NeurIPS 2026 Papers

It is often easier to destroy the causal content of a training sample than to isolate it. We use this observation to expose shortcut gradients during training. If an intervention removes the semantic evidence that justifies a sample's label while preserving nuisance structure, then any predictive gradient the model still produces on the destroyed view points toward features that can support the label without the causal signal. The destroyed view is constructed from the same sample as the clean view, and the implemented optimizer estimates this shortcut direction on the current minibatch and applies the steering step periodically. Thus CGS injects a recurring within-sample shortcut-correction signal while remaining domain-label-free and close to ERM in cost. We formalize this principle through a nuisance-only Distributionally Robust Optimization geometry, in which an adversary may perturb nuisance factors while holding the semantic component fixed. The resulting local Danskin majorizer induces a first-order robust-feasible cone in parameter space, and Causal Gradient Steering (CGS) is the closed-form projection of the ERM step onto a tractable single-normal approximation of this cone. We further prove target-risk and probe-admissibility guarantees, showing that exact counterfactual generation in pixel space is unnecessary. CGS is compatible with standard first-order training and can act either as a standalone optimizer or as a plug-in correction for existing DG algorithms. It achieves state-of-the-art performance across five standard domain generalization benchmarks. Moreover, using a single locked CGS hyperparameter configuration, it improves seventeen prior DG methods by up to +15.8 percentage points without method-specific retuning, improves OSTrack-256 across GOT-10k, UAV123, and OTB2015, and establishes new matched-protocol state of the art for domain-generalized semantic segmentation by improving SCSD from 51.42 to 52.35 mIoU on GTAV+SYNTHIA$\rightarrow$\{Cityscapes, BDD, Mapillary\} and from 35.66 to 36.99 mIoU on GTAV$\rightarrow$ACDC. Beyond this algorithm, causal signal destruction defines a research direction parallel to data augmentation. The destruction operator is a design axis, and task-specific destroyers can turn shortcut suppression into a reusable tool for broader vision problems.

Causal discovery methods produce data-driven hypotheses about causal relationships, which may become new scientific findings or inform decisions about downstream interventions. In such settings, false positive causal claims can be more consequential than false negatives. Yet few methods target false positive error control in causal discovery, and existing error guarantees are often asymptotic and require strong versions of the faithfulness assumption. We introduce the $m$-conservative PC algorithm and prove that it controls false discovery rate in the linear Gaussian setting under an extremely weak version of the faithfulness assumption. In our framework, false positive error for causal graphs is defined based on the conditional-independence information they entail, yielding a metric that penalizes both false adjacencies and incorrect edge orientations. The parameter $m$ quantifies a trade-off between algorithmic complexity and the strength of the required faithfulness assumption. The $m$-conservative PC algorithm combines undirected graph learning, a Benjamini-Yekutieli-style procedure for conditional independence testing, and a conservative orientation step that marks unresolved or contradictory edge directions as ambiguous. Our algorithm produces valid outputs and retains error guarantees even in the finite-sample setting, despite possible random errors in the conditional independence tests.

We propose Low-Rank Quantile Surfaces (LRQS), a bivariate causal model in which, in the causal direction, an unknown monotone transformation of the conditional quantile surface admits a low-rank functional decomposition. LRQS subsumes location-scale noise models and post-nonlinear heteroscedastic noise models, while allowing multiple quantile bases to represent changes beyond location-scale effects. We prove generic identifiability of LRQS: the transformed quantile surface is low rank in the causal direction, whereas reverse representability under the corresponding constraints occurs only for exceptional, fine-tuned cause marginals. We provide a simple-yet-powerful causal score using a nonparametric fitting procedure that alternates between rank-constrained approximation of discretized quantile surfaces and isotonic estimation of the unknown monotone transformation. Experiments on synthetic mechanisms with higher-rank distributional shape variation and strong nonlinear distortions, together with standard bivariate benchmarks, show that LRQS is especially effective when conditional distributional shape or observation distortion goes beyond existing location-scale assumptions.

Causal discovery aims to uncover the causal relationships among variables beyond correlations from observational data. On time series, a major challenge is nonstationarity, which is typically modeled as regime-based shifts or drifting causal strength. In contrast, we consider non-stationarity arising from varying cause-to-effect delay, and introduce a causal model that is identifiable with few assumptions. To discover causal relationships with varying causal delay in practice, we formalize the problem in terms of the algorithmic model of causation, and propose STRETCH to discover causal graphs. We show on synthetic data that our method correctly recovers the causal relationships, and show the relevance of this causal model on a case study on the impact of El Niño climatic phenomenon on Indian monsoon.

Existing causal discovery methods for interventional data typically follow one of two paradigms: they either require explicit environment labels and known intervention targets, or, in the absence of such metadata, they rely on computationally intensive procedures such as first inferring intervention targets or employing complex models to account for the latent variables of environment labels. Surprisingly, we show that neither explicit environment labels nor auxiliary inference algorithms are strictly necessary: under certain conditions, the classical ICA-LiNGAM algorithm consistently recovers the causal graph from simply pooled interventional and observational data. We first demonstrate that in linear Gaussian structural equation models where interventions independently perturb the noise distributions across nodes, pooling produces exactly independent, non-Gaussian sources, the appropriate setting for Independent Component Analysis (ICA). Because the assumption of strictly independent interventions can be overly restrictive, we extend our analysis to the practical setting of single-node (atomic) interventions. While pooling atomic interventions induces the necessary non-Gaussianity, it also introduces source *dependence*, violating a core ICA assumption. However, theoretical analysis establishes that this dependence decays as $\mathcal{O}(1/n^2)$ with the number of variables $n$, whereas non-Gaussianity decays only as $\mathcal{O}(1/n)$. This yields a regime of mild misspecification at moderate $n$ where sources are near-independent yet sufficiently non-Gaussian for ICA to succeed. In synthetic experiments, where data is pooled across many different environments, our label-free approach matches or exceeds label-aware methods. On real-world data, our approach performs comparably to methods that explicitly require environment labels. Ultimately, our work challenges the assumed necessity of environment labels and complex inference mechanisms in interventional causal discovery and suggests a re-evaluation of the often-overlooked classical ICA-LiNGAM algorithm.

Selection bias is a difficult yet widespread problem in causal discovery, occurring whenever non-random selection processes lead to data that is not representative of the underlying populations. Due to its practical importance, related works have been proposed to address the problem under local [Versteeg et al., 2022] or interventional settings [Dai et al., 2025a], but general algorithms for observational data remain elusive. In this paper, we focus on truncated data (hard selection), and provide a general result for Additive Noise Models (ANM). We show that score-based methods are a surprisingly suitable candidate due to a special property of the score function ($\nabla \log p(x)$): *deterministic truncation preserves both the score* of the joint distribution as well as the Jacobian of the score. While established score-matching algorithms still fail in most settings, we actively leverage this observation to propose a new method for causal discovery that is robust under truncated data with ANMs. Overall, our approach offers a general, robust solution that is agnostic to external information about the selection process and still achieves comparable performance to the state-of-the-art approaches when selection is not present.

We introduce a categorical framework for causal abstraction that unifies and extends existing approaches. Modeling causal systems as Markov functors from free Markov categories generated by directed acyclic graphs, we define a causal abstraction as a deterministic natural transformation together with an embedding of restricted free Markov categories. This separates graphical compatibility under interventions from domain-level clustering of variables or values. Our framework provides an explicit characterization of admissible high-level graphs and recovers prior notions such as constructive -abstractions and cluster-DAG abstractions with unobserved confounders. We give concise categorical proofs that interventional distributions factorize over graphical abstractions and that do-calculus applied to the high-level graph yields valid conclusions for the low-level model.

Causal inference is central to scientific discovery, yet choosing appropriate methods remains challenging due to the complexity of statistical methodology and real-world data. Inspired by the success of artificial intelligence in accelerating scientific software, we introduce an evolutionary framework that uses large language models to discover and iteratively refine causal methods. Across benchmarks, our estimators consistently outperform established baselines: our best estimator lay on the Pareto frontier of 58 human submissions for a recent community competition. We also extend the algorithm to achieve competitive results in settings with estimated rewards. Analysis of the evolutionary trajectories shows that agents progressively discover sophisticated strategies tailored to unrevealed data-generating mechanisms. Our findings suggest that language-model-guided evolution could be used in scientific settings with partially observed rewards such as causal inference.

Directed Acyclic Graphs (DAGs) are foundational to many areas of AI research, providing a formal language for causal reasoning and model interpretability. However, learning DAGs remains challenging, due to super-exponential computational cost and diminished accuracy in small sample regimes. To address these challenges, we introduce Attention-DAG (ADAG), a novel linear transformer architecture for unsupervised amortized DAG learning. Unlike traditional unsupervised DAG learning methods which recover the graph structure from data of each individual domain, ADAG leverages the knowledge from multiple domains. It provides a nonlinear mapping from observational data of each domain to both the corresponding graph structure and the underlying parameters of Structural Equation Models (SEMs). This enables efficient zero-shot inference of causal structures in new domains with unseen SEM parameters. Remarkably, we demonstrate that for DAG learning problem attention acts as a fixed-point iterative scheme, so the training on multiple domains effectively discovers an efficient solver for the constraint optimization problem. Extensive evaluations on synthetic and realistic benchmarks demonstrate that ADAG significantly outperforms existing baselines in accuracy and efficiency, particularly when data is scarce.

Causal Bayesian optimization (CBO) typically relies on the unrealistic assumption of a perfectly known causal graph. Recent methods relax this constraint by coupling optimization with structure learning, but they often waste sample budgets on structural uncertainties that are irrelevant to the optimizer. In this paper, we formalize \emph{routing-equivalence} to shift the objective from full causal-graph recovery to causal belief routing, where structural differences only matter when they alter optimizer-facing objects such as admissible exploration sets and \emph{do}-priors. Furthermore, we propose \agentcbo{}, a graph-belief routing framework that incorporates LLM causal priors through guarded proposal and commit mechanisms. Specifically, a \textsc{Language-Prior Agent} combines LLM beliefs with constraint-based discovery to extract a protected causal backbone alongside residual uncertain edges. A \textsc{Calibration Agent} and a \textsc{Residual Repair Agent} then refine only these uncertain structures through score-gated bounded local edits. Finally, a deterministic commit gate evaluates candidate updates using routing-proxy checks before allowing them to influence intervention selection. Across ten benchmarks, \agentcbo{} performs comparably to known-graph CBO, demonstrating that guarded LLM priors can improve fixed-budget CBO performance.

Every control action on a physical system is already a do-operator intervention, yet causal discovery and control are typically treated as separate stages. This separation leaves deployed controllers unable to test whether the causal graph they rely on remains valid under changing operating conditions. We present \textsc{PolicyGRID}, a closed-loop framework that uses actuator interventions to validate candidate causal edges, fits a structural causal model over the validated graph, and reuses that graph for both policy optimization and latent-regime monitoring. In a multi-actuator physical simulation with latent operating regimes (building energy management), interventional graph validation reduces closed-loop energy use by 21\% at a standard comfort target relative to an otherwise identical observation-only graph, while improving four-way latent-context identification from 61.2\% to 80.8\%. A targeted ablation shows that the gains originate in graph pruning. Validation removes 16 of 47 candidate edges; with coefficient training held fixed, the validated graph reduces closed-loop energy relative to the unvalidated candidate set, while refitting coefficients on the same graph does not. On a live physical testbed, the same pipeline runs without code changes, performs 21 physical interventions, discovers 16 edges, and produces a target-responsive control policy where the observation-only baseline is insensitive to the comfort-energy target. These results show that physical controllers can use their own actions to validate causal structure and improve downstream control under latent regime shifts.

Causal reasoning from observational data becomes significantly challenging when the underlying causal structure is only partially known. In this work, we study the the equivalence class of structural causal models (SCMs) with latent variables sharing the same set of conditional independencies, as represented by a partial ancestral graph (PAG). Specifically, we provide a new characterization of SCM-induced causal diagrams in this equivalence class using differentiable parameters. Building on this characterization, we introduce a new model class called PAG-constrained neural causal models ($\mathcal{P}$-NCMs) which parameterize this equivalence class of SCMs. We prove that $\mathcal{P}$-NCMs are expressive enough to represent counterfactual distributions induced by any SCM in the class, while remaining consistent with the structural constraints shared across all its members. Finally, we demonstrate how the differentiable parameterization of this model class enables causal inference under Markov equivalence by reducing counterfactual partial identification to an optimization problem over $\mathcal{P}$-NCMs. We establish the theoretical soundness of this approach and validate its performance on simulations.