NeurIPS 2026 Papers

This paper studies the task of estimating heterogeneous treatment effects in causal panel data models with covariate effects. We propose a novel **Co**variate-Adjusted **DE**ep C**A**usal **L**earning (**CoDEAL**) framework, that cohesively deal with the underlying heterogeneity and nonlinearity of both panel units and covariate effects. CoDEAL integrates nonlinear covariate effect components (parameterized by a feed-forward neural network) with nonlinear factor structures (modeled by a multi-output autoencoder) to form a heterogeneous causal panel model. The nonlinear covariate component flexibly captures complex covariate influences on outcomes, and the nonlinear factor decomposition enables CoDEAL to effectively capture both cross-sectional and temporal dependencies inherent in the data panel. This latent structural information is subsequently integrated into a customized matrix completion algorithm, thereby facilitating more accurate counterfactual imputation. Moreover, the use of a multi-output autoencoder explicitly accounts for heterogeneity across units and enhances the model interpretability of the latent factors. We establish theoretical guarantees on the convergence of the estimated counterfactuals and demonstrate the compelling performance of the proposed method using extensive simulation studies and real-world data applications.

Building hydrogen station networks, electric vehicle (EV) charging grids, or vaccine distribution systems requires coordinating two separately operated graphs - demand-side facilities and the supply-side networks they depend on - where each operator's payoff depends on the other's choices. We formalize this as the Co-Evolving Graph Game (CEGG), a setting that sits between facility location, interdependent-network analysis, and graph-based multi-agent reinforcement learning (MARL) but is not jointly addressed by any of them. We propose Cross-Graph Attention with Policy Mirror Descent (CGA-PMD), pairing cross-graph attention - which lets each agent read only the partner-graph nodes structurally coupled to its own - with a policy mirror descent update for stable training. Across three reward domains and a range of practical network scales, we find that the structure of the coupling selects which method wins: at small scale most methods are competitive, but as scale grows or coupling becomes irregular, only CGA-PMD remains productive while own-only, unmasked-attention, and Proximal Policy Optimization (PPO)-based variants all fail in distinct ways. Our theoretical analysis explains why: PMD's Kullback-Leibler (KL) regularization admits an iteration-uniform cumulative drift bound while PPO's clip update does not, predicting CGA-PMD's stability in the hard regime where PPO-based methods collapse.

Generative modeling over discrete structures underpins applications across deep learning, from biological sequence design and code generation to large language models, yet generation often remains sequential, relying on autoregressive decoding or iterative refinement. We introduce Coupling Models, a one-step discrete generative model that learns a direct coupling between discrete sequences $x$ and Gaussian latents $z \sim \mathcal{N}(0,I)$. Unlike recent distillation methods that compress a pretrained multi-step sampler into fewer steps, Coupling Models train a purpose-built decoder to invert this coupling and generate samples in a single forward pass. The method also avoids complex continuous flows over the simplex and hand-specified data-to-noise couplings. Empirically, Coupling Models improve the strongest one-step baselines in each domain, reducing LM1B text-generation perplexity by 33% at its lowest-perplexity operating point, Fly Brain enhancer-design FBD by 18%, and MNIST-Binary FID by 46%. These results suggest that effective one-step discrete generation depends strongly on how data and noise are coupled before decoding.

We investigate the problem of learning neural operators for coupled multi-physics PDEs, where multiple physical processes co-evolve and influence one another via bidirectional coupling. For example, in subsurface CO$_2$ storage, fluid flow, heat transfer, and geo-mechanical deformation evolve in a tightly coupled manner. Prior work, including neural operators and generative PDE solvers, mostly focuses on single-physics settings or relies on iterative inference, limiting their effectiveness in coupled PDEs. This paper introduces coupled-flow, a one-step generative neural operator that revisits coupled operator learning as solving a distributional transport problem. It parameterizes process-specific average velocity fields conditioned on the full coupled state, enabling cross-process interactions to emerge naturally from the transport dynamics. We further establish a Wasserstein-2 generalization bound that ties the prediction error of coupled-flow to its training losses through the regularity of the induced flow. Experiments on a wide variety of multi-physics benchmarks demonstrate that coupled-flow achieves significant performance improvements over coupled neural-operator and generative PDE baselines.

Physics-Informed Neural Networks (PINNs) solve forward PDEs by minimizing residual losses from the governing equations with initial and boundary conditions, but they often struggle with discontinuities such as shocks. In contrast, finite volume methods (FVM) handle discontinuities by enforcing integral conservation, which admits weak solutions. Motivated by this, we propose a \emph{Coupled Integral PINN (CI-PINN)} that augments a standard PINN with an auxiliary network for integral potentials and coupled integral constraints. This improves robustness near shocks while avoiding meshing and the numerical flux integration/reconstruction used in classical schemes. We validate CI-PINN on forward benchmarks including Burgers, Buckley--Leverett, the Euler system, and the Shallow-Water equations.

Guidance methods are essential tools for steering the generation process in diffusion models, improving the generalizability of stochastic robotic controllers and enabling high-quality controlled image synthesis. Despite strong parallels between flow-matching and diffusion, integrating guidance into flow-matching models remains quite challenging. Recent work has proposed general guidance frameworks for flow-matching, however, they are direct adaptations of diffusion guidance methods and can prove unstable. In this work, we conduct a theoretical analysis of guidance in flow-matching and show that a naive translation of diffusion-based guidance to flow-matching breaks the coupling distribution used during training, resulting in weaker control over sampling accuracy. Building on this insight, we propose **Coupled Guidance**, a flow-matching-specific guidance mechanism derived from a geometric perspective that leverages the coupling structure inherent to flow-matching training. To validate the effectiveness of our approach, we conduct extensive experimentation on a custom robotic *collision avoidance* task using Maniskill3, four robotic *dexterous manipulation* tasks from the Adroit benchmark, and three image generation tasks, namely *inpainting*, *super-resolution*, and *deblurring*, using the ImageNet-128 and CelebA-HQ-256 datasets. Our findings show that our framework improves sample quality and guidance stability across all tasks, without imposing any additional overhead.

Crowd counting is a vital computer vision task with wide-ranging applications, from public surveillance to urban planning. A persistent challenge is achieving scale invariance despite noisy labels, as humans often make counting errors with similar objects. Most existing methods struggle to maintain consistency and robustness when testing images differ in scale from the training data. We propose ScaLe-aware Invariance and Correcting Errors (SLICE) for robust crowd counting, a novel scale-aware loss function that improves scale invariance, enabling consistent and robust predictions under varying scales and annotation noise. The loss function combines two components: a scale-invariance term that applies multiscale supervision to enforce consistency across density maps of the same scene, and an error correction term that addresses inevitable annotation noise by modeling label uncertainty with probabilistic methods such as a mixture of Gaussians. SLICE is model-agnostic and integrates easily into existing crowd counting architectures without extra computational overhead during inference. Extensive experiments on five benchmark datasets show that SLICE greatly improves scale invariance and cross-dataset generalization, achieving the state-of-the-art results in challenging scenarios. Using CrowdDiff, Steerer, and CrowdFormer as baselines, SLICE lowers mean absolute error (MAE) by 5–7\% by addressing annotation noise and scale variation. Applying the scale-invariance term across multiple scales further cuts MAE by up to 15\%.

Reinforcement learning has rapidly become the dominant paradigm for training software engineering (SWE) agents on long-horizon, multi-turn tasks such as resolving real-world GitHub issues. Yet existing pipelines suffer from a fundamental credit-assignment bottleneck: rewards arrive only at the end of trajectories that may span dozens of file edits, shell commands, and test invocations, leaving every intermediate decision indistinguishable from luck. We observe that containerised SWE tasks provide a particularly useful form of environment forkability: a commit hash plus a container image specifies a real executable software state that can be restored cheaply and exactly, with auditable provenance and without a simulator-to-reality gap. We exploit this property by introducing Counterfactual Rollout Replay (CRR), a training-time procedure that re-executes the environment from selected decision points with alternative actions and assigns each selected step an advantage equal to the sampled on-policy versus counterfactual return differential. CRR requires no learned process reward model, no human rubric annotation, and no oracle hindsight signal; it is free of auxiliary process labels and reward-model training, while still incurring extra environment-replay compute. Applied to a 14B base model on SWE-Gym and evaluated on SWE-bench Verified and SWE-rebench, CRR-trained agents reach higher resolution rates with substantially fewer trajectories than outcome-only GRPO and complement orthogonal advances such as PRM-based scoring and trajectory search.

We study finite-horizon two-player zero-sum perfect-recall partial-information games and ask for the minimal finite-dimensional state sufficient to answer all rooted observation-measurable unilateral continuation queries. For each player $i$ and information set $I$, we consider the span $\mathcal L_i(I)$ of feasible counterfactual beliefs and the effective local query space $\mathcal E_i(I)$ generated by rooted continuation queries restricted to $\mathcal L_i(I)$. We prove that its dimension $d_i(I)$ is simultaneously the rank of the local counterfactual query operator, the minimum core-query basis size, the minimum exact local realization dimension, and the dimension of the canonical quotient $\mathcal L_i(I)/\mathcal N_i(I)$, yielding reduced counterfactual predictive-state representations, unique up to similarity, with exact first-return update operators. Aggregating the local ranks defines the deviation-conditioned predictive-state dimensions $d_t^i$, $d_t$, $d_\star$, and $D_\star$. We then prove that local rooted payoff-query control transfers to global exploitability, and under local design richness and bounded one-step parameter norms obtain a rollout-based upper bound in these minimal coordinates. We complement this with a minimax lower bound showing that $\Omega(d/\gamma^2)$ local rollouts are necessary even when the peak DCPSD equals $d$, and with an exponential separation theorem exhibiting games with $d_\star=m$ but observable continuation-trace complexity $2^m$. Finally, we show that DCPSD recovers finite-rank predictive-state, observable-equivalence, and linearly parameterized continuation-law models as special cases.

Counterfactual explanations are a central tool in interpretable machine learning, yet computing them exactly for complex models remains challenging. For tree ensembles, predictions are piecewise constant over a large collection of axis-aligned hyperrectangles, implying that an optimal counterfactual for a point corresponds to its projection onto the nearest rectangle with an alternative label under a chosen metric. Existing methods largely overlook this geometric structure, relying either on heuristics with no optimality guarantees or on mixed-integer programming formulations that do not scale to interactive use. In this work, we revisit counterfactual generation through the lens of nearest-region search and introduce *counterfactual maps*, a global representation of recourse for tree ensembles. Leveraging the fact that any tree ensemble can be compressed into an equivalent partition of labeled hyperrectangles, we cast counterfactual search as the problem of identifying the *generalized Voronoi cell* associated with the nearest rectangle of an alternative label. This leads to an exact, amortized algorithm based on volumetric k-dimensional (KD) trees, which performs branch-and-bound nearest-region queries with explicit optimality certificates and sublinear average query time after a one-time preprocessing phase. Our experimental analyses across several real datasets from high-stakes application domains show that this approach delivers globally optimal counterfactual explanations with millisecond-level latency, achieving query times that are orders of magnitude faster than existing exact, cold-start optimization methods.

Vision-Language-Action (VLA) models inherit rich semantic priors from pretrained vision-language models, yet these priors do not guarantee persistent instruction sensitivity after narrow-domain fine-tuning. We observe a systematic failure mode: although VLA models remain visually reactive, their later actions can become weakly constrained by the commanded instruction, leading to unstable object interaction and visually plausible but instruction-inconsistent behavior. We trace this behavior to a collapse of instruction-conditioned representations across network depth and task progress. More fundamentally, this collapse is enabled by the learning objective itself: standard imitation learning admits Bayes-optimal solutions that are invariant to language. We address this by recasting instruction grounding as identifying the commanded instruction among counterfactual alternatives. Based on this view, we propose Counterfactual Instruction Grounding (CIG), a contrastive objective that encourages the generated trajectory to remain identifiable with the commanded instruction among counterfactual alternatives. CIG applies to both autoregressive and flow-matching VLA models, using exact action-chunk likelihoods for autoregressive models and an energy-based pseudo posterior for flow-matching models to avoid intractable trajectory likelihood estimation. Practically, CIG can be applied directly to already fine-tuned models as a continuation-stage grounding objective, restoring instruction sensitivity without retraining from scratch or changing the architecture. Extensive experiments on RoboCasa and LIBERO-Plus demonstrate that CIG achieves strong instruction-following performance with success rates of 71.3% and 86.3%, respectively. Real-world deployment further shows that CIG transfers to kitchen manipulation and preserves instruction-conditioned behavior in visually ambiguous scenes.

Counterfactual explanations for time-series classification generate synthetic instances that flip a prediction to a desired class while remaining plausible and making small, local changes. Existing methods often rely on classifier gradients, and many do not naturally extend to one-class settings. To bridge this gap, we propose CTCF, a model-agnostic method for hard-decision classifiers in supervised and one-class settings. CTCF decouples generation from classifier-specific control by reusing an unconditional Flow Matching generator and learning a flow-time-dependent desired-class region from interpolation states labeled by endpoint hard decisions, without classifier gradients or class probabilities. At inference time, CTCF uses a dual-control mechanism: fused-lasso endpoint-objective steering encourages small, segment-local changes, while linearized projection correction reduces violations of a conservative desired-class region. Theoretically, under ideal marginal matching, we show that the surrogate risk on interpolation states equals the corresponding ODE-trajectory risk. Experiments on UCR datasets demonstrate CTCF's effectiveness across quantitative metrics and qualitative case studies.

Estimating counterfactual outcomes when multiple treatments are applied simultaneously, the composite treatment setting, is fundamentally harder than the single-cause case: the treatment space grows combinatorially, most combinations are unobserved, and confounding is entangled across dimensions. We propose PACE (Progressive Alignment for Composite Effects), which exploits a known causal DAG over treatment variables to progressively transform the observational data distribution into the target interventional distribution. PACE performs K sequential augmentation steps in reverse topological order, each isolating a single treatment component and conditioning only on its parents in the DAG. We derive the closed-form optimal augmentation density minimizing KL divergence at each step, establish finite-sample bounds prescribing the augmentation budget via DAG-aware selection bias ratios, and show that the DAG provides a deterministic processing order that eliminates the need for random permutation averaging. On semi-synthetic benchmarks with real covariates (IHDP, Twins, Hillstrom) and controlled synthetic environments, PACE substantially outperforms seven baselines on both continuous and binary outcomes, with the largest gains on rare treatment combinations where confounding is most severe. Ablations confirm consistent improvements over the closest prior method across varying DAG topologies, confounding strengths, and under DAG misspecification.

Large language models are increasingly deployed as autonomous agents that plan and act over long-horizon interactions, learning from both final outcomes and rich environmental feedback. However, optimizing from such interaction experience remains challenging, as feedback is heterogeneous and rarely carries explicit reward information. Existing post-training approaches rely on outcome-driven methods, such as reinforcement learning with verifiable rewards (RLVR), which primarily exploit final success signals while leaving interaction experience and feedback underutilized. In sparse-reward, long-horizon tasks, this often results in **distribution sharpening**: the policy reinforces a narrow set of already-successful behaviors, without substantially improving the feedback-grounded agency needed for broader problem-solving capacity (e.g., Pass@$k$). We propose ***Counterfactual Distillation***, a framework that converts exploration-derived experience into trainable policy supervision. Specifically, we organize exploration as a tree-structured search process, where the agent reflects on past decision points and makes new experience-guided decisions to form alternative branches. These corrections are then distilled as counterfactual targets: we train the model to predict the revised action from the original history without explicitly providing the experience, thereby introducing out-of-distribution behavior patterns and expanding exploration capacity. Across diverse interactive coding and agentic tasks, our method outperforms outcome-driven baselines such as GRPO and experience-based methods such as Early Experience, with gains of up to **14%** on Pass@128. When interleaved with reinforcement learning updates, it further raises the performance ceiling, yielding over **10%** improvement in Pass@1. We provide an [anonymized implementation](https://anonymous.4open.science/r/Counterfactual-Distillation-0E71).

Policies achieving strong performance in simulators or learned world models can fail when deployed into the real environment. While there must be environmental differences that account for these failures, not all differences are equally responsible. A benign error of irrelevant visual details may co-exist with a failure to predict a single critical transition causing an inevitable catastrophic failure. In this paper, we introduce \emph{counterfactual debugging} as an approach for \emph{world model transfer gap attribution} to identify the time steps whose transition or reward errors are \emph{causally responsible} for a performance degradation exhibited in a real trajectory, rather than only visually or statistically different. We develop a scalable algorithm for computing these attributions that exploits the sparsity of causal errors by recursively divide-and-conquer, significantly reducing computational costs and achieving an exponential speedup. The resulting ranked attribution report can better explain the performance gap in the real trajectory. Experiments across several distinct environments with a variety of injected world-model failures (observation corruption, reward misprediction, and physics violations) demonstrate that counterfactual debugging correctly identifies the errors that are responsible for performance gap, providing theoretically grounded, actionable insights for model improvement.

Large-scale human demonstrations have been a key ingredient in training interactive agents, from robot policies to computer-use agents and game world models. But for multi-agent world modeling, the open data landscape is missing a crucial combination: expert humans acting together in the same evolving world, observed from every participant’s viewpoint, with precise controls and state. Internet-scale video captures human behavior, but its controls are inferred and its viewpoints are not synchronized; simulator and policy rollouts provide exact labels and all-player views, but not strategic, collaborative human play. We present CounterStrike-1K, a public benchmark dataset built from professional Counter-Strike 2 match replay files. It contains 1,490 rendered player-view hours across seven maps, with every released round synchronized across all ten active player viewpoints. Each view is paired with audio, replay-derived game controls, player state, world position, and sparse game event annotations. Because each round records expert human teams coordinating under partial observability, CounterStrike-1K tests whether models can simulate not just game physics or single-view visual plausibility, but skilled decisions and their consequences across all players’ views. We provide fixed splits and benchmarks for action-conditioned prediction, cross-POV retrieval, multi-POV action coverage, and shared-state recovery. By releasing round-complete multi-perspective demonstrations at this scale, CounterStrike-1K provides a grounded training and evaluation testbed for multi-agent world-model research.

Counterfactual explanations (CFs) provide human-interpretable insights into model's predictions by identifying minimal changes to input features that would alter the model's output. However, existing methods struggle to generate multiple high-quality explanations that (1) affect only a small portion of the features, (2) can be applied to tabular data with heterogeneous features, and (3) are consistent with the user-defined constraints. We proposeCounterFlowNet, a generative approach that formulates CF generation as sequential feature modification using conditional Generative Flow Networks (GFlowNet). CounterFlowNet is trained to sample CFs proportionally to a user-specified reward function that can encode key CF desiderata: validity, sparsity, proximity and plausibility, encouraging high-quality explanations. The sequential formulation yields highly sparse edits, while a unified action space seamlessly supports continuous and categorical features. Moreover, actionability constraints, such as immutability and monotonicity of features, can be enforced at inference time via action masking, without retraining. Experiments on eight datasets under two evaluation protocols demonstrate that CounterFlowNet achieves superior trade-offs between validity, sparsity, plausibility, and diversity with full satisfaction of the given constraints.

We consider the problem of Cost-Aware Learning, where sampling different components of a finite-sum objective incurs different costs. The objective is to reach a target error while minimizing the total cost. We propose Cost-Aware SGD, which uses a distribution based on gradient norms and costs to sample components. We provide a thorough analysis of this algorithm, including cost-improvement bounds over baselines, a characterization of distribution proxy sub-optimality, and a lower bound. We apply our theoretical insights to reinforcement learning with language models, where the computational cost of sequence-level policy gradients varies with length. We find that the advantage magnitude serves as a high-fidelity proxy for gradient norms, and use this to introduce Cost-Aware GRPO. Empirical results on 1.5B, 4B, and 8B LLMs demonstrate that this algorithm significantly reduces the tokens used in policy optimization while matching or exceeding baseline accuracy.

We study the problem of auditing the fairness of a given classifier under partial feedback, where true labels are available only for positively classified individuals (e.g., loan repayment outcomes are observed only for approved applicants). We introduce a novel cost model for acquiring additional labeled data, designed to more accurately reflect real-world costs such as credit assessment, loan processing, and potential defaults. Our goal is to find optimal fairness audit algorithms that are more cost-effective than random exploration and natural baselines. In our work, we consider two audit settings: a black-box model with no assumptions on the data distribution, and a mixture model, where features and true labels follow a mixture of exponential family distributions. In the black-box setting, we propose a near-optimal auditing algorithm and show that a natural baseline can be strictly suboptimal. In the mixture model case, we design a novel algorithm that achieves significantly lower audit cost than the black-box case under mild assumptions. Our approach develops novel connections between partial feedback and learning from truncated samples. We also extend known results on maximum-a-posteriori oracles for spherical Gaussian mixtures to handle exponential family mixtures, which may be of independent interest. Moreover, our algorithms apply to popular fairness metrics including demographic parity, equal opportunity, and equalized odds. Empirically, we demonstrate strong performance of our algorithms on real-world fair classification datasets like Adult Income and Law School, consistently outperforming natural baselines by around 50% in terms of audit cost.