NeurIPS 2026 Papers

It is now common to use 2D diffusion priors for problems where the underlying object is 3D (e.g., medical imaging). We would pick a noise schedule from the EDM literature, anneal a tilted prior, and then use the formulation as a 3D generative model. It works empirically. But we know very little about what it converges to and how fast. We study this question for a natural target: the multi-marginal Schrödinger bridge, the relative-entropy projection of a 3D prior onto the distribution whose rendered slices match the 2D marginals. But computing it is intractable. The annealed 2D-tilted surrogate is what one actually uses in applications. The main question is how close the latter object is to the former. Our main idea is that the discrepancy between these two laws — a comparison of two high-dimensional, fully coupled distributions — can be reduced to the size of a *single* scalar correction field. This field has a nice two-piece form: residual coupling across slices and tempering mismatch from the annealed discrete schedule. Using a Gaussian-smoothed filtration, Wasserstein screening, and conditional concentration, we obtain an explicit discrepancy bound in which the relevant terms separate into latent and posterior-residual contributions. When the smoothing scale is identified with the EDM noise level $\sigma(\tau)$, our bound yields $\mathrm{KL}(\Pi_\tau\|P^\star)=O\left(N\sigma(\tau)^2\right)$ and $\|\Pi_\tau-P^\star\|_{\mathrm{TV}}=O\left(\sqrt{N}\sigma(\tau)\right),$ if the latent scale remains bounded and the surrogate log-discrepancy is noise-aligned. So, the 2D-tilted construction converges to the Schrödinger-bridge lift at a rate governed by user-checkable quantities like the surrogate Lipschitz constants and the posterior concentration constant.

In emotional support conversations, user needs are dynamic, shifting across turns between emotional soothing, cognitive guidance, and their combinations. Existing methods often optimize a single user-state objective, such as emotional relief or cognitive growth, making it difficult to capture such need shifts. In this paper, we formulate emotional support dialogue as a need-aware multi-objective optimization problem, where agents learn to generate responses that balance multiple support objectives according to users' evolving needs. We propose \textbf{MindFlow}, a psychologically grounded user simulator that tracks users' emotional and cognitive needs at each turn, derives state-dependent preference vectors from personalized arousal curves, and models mental-state transitions with a dual-process system. Building on MindFlow, we introduce \textbf{NeMo}, a need-aware multi-objective reinforcement learning framework that estimates local multi-turn effects through forward simulation and dynamically aggregates emotional and cognitive rewards based on current support preferences. By converting delayed, multi-dimensional feedback into step-level optimization signals, NeMo improves credit assignment and aligns policy learning with long-term user-state improvement. Experiments show that NeMo consistently improves user-side state metrics and response-level supportive quality, with robust generalization under both Sim2Sim and Sim2Real evaluations. Code and data are available at https://anonymous.4open.science/r/NeMo-6EB9.

We study a structured stochastic multi-armed bandit problem in which each decision simultaneously determines the learner's reward and the feedback available for learning. At each round, the learner selects a task and an option. Each task is associated with an unknown parameter that governs its reward, while each option has a known reward function of this parameter and determines how information about that reward is observed. Some options may provide fine-grained feedback at the cost of lower immediate reward, whereas others may yield higher reward but return only coarse feedback. This creates an intrinsic trade-off between reward maximization and information acquisition. We formalize this setting as parametric bandits with action-dependent coarsened feedback. For stationary tasks, we propose ACF-UCB, an optimistic algorithm that constructs task-level confidence sets by aggregating information from all atoms of the option-dependent feedback distributions. For piecewise-stationary tasks, we develop SW-ACF-UCB, a sliding-window variant that adapts to temporal changes. We prove high-probability regret bounds for stationary environments and dynamic regret guarantees for piecewise-stationary environments. We also establish lower bounds showing that the dependence on the number of tasks and the horizon is unavoidable, while methods that ignore the shared parametric structure suffer substantially larger regret.

Reconstructing accurate camera poses and floor-plan layouts from sparse, unposed, wide-baseline RGB panoramas remains a challenging open problem. Direct multi-room floor-plan prediction is especially difficult in this setting: pose, geometry, semantics, and global layout structure are tightly coupled, yet a complete floor-plan is hard to learn as a single global output. Our key insight is to keep the model's predictions strictly local. Multi-view Ordered Wall Instance Segmentation (MOIS) is designed around this concept. Each panorama column predicts only the wall it observes plus the next two adjacent walls in clockwise order. The global wall partition, room layouts, and shared coordinates emerge from deterministic aggregation of overlapping local predictions. Building on MOIS, we propose Multi-view floor-plan Feed-Forward Network (MvFFN), which jointly predicts coarse camera poses, dense global geometry, and per-wall semantic outputs. A downstream Layout Chaining (LC) post processing pipeline then assembles these predictions into multi-room floor-plans with shared global coordinates, consistent wall identities, and connected room structure. The dense MOIS predictions recover cross-view wall identity and local within-room connectivity more accurately than composed modular baselines, and the assembled layouts substantially outperform prior methods on wall and junction level accuracy. We also introduce the ZInD-CrossView dataset, which augments ZInD with globally unique wall instances and cross-view segmentation labels for this task.

Conformal prediction constructs prediction sets with finite-sample coverage guarantees, but its calibration stage is structurally constrained to a scalar score function and a single threshold variable — forcing shapes of prediction sets to be fixed before calibration, typically through data splitting. We introduce multi-variable conformal prediction (MCP), a framework that extends conformal prediction to vector-valued score functions with multiple simultaneous calibration variables. Building on scenario theory as a principled framework for certifying data-driven decisions, MCP unifies prediction set design and calibration into a single optimization problem, eliminating data splitting without sacrificing coverage guarantees. We propose two computationally efficient variants: RemMCP, grounded in constrained optimization with constraint removal, which admits a clean generalization of split conformal prediction; and RelMCP, based on iterative optimization with constraint relaxation, which supports non-convex score functions at the cost of possibly greater conservatism. Through numerical experiments on ellipsoidal and multi-modal prediction sets, we demonstrate that RemMCP and RelMCP consistently meet the target coverage with prediction set sizes smaller than or comparable to those of baselines with data split, while considerably reducing variance across calibration runs — a direct consequence of using all available data for shape optimization and calibration simultaneously.

Mathematical optimization drives decisions in supply chains, logistics, energy, and scheduling, but translating natural-language problems into solver-executable formulations remains a bottleneck. While frontier models show promise for this task, many deployments require small language models (SLMs) that run locally under privacy, latency, and cost constraints. Existing SLMs are limited by noisy data, ambiguous benchmarks, and one-shot inference that ignores the iterative, feedback-driven nature of optimization modeling. We introduce \textsc{OptiMind}, a framework for improving SLMs through formulation-centric data cleaning, class-conditional priors, and multi-turn reinforcement learning with solver feedback. \textsc{OptiMind} repairs ambiguous problems, regenerates solution trajectories, audits benchmark labels, constructs accepted objective-value sets, and distills class-level hints from recurring formulation errors. It then trains models to formulate, execute, and revise GurobiPy programs using solver-verified correctness as reward. On expert-cleaned IndustryOR, Mamo-Complex, and OptMATH benchmarks, a 20B \textsc{OptiMind-RL} model outperforms strong open-source baselines and reaches frontier-model performance under the same protocol. Our results suggest that optimization formulation is better treated as an interactive solver-grounded decision process than as one-shot code synthesis. We release our inference framework, cleaned benchmarks, and sample error analyses at \url{https://anonymous.4open.science/r/OptiMind-NeurIPS-1DB020}, with full data and model to follow.

Reinforcement learning with verifiable rewards (RLVR) plays a pivotal role in improving the reasoning ability of large language models. However, widely used PPO surrogate objectives are fundamentally *local*, as they rely on a local approximation of the exact policy gradient objective. While this approximation improves stability by reducing the variance induced by importance sampling, it also introduces structural bias into the surrogate objective, which must be controlled through trust region mechanisms. In this work, we introduce the $N$-step forward trace, which augments the PPO surrogate objective using the cumulative likelihood ratio of the next $N-1$ tokens. Building on this idea, we propose $N$-Step Forward-Trace Policy Optimization (NFPO), a practical RLVR algorithm that integrates the $N$-step forward trace into the masked policy gradient framework. NFPO provides a continuous bridge between the PPO surrogate objective and the exact policy gradient objective, offering a principled mechanism for controlling the bias–variance trade-off. Our theoretical analysis shows that, with an appropriate choice of $N$, the proposed objective yields a tighter policy-improvement bound than the standard PPO surrogate. Experiments on comprehensive reasoning benchmarks demonstrate that NFPO consistently improves performance, supporting our theoretical findings.

Multi-objective reinforcement learning (MORL) is a fundamental problem for modern AI, with applications spanning robotics, LLMs, and reasoning. A central challenge is to learn policies that balance competing objectives, such as speed versus energy in robotics, or helpfulness versus honesty in alignment. Optimal policies can vary sharply with the preferred objective weights, and the severity of this variation depends crucially on the degree of misalignment among objectives, making per-preference learning sample-inefficient. To formalize this, we introduce an *objective-conflict coefficient* and use it to derive near-optimal regret bounds for online MORL that quantify the impact of misalignment on learning efficiency. Motivated by this analysis, we propose *routed ensemble policy learning*, an algorithm that maintains a small set of basis policies and dynamically routes trajectories to the policy with the highest potential reward. We further design a scalable, kernel-based attribution algorithm that estimates how feedback signals from one set of trajectories influence policy learning on others. Unlike existing attribution methods, our approach captures nonlinear interactions, such as synergy and antagonism between trajectories, to explain objective conflict. We extensively evaluate our approach across diverse environments and benchmarks: routed ensembles improve average performance by 4.3\% over MORL baselines on several environments from the Meta-World and MO-Gymnasium benchmarks, and kernel-based attribution improves correlation with leave-one-out analysis over existing baselines by 50\%. When applied to downstream task selection, kernel-based attribution yields a 27\% improvement in reward over baseline attribution methods.

Many decision-making problems involve multiple objectives, where actions affect several performance metrics, fairness criteria, or safety constraints. We study multi-objective causal bandits with multiple reward nodes, where actions correspond to interventions on subsets of variables in a causal graph and performance is evaluated through Pareto optimality. Existing approaches to multi-objective bandits typically define optimality at the level of individual actions, using pairwise dominance or scalarization. In contrast, randomized decision rules induce convex combinations of action-level reward vectors, so the relevant achievable set is the convex hull of these rewards. Thus, an intervention may be suboptimal even if no single intervention dominates it, because it can be dominated by a randomized policy over other interventions. We formalize this policy-level phenomenon and show that it has consequences for both causal action-space reduction and online learning. First, we provide a necessary-and-sufficient graphical characterization of possibly Pareto-optimal minimal intervention sets (PPOMISs). Our characterization yields a minimal, sound, and complete candidate intervention family from the graph alone, correcting prior formulations that may include intervention sets that are never Pareto-optimal under any compatible structural causal model. Second, over this reduced intervention space, we design an online UCB-style algorithm that eliminates actions using dominance tests against convex combinations of other actions, and prove logarithmic gap-dependent Pareto regret. Finally, we study constrained multi-objective causal bandits, where feasibility and optimality may be realized only with randomized policies, and develop an online UCB-style constrained bandit algorithm with sublinear regret and constraint-violation guarantees.

We study stochastic multi-objective optimization when each objective may be non-smooth and non-convex. We introduce the notion of $(\delta,\epsilon)$-Pareto Goldstein stationary points (PGSP) to characterize the convergence of solving multi objective optimization. The $(\delta,\epsilon)$ generalizes the definition of $(\delta,\epsilon)$-Goldstein stationary point for single objective non-smooth non-convex optimization and the $\epsilon$-Pareto stationary point for solving multi objective optimization with smooth objectives. We propose the multi-gradient-free method (MGFM), which finds $(\delta,\epsilon)$-PGSP with $\tilde{\mathcal{O}}(m^2d^{3/2}\delta^{-1}\epsilon^{-4})$ oracle complexity to the stochastic function values, where $m$ is the number of objectives and $d$ is the problem dimension. We further propose MGFM+, a faster multi-gradient-free method based on variance reduction, which improves the complexity to $\tilde{\mathcal{O}}(m^2d^{3/2}\delta^{-1}\epsilon^{-3})$. These provide the first non-asymptotic analysis for multi-nonsmooth-nonconvex-objective optimization. \end{abstract}

Realizing stable neural decoding over extended periods remains a significant challenge, primarily because invariant task-related neural dynamics are inextricably entangled with inherent signal non-stationarity and the physical drift of electrode-neuron interfaces. This work introduces LNDN (Long-term Neural Decoding Network), a hierarchical framework designed to decouple category-specific neural dynamic manifolds from representational drift, sustaining decoding precision without periodic recalibration. The proposed architecture addresses representational drift through an integrated tri-level alignment strategy. At the physical feature level, a decoupled representation and dynamic gating module isolates the physical identity of neurons from their transient states, adaptively filtering stochastic neural noise. This is further strengthened at the decision level by a Mixture-of-Experts (MoE) architecture, which employs a parallel soft-voting mechanism to suppress high variance induced by local representational distortions. Finally, at the manifold level, Adaptive Batch Normalization (AdaBN) and latent contrastive learning, combined with second-order correlation alignment, explicitly anchor the geometric consistency of the low-dimensional neural manifold over a period of months. Systematic evaluations on a longitudinal olfactory dataset, involving 9 mice performing a four-odor decoding task, demonstrate the efficacy of this approach. When trained exclusively on data from the initial four weeks, LNDN maintains an average accuracy of 83.67\% on completely unseen tests spanning the subsequent eight weeks, significantly outperforming mainstream domain adaptation and advanced neural decoding baselines. This framework offers a scalable, "set-and-forget" solution for robust, long-term invasive brain-computer interface applications.

Partially Observable Markov Decision Processes (POMDPs) are systems in which one agent interacts with a stochastic environment, and receives only partial information about the current state. In a multi-environment POMDP (MEPOMDP), the initial state is unknown, and assumed to be adversarially chosen. In this work we focus on computing the optimal value and policy in MEPOMDPs with finite-horizon objectives. That problem is known to be PSPACE-complete in POMDPs. Our main results are as follows: (1) we establish that it is also PSPACE-complete in the more general setting of MEPOMDPs; (2) we present a practical algorithm and evaluate it on classical benchmarks, significantly outperforming the only previously known algorithm.

Randomized Smoothing (RS) is a principled and widely adopted approach for certifying the robustness of black-box models, such as neural networks, against adversarial perturbations. We propose an optimization perspective that unifies several prior randomized smoothing certificates. We then show how to reduce the underlying high-dimensional worst-case optimization problem to an equivalent two-dimensional formulation under a double- or multi-sampling scheme, enabling efficient solutions via convex optimization. By exploiting additional information about the variance of the smoothed classifier across different smoothing distributions, we derive certified bounds that improve upon standard certificates. We show results on both classification and regression tasks.

When researchers iteratively refine ideas with large language models, do the models preserve fidelity to the original objective? We introduce DriftBench, a benchmark for evaluating constraint adherence in multi-turn LLM-assisted scientific ideation. Across 2,146 scored benchmark runs spanning seven models from five providers (including two open-weight), four interaction conditions, and 38 research briefs from 24 scientific domains, we find that iterative pressure reliably increases structural complexity and often reduces adherence to original constraints. A restatement probe reveals a dissociation between declarative recall and behavioral adherence, as models accurately restate constraints they simultaneously violate. The knows-but-violates (KBV) rate, measuring constraint non-compliance despite preserved recall, ranges from 8\% to 99\% across models. Structured checkpointing partially reduces KBV rates but does not close the dissociation, and complexity inflation persists. Human validation against blind raters confirms that the LLM judge under-detects constraint violations, making reported constraint adherence scores conservative. Sensitivity analyses confirm the findings are robust to temperature (0.7 vs.\ 1.0) and pressure type (novelty vs.\ rigor). We release all briefs, prompts, rubrics, transcripts, and scores as an open benchmark.

Most work on improving large language models treats accuracy as the sole objective. We argue that the harness — the Python code surrounding the model that constructs prompts, routes calls, and parses outputs — is a first-class design surface whose quality is inherently multi-objective: an accurate harness that refuses no unsafe request, or that consumes an order of magnitude more tokens, is not a good harness. We present Meta-Harness, a system that casts harness design as search over three per-domain objectives — accuracy, behavioural safety, and token cost — solved by an agentic proposer (Claude Code) with full filesystem access to prior harness source, execution traces, and scoring artifacts. Our central finding is that a single-phase joint-reward proposer (MoMHa) outperforms every alternative, including a two-phase "accuracy then tokens" ablation, scalar-only feedback, and an accuracy-only baseline. We evaluate on seventeen domains: seven synthetic capability suites, seven real-world public benchmarks (HumanEval, MBPP, Spider, FEVER, MMLU-Pro, LawBench, NuminaMath), and three U-SafeBench-derived user-specific safety domains, using a 12-model fleet spanning four families. On the synthetic track MoMHa achieves a joint mean of 0.482 versus 0.198–0.422 for ten baselines, winning 7/10 per-domain columns; on the real-world track it scores 0.461 versus 0.377 for the strongest baseline (DSPy), winning 5/7 columns — demonstrating that harness strategies transfer to unseen benchmarks without retraining on 8 of 12 target models. MoMHa attains the highest measured behavioral safety composite (U-SafeBench, 0.781) and uses 95 fewer tokens per example than the two-phase alternative. We will release all harness code, evaluation infrastructure, and cross-model logs.

Language models fine-tuned with reinforcement learning frequently learn to exploit their reward source rather than solve the underlying task. Existing fixes are typically reactive: detect a specific exploit, then patch the reward. We instead ask whether reward hacking can be prevented by constraining how the model represents the task. We introduce prompt KL regularization, a single auxiliary loss that adds a KL penalty between the actor's and reference model's per-token distributions on the prompt only, leaving the response distribution free. Across three reward hacking tasks of different sizes, prompt KL regularization maintains low hack rates (under 3\%) when standard training yields up to 100\% hack rates. Additionally, it matches or improves ground-truth accuracy, with no changes to the reward or environment. We aim to understand why prompt KL regularization is effective. Two independent mechanistic studies suggest that changes in prompt representations are key to models learning reward hacking behavior. First, we show that prompt-space activation steering Pareto-dominates response-space steering on hack rate and accuracy. Then, we demonstrate that swapping prompt activations between models can transfer and reduce reward hacking. Together, these results suggest that the way models internally represent the task is central to reward hacking, and that this representation can be directly constrained to prevent it.

Long-tailed visual recognition is limited not only by biased optimization, but also by the under-retention of rare-class evidence in parameters learned from imbalanced data. MemTailor addresses this limitation by augmenting a frequency-aware multi-expert backbone with a hierarchical class-aware memory that preserves visual evidence outside the backbone. The memory stores per-class prototypes and bounded instance slots for each expert, allocates proportionally richer capacity to rare classes, and records both shallow and deep features to retain complementary discriminative cues. During training, same-class memory retrieval constructs class-adaptive feature augmentation and provides an auxiliary supervised objective on the augmented features. At inference, class-level memory quality and prediction uncertainty determine when stored evidence is allowed to correct expert logits, and the final prediction fuses memory-corrected logits across multiple input scales. Experiments on long-tailed visual recognition benchmarks show that MemTailor improves balanced recognition, especially for under-represented classes.

We evaluate the autonomous offensive cyber capabilities of frontier AI agents on two purpose-built cyber ranges---a 32-step corporate network attack and a 7-step industrial control system attack targeting a simulated cooling tower---complemented by a private 82-task CTF suite spanning four difficulty tiers to measure narrow cyber skills. Estimated human-expert solve times are roughly 20 hours for the corporate range, 22 hours for the cooling tower, and from 1 minute to 40 hours across the CTF suite. Across twelve models released over a twenty-month period---from GPT-4o in August 2024 to early predeployment checkpoints of Mythos and GPT-5.5---we observe two trends. First, performance increases approximately log-linearly with inference-time compute, with no plateau observed for the strongest models up to 100M tokens. Second, newer frontier models generally complete more steps at fixed token budgets. GPT-5.5 and the Mythos Preview checkpoint each completed all 32 steps in at least one run, the first end-to-end completions of the corporate range; GPT-5.5 averaged 22.3 of 32 steps across ten 100M-token runs. On the control system range, the latest models reached 4 of 7 steps, primarily by directly probing the operational-technology protocol rather than following the intended chain of IT compromise and authenticated control. These results indicate rapid improvements in autonomous cyber capability and suggest that complex but undefended multi-step ranges are no longer reliably distinguishing the strongest frontier models. Future evaluations should emphasise hardened environments, active defences, defensive-control effectiveness, and operational security---priorities that grow more pressing as the threat of AI-driven cyber attacks becomes increasingly realistic.

We study Metrical Task Systems, a broad class of problems in online algorithms, under a model where input requests are generated by a stochastic process. We first consider the case of requests drawn IID from an unknown distribution, and then extend the model to requests generated by a finite-state Markov chain, where the algorithm observes both the current request and the current state of the chain before making its next move. This formulation captures practical settings in which requests are generated by an evolving environment. In both settings, we show how to find in polynomial time an algorithm whose expected cost per step is arbitrarily close to the cost of the best possible online algorithm. Our theoretical results are complemented by a brief empirical evaluation of our algorithms.