NeurIPS 2026 Papers

Membership Inference Attacks (MIAs) aim to distinguish training points (members) from unseen data (non-members), and are widely used to quantify memorization and assess privacy risks. Standard MIA evaluation requires repeated retraining, which is computationally costly for large models. One-run (single training with randomized data inclusion) and zero-run (post hoc evaluation) methods are often used instead, but their statistical validity remains unclear. We address this gap by framing MIA evaluation as a causal inference problem, defining *memorization as the causal effect of including a data point in the training set*. This novel formulation reveals and formalizes key sources of bias in existing protocols: one-run methods suffer from interference between jointly included points, while zero-run evaluations are additionally confounded by distribution shift between member and non-member evaluation data. We derive causal analogues of standard MIA metrics and propose practical estimators for multi-run, one-run, and zero-run regimes with non-asymptotic consistency guarantees. We validate our approach in several settings, including pretrained and fine-tuned LLMs, showing that it enables reliable measurement of MIA performance without retraining and under distribution shift. Overall, our framework provides a principled foundation for privacy evaluation in modern AI systems.

We study experiments on interacting populations of humans and AI agents, where both unit types and the interaction network remain unobserved. Although causal effects propagate throughout the system, the goal is to estimate effects on humans. Examples include online platforms where human users interact alongside AI-driven accounts. We assume a human–AI prior that gives each unit a probability of being human. While humans cannot be distinguished at the unit level, the prior allows us to compute the average human composition within large subpopulations. We then model outcome dynamics through a causal message passing (CMP) framework and analyze sample-mean outcomes across subpopulations. We show that by constructing subpopulations that vary in expected human composition and treatment exposure, one can consistently recover human-specific causal effects. Our results characterize when distributional knowledge of population composition (without observing unit types or the interaction network) is sufficient for identification. We validate the approach on a simulated human–AI platform driven by behaviorally differentiated LLM agents. Together, these results provide a theoretical and practical framework for experimentation in emerging human–AI systems.

Latent confounding poses a significant obstacle to identifying the causal effect of a treatment on an outcome. To address this, many existing studies leverage proxies of the latent confounder to indirectly adjust for the confounding bias. However, they impose specific structural constraints on the proxies and typically require multiple proxies. In this paper, focusing on the latent variable linear non-Gaussian acyclic model (lvLiNGAM), we propose a causal effect identification procedure requiring only a single agnostic proxy. Crucially, the term "agnostic" means that the causal connections between the proxy and the treatment-outcome pair can be arbitrary and are not required to be known a priori. This structural complexity precludes identifying the causal effect via a simple closed-form formula. Consequently, our identification procedure is designed to first derive candidate solutions from cumulants and then isolate the valid solution by examining certain independence relationships. We present a series of new theoretical results, which collectively establish the soundness of our identification procedure: given the observational population distribution, it correctly identifies the true causal effect when identifiable, and correctly reports unidentifiability otherwise. Finally, we empirically validate our theoretical results.

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.

Automated systems built on artificial intelligence (AI) are increasingly deployed across high-stakes domains, raising critical concerns about fairness and the perpetuation of demographic disparities that exist in the world. In this context, causal inference provides a principled framework for reasoning about fairness, as it links observed disparities to underlying mechanisms and aligns naturally with human intuition and legal notions of discrimination. Prior work on causal fairness primarily focuses on the standard machine learning setting, where a decision-maker constructs a single predictive mechanism $f_{\widehat Y}$ for an outcome variable $Y$, while inheriting the causal mechanisms of all other covariates from the real world. The generative AI setting, however, is markedly more complex: generative models can sample from arbitrary conditionals over any set of variables, implicitly constructing their own beliefs about all causal mechanisms rather than learning a single predictive function. This fundamental difference requires new developments in causal fairness methodology. We formalize the problem of causal fairness in generative AI and unify it with the standard ML setting under a common theoretical framework. We then derive new causal decomposition results that enable granular quantification of fairness impacts along both (a) different causal pathways and (b) the replacement of real-world mechanisms by the generative model's mechanisms. We establish identification conditions and introduce efficient estimators for causal quantities of interest, and demonstrate the value of our methodology by analyzing race and gender bias in large language models across different datasets.

This position paper argues that causal benchmarks for multimodal AI should measure categorical difference, not capability gap. The field reports machine causal performance against human performance and interprets progress as gap-closing along a shared scale. The shared-scale assumption rests on a flattened reading of Hume's regularity theory in which causation reduces to constant conjunction across instances and the temporal experience of the observer has no role. When understood in terms of its presuppositions, Hume's regularity is inseparable from a temporally extended subject who undergoes the conjunctions over time. Human and machine causal cognition therefore have different temporal architectures. The two are grounded in time as substrate and time as dimension, a categorical difference that scale or additional intervention machinery cannot close. Evaluation paradigms that treat the two as commensurable produce inflated assessments of machine causal competence that independently scored probes cannot capture. We propose \textit{Anthropomorphic Competence Inflation} as a construct the field can develop into a broader measurement instrument and formalize it through the \textit{Inflation Score}. Preliminary observations on two recent vision-language models match the pattern predicted by the categorical claim. The implications affect evaluation practice, deployment in causal-decision domains, and the next phase of AI causality research.

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.

Cauchy activations and Cauchy-adaptive layers can give large gains on scientific learning tasks, but the gains are selective and not uniquely Cauchy-specific. We organize this selectivity with an empirical loss-architecture alignment taxonomy: an architecture can help when the objective exposes structures it can use, and can lose under a mismatched objective. In score learning, Cauchy score networks improve over SiLU under a Fokker-Planck PDE loss, but the same advantage disappears under denoising score matching and a Gaussian activation is comparable to Cauchy under the PDE loss. In loss-activation factorials, robust residual losses explain more of the heavy-tailed and spectral gains than the activation alone; an Allen-Cahn trap initially escaped by CauchyAct+Cauchy loss is also escaped, sometimes more strongly, by CauchyAct+L1, CauchyAct+Huber, and ReLU+Cauchy loss. We also analyze ResidualCAN, a CauchyAct main path plus a softmax-weighted Cauchy Adaptive Node residual. It achieves 1520x lower stationary Allen-Cahn error than a SiLU MLP at epsilon = 1.0 and remains strongest or second strongest against KAN-style, tuned SIREN/Fourier, and adaptive PINN baselines across an Allen-Cahn epsilon-suite. Ablations show that most of this gain comes from a dense local-basis residual rather than from Cauchy activation alone. A Poisson/Burgers boundary check prevents a broad PDE dominance claim: tuned SIREN/Fourier and KAN-style baselines can dominate away from transition-layer structure. The resulting claim is deliberately bounded: Cauchy components are one useful instance of robust/local-basis co-design in low-dimensional scientific tasks, not a universal activation or a uniquely rational mechanism.

Message-passing graph neural networks (MPGNNs) dominate modern graph learning. Typical efforts enhance MPGNN's expressive power by enriching the adjacency-based aggregation. In contrast, we introduce a graph-level aggregation over walk incidence-based matrices that are constructed to deliberately trade off some expressivity for stronger and more structured inductive bias. This approach allows for gradual scaling between classical message-passing and simpler methods based on walks. Our second result characterizes the expressive power at each scale using homomorphism counts over a hierarchy of generalized caterpillar graphs. Based on these foundations, we propose Caterpillar GNNs that substantially reduce the number of nodes in the hidden layers of the computational graphs on real-world datasets. This gradual reduction does not obstruct learning, enabling a systematic study of lower-order expressivity. We further describe benchmark settings where a task-aligned expressivity supports learning.

Adaptive learning requires distinguishing environmental volatility from observation stochasticity, two sources of uncertainty that demand opposite adjustments to the learning rate but inflate experienced variance similarly. Disentangling them is computationally difficult with no tractable closed-form solution. Particle-filter methods are the natural tool for this kind of joint inference, but their stochastic likelihoods and non-differentiable objectives force derivative-free fitting protocols and discourage the individual-difference analyses central to cognitive modeling, where small effect sizes leave little room for additional estimator noise. We introduce the Categorical Bayes Filter (CBF), a deterministic alternative that preserves the conditional structure of recent particle-filter accounts but replaces the stochastic outer layer with a categorical distribution on a quantile grid parameterized through differentiable Beta quantile functions. The procedure performs evidence maximization with an exact, deterministic marginal likelihood that is fully differentiable in the grid parameters. In a volatility-stochasticity task with N = 643 participants, fitted CBF dispersion parameters reveal a cross-over phenotyping pattern between volatility-blind and stochasticity-blind subjects that is not recoverable from particle-filter parameters fit to the same data under a state-of-the-art protocol. The deterministic structure also yields a trial-by-trial ambiguity signal that predicts response times not used in fitting. More broadly, the approach opens individual-level analyses in cognitive modeling and computational psychiatry that stochastic methods have effectively foreclosed.

Within the landscape of inference-time scaling methods for foundation models, a _width-based_ approach to scaling—which involves the insertion of \ tokens in the input stream to delay model responses—offers a unique advantage by increasing model expressivity while remaining highly parallelizable at both training and inference. The existing literature on training models to utilize \ tokens relies on the standard cross-entropy objective in which the model output is read out and evaluated only at the final step of a pause sequence. This approach provides no mechanism for the model to regulate its own processing or to signal readiness to respond, treating the additional compute steps as a static barrier rather than a resource to be used adaptively. We propose a supervised loss, _Catch Your Breath_ (_CYB_), framed as a sequential-decision problem, that trains a model to dynamically and autonomously scale the number of compute steps used for each input token. The model indicates the need for additional compute steps by emitting a special \ output, delaying its response via a \. The model can abstain multiple times to obtain longer delays. Our experiments demonstrate that CYB significantly outperforms standard cross-entropy when introduced either in pretraining or fine-tuning, reducing perplexity and enhancing downstream accuracy with no additional computational or memory cost.

Humans develop perception through a bottom-up hierarchy: from basic primitives and Gestalt principles to high-level semantics. Current Multimodal Large Language Models (MLLMs) are trained directly on complex downstream tasks. Does it guarantee their performance on these foundational visual capabilities? To systematically investigate this gap, we introduce VisFactor, a benchmark that digitizes 20 vision-centric subtests from FRCT, a well-established cognitive psychology assessment spanning four domains of human visual cognition. Furthermore, we design algorithms to automatically construct and validate unlimited test cases with controllable difficulty. Using VisFactor, we evaluate 39 frontier MLLMs, including both proprietary (e.g., GPT, Gemini) and open-source (e.g., LLaMA, Qwen) models. The best model achieves a score of only 55.9%. Analysis reveals good internal consistency (Cronbach's alpha = 0.94) and construct validity (compared to existing vision benchmarks). Models consistently fail on tasks such as mental rotation, spatial relation inference, and figure–ground discrimination, regardless of model size or prompting strategy. These findings suggest that performance improvements on existing general benchmarks might represent castles in the air instead of a genuine mastery of human-like visual cognition.

Reinforcement learning (RL) is a promising way to improve the clinical reasoning abilities of large language models (LLMs), but current pipelines often rely on expert-labeled questions or costly synthetic-data generation. Meanwhile, the medical literature offers a wealth of high-quality unlabeled documents, including clinical case reports that trace the full clinical course from initial presentation to final treatment decisions. We study whether document-grounded self-play can convert these reports into effective RL training signals. We identify two challenges that limit existing self-play methods in this setting: knowledge-point fixation, where the proposer repeatedly asks about a narrow set of salient clues in a source report, and difficulty-quality mismatch, where appropriately difficult questions may still be poorly formed or shallow, limiting their value for reasoner training. To address these challenges, we propose CasePlay, a self-play framework with two key components: (a) a Knowledge-Conditioned Proposer, which anchors question generation to case-specific knowledge points so that questions draw on a broader range of evidence from the source report; and (b) a Rubric-Judge Reasoner, which augments answer-accuracy feedback with rubric-based quality feedback on clue integration, reasoning depth, and option quality, guiding the proposer toward reasoning-intensive questions that better support reasoner training. Extensive experiments across seven medically related benchmarks demonstrate that CasePlay outperforms existing self-play baselines and improves the SFT warm-start model by 3.0 points on average, highlighted by a 6.9-point gain on LiveClin. This approach offers an effective path toward continually improving medical reasoning ability through self-play RL. Code is available at \url{https://anonymous.4open.science/r/CasePlay}.

Multimodal Large Language Models (MLLMs) have shown strong performance on medical public benchmarks, but existing evaluations remain limited as clinically grounded assessments because they often rely on isolated inputs lacking study-level structure and simplified, recognition-style tasks that are far from real diagnostic workflows. We introduce \textbf{CardioLens}, a leakage-resistant evaluation testbed using multi-sequence Cardiovascular Magnetic Resonance (CMR), constructed from private hospital archives via a rigorous report-to-QA construction and verification pipeline. CardioLens is built from 473,896 slices and 13,494 verified QA pairs across 4D Cine, LGE, perfusion, and T2-weighted imaging, and evaluates three stages of CMR interpretation: image understanding, report generation, and disease diagnosis. Across 24 state-of-the-art MLLMs, CardioLens reveals a substantial clinical reality gap. Models perform poorly overall, with performance degrading along the real CMR workflow. Confusion analysis further reveals a category-collapse failure mode: models often default to frequent abnormal categories rather than reliably telling distinct clinical findings. To rule out MLLM-compatible input construction as the failure cause, we compare random, clinically-motivated, and data-driven selection protocols under different slice budgets; performance changes only marginally, typically by about 1\%. Explicit reasoning prompts also fail to rescue performance, often driving models toward conservative predictions rather than improving visual evidence use. These results show that current MLLMs remain far from reliable CMR interpretation, where clinical decisions require integrating distributed evidence across sequences, views, and temporal phases. By exposing where and how current MLLMs fall short, CardioLens provides a clinically grounded testbed for developing the next generation of MLLMs toward real-world clinical depolyment.

Characterizing the properties of neuronal cell types is central to understanding brain function. Yet, biophysically realistic neuron models remain difficult to scale to large populations while preserving the richness of cellular dynamics and within-cell-type variability. We present a cell-type-specific neural-operator framework for scalable neuronal population modeling. Rather than training separate surrogate models for individual neurons, the proposed framework learns a shared operator across multiple modeled neurons from the same cell type, conditioned on biologically interpretable electrophysiological features. This enables efficient generation of large ensembles of somatic voltage responses while preserving variability across cells and model configurations. We evaluate the approach using membrane dynamics metrics, action potential waveform metrics, spike timing accuracy, input-output firing relationships, and electrophysiological feature distributions. Our framework reproduces subthreshold membrane dynamics, spike waveforms, and firing-rate responses across major cortical inhibitory neuron types, while accurately preserving spike timing despite the sensitivity of threshold-crossing dynamics. The predicted electrophysiological feature distributions show strong agreement with detailed simulator outputs and human experimental recordings, including high explained variability in properties such as inter-spike intervals, firing frequency, action-potential shape, and post-spike recovery. By enabling fast ensemble simulation of cell-type-specific neuronal responses, the proposed framework provides a scalable tool for studying cellular diversity, probing variability near functional thresholds, and generating synthetic but biophysically grounded neuronal populations.