NeurIPS 2026 Papers

Memory consumption of the key-value (KV) cache remains a central bottleneck for long-context LLM inference. We introduce PRKV, a training-free KV eviction method that estimates multi-hop global token importance by applying Personalized PageRank over attention-induced transition graphs. This enables importance propagation beyond recency or instantaneous attention, without modifying the model. We benchmark PRKV on long-context understanding, sparse retrieval, and chain-of-thought reasoning tasks using multiple LLM families. Under moderate to aggressive compression ratios, including up to 90\%, PRKV achieves competitive task performance against established eviction baselines while reducing peak memory usage with low end-to-end overhead. These results demonstrate that multi-hop global influence estimation yields a favorable accuracy--memory trade-off for scalable long-context inference.

Persistence diagrams are common representations in topological data analysis, yet they lack both the vector space structure required by machine learning algorithms and a principled framework for statistical comparison. We introduce STRAND (Survival Topological Representation ANalysis of Diagrams), which treats (collections of) PDs as survival data: each topological feature with persistence value $p = d - b$ is a fully observed time-to-event, and the persistence survival function $S(t) = \mathbb{P}(p > t)$ is the central object for comparing diagrams. From this single representation we derive (i) a non-parametric two-sample test with calibrated Type~I error and high power from a small number of diagrams; (ii) interpretable effect sizes; and (iii) a 1-Wasserstein-stable feature vector for downstream machine learning. We validate calibration and power on synthetic manifolds with controlled topology, demonstrate competitive vectorisation across 14 graph and 3D point cloud benchmarks, and apply the method to study functional brain connectivity in fMRI/neuroscience data. To our knowledge, STRAND is the first method to provide hypothesis testing and vectorisation for persistence diagrams from a single coherent and interpretable representation.

Free energy estimation is a fundamental yet challenging problem, from physics to statistics. Classical approaches rely on thermodynamic transformations, ranging from direct estimation, quasistatic integration, to finite-time averaging. Recent work learns neural transports to significantly accelerate the efficiency in the finite-time regime. In this paper, we generalize this framework to arbitrary state spaces. Building on this view, we develop a generalized neural transport learning approach for efficient estimation. Experiments validate the effectiveness and efficiency of the proposed method beyond continuous settings, extending to discrete and multimodal spaces as well as autoregressive settings.

Monocular depth foundation models generalize well across scenes, yet they are typically optimized with uniform pixel-wise objectives that do not distinguish user-specified or task-relevant target regions from the surrounding context. We therefore introduce Focusable Monocular Depth Estimation (FDE), a region-aware depth estimation task in which, given a specified target region, the model is required to prioritize foreground depth accuracy, preserve sharp boundary transitions, and maintain coherent global scene geometry. To prioritize task-critical region modeling, we propose FocusDepth, a prompt-conditioned monocular relative depth estimation framework that guides depth modeling to focus on target regions via box/text prompts. The core Multi-Scale Spatial-Aligned Fusion (MSSA) in FocusDepth spatially aligns multi-scale features from Segment Anything Model 3 to the Depth Anything family and injects them through scale-specific, gated conditional fusion. This enables dense prompt cue injection without disrupting geometric representations, thereby endowing the depth estimation model with focused perception capability. To study FDE, we establish FDE-Bench, a target-centric monocular relative depth benchmark built from image-target-depth triplets across five datasets, containing 252.9K/72.5K train/val triplets and 972 categories spanning real-world and embodied simulation environments. On FDE-Bench, FocusDepth consistently improves over globally fine-tuned DA2/DA3 baselines under both box and text prompts, with the largest gains appearing in target boundary and foreground regions while preserving global scene geometry. Ablations show that MSSA's spatial alignment is the key design factor, as disrupting prompt-geometry correspondence increases AbsRel by up to 13.8%.

Data collection is a critical component of modern machine learning pipelines. In many settings, multiple agents, such as hospitals or research labs, can collaborate to share the burden of data collection rather than each bearing it alone. But how should the work be divided among these agents fairly? Studying this question is complicated by heterogeneity in agents' data collection costs and data quality, and by the fact that fairness itself is subjective and use-case-dependent. We study these challenges in the context of PAC mean estimation, where agents wish to estimate an unknown scalar $\mu$ to within accuracy $\epsilon$ with probability at least $1-\delta$, via samples from distributions with common mean $\mu\,$. Agents may incur different costs to collect their samples, and their distributions may have different variances (data qualities). Our first contribution is a framework that casts collaborative data collection as a bargaining problem, where agents specify a notion of utility (e.g., negative cost incurred, or cost savings relative to working alone) and a welfare function over agent utilities. By maximizing the welfare over the feasible set of data collection amounts (i.e. there is enough data to satisfy $(\epsilon,\delta)$-PAC mean estimation), we obtain a fair division of work. Drawing on classical fairness axioms from the microeconomics literature, the family of admissible welfare functions takes a specific one-parameter form that includes utilitarian, egalitarian, and Nash bargaining as special cases. When agents' noise variances (data qualities) are known, this yields a clean characterization of the fair division. Our second contribution addresses the more challenging setting where variances are unknown. As the feasible set of data collection amounts itself depends on the variances, it is impossible to specify a fair division of work upfront. We propose an online algorithm that combines plug-in variance estimates with carefully calibrated forced sampling, and show that it is asymptotically optimal: the ratio of the achieved welfare to the welfare of the true fair division converges to 1 almost surely as either $\epsilon$ or $\delta$ goes to 0. We further show that our estimator asymptotically exactly meets the specified error tolerance and failure probability.

We introduce a novel Mutual Information (MI) estimator that fundamentally reframes the discriminative approach. Instead of training a classifier to discriminate between joint and marginal distributions, we learn a normalizing flow that transforms one into the other. This technique produces a computationally efficient and precise MI estimate that scales well to high dimensions and across a wide range of ground-truth MI values.

Explainability, the capability of an artificial intelligence system (AIS) to explain its outcomes in a manner that is comprehensible to human beings at an acceptable level, has been deemed essential for critical sectors, such as healthcare. Is it really the case? In this perspective, we consider two extreme cases, Oracle (without explainability) versus AI Colleague (with explainability) for a thorough analysis. We discuss how the level of automation and explainability of AIS can affect the determination of liability among the medical practitioner/facility and manufacturer of AIS. We argue that explainability plays a crucial role in setting a responsibility framework in healthcare, from a legal standpoint, to shape the behavior of all involved parties and mitigate the risk of potential defensive medicine practices.

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.

In networks, effective dynamic treatment allocation requires deciding both whom to treat and also when, so as to amplify policy impact through spillovers. An early intervention at a well-connected node can trigger cascades that change which nodes are worth targeting in the next period. Existing treatment strategies under network interference are largely static while dynamic treatment frameworks typically ignore network structure altogether. We integrate these perspectives and propose Q-Ising, a three-stage pipeline that (i) estimates network adoption dynamics via a Bayesian dynamic Ising model from a single observed panel, (ii) augments treatment adoption histories with continuous posterior latent states, and (iii) learns a dynamic policy via offline reinforcement learning. The Bayesian mechanism enables uncertainty quantification over dynamic decisions, yielding posterior ensemble policies with interpretable spillover estimates. We provide a finite-sample regret upper bound that decomposes into standard offline-RL uncertainty, network abstraction error, and first stage error in Ising state estimation. We apply our method to data from Indian village microfinance networks and synthetic stochastic block models under simulated heterogeneous susceptible-infected-susceptible (SIS) dynamics and demonstrate that adaptive targeting outperforms static centrality benchmarks.

The canonical orientation of a 3D object is often not unique but inherently ambiguous: many objects admit multiple equally valid canonical frames that no single-output regressor can faithfully represent. Rotational symmetry is the most structured manifestation of this phenomenon, where the set of valid orientations forms an orbit of the symmetry group. Existing methods fall short in one of three ways: they predict only a single orientation, handle symmetry only under pre-defined group assumptions, or resort to test-time augmentation to approximate the full set of valid orientations. We instead introduce a general framework for ambiguity-aware orientation estimation that is at once $SO(3)$-equivariant by construction, distributional in its output, and free of any restriction on the symmetry group. It effectively predicts multiple valid orientations as a continuous multi-modal distribution over $SO(3)$ via a truncated Wigner-D expansion, without any symmetry-group assumption. The proposed method outperforms recent equivariant regressors and fixed-quotient classifiers on the ShapeNet orientation benchmark, particularly on categories with continuous rotational symmetry, showing that supervision on discrete symmetry labels generalises to continuous bands.

Learning a risk-sensitive individualized treatment rule (ITR) with patient covariates is challenging when the treatment criterion depends on the full conditional outcome distribution rather than only its conditional mean. Existing methods are largely criterion-specific, making it difficult to compare multiple treatment criteria within a common pipeline, such as quantiles, conditional value-at-risk (CVaR), and complex preference-based objectives such as cumulative prospect theory (CPT). We propose a distribution-first framework for risk-sensitive ITR learning that first estimates treatment-specific conditional outcome distributions and then constructs the target ITR by plug-in criterion evaluation. The proposed framework unifies treatment rule learning across multiple criteria and accommodates hard-to-optimize objectives within the same estimation pipeline. On the theoretical side, it yields a general error propagation result for Lipschitz treatment criteria, linking first-stage distribution estimation error to downstream criterion estimation and treatment regret, together with sharper regret bounds under standard margin conditions. Empirically, we show that the proposed framework outperforms direct criterion-specific methods in multiple settings and further evaluate it on the ACTG175 HIV clinical trial, a randomized study comparing several antiretroviral regimens in HIV-infected adults.

Individualized treatment selection with continuous actions requires accurate causal response estimation in decision-relevant regions, rather than uniformly over the entire action space. Estimating a global causal response surface and then choosing the treatment that maximizes it can therefore be suboptimal, since standard estimation objectives allocate modeling effort according to the observed treatment distribution rather than the regions that determine the optimal decision. While decision-aware approaches have been studied in unconfounded settings, this problem remains underexplored in proximal causal inference, where proxy variables and bridge functions enable identification under suitable assumptions even in the presence of hidden confounding. Despite recent progress, proximal methods have primarily focused on treatment-effect and potential-outcome estimation rather than treatment selection and optimal decision-making. To bridge this gap, we introduce a policy-targeted weighted bridge loss that emphasizes decision-relevant treatment regions while retaining global stabilization. We prove a regret bound showing that the proposed weighted bridge loss controls treatment-selection regret through a weighted ill-posedness constant. We instantiate the framework in decision-aware variants of several proximal bridge solvers, yielding practical algorithms that alternate between weighted bridge estimation, response-surface projection, policy update, and weight refinement. Empirically, we find that decision-aware weighting reduces regret across several bridge solvers, suggesting improved treatment selection in proximal settings.

Estimating causal effects from observational data requires identifying valid adjustment sets. This task is especially challenging in realistic settings where latent confounding and feedback loops are present. Existing approaches typically assume acyclicity or rely on global causal structure learning, limiting applicability and computational efficiency. In this work, we study a local, data-driven method for covariate selection based on conditional independence information. While this method is known to be sound and complete in acyclic causal models, its validity in the presence of cycles has remained unclear. Our main contribution is to show that these guarantees extend to cyclic causal models. In particular, our result relies on the invariance of conditional independence assertions under $\sigma$-acyclification. These findings establish a unified, cycle-agnostic perspective on covariate selection and causal effect estimation, showing that the method applies across cyclic and acyclic settings without modification. Empirically, we validate this on extensive synthetic data, showing reliable performance in cyclic causal models.

Randomized controlled trials typically assume that prognostic covariates are known and available at no cost. In practice, obtaining high-dimensional pretreatment data is costly, forcing a trade-off between covariate-adaptive precision and a measurement budget. We introduce Dynamic Adaptive Rerandomization via Thompson Sampling (DARTS), which treats covariate acquisition as a sequential optimization problem embedded within a design-based causal inference task. A budgeted combinatorial Thompson sampler learns which covariates are most prognostic across successive batches; selected covariates then drive rerandomization and regression adjustment to reduce batch-level average treatment effect variance. Our primary theoretical contribution is a decoupling result: adaptive covariate selection based on past batches preserves batch-level randomization validity, and the cumulative inverse-variance weighted estimator achieves at least nominal asymptotic coverage. We further derive a Bayes risk bound for the acquisition layer that matches the minimax lower bound up to logarithmic factors. Empirically, DARTS systematically concentrates budget on informative features, significantly closing the efficiency gap to oracle designs while maintaining strict inferential validity.

Simulation-based inference with neural posterior estimation (NPE) often yields overconfident and unreliable posteriors under limited simulation budgets. To address this, we propose DRO-NPE, a distributionally robust approach that replaces the standard NPE objective with a worst-case loss over a Wasserstein ambiguity set. We introduce KL-based metrics for miscoverage and miscalibration, and use these to show that the DRO-NPE objective controls overfitting and reduces posterior overconfidence. Our method is tractable, parallelisable, and readily integrates with standard normalising flows. Across benchmark SBI tasks, DRO-NPE consistently improves coverage and calibration, while narrowing the gap between empirical and population NPE loss, leading to more reliable inference in low-simulation regimes.

We propose a conservative continuous-time stochastic control framework for treatment optimization from irregularly sampled patient trajectories. We model the unknown patient dynamics as a controlled stochastic differential equation where treatment is a continuous-time control input. Naive model-based optimization can exploit model errors and propose out-of-distribution controls that appear optimal under the learned model but perform poorly under the true dynamics. To mitigate such extrapolation, we introduce a consistent, signature kernel MMD regularizer on path space, which penalizes controls whose predicted trajectories deviate from observed ones. The resulting conservative objective minimizes a tractable upper bound on the true cost. Experiments on pharmacometric simulators show improved robustness and performance compared to non-conservative baselines.

A complete understanding of heterogeneous treatment effects requires fully capturing the conditional distribution of the counterfactual outcomes. To this end, we propose the *Conditional Counterfactual Mean Embeddings* (CCME), a framework that embeds conditional distributions of counterfactual outcomes into a reproducing kernel Hilbert space (RKHS). Under this framework, we develop a two-stage meta-estimator for CCME that accommodates any RKHS-valued regression in each stage. Based on this meta-estimator, we develop three practical CCME estimators: (1) *Ridge Regression* estimator, (2) *Deep Feature* estimator that parameterizes the feature map by a neural network, and (3) *Neural-Kernel* estimator that performs RKHS-valued regression, with the coefficients parameterized by a neural network. We provide finite-sample convergence rates for all estimators, establishing that they possess the double robustness property. Our experiments demonstrate that our estimators accurately recover distributional features including multimodal structure of conditional counterfactual distributions.

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.

Treatment assignment problems arise wherever limited budget must be allocated to heterogeneous users, with applications ranging from personalized recommendations to online advertising and healthcare. In such settings, individuals exhibit heterogeneous responses to different treatments, making it essential to learn cost-aware personalized treatments. This paper introduces the Cost per Unit Value Equalization Tree (CUVET) algorithm, a novel treatment assignment approach that partitions the user space. Under a diminishing-returns (power-law) assumption, CUVET solves the within-cohort allocation problem by equalizing the marginal cost per unit value across each user group, yielding a closed-form cost-aware treatment assignment suited for large-scale industrial deployment. We also release CUVET-policy, an 86.7-million-impression public benchmark derived from real-world industrial A/B tests, providing an open-source evaluation framework for decision-focused learning. Across a multi-method benchmark suite, the Bayesian variant of CUVET achieves the largest cost-feasible value uplift on the public MT-LIFT dataset +11.1% under LP, vs. at most +1.3% for all baselines, while on CUVET-policy, where treatment effects are sub-percent, CUVET variants are the most efficient and strongest cost-feasible methods.