NeurIPS 2026 Papers

We study identifiability and estimation of the direct causes, that is, the parents, of a designated target $Y$ in a structural causal model using only observational data. Our main assumption is an additive-noise model for $Y$: the value of $Y$ equals some function of its parents plus noise that is independent of those parents. We allow for general functional relationships and hidden confounding among all other variables. We prove that under a `no-backward' additive-noise condition the true parent set, $\mathrm{PA}(Y)$, is identified from the observational distribution by a simple population principle: among all candidate variable sets that make the regression residual of $Y$ independent of the regressors, choose the one with the smallest residual variance, and—if several tie—the smallest set. To justify the ``no-backward'' condition, we propose a novel identifiability scheme based on identifiability witnesses: we prove that in finite-dimensional analytic model classes, for which we have an identifiability witness (that is, a single identifiable model), residual independence for sets containing descendants of \(Y\) holds only on Lebesgue-null exceptional parameter sets. This scheme is strong enough to recover known identifiability results. For finite data, we propose Independent Risk Minimization (IndRM), which offers a simple, local, and non-interventional route to isolating the direct causes of $Y$ in multivariate systems, avoiding global model assumptions and full-graph search.

A central goal of science is to produce valid explanations of complex systems: high-level causal accounts that faithfully reflect the behavior of lower-level mechanisms. Yet no consensus exists on how to measure whether a proposed high-level explanation is actually valid. We introduce a benchmark of ten complex systems spanning discrete and continuous state spaces and static and dynamical regimes, each equipped with consensual ground-truth causal explanations and invalid contrastive conditions. Within a unified causal abstraction framework, we systematically evaluate over thirty candidate metrics drawn from observational, functional, information-theoretic, and causal families. Our results show that only the latter reliably discriminates valid from invalid abstractions, and only when incorporating faithfulness testing over unmapped variables. Building on these findings, we introduce the Causal Abstraction Error (CAE), a continuous validity metric with an explicit faithfulness test, which passes all discrimination tests across every system and converges with as few as 30 sampled interventions. We offer it as a general-purpose metric for the discovery and validation of high-level explanations of complex systems.

Advances in deep reinforcement learning have enabled the development of policies capable of solving complex, high-dimensional problems, allowing AI agents to strategize and reason purely through interaction without supervision. Despite these successes, our knowledge on the functional properties and the underlying structure of the deep neural policy manifold remains limited. In this paper, we uncover a fundamental functional property in reinforcement learning: the intrinsic alignment between the advantage function and the gradient of the loss targeting directions of incoherence. We provide a rigorous theoretical foundation for this relationship, demonstrating that this intrinsic alignment characterizes how policies learn and internalize the underlying value function and how this process governs policy decisions. By leveraging this fundamental functional property, we propose a novel algorithm that can diagnose and identify deep neural policy decision volatilities. We conduct extensive empirical analysis in high-dimensional MDPs. From algorithmic and architectural changes to natural distributional shifts and worst-case perturbations, our proposed method can identify and audit the differences by leveraging the underlying structure of the deep neural policy manifold and the intrinsic correlation. Our analysis reveals foundational properties of policies trained in high-dimensional MDPs, and our paper provides a principled step toward constructing scalable, stable, and generalizable deep reinforcement learning agents.

We partially resolve Conjecture 1 of \textit{Karagodin et al., Clustering in Causal Attention Masking (NeurIPS 2024)} and extend it to time-dependent parameter regimes. The conjecture predicts that causal attention dynamics converge to two clusters aligned with the eigenvectors associated with the largest eigenvalue $\lambda_{\max}$ of the value transformation. We prove that this behavior holds when $\lambda_{\max}>0$ and is generally false when $\lambda_{\max}\le0$. The resulting two-cluster regime is common in practice and substantially more challenging than the classical single-cluster setting studied previously. A central contribution of our work is the identification of a rigorous dimension deduction phenomenon: despite evolving in a high-dimensional embedding space, token trajectories collapse onto a two-dimensional structure governed by a small number of dominant directions. Building on this insight, we introduce a new analytical framework--instability within the flow--inspired by instability phenomena in physical systems. This framework enables the analysis of steady-regime behavior in non-monotone, non-autonomous attention dynamics. Our theoretical findings are illustrated through simulations and experimental studies using Group Query Attention (GQA) layers.

Despite the importance of causal reasoning, training LLMs to perform causal reasoning remains underexplored. Existing data efforts mostly focus on benchmarking LLMs on specific aspects of causality, rendering them less suitable for training generalizable causal reasoners. To address this, we propose UniCo, a data generation framework that both (1) addresses 18 causal query types across Pearl's Causal Ladder and (2) translates symbolic samples into code and narrative domains to simulate real-world use cases where causal terms are not explicitly specified. To ensure data quality, UniCo grounds answers with exact causal inference and filter cases with reasoning shortcuts. Upon supervised-finetuning with 66.6K UniCo-generated instances, Qwen3-4B, Qwen3-8B and Olmo-3-7B-Instruct achieve an average of 22.9% improvements across all 18 in-distribution query types, and 8.1% over state-of-the-art causal data generation frameworks on 7 established causal benchmarks outside the training distribution. Furthermore, in real-world medical understanding, legal decision, and tabular reasoning, UniCo-trained models consistently display more faithful reasoning traces, outperforming the base models by an average of 20.2% in faithfulness metrics. These suggest that causality-centered training not only strengthens causal reasoning, but also equips LLMs with a causal mindset in general reasoning tasks.

We introduce structural causal bottleneck models (SCBMs), a novel class of structural causal models in which causal effects between high-dimensional variables are mediated by low-dimensional summary statistics, or *bottlenecks*. SCBMs provide a flexible framework for mechanism-specific, target-dependent dimension reduction while remaining estimable via standard learning algorithms. We prove that bottleneck variables are identifiable up to bijection from observational data, and validate this experimentally. We then study causal effect estimation in linear SCBMs under three standard adjustment strategies. For instrumental variables, we identify a population-level non-identifiability of naïve two-stage least squares when all variables are high-dimensional, and show that bottleneck representations restore identification. For mediation and backdoor adjustment, we prove that conditioning on bottleneck variables yields valid effect estimates with explicit finite-sample efficiency gains over conditioning on full high-dimensional variables. We argue that SCBMs provide a principled alternative to existing causal dimension reduction frameworks such as causal representation learning and causal abstractions.

Many causal quantities are only partially identifiable due to the inherent missingness of potential outcomes, and the associated partial identification (PI) sets can be obtained by solving an optimal transport (OT) problem. Covariates often provide additional information about the potential outcomes and thus yield tighter PI sets, which can be obtained via conditional optimal transport (COT). However, COT-based PI set estimators are susceptible to the curse of dimensionality in the covariates, which precludes the asymptotic normality and hinders statistical inference. In this paper, we exploit the smoothness in the marginal densities of covariates and potential outcomes, and develop a wavelet-based primal approach for COT that attains a faster convergence rate. Moreover, for quadratic cost functions, we establish a stability result for COT and prove asymptotic normality of the proposed estimator, enabling valid statistical inference for the PI set. Empirically, we validate the estimation and inference performance of our approach through numerical experiments in comparison with existing benchmarks.

Temporal causal structure learning aims to recover lag-aware causal relations from multivariate time series. While prior knowledge has been widely used to improve static structure learning, its integration into lag-aware structure learning remains limited, because available priors are often lag-agnostic. Recent studies have explored lag-agnostic edge presence priors, but partial order priors, which can prune the ordering space and improve structure learning, remain underexplored. A key challenge is that variables may influence each other at different lags, leading to cyclic variable-level relations where ordering is no longer naturally defined. Moreover, directly applying static differentiable formulations of partial order constraints can be unstable due to repeated-walk accumulation on cycles. To address this gap, we represent partial order priors on the summary graph and follow the natural idea of the order relation that only allows a single direction of possible causality between two variables, which is equivalent to forbidding all reversed causality, direct or indirect. This converts partial order constraints into path prohibition constraints that can be extended to cyclic summary structures. For stable differentiable characterization, we propose a decoupled partial order constraint method. The method preserves the original lag-aware structure for data fitting, imposes partial order constraints through a normalized summary representation, and captures higher-order reachability with a closed-form connectivity characterization. Experiments further demonstrate its effectiveness in nonstationary settings.

Generalized category discovery (GCD) becomes substantially more challenging when the number of novel classes is unknown. We argue that, after the backbone is fixed, this stage should be treated as seen-constrained model-order selection rather than as an auxiliary clustering detail. The selector must estimate the class count without novel labels while remaining consistent with the labeled seen categories available in the standard GCD setting. We instantiate this view by constructing a nested merge path from a seen-constrained overclustering and selecting the coarsest near-optimal cut under observable surrogate decision risks. These risks combine seen-class consistency, cross-seed stability, unlabeled-side compactness, and a tiny-cluster degeneracy penalty. The resulting protocol separates class-count error, downstream clustering quality, and robustness. Where an aligned public unknown-$K$ baseline is available, namely on SelEx, the selector reduces class-count error on all four fine-grained datasets, including a reduction from 342 to 15 classes on Herbarium-19. Broader-domain diagnostics further distinguish ImageNet100, where the default selector can underestimate the class count toward the seen-class regime, from CIFAR100, where the selector landscape exposes an accuracy-count operating-point trade-off. The mixed accuracy outcomes reveal distinct count-, path-, and representation-level bottlenecks, supporting unknown-$K$ selection as a decision layer that should be evaluated separately from representation learning.

Causal discovery from nonlinear multivariate time series is challenging in high-dimensional systems, where the number of candidate directed relations grows quadratically with the number of variables. Existing methods are often limited by target-wise model fitting, repeated conditional testing, or expensive graph-search procedures. We propose SCDM, a shared-parameter meta-learning framework for scalable temporal causal discovery. SCDM treats each target variable as a task while learning a shared temporal predictor and a shared causal-strength matrix across tasks. Each meta-episode updates only a subset of target-variable tasks, allowing the model to accumulate structural evidence across the full system without exhaustive target-wise optimization. After training, a post-training graph readout converts the learned predictor into continuous directed causal scores for threshold-independent evaluation. We also provide a finite-error recovery principle showing that, under fully observed delayed-system assumptions and a positive risk-gap condition, thresholding SCDM scores recovers the graph when statistical, meta-optimization, and readout errors are below the population margin. Experiments on controlled synthetic, neuroimaging-inspired, high-dimensional, and real-world temporal benchmarks demonstrate competitive causal recovery and improved scalability in large temporal systems.

Learning directed causal graphs from time-series data poses significant challenges, especially in fMRI where slow sampling rate obscures fast neural interactions. This temporal mismatch leads to undersampling, which can make multiple graphs equally plausible. We address this problem by explicitly modeling undersampling effects when recovering causal graphs. Our approach employs answer set programming (ASP) to enforce domain-specific constraints and optimize soft observational constraints, thereby identifying a Markov equivalence class for the resulting graph solutions. By customizing an ASP solver to collect multiple near-optimal solutions, we obtain not only the single best-fitting graph but an equivalence class of high-scoring graphs for expert consideration. This method, called Real-world noisy RASL (RnR), can also act as a meta-solver: it refines the output of other causal discovery algorithms by accounting for undersampling biases. In synthetic data and empirical brain network data, RnR produces more accurate causal graphs than state-of-the-art methods. When applied as a meta-solver (refining outputs of existing algorithms), it improves F1 scores by an average of 46\% over baseline methods; on standalone synthetic data benchmarks, it achieves a 64\% improvement. We demonstrate that RnR is robust to varying undersampling rates, maintaining high precision and recall even as sampling becomes more sparse, whereas baseline methods degrade significantly. Finally, we test RnR on real-world settings where ground truth connectivity is unknown such as human brain fMRI data, showing that incorporating undersampling-aware constraints via ASP yields more reliable and interpretable brain connectivity estimates from fMRI time series, bridging the gap between neural dynamics and observational data.

Constraint-based causal discovery requires a large number of conditional independence (CI) tests. In nonlinear and high-dimensional settings, generative CI methods offer strong expressive power, but often suffer from high per test cost and limited reusability across the many query dependent conditional resampling tasks arising in graph search. We propose a generative nonlinear CI testing and graph search framework for PC-style causal discovery. First, we develop the Flow Matching based Conditional Independence Test (FMCIT), which combines joint flow matching modeling with conditional imputation to reformulate generative CI testing from query specific conditional modeling into a conditional resampling process that can be reused across queries. This allows the same generative model to repeatedly generate the randomized copies required by CI testing throughout the entire graph search procedure. We then introduce GPC‑FMCIT, which embeds FMCIT into a guided PC pipeline with screening, guidance, refinement, and orientation. By using low-cost screening to shrink the search space, constructing edge-specific candidate conditioning sets from local graph structure, and invoking FMCIT only in a budget-controlled refinement stage, GPC-FMCIT reduces both the deployment cost of individual nonlinear CI queries and the overall query complexity. Experiments on synthetic datasets and real-data analyses show that the proposed method achieves a strong accuracy--efficiency trade-off under nonlinear and high-dimensional structures. Overall, our results suggest that, through the joint design of reusable conditional resampling and controlled graph search, generative nonlinear CI testing can become a practical system level module for high‑dimensional PC‑style causal discovery.

Although Large Multimodal Models (LMMs) have achieved strong performance on general video understanding, their susceptibility to textual prior shortcuts during causal discovery has been recognized as a critical deficit. The underlying mechanisms of this phenomenon remain incompletely understood, as existing benchmarks only measure response accuracy without revealing the sources and extent of the deficit. We introduce ProCauEval, a perturbation-based evaluation protocol that shifts from outcome assessment to mechanism diagnosis, probing causal discovery through five controlled configurations that systematically manipulate visual and textual modalities to decompose their respective contributions to model behavior and dissect the failure modes. Evaluating 17 mainstream LMMs, we find that models faithfully perceive video content yet systematically underexploit it during causal reasoning. We further observe that stronger post-training amplifies rather than mitigates textual prior reliance, and that higher baseline performance correlates with greater fragility under perturbation. To address these, we propose Anti-Distillation Policy Optimization (ADPO), a reinforcement learning framework built on negative teacher alignment, which augments GRPO by explicitly pushing the policy away from a prior-only counterfactual teacher induced by visual corruption. Specifically, ADPO maximizes the divergence between the policy distributions conditioned on the original and visually corrupted inputs, thereby forcing the model to ground its reasoning in visual evidence rather than textual shortcuts. Extensive experiments show that ADPO improves visual engagement without sacrificing fundamental comprehension, thus offering a preliminary step toward reliable causal discovery.

The standard constraint-based paradigm for causal discovery with incomplete data---impute first, test second---is frequently miscalibrated: any consistent conditional independence (CI) test rejects a true null with probability approaching 1 when imputation error induces spurious conditional dependence. We introduce *PAIR-CI*, a nonparametric CI test that restores calibration by integrating multiple imputation directly into the inferential procedure via a paired permutation design. PAIR-CI compares cross-validated models that include and exclude the candidate variable while receiving the same imputed conditioning set, forcing imputation error to cancel in their loss difference rather than contaminate the test statistic. A provably consistent variance estimator jointly accounts for uncertainty arising from cross-validation and multiple imputation---to our knowledge, the first formal unification of these two inferential frameworks. In simulations, existing imputation-based CI tests exhibit false positive rates of 28--45\% when data are missing not at random (MNAR), whereas PAIR-CI averages below the nominal 5\% level across data-generating processes and missingness mechanisms. These gains are largest in nonlinear settings and grow with causal graph size: when integrated into the PC algorithm, PAIR-CI reduces structural Hamming distance by 8\% on 10-variable nonlinear graphs, 15\% on 30-variable equivalents, and up to 44\% on the 56-variable HAILFINDER network, with stable performance in all settings.

Differentiable structure learning transforms DAG discovery from a combinatorial search into a continuous optimization problem, enabling gradient-based recovery of causal structures. In many applications, researchers possess partial-order priors over the variables (e.g., from biological signaling cascades or temporal ordering), which substantially narrow the space of plausible causal graphs. Existing approaches integrate such priors by decomposing the prior order graph into a collection of paths and evaluating prior-aware acyclicity constraints path by path; this is correct but its constraint-evaluation cost scales linearly with the number of induced maximal paths, a bottleneck for multi-chain priors. We propose PACO, Partial-order-Augmented Continuous Optimization, which encodes the same partial-order compatibility through a single masked-reachability matrix, that masks the matrix exponential of the learned graph by the strict transitive closure of the prior. The constraint and its Frechet-adjoint gradient are computed in a single $2d{\times}2d$ block matrix exponential whose dominant cost is independent of the number of induced prior paths. We prove that PACO has the same exact zero-level feasible set as the path-decomposition formulation. Across synthetic and real-data experiments under matched priors and dataset seeds, PACO matches path-decomposition on structural recovery and substantially reduces wall-clock cost in multi-chain prior settings.

Neural causal models can simulate interventions in complex, high-dimensional settings, but typically require a known causal graph. Observational data, however, generally identifies only a Markov equivalence class of graphs, represented by a CPDAG, and causal queries may vary across DAGs in that class. We introduce \textit{Masked Neural Causal Models }(NCMs), a provably expressive nonparametric framework for simulating and bounding interventional queries over all models compatible with a given CPDAG given observational data. We give an optimization objective in the space of Masked NCMs that asymptotically recovers the true bounds of the causal effect. To enable this optimization in practice, we introduce an attention-based architecture and a novel optimization strategy that recovers highly accurate bounds in discrete nonparametric settings.

Inspired by long-standing open problems in algebraic combinatorics, we show that modern machine learning can meaningfully contribute to verifiable mathematical discoveries. In particular, we focus on the construction of simple mathematical functions under exact distributional constraints, a setting we formalize as Simple Learning Under Rigid Proportions (SLURP). We tackle this problem by introducing two methods: MapSeek-Functional, which models the desired function alternating pseudo-labeling and supervised training steps; and MapSeek-Symbolic, designed to directly produce symbolic formulas. We successfully apply both methods to a research problem in algebraic combinatorics, discovering a new combinatorial interpretation of the $q,t$-Narayana polynomials arising from representation theory. To our knowledge, this is the first such interpretation based on noncrossing partitions. Using one discovered statistic, we find a combinatorial proof of the symmetry of these polynomials in a previously unsolved case. To streamline verification and reproducibility, we release all code, including a formalization of the mathematical discoveries of this paper in Lean 4.

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.

Modeling event sequences requires understanding when future events will occur and how event types causally influence one another over time. Existing temporal point process (TPP) models typically assume static or first-order dependence structures, which limits their ability to capture the dynamic and multi-order causal mechanisms commonly observed in real-world systems. We propose MOCHA, a Multi-Order Causal Hierarchical Architecture for multivariate TPP that jointly models time-varying causal structure and multi-hop influence propagation in continuous time. MOCHA learns latent dynamic weighted directed acyclic graphs (DAG) over event types, where acyclicity and sparsity constraints promote structurally valid causal graphs. Based on the learned graph, the model decomposes event dynamics into multi-order causal paths, and incorporate both direct influence and indirect propagation into the intensity function. The entire framework is end-to-end differentiable and optimized jointly for event prediction and causal structure discovery. Experiments on seven real-world datasets from different domains show that MOCHA consistently achieves superior negative log-likelihood, while also recovering dynamic causal patterns that align with domain knowledge. These results demonstrate that MOCHA provides an effective framework for dynamic causal structure learning in TPP.