter out-of-distribution generalization bound than optimization-centric methods and reduces task gradient interference without explicit gradient projection or reweighting. Empirically, CORE-MTL consistently outperforms existing methods on visual multi-task benchmarks in both in-distribution and out-of-distribution settings. Code is publicly available at https://github.com/Hope-Rita/CORE-MTL.

Bayesian optimization is a popular way to optimize expensive systems, where every experiment, simulation, or intervention costs time or money. In its standard form, it treats the variables we control as plain inputs to a black box and cannot tell apart mere correlation from a real cause and effect. Causal Bayesian optimization closes part of this gap by using a known causal graph together with observational data to decide which variables are worth intervening on. Existing methods, however, learn the effect of each possible intervention almost in isolation, even though in a causal system these effects usually share the same underlying mechanisms. We propose graph-coupled causal Bayesian optimization, which ties the different intervention effects together through the uncertainty we have about a small set of shared causal parameters. The result is a causal kernel that lets evidence collected from one intervention improve our estimate of related interventions. For identifiable linear Gaussian causal models, we show that this kernel has low rank, bounded by the number of shared parameters rather than by the size of the intervention menu. This in turn yields an information-gain bound that grows only logarithmically in the optimization horizon, and a regret bound that cleanly separates three sources of error: optimization, causal estimation, and the choice of which intervention sets to consider. We also describe nonlinear and adaptive extensions. Across theory-aligned Gaussian systems, shared-mechanism stress tests, and standard causal optimization benchmarks, the method keeps the benefits of causal Bayesian optimization while transferring information across related interventions, with the clearest gains when direct interventions on the target's parents are unavailable and sparse interventional data must be reused across a large family of candidate interventions.

Predictive models trained on observational data often fail to generalise to the distributions they encounter when deployed, especially when the training data is a product of the system being optimised. Recommender systems are a canonical example: they are trained on interaction logs confounded by the deployed policy, past user behaviour, and platform filtering. As a result, the training distribution differs substantially from the candidate distribution scored at serving time, a gap that makes offline metrics unreliable predictors of online performance. We address the distribution shift problem with a method motivated by causal representation learning (CRL). We propose an information-theoretic disentanglement criterion and prove that its optimum depends only on the causal components of the input. We then derive a tractable variational lower bound that makes the criterion optimisable from finite observational data alone. The scope of our method is narrower than that of much of the CRL literature, in that we target better generalisation under distribution shift, not full identification of all latent causal factors. This narrower target is what makes the method practical, requiring only the existing confounded logs, applying to any standard supervised model, and adding no inference-time cost. Our headline evaluation is an A/B test with millions of users on Spotify, applied to a production ranker for personalised playlist generation. A capacity-matched CRL variant performed on par offline but delivered substantial online gains in listener engagement. Complementary evidence on the public KuaiRand recommendation dataset and a synthetic benchmark with known causal structure shows the same pattern: offline parity with baseline, gains under distribution shift. Across all three settings, adding our causal disentanglement objective yields meaningfully better out-of-distribution generalisation.

Single-cell perturbation prediction aims to infer how cells respond to unseen interventions and to achieve out-of-distribution (OOD) generalization, providing a computational route to understanding how perturbations reshape cellular programs over time. Existing machine learning methods have made important progress, but typically capture only one side of the response. Latent causal approaches seek mechanisms that support generalization and interpretation, yet often treat perturbation effects as static outcomes. Temporal models describe how gene expression changes across time, but usually do not explicitly recover the latent causal generative mechanisms driving these changes. In practice, perturbation effects are both latent and dynamical: interventions act through unobserved cellular programs, whose states evolve over time and give rise to observed expression profiles. Motivated by this view, we propose a latent dynamical causal generative model for single-cell perturbation data that jointly captures latent cellular programs, perturbation-conditioned mechanisms, and temporal evolution. We further provide an identifiability analysis showing that, under suitable conditions, the latent causal variables are recoverable up to standard equivalence classes. Guided by this analysis, we develop CITE-VAE, a learning framework for recovering latent cellular programs and their perturbation-driven dynamics from single-cell sequencing data. Experiments on Causal-3DIdent validate the theoretical results and the effectiveness of the proposed method in controlled settings. Additional experiments on real-world CRISPR-based single-cell perturbation data show improved generalization to unseen perturbations compared with state-of-the-art baselines, highlighting the practical robustness of our approach.

Prediction models trained under the source distribution do not generalize well to a different target distribution. A valid inference about an unseen data distribution must be anchored by the invariance of certain causal mechanisms that generate the source and target data, however, these structural invariances are non-identifiable from the source data alone. Under mild causal assumptions about the data, we show that the optimal prediction in the target is in fact partially identifiable by the source distribution. The result rests on a simple observation: In any domain, the optimal prediction can be factorized into what we call a pair of abduction and deduction maps, where the abduction map makes inference about some unobserved variables (possibly confounders) from the observed variables and the deduction map predicts the label using both the observed and inferred quantities. Access to large source data pins down the optimal prediction, thus constrains the valid abduction-deduction ensembles that produce it -- a non-identifiability that we call the abduction-deduction entanglement. To leverage this, we parameterize the constrained family using what we call a representation transplant, that is a specific linear transformation in the representation space that manipulates the abduction content of the representation while retaining the deduction component. Invariance of the causal mechanism generating the label implies existence of an invariant deduction map between source and target. Thus, we can search the space of plausible target distributions via a parametric transplant. We use this scheme in a learner-adversary game that, under an idealistic optimization, provably terminates with the learner having the minimax-optimal target prediction. Evaluations verify the theory, showing that the method is competitive in DG benchmarks.

Causal representation learning (CRL) and traditional representation learning have largely developed along different trajectories. Traditional representation learning has been driven mainly by applications and empirical objectives, whereas CRL has focused more on theoretical questions, particularly identifiability. This difference in emphasis has created a gap between the two fields in terminology, problem formulation, and evaluation, limiting communication and sometimes leading to disconnected or redundant efforts. In this paper, we argue that these two fields should be brought into dialogue rather than treated as separate paradigms. To this end, we introduce a unified formulation in which the representation learning is characterized by two components: a task component, which specifies what information the learned representation is required to preserve, and a constraint component, which specifies what structure is imposed on the latent space. Under this formulation, the benefits run in both directions. CRL provides theoretical tools for understanding when structured latent constraints are useful or necessary, while traditional representation learning offers practical insights on task design and objective choice that can improve the development of CRL methods. To illustrate this interaction, we experimentally study how different task components affect the behavior of CRL methods under different structured constraints. Results on CausalVerse show that the effectiveness of causal constraints depends strongly on the tasks with which they are paired.

Identifying latent variables and the causal structure involving them is essential across various scientific fields. While many existing works fall under the category of constraint-based methods (with e.g. conditional independence or rank deficiency tests), they may face empirical challenges such as testing-order dependency, error propagation, and choosing an appropriate significance level. These issues can potentially be mitigated by properly designed score-based methods, such as Greedy Equivalence Search (GES) (Chickering, 2002) in the specific setting without latent variables. Yet, formulating score-based methods with latent variables is highly challenging. In this work, we develop score-based methods that are capable of identifying causal structures containing causally-related latent variables with identifiability guarantees. Specifically, we show that a properly formulated scoring function can achieve score equivalence and consistency for structure learning of latent variable causal models. We further provide a characterization of the degrees of freedom for the marginal over the observed variables under multiple structural assumptions considered in the literature, and accordingly develop both exact and continuous score-based methods. This offers a unified view of several existing constraint-based methods with different structural assumptions. Experimental results validate the effectiveness of the proposed methods.

Single-cell perturbation modeling is fundamental for understanding and predicting cellular responses to genetic perturbations. However, existing approaches, from causal representation learning to foundation models, often struggle with an overlooked challenge: gene expression is dominated by perturbation-invariant information, while perturbation-specific signals are intrinsically sparse. As a result, learned representations either entangle invariant and perturbation-specific information, leading to spurious and non-generalizable predictors, or suppress perturbation-specific signals altogether, rendering them ineffective for prediction. To address this, we propose PerturbedVAE, a general framework designed to resolve this signal imbalance. The framework explicitly separates perturbation-specific information from dominant invariant structure and recovers causal representations to effectively utilize such information for prediction. We further provide an identifiability analysis that characterizes the conditions under which sparse perturbation effects can be reliably recovered, thereby clarifying how the framework can be concretely specified under such conditions. Empirically, PerturbedVAE achieves state-of-the-art performance on a widely used benchmark across multiple evaluation settings, yielding significant gains on out-of-distribution combinatorial predictions and uncovering interpretable perturbation-response programs.

Causal representation learning (CRL) seeks to uncover meaningful latent variables and their corresponding causal structure from high-dimensional observational data. Although its significance, CRL identifiability remains a crucial property, as it ensures the recovery of the mechanisms behind the data generation process, and hence the interpretability and robustness of the representation. Proving identifiability in CRL is intrinsically difficult, and we address in this work an even more challenging setting: multimodality. We consider multimodal observed data with a latent partially shared structure. Each modality is generated, through non linear mixing functions, from a specific subset of causal latent variables. Under flexible assumptions and without imposing any parametric distribution on the latent variables, we establish component-wise identifiability guarantees for the causal latent representation. Our identifiability results, furthermore, apply to the undercomplete scenario where we have, for each modality, more observed than latent variables. To instantiate our theoretical analysis, we introduce a Wasserstein-based module to recover the partially shared latent structure. Due to its differentiability, the latter can be easily integrated into all types of architecture, only requiring minimal changes. Extensive experiments on synthetic and realistic datasets validate the superiority of our approach over SOTA methods.

Automatic misinformation detection performs well when deception is visible in what an article explicitly states. However, some misinformation articles remain locally coherent and only become misleading once compared with contemporaneous reports that supply background facts the article omits. We study this omission-relevant setting and observe that current omission-aware approaches typically either attach retrieved context as auxiliary evidence or infer a categorical omission signal, leaving the specific missing fact implicit. We propose \emph{Latent Causal Void} (LCV), a retrieval-guided detector that explicitly reconstructs the missing fact for each target sentence and uses it as a textual cross-source relation in graph reasoning. Concretely, LCV retrieves temporally aligned context articles, asks a frozen instruction-tuned large language model to generate a short missing-context description for each sentence--article pair, and feeds the resulting relation text into a heterograph over target sentences and context articles. On the bilingual benchmark of Sheng et al., LCV improves over the strongest omission-aware baseline by $2.56$ and $2.84$ macro-F1 points on the English and Chinese splits, respectively. The results indicate that modeling the missing cross-source fact itself, rather than only attaching retrieved evidence or predicting an omission signal, is a useful representation for omission-aware misinformation detection.

Recent work on causal abstraction, in particular graphical approaches focusing on causal structure between clusters of variables, aims to summarize a high-dimensional causal structure in terms of a low-dimensional one. Existing methods for learning such summaries from data assume that both the high- and low-dimensional structures are acyclic, which is helpful for causal effect identification and reasoning but excludes many high-dimensional models and thus limits applicability. We show that in the linear non-Gaussian (LiNG) setting, the high-dimensional acyclicity assumption can be relaxed while still allowing recovery of a low-dimensional causal directed acyclic graph (DAG). We further connect identifiability of this low-dimensional DAG to existing results: LiNG models with cycles are observationally identifiable only up to an equivalence class whose members differ by reversals of directed cycles; our low-dimensional DAG, which is invariant across all members of a given equivalence class, thus forms a natural representative of the class. While existing approaches for learning this observational equivalence class over high-dimensional variables have exponential time complexity, our low-dimensional summary is learned in worst-case cubic time and comes with explicit bounds on the sample complexity. We provide open source code and experiments on synthetic data to corroborate our theoretical results.

Query-separated computation forces a representation to play an operational role: data are encoded before a query is known, and a later decoder can answer only through the intermediate interface. In this regime the representation functions as a message rather than merely as a feature map. We formalize this observation by embedding information causality (IC) into representation learning, obtaining a framework called neural information causality (Neural-IC). The revised formulation separates two logically distinct statements. First, every query-separated architecture induces a random-access communication experiment and obeys the embedding inequality $I_{\mathrm{N\text{-}RAC}}\le I(\vec a:H,B)$. Second, any independently certified physical capacity bound on the interface, such as a hard $m$-bit alphabet, a finite-precision register, or a power-constrained noisy channel, implies $I_{\mathrm{N\text{-}RAC}}\le C_H$. This separation avoids treating capacity as a post hoc definition and makes Neural-IC an operational diagnostic for query leakage, precision leakage, and episode-specific memory. We also provide an exact one-bit classical RAC benchmark, showing explicitly that the relevant quantum enhancement is not total information beyond the bottleneck, but fair query-conditioned access. For CHSH-type correlation layers, nested Neural-RAC protocols multiply correlation biases across depth; requiring stability of a one-bit bottleneck for arbitrary depth selects the Tsirelson threshold. We extend the analysis to asymmetric seed biases, to multi-capacity finite-depth phase diagrams, and to correlated data via a conditional information score. Controlled simulations, including straight-through binary bottlenecks and deliberately leaky ablations, verify that apparent violations are accounted for by broken query separation or undercounted capacity.

Natural Language Processing is rapidly evolving into a primary instrument for Computational Social Science, with researchers increasingly using embeddings to measure latent constructs such as novelty, creativity, and bias. However, this transition faces a fundamental validity challenge: the ''Proxy Presumption,'' or the reliance on geometric properties (e.g., cosine distance) as direct measures of social concepts. We argue that without explicit validation, unsupervised representations remain entangled mixtures of the target construct ($C$) and confounding attributes ($Z$) like topic, style, and authorship. To bridge the gap between semantic embeddings and valid social measures, we introduce the Construct Validity Protocol (CVP). Drawing on causal representation learning and psychometrics, the CVP offers a rigorous pipeline from conceptualization to quantitative verification. We further propose Counterfactual Neutralization, a novel method using LLMs to reduce confounding in embedding space. By providing a standardized Validity Suite -- including tests for discriminant, incremental, and predictive validity -- this work offers the community a toolkit to transform heuristic proxies into robust, scientifically defensible instruments.

Online reinforcement learning (RL) relies on the Markov property for guaranteed performance, but real-world applications often lack well-defined states given raw observed variables. While causal RL has attracted growing interest, existing work typically assumes Markovian states are provided and focuses on using causality to accelerate learning, leaving a fundamental gap: \emph{given a longitudinal causal graph over observed variables, how does one construct MDP states that provably satisfy the Markov property?} We address this by providing a procedure that constructs a provably minimal state representation. In deep RL, we observe that the minimal representation alone empirically fails to improve performance, indicating that neural networks cannot directly exploit Markovian minimality. To address this, we propose \textbf{MOSE} (Multi-Order State Exposure), which feeds multi-order historical state constructions into the same $Q$-function. MOSE consistently outperforms both the minimal state construction and single-window policies on common benchmarks and synthetic datasets. Including the minimal representation alongside MOSE can further improve performance. Our results establish a core principle for causal deep RL: minimal sufficiency is not enough, and \emph{controlled redundancy} is necessary to unlock the benefit of causal state information.

Estimating individualized treatment effects from longitudinal observational data is central to data-driven medicine, yet existing methods face a fundamental limitation: reducing confounding bias often suppresses clinically informative heterogeneity, degrading patient-specific predictions. Here, we identify this tension as a bias-precision paradox in causal representation learning and introduce sampling-based maximum mean discrepancy (sMMD), a stochastic alignment strategy that replaces global adversarial balancing with subset-level matching. We instantiate this approach in a framework for counterfactual outcome prediction with attribution-grounded interpretability. Across two large-scale ICU cohorts (n = 27,783), our framework improves accuracy under distribution shift, reducing error by up to 11.5% and substantially increasing recall in high-risk tasks. Mechanistic analyses show that sMMD selectively preserves clinically decisive variables. In human-AI evaluation, our method outperforms clinicians-in-training and large language models, and improves clinician accuracy by 14.7% while reducing decision time, enabling interpretable, real-time clinical decision support.

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.

We report a systematic failure mode in predictive representation learning. Across 2695 neural network configurations trained to predict linear-Gaussian dynamics, the optimal encoder tracks the environment rather than the system it is meant to model. The mean causal fidelity -- the fraction of encoder sensitivity allocated to system degrees of freedom -- is 0.49, and only 2.5% of configurations exceed 0.70. The failure intensifies with dimension: at N=100, the optimal encoder becomes causally blind (fidelity ~10^{-8}) while achieving 92% lower prediction error than the causal representation. We prove this is not an optimization artifact but a structural property of the predictive objective: when environment modes are slower or less noisy than system modes, every minimizer of the population risk encodes the former. The set of dynamics exhibiting this predictive-causal gap is open and of positive measure in parameter space. In a nonlinear Duffing-GRU sweep, unconstrained predictors learn environment-dominant representations in 55% of tasks (95% CI 41--68%) versus 24% under operational grounding (p=2.3e-3); the median out-of-distribution MSE inflation under environment shift is 1.82x versus 1.00x. Operational grounding -- restricting the loss to system observables -- partially suppresses the gap, but causal fidelity is never recovered without an explicit system-environment boundary. The results identify the predictive-causal gap as a structural limit of learning, with implications for self-supervised representation learning, world models, and the scaling paradigm.

We consider learning from labeled data collected across multiple environments, where the data distribution may vary across these environments. This problem is commonly approached from a causal perspective, seeking invariant representations that retain causal factors while discarding spurious ones. However, this framework assumes that the environment has no direct effect on the target. In contrast, we consider settings in which this assumption fails, but still aim to learn representations that support robust prediction on average across previously unseen environments. To this end, we study representations learned by explicitly modeling variation across environments and then marginalizing that variation out. We analyze the resulting representations and characterize when they are preferable to those learned by causal invariant-representation methods. We propose a concrete method based on generalized random-intercept models, a class of predictors in which such marginalization is possible, and study their generalization properties. Empirically, we show that these models outperform invariant-learning methods across a range of challenging settings.

Causal representation learning aims to recover the latent causal variables and their causal relations, typically represented by directed acyclic graphs (DAGs), from low-level observations such as image pixels. A prevailing line of research exploits multiple environments, which assume how data distributions change, including single-node interventions, coupled interventions, or hard interventions, or parametric constraints on the mixing function or the latent causal model, such as linearity. Despite the novelty and elegance of the results, they are often violated in real problems. Accordingly, we formalize a set of desiderata for causal representation learning that applies to a broader class of environments, referred to as general environments. Interestingly, we show that one can fully recover the latent DAG and identify the latent variables up to minor indeterminacies under a nonparametric mixing function and nonlinear latent causal models, such as additive (Gaussian) noise models or heteroscedastic noise models, by properly leveraging sufficient change conditions on the causal mechanisms up to third-order derivatives. These represent, to our knowledge, the first results to fully recover the latent DAG from general environments under nonparametric mixing. Notably, our results match or improve upon many existing works, but require less restrictive assumptions about changing environments.

We address Human Activity Recognition (HAR) utilizing Wi-Fi Channel State Information (CSI) under the joint requirements of causal interpretability, symbolic controllability, and direct operation on high-dimensional raw signals. Deep neural models achieve strong predictive performance on CSI-based HAR (CHAR), yet rely on continuous latent representations that are opaque and difficult to modify; purely symbolic approaches, in contrast, cannot process raw CSI streams. We propose a fully automatic and strictly decoupled pipeline in which CSI magnitude windows are compressed by a categorical variational autoencoder with Gumbel-Softmax latent variables under a capacity-controlled objective, yielding a compact discrete representation. The encoder is then frozen and used as a deterministic mapping to one-hot latent trajectories. Causal discovery is performed on these trajectories to estimate class-conditional temporal dependency graphs. Statistically supported lagged dependencies are translated into Linear Temporal Logic (LTL) rules, producing a fully symbolic and deterministic classifier based solely on rule evaluation and aggregation, without any learned discriminative head. Because rules are defined over discrete latent variables, antenna-specific rule sets can in principle be combined at the symbolic level, enabling structured multi-antenna fusion without retraining the encoder. Results from CHAR Latent Temporal Rule Extraction (CHARL-TRE) indicate competitive performance while preserving explicit temporal and causal structure, showing that deterministic symbolic classification grounded in unsupervised discrete latent representations constitutes a viable alternative to end-to-end black-box models for wireless HAR.

Multimodal affective computing aims to predict humans' sentiment, emotion, intention, and opinion using language, acoustic, and visual modalities. However, current models often learn spurious correlations that harm generalization under distribution shifts or noisy modalities. To address this, we propose a causal modality-invariant representation (CmIR) learning framework for robust multimodal learning. At its core, we introduce a theoretically grounded disentanglement method that separates each modality into causal invariant representation' and environment-specific spurious representation' from a causal inference perspective. CmIR ensures that the learned invariant representations retain stable predictive relationships with labels across different environments while preserving sufficient information from the raw inputs via invariance constraint, mutual information constraint, and reconstruction constraint. Experiments across multiple multimodal benchmarks demonstrate that CmIR achieves state-of-the-art performance. CmIR particularly excels on out-of-distribution data and noisy data, confirming its robustness and generalizability.

Joint-embedding self-supervised learning (SSL), the key paradigm for unsupervised representation learning from visual data, learns from invariances between semantically-related data pairs. We study the one-to-many mapping problem in SSL, where each datum may be mapped to multiple valid targets. This arises when data pairs come from naturally occurring generative processes, e.g., successive video frames. We show that existing methods struggle to flexibly capture this conditional uncertainty. As a remedy, we introduce a latent variable to account for this uncertainty and derive a variational lower bound on the mutual information between paired embeddings. Our derivation yields a simple regularization term for standard SSL objectives. The resulting method, which we call AdaSSL, applies to both contrastive and distillation-based SSL objectives, and we empirically show its versatility in causal representation learning, fine-grained image understanding, and world modeling on videos.

Temporal causal representation learning methods assume that causal mechanisms switch instantaneously between discrete domains, yet real-world systems often exhibit continuous mechanism transitions. For example, a vehicle's dynamics evolve gradually through a turning maneuver, and human gait shifts smoothly from walking to running. We formalize this setting by modeling transitional mechanisms as convex combinations of finitely many atomic mechanisms, governed by time-varying mixing coefficients. Our theoretical contributions establish that both the latent causal variables and the continuous mixing trajectory are jointly identifiable. We further propose TRACE, a Mixture-of-Experts framework where each expert learns one atomic mechanism during training, enabling recovery of mechanism trajectories at test time. This formulation generalizes to intermediate mechanism states never observed during training. Experiments on synthetic and real-world data demonstrate that TRACE recovers mixing trajectories with up to 0.99 correlation, substantially outperforming discrete-switching baselines.

We treat the internals of generative models as mechanistic objects rather than black boxes. We introduce \textbf{Attribution Graphs} (AGs), which extend GradCAM++ to circuit-level representations, and \textbf{Causal Probing}, a do-calculus intervention method for identifying causal latent structures, enabling detection and correction of spurious correlations, demographic biases, and misaligned decision circuits during training. We further propose the \textbf{Cognitive Alignment Score (CAS)}, quantifying agreement between model-internal representations and human concepts, a \textbf{saliency-first privacy mechanism} sharing only thresholded attribution nodes, a bias-aware regularizer aligning subgroup statistics, and a Reveal-to-Revise loop integrating attribution signals into parameter updates without separate fine-tuning. Evaluated on CelebA, FairFace, Jigsaw, and HateXplain, our method achieves \textbf{94.1%} accuracy, \textbf{92.3%} macro F1, \textbf{79.4%} IoU-XAI, and \textbf{12.7} FID at 72--76% adversarial robustness, while reducing subgroup disparity $Δ_{\mathrm{bias}}$ by \textbf{41%}, demonstrating that mechanistic interpretability, fairness, and generative performance can be jointly optimized.

In this work, we establish the sufficient conditions under which nonlinear Canonical Correlation Analysis (CCA) recovers ground-truth latent factors up to an affine transformation. By transporting the analysis from the observation space to the source space, we extend classical statistical results on orthogonal polynomial expansions of bivariate distributions to representation learning, proving affine identifiability under specific distributional priors. We formally demonstrate that whitening is strictly necessary to ensure the boundedness and well-conditioning of the learned mappings. Furthermore, we bridge the gap between theory and practice by proving that ridge-regularized empirical CCA converges to its population counterpart in the finite-sample regime. Finally, our findings provide a rigorous theoretical foundation explaining the empirical success of recent correlation-based non-contrastive learning methods. Experiments on synthetic and rendered image datasets, alongside systematic ablations, validate the predicted recovery behavior and illustrate the failure modes that arise when the assumptions are violated.

We evaluate methods for causal representation learning (CRL) on a simple, real-world system that satisfies the basic problem setup of CRL. The system consists of a controlled optical experiment producing a variety of measurements where the underlying causal factors---the control inputs to the experiment---are known, providing a ground truth. We select methods representative of different approaches to CRL and find that they all fail to consistently recover the underlying causal factors. To understand the failure modes of the evaluated algorithms, we perform an ablation on the data by substituting the real data-generating process with a simpler synthetic equivalent. The results reveal a reproducibility problem, as most methods already fail on this synthetic ablation despite its simple data-generating process. Additionally, we observe that common assumptions on the mixing function are crucial for the performance of some of the methods but do not hold in the real data. Our efforts highlight the contrast between the theoretical promise of the state of the art and the challenges in its application. We hope the benchmark serves as a simple, real-world sanity check to further develop and validate methodol- ogy, bridging the gap towards CRL methods that work in practice.