NeurIPS 2026 Papers

Expert background knowledge is often available in practical applications of causal discovery. Such constraints on the true causal graph can help causal discovery in terms of identifiability of causal effects and accuracy of the learned structure, but also in reducing the space of candidate causal graphs. As causal discovery can become computationally expensive for large number of variables, it is crucial to utilize background knowledge effectively \emph{during} the causal discovery process. However, most current methods only use background knowledge in a postprocessing step after causal discovery to refine the learned graph. In this work, we develop a framework for utilizing background knowledge during the causal discovery process, focusing especially on scalable causal discovery methods that recover only a subset of the whole graph. We implement our framework for multiple algorithms and empirically show that utilizing background knowledge can both reduce computational requirements and increase the quality of the learned structures.

We extend the Bayesian learning rule by explicitly incorporating the compositional structure of neural networks. The central observation is that backpropagation and exponential family variational inference share a common Lagrangian duality structure. Leveraging this connection, we develop a new Bayesian learning framework in which adjoint variables backpropagate layerwise sensitivity signals that converts into loss-site natural parameters. For Gaussian weight posteriors and Gaussian layer-state projections, the framework recovers deterministic back-propagation and Hessian backpropagation via delta-method approximations, while providing a unified perspective on localization-style prediction rules and moment matching methods. We also derive a new variant of IVON, clarify how its gradient and Hessian estimates differ from those of the standard version, and demonstrate how neural network structure can be incorporated into Bayesian learning in practice.

Constraint-based causal discovery recovers causal DAG structure from conditional independence (CI) relations. Classical methods such as PC orient v-structures first, then propagate edge directions from these seeds, relying on accurate CI tests and rich separating-set searches. In practice, these conditions often fail, causing cascading orientation errors. Recent work uses large language models (LLMs) as experts to augment edge orientation when standard assumptions fail, but often treats LLM outputs as reliable or assumes stable error behavior, despite hallucinations and instability. We propose MosaCD, a constraint-based framework that robustly combines CI tests with LLM inference to obtain high-confidence orientation seeds, then propagates them with Seeded Propagation Rules (SPR), which mitigate the fragility of collider-first orientation. We prove oracle-level soundness for SPR under explicit assumptions on the skeleton, separating-set record, and seed orientations, and give a stylized finite-sample analysis showing why prioritizing non-collider evidence can reduce orientation errors. Across 13 real-world benchmarks, MosaCD and SPR achieve substantially higher accuracy than existing methods through more reliable seeds and more robust propagation.

Explaining model predictions in high-stakes settings requires knowing *why* a prediction was made, a central challenge in modern AI. Yet existing methods lack a principled causal framework for explanation, leading to a disagreement problem: explanation methods produce conflicting attributions with no way to determine which is correct. Based on the literature in cognitive science, law, and philosophy, and using the language of causality, we formalize four desiderata for explanation methods that assign numerical credit to variables. We show that no prior explanation method including SHAP and LIME satisfies all desiderata, and prove the Explanatory Impossibility Theorem, which shows that even in principle, no method can satisfy all desiderata without causal assumptions. We introduce *counterfactual Shapley values*, an aggregation of a novel counterfactual quantity we call the *natural total effect*, and prove they satisfy all desiderata. We develop an algorithm for computing tight bounds on counterfactual Shapley values. Experiments corroborate our theory.

Causal discovery methods commonly assume that all data is independently and identically distributed (i.i.d.) and that there are no unmeasured variables affecting the system. In practice, these assumptions are often violated, leading to inaccurate inference. In this paper, we study how to identify hidden confounding and selection biases from causal mechanism shifts. In particular, we show that structural biases lead to dependent mechanism shifts. That is, by considering for which variables the mechanisms change given data from different environments, we can tell which variables are unbiased, which are subject to hidden confounding, and which are undergoing selection bias. We formalize this into an empirically testable criterion based on mutual information, and show under which conditions it identifies structural biases. To tell which nodes are subject to what kind of bias, we introduce the StruBI algorithm. Experiments on synthetic and real-world data show that StruBI works well in practice, accurately recovering affected variable sets and types of biases, outperforming the state-of-the-art by a wide margin.

Uncertainty quantification is central to many applications of causal machine learning, yet principled Bayesian inference for causal effects remains challenging. Standard Bayesian approaches typically require specifying a probabilistic model for the data-generating process, including high-dimensional nuisance components such as propensity scores and outcome regressions. Standard posteriors are thus vulnerable to strong modeling choices, including complex prior elicitation. In this paper, we propose a \textit{generalized Bayesian framework for causal inference}. Our framework avoids explicit likelihood modeling; instead, we place priors directly on the causal estimands and update these using an identification-driven loss function, which yields generalized posteriors for causal effects. As a result, our framework turns existing loss-based causal estimators into estimators with full uncertainty quantification. Our framework is flexible and applicable to a broad range of causal estimands (e.g., ATE, CATE). Further, our framework can be applied on top of state-of-the-art causal machine learning pipelines (e.g., Neyman-orthogonal meta-learners). For Neyman-orthogonal losses, we show that the generalized posteriors converge to their oracle counterparts and remain robust to first-stage nuisance estimation error. With calibration, we thus obtain valid frequentist uncertainty even when nuisance estimators converge at slower-than-parametric rates. Empirically, we demonstrate that our proposed framework offers causal effect estimation with calibrated uncertainty across several causal inference settings. To the best of our knowledge, this is the first flexible framework for constructing generalized Bayesian posteriors for causal machine learning.

Prior work has shown that grokked Transformers implement discrete Fourier transforms or group character representations for modular arithmetic. We unify these findings under the Wedderburn--Artin decomposition: using interchange intervention accuracy (IIA), a causal method stronger than ablation, we show that grokked models decompose computation along the Wedderburn components of the target algebra. Across 11 commutative algebras over $\F_p$ ($p = 2,3,5,7$)---including 6 with nontrivial Jacobson radical---all grokked models achieve raw IIA $\geq 0.97$. When models predict incorrectly, errors remain compartmentalized by component ($3.8\times$ chance), confirming that independence is structural, not a byproduct of accuracy. Training dynamics reveal that Wedderburn alignment emerges synchronously with grokking. For non-commutative groups, models exhibit \emph{selective} Wedderburn alignment; non-commutativity raises a capacity threshold that larger models overcome.

Causal discovery often starts from a set of variables that were measured together because they are believed to describe related parts of the same underlying process. Standard continuous DAG learners encode data fit, sparsity, and acyclicity, but they can still return graphs that fragment into isolated variables or disconnected components. We study a simple structural prior for this setting: the learned causal DAG should remain sparse while its undirected skeleton should be weakly connected. We introduce Fiedler regularization, a differentiable spectral penalty based on the algebraic connectivity of a smooth support-preserving skeleton of the learned weighted adjacency matrix. The resulting penalty can be added modularly to differentiable causal discovery objectives, providing connectivity control without changing the underlying learner. We instantiate the approach for GOLEM, graph autoencoder, and DAG-GNN models. Across sparse connected synthetic DAGs up to 200 variables, including connected-conditioned Erdős-Rényi, sparse connected, scale-free, and small-world graph families, Fiedler-regularized learners improve fragmentation control and structural recovery across learner families. These results position algebraic connectivity as a principled and practical prior for learning sparse causal DAGs in settings where the measured variables are expected to have a connected causal structure.

Humans have a remarkable ability to judge causal relationships from a limited number of unreliable observations. Past work on causal cognition has largely focused on normative accounts of human behavior, leaving unknown how biologically plausible neural systems could learn causal relationships from observations and update their representations of causal structure with additional evidence. Here, we leverage task-optimized recurrent neural networks to discover candidate implementation-level neural mechanisms of causal judgment. We propose a novel cognitive task in which a subject observes stochastic samples from an unknown causal structure (e.g. among variables A, B, and C with unknown causal relationships), and must judge whether a specific causal relationship is present given a query (e.g. "does A cause C?"). We found that, after training, recurrent neural networks perform the task with high accuracy, adopt strategies that incorporate the behavior of non-queried variables to form their judgments, and, despite being trained only on pairwise queries ("does A cause B?", "does C cause A?", etc), form implicit beliefs about the complete graphical structure underlying the observations. Lastly, we use dynamical systems analysis to identify a set of low-level neural mechanisms that implement causal judgment and representation of causal graphical structure. Together, these findings lay the groundwork for a "bottom-up" approach to causal cognition, providing a potential basis for subsequent experimental study in the brain.

Causal discovery is increasingly used to analyze telemetry from interactive systems, but a plausible graph does not guarantee an identifiable or reliable product decision. We study this problem for one query: whether early competitive gameplay increases Day-1 retention in a deployed Role-playing game (RPG). We propose an admissibility-first framework that treats discovered graphs as structural hypotheses, keeps only graphs that identify the target effect and have adequate treatment-control overlap, and validates admissible effects through cross-algorithm stability, placebo, subsampling, and E-value diagnostics. On real telemetry, only about one third of discovery runs support the target effect after temporal and semantic constraints. Some admissible Directed Acyclic Graphs (DAGs) converge to a positive risk-difference average treatment effect (ATE), down from a raw retention gap, and the estimate survives all refutation checks. Graph-level recovery is therefore an inadequate proxy for causal reliability; discovery pipelines for decision support should be evaluated at the query and effect level.

Structural causal models (SCMs) provide a principled foundation for causal reasoning, and neural causal models (NCMs) extend this framework by parameterizing causal mechanisms with neural networks. The classical formulation of NCMs assumes a specific architectural choice: a single function approximator per structural equation. In this work, we revisit this assumption and show that it represents only one point in a broader family of valid neural causal model parameterizations. Using interventions as an analytical lens and graph-based neural architectures as a concrete construction, we characterize how different parameter-sharing schemes over sub-mechanisms induce distinct members of the NCM family while preserving the same causal graph. This perspective yields two additional regimes beyond the classical formulation, which differ in how causal mechanisms are decomposed and parameterized within a unified structural framework. Together, these regimes demonstrate that architectural choices shape the causal semantics and expressivity of neural causal models, even when graphical structure is fixed. Relaxing structural assumptions further, we identify a class of partially causal models (PCMs) that support limited interventional or counterfactual queries without satisfying full SCM requirements, offering alternative trade-offs between causal fidelity and tractability. We place NCMs and PCMs within a unified expressivity spectrum between purely associational models and fully causal generative models, and illustrate these distinctions empirically using a graph-based variational autoencoder with interventional structure.

Investigating the causal structures of transformers often entails a trade-off between the granularity of the explanation and computational overhead. Existing approaches either bypass the full internal chain, potentially missing critical decision-relevant links, or struggle with the combinatorial explosion of path enumeration. To address these challenges, we propose an efficient automated path-tracing method that ensures both causal reliability and algorithmic feasibility. Through extensive verification, we find that (i) the identified paths are the primary sources for decision signals, as evidenced by a marked decrease in self-repair compared to non-path components; and (ii) transformers utilize modular, class-shared path mechanisms to process categorical information. Beyond these findings, we show that the potential implications of our method can stem from sparse manipulation, highlighting efficient applicability to downstream tasks such as model debugging and pruning.

Consider two large vision models. They process the same image and both correctly predict the class ``rabbit.'' How much of the circuit computation along the way was shared? Model diffing offers a natural lens on this question. So far, however, it has largely operated on a single layer and at the level of representations rather than circuits. In this work, we introduce Universal Circuits (UCs), enabling model diffing at the circuit level. Specifically, we extend CLTs across both layers and models, with losses that encourage sparsity for interpretability and output fidelity for faithfulness. We train UCs between pairs of standard large vision models. We find that a compact cross-model intersection of pruned class circuits, typically a few hundred universal (shared) features per pair, produces $89$-$98\%$ of full-circuit classification accuracy in both models, while a complementary set of universal features (hundreds per pair) is kept by only one model's circuit, reflecting how each model weights shared concepts differently in its own representations. To demonstrate a downstream use of UC, we perform model \textit{surgery}: a class is successfully transferred from one model to another with no gradient steps taken in the new model. More broadly, our work demonstrates that large vision models leverage shared multi-layer algorithms for downstream performance, and that these algorithms can be discovered, compared, and reused across models.

Self-supervised Vision Transformers (ViTs) like DINO encode rich semantics, enabling training-free segmentation of objects from the background and discovery of their parts via feature clustering. This paper focuses on part discovery: partitioning a foreground object into semantic parts. Existing approaches produce imprecise part boundaries. We trace this to the rigid ViT patch grid used in training DINO, where patches straddling boundaries contain pixels from multiple parts. While DINO's invariance-based training could absorb this pixel-level mixing into clean features, experiments with over 26K foreground patches show it does not: boundary-overlapping patches produce features with higher entropy and lower assignment confidence, blurring predicted part boundaries. Rather than make the massive effort of retraining DINO over geometrically coherent regions, an easier approach is to take boundaries directly from a boundary detector, which supplies the geometric information DINO's features lack. Motivated by this, we introduce Part-DINO, a training-free framework that combines boundaries from low-level image segmentation with DINO's semantic features. We use the boundaries to partition the image into regions, pool DINO features within each region, and group them to discover parts. Without any training, Part-DINO produces structurally coherent part assignments, outperforming training-free baselines across four standard benchmarks (CUB, CelebA, PartImageNet-OOD, PartImageNet-Seg) and remaining competitive with weakly-supervised and unsupervised methods.

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.

Causal discovery aims to recover directed causal relations from observational and interventional data, providing a basis for mechanistic understanding and reliable decision-making. Causal discovery foundation models (CDFMs) seek to amortize this problem by mapping a dataset directly to a causal graph in a single forward pass, avoiding per-dataset testing, search, or optimization. However, existing CDFMs remain limited, often failing to consistently match strong classical methods, and we find that a key bottleneck lies not only in model architecture but also in how causal pretraining tasks are constructed. Based on this observation, we propose CausalTab, a data-driven CDFM trained with broad causal pretraining over diverse graph priors, structural mechanisms, noise models, dimensions, sample sizes, and intervention regimes. A dynamic task construction strategy composes these causal environments into varied discovery tasks, enabling more transferable structural learning from observational and mixed-interventional data. On large-scale synthetic benchmarks, CausalTab achieves stronger and more robust performance than diverse causal discovery baselines. To further bridge abstract synthetic generators and realistic causal reasoning scenarios, we introduce an expert-knowledge-guided and LLM-audited semantic causal environment benchmark, where domain-grounded SCMs generate interpretable observational and interventional datasets for out-of-distribution analysis. Across both synthetic and semantic environments,CausalTab demonstrates robust structure recovery, especially under interventional evidence, highlighting broad causal pretraining as a key ingredient for transferable amortized causal discovery.

Causal discovery, the problem of inferring the direction of causality, is generally ill-posed. We use the language of structural causal models (SCM) to show that assuming that the causal relations are acyclic and invariant across multiple environments (e.g., the way minimum wage affects employment rate is stable across different geographical regions), \textit{only} two auxiliary environments are sufficient to infer the causal graph for arbitrary nonlinear mechanisms. Moreover, we demonstrate that this implies identifiability of the SCM functional mechanisms: as a corollary, we show that \textit{two} auxiliary environments are sufficient to guarantee correct counterfactual inference. We empirically support our theoretical results on synthetic data.

There are many causal discovery algorithms, but few guiding principles for choosing between them. Methods are usually compared through three lenses: identifiability, consistency, and benchmarks. Each introduces assumptions about the data-generating process that are often untestable. We argue that there are no shared standards for comparing, prioritizing, or even discussing those assumptions. We support this claim by showing that (i) identifiability assumptions are often preferred by convention rather than by principle, (ii) uniform consistency requires further untestable assumptions, while also the weaker pointwise consistency has arguably narrowed algorithm design, and (iii) benchmarks are not neutral tests but carry an epistemic role of their own: they quietly fix which regimes matter, which guarantees come into play, and what counts as success. In doing so, they shape what algorithm comparisons are taken to show and thus perform some of the same epistemic work as theory, but less transparently. In this position paper we argue for a more transparent, integrated practice: Make the epistemic standards for discussing identifiability and consistency assumptions explicit, especially their failure modes and scope conditions; design benchmarks to operationalize those standards, by stress-testing and ablating both. Then, theoretical and empirical results jointly clarify when, why, and how algorithms may work rather than accumulate as disconnected advances.

We study heterogeneous treatment-effect (HTE) estimation in observational survival studies commonly associated with both censored outcomes and unmeasured confounding. We integrate causal survival forests (CSF) with negative controls (NC) from proximal causal inference and introduce Negative Control Causal Survival Forests (NC-CSF), a flexible nonparametric HTE learner for survival analysis. In particular, our approach uses a loss that incorporates proxy variables and Neyman orthogonalization to train the random forest, thereby mitigating bias from unobserved confounding and gaining robustness to nuisance estimation. Through extensive simulations spanning varying levels of confounding, proxy relevance, and censoring mechanisms, we demonstrate that NC-CSF substantially reduces bias and estimation error (root mean squared error) relative to existing baselines. We further demonstrate the practical utility of our method on real-world clinical datasets, where it confirms several existing findings and also reveals new interpretable patterns of treatment-effect heterogeneity. To facilitate practical use, we provide an end-to-end Python implementation of NC-CSF that carefully handles implementation details such as nuisance estimation and clipping.