NeurIPS 2026 Papers

Optical Music Recognition (OMR), the task of transcribing sheet music into a structured textual representation, is currently bottlenecked by a lack of large-scale, annotated datasets of real scans. This forces models to rely on either few-shot transfer or synthetic training pipelines that remain overly simplistic. A secondary challenge is encoding non-uniqueness: in the popular Humdrum **kern format for transcribing music, multiple different text encodings can render into the same visual sheet music. This one-to-many mapping creates a harder learning task and introduces high uncertainty during decoding. We propose Transcoda, an OMR system built on (i) an advanced synthetic data generation pipeline, (ii) a normalization of the **kern encoding to enforce a unique normal form and (iii) grammar-based decoding to ensure the syntactic correctness of the output. This approach allows us to train a compact 59M-parameter model in just 6 hours on a single GPU that outperforms billion-parameter baselines. Transcoda achieves the best score among state of the art baselines on a newly curated benchmark of synthetically rendered scores at 18.46% OMR-NED (compared to 43.91% for the next-best system, Legato) and reduces the error rate on historical Polish scans to 63.97% OMR-NED (down from 80.16% for SMT++). We will make our model, data and generation pipeline publicly available upon publication of the paper.

Meta pseudo-labeling improves semi-supervised learning by updating a teacher according to whether its pseudo-labels help a student improve on labeled data. Existing one-step meta-gradient methods, however, differentiate through the student update, introducing mixed higher-order derivatives, extra memory cost, and noisy minibatch meta-gradients. We propose Trajectory-Matching Meta Pseudo-Labeling (TMPL), a first-order alternative that extracts labeled-data feedback from recent student optimization trajectories. We show that the one-step meta objective is locally equivalent, up to second-order terms in the student step size, to maximizing alignment between the outer gradient and the pseudo-label-induced student gradient. TMPL approximates this alignment without differentiating through the student update by matching finite differences of the outer objective and the pseudo-label-induced student objective along recent student displacements. Its implementation stores only a FIFO cache of detached scalar objective values, rather than student computation graphs or past student networks. We prove that small trajectory-matching error controls the gradient mismatch within the span of recent displacements, with an explicit residual for unexplored directions. On CIFAR10, CIFAR100, SVHN, and STL10, TMPL improves over MPL in all eight evaluated label regimes, obtains the best result in five settings, and remains competitive with strong SSL baselines. On CIFAR100 with 2500 labels, TMPL reduces peak memory by 39.7\% relative to MPL and 54.0\% relative to a raw differentiable meta-gradient implementation. Ablations identify the directional trajectory-matching term as the main source of improvement, while alignment diagnostics show that TMPL recovers MPL-like gradient alignment after a short warm-up.

Hamiltonian Neural Networks (HNNs) produce stable long-horizon rollouts by integrating a learned Hamiltonian with a symplectic scheme. Standard Monte Carlo (MC) dropout conflicts with this per-trajectory interpretation because resampling the dropout mask inside a leapfrog integrator means successive substeps follow different subnetworks, so a single MC rollout no longer corresponds to any one sampled Hamiltonian. We propose trajectory-consistent dropout, implemented as Fixed-mask MC, where each stochastic rollout selects one mask from a finite bank and reuses it across the full integration path. This restores a coherent per-rollout Hamiltonian sample and makes uncertainty decomposition operational. Crossing the mask axis with an initial-condition ensemble separates model-sample uncertainty from sensitivity to the initial state. On coupled-pendulum rollouts, Fixed-mask MC reduces mean energy drift by 72% relative to Standard MC. Under held-out mass ratios, Fixed-mask MC increases the epistemic share of predictive variance by 16.9 percentage points from in-distribution to out-of-distribution, compared with 4.2 percentage points for Standard MC, indicating a substantially stronger shift of the uncertainty budget toward model uncertainty when the physics moves outside training support. Spring-chain and transverse-field Ising experiments show that the same axis-preserving decomposition transfers to structured pairwise and latent quantum dynamics, although point-prediction and likelihood gains remain system-dependent. These results position Fixed-mask MC as a single-training-run route to trajectory-consistent, physically interpretable uncertainty in structured neural dynamical models.

Diffusion policies have emerged as a powerful policy class for offline reinforcement learning (RL) due to their ability to model complex, multimodal action distributions through iterative denoising. However, in offline RL, expressivity alone is not enough. Generated actions are supposed to remain within value-reliable regions of the action space to avoid extrapolation error. We find that standard diffusion policies often produce unstable denoising trajectories whose intermediate and final action candidates drift toward weakly supported regions, making critic-guided action selection unreliable and degrading teacher quality for one-step distillation. This issue is particularly pronounced on mixed-quality offline datasets, where suboptimal behaviors amplify trajectory instability. To address this problem, we propose Trajectory Consistency Rectification (TCR), a framework designed to promote denoising stability during both training and inference. At inference time, TCR aggregates locally consistent, high-value action candidates across denoising steps to suppress critic-unreliable outliers. During training, it adaptively reweights denoising steps to improve trajectory-level coherence. We show that this stabilization provides a more reliable teacher for one-step flow-matching distillation. Extensive experiments on D4RL and OGBench show that TCR consistently improves over diffusion-policy baselines, with significant gains in sparse-reward domains like AntMaze and Adroit. Moreover, one-step policies distilled from TCR achieve competitive performance among efficient single-step methods. These results suggest that enhancing the temporal consistency of denoising trajectories is a key ingredient for robust offline diffusion reinforcement learning.

Discrete flow matching generates text by iteratively transforming noise tokens into coherent language, but may require hundreds of forward passes. Distillation uses the multi-step trajectory to train a student to reproduce the process in a few steps. When the student underperforms, the usual explanation is insufficient capacity. We argue the opposite: the trajectory is the bottleneck, not the student. Each training trajectory is built through a chain of blind stochastic jumps with no evaluation of sequence quality; a single bad decision at an early midpoint propagates through subsequent steps, yet the student must imitate the result. Trajectory-Shaped Discrete Flow Matching (TS-DFM) replaces these blind jumps with guided navigation: a lightweight energy compass evaluates candidate continuations at each midpoint, selecting the most coherent. All shaping is training-only; inference cost is unchanged. On 170M-parameter language modeling, the shaped student at 8 steps achieves 32% lower perplexity than the 1 024-step teacher while being 128×faster, with gains consistent across source distributions and three evaluators of increasing scale. TS-DFM achieves the best perplexity of any discrete-generation baseline we compare against, including methods trained on 6×more data or using 5×larger models.

A common way for trajectory planning is to leverage generative models trained on large collections of expert trajectories. At inference time, the model generates executable trajectories by conditioning on task goal constraints. However, trajectory-based methods rely on costly supervision, scale poorly with sequence length, and often generalize poorly to unseen constraints such as novel start-goal pairs. We propose an alternative to learn the underlying state-space manifold and use the geometry of the manifold for trajectory planning. This approach requires only state observations and enables generalization to unseen constraints by constructing trajectories on the learned manifold of the state space. Experiments on classical planning problems in maze demonstrate the effectiveness of our work. We further show that the method can be used in higher dimension space where table-top robot arms are considered. Our method is able to find feasible path given only infeasible straight line reference, and be comparable to State-of-the-Art trajectory-based model without actually learning on trajectory data.

Although existing candidate trajectory evaluators have substantially improved end-to-end planning accuracy, their underlying mechanism remains suboptimal. Model-based evaluators typically make scoring future-aware by explicitly predicting candidate-conditioned future states over the planning horizon, which we term rollout. However, rollout incurs high inference cost and accumulates prediction errors. We argue that planning does not require reconstructing a full future scene for each candidate, but only future-relevant information for reliable comparison. We therefore propose RFWorld, a Rollout-Free World model for end-to-end trajectory evaluation. RFWorld constructs a shared scene memory and shapes it into a future-readable representation via lightweight training-time temporal readout with semantic supervision, keeping training overhead low. At inference time, candidate trajectories directly query the shared memory via sparse spatial readout for scoring, reducing computation by roughly the planning horizon times the number of candidate trajectories, while avoiding recursive rollout errors. Experiments on NAVSIM show that RFWorld learns a more planning-aligned world representation and achieves state-of-the-art performance.

Large language model agents have shown strong capabilities in generating coherent and contextually appropriate responses, yet robust long-horizon dialogue remains limited by the lack of external memory that is traceable, updatable, and diagnostically transparent. Existing memory-augmented agents often store memories as isolated records or overwritable states, making it difficult to preserve how information originates, evolves, conflicts, or becomes obsolete over time. We propose TrajWiki, a trajectory-based memory framework for long-horizon conversational agents. Instead of treating memory as static entries, TrajWiki represents each memory as a source-grounded evolution trajectory, maintained through immutable episodic snapshots and claim-level operations such as ADD, REVISE, and DEPRECATE. To reduce fragmentation and retrieval cost, TrajWiki further introduces Memory Wiki, a persistent intermediate layer that incrementally compiles dialogue history into structured and interlinked wiki pages capturing salient entities, events, quantities, topics, and conflicts. At inference time, queries are routed hierarchically from relevant wiki pages to linked memory trajectories, then to corresponding snapshots and source messages for evidence-grounded answer synthesis. Experiments on LoCoMo and MedMT show that TrajWiki improves long-horizon dialogue performance across both open-source and closed-source LLM backbones, while providing greater interpretability and diagnostic visibility into memory evolution, retrieval failures, and answer generation. Code is available at https://anonymous.4open.science/r/TrajWiki-F0EC/.

Controlling the motion of multiple objects in image-to-video (I2V) generation requires preserving object identities while enforcing adherence to distinct target trajectories. This becomes particularly challenging as the number of objects increases and their paths intersect or occlude one another. Existing approaches entangle multiple trajectories within a shared, dense conditioning signal, making object-level correspondence difficult to preserve in crowded scenes. We depart from this paradigm and enforce a strict, per object spatial constraint that isolates instances independently. Our method, TrajLoc, achieves this directly within the attention layers by substituting the cross-attention weights of each object token with a Gaussian heatmap centered on its target location at every frame. The same per object token interface carries trajectory and depth through a learned embedding and preserves identity by encoding first frame appearance in place of an object token. Evaluations across six datasets, featuring up to 20 simultaneously controlled objects and out of distribution real world scenes, demonstrate that our method consistently improves both visual fidelity and trajectory adherence. Applied to two architecturally distinct backbones (CogVideoX 5B and WaN 2.1 14B), our approach achieves average gains of +4.3 dB PSNR and a 51\% reduction in trajectory end point error compared to the strongest baselines. Code will be made publicly available upon publication.

In this work, we introduce a novel training-free encoding framework, dubbed **XShapeEnc**, that encodes an arbitrary spatially grounded 2D geometric shape into a compact representation exhibiting five favorable properties, including invertibility, adaptivity, generality and controllability. Specifically, a 2D spatially grounded geometric shape is decomposed into its normalized geometry within the unit disk and its pose vector, where the pose is further transformed into a harmonic pose field that also lies within the unit disk. A set of orthogonal Zernike basis is constructed to encode shape geometry and pose either independently or jointly, with controllable relative emphasis on shape geometry or shape pose. We demonstrate the theoretical validity, efficiency, discriminability, and wide applicability of **XShapeEnc** via extensive analysis and experiments across a wide range of shape-aware tasks and our self-curated XShapeCorpus dataset. We envision **XShapeEnc** as a foundational tool for research beyond one-dimensional sequential data and data-driven, learning-based encoding paradigms, paving the way for a unified spatial encoding framework for frontier 2D spatial intelligence.

Transformers perform inference by iteratively transforming token representations across layers. This layerwise computation has been studied empirically, and recent mean-field theories of Transformer dynamics explain how attention can drive token distributions toward clustering. However, existing mean-field analyses largely treat model parameters as prescribed, leaving open how training reshapes this clustering picture. We study this question in a noisy mean-field Transformer in which only a parameter-linear FFN is trained under $L^2$ regularization. We find and analyze a training-induced phase in the dynamics: after initially following attention-driven clustering, the token distribution can leave the clustered regime near the final layers. Our mathematical analysis is based on an entropy-regularized interaction energy that captures the clustering bias of attention. More broadly, our results point toward a training-aware mean-field theory of Transformer dynamics, in which training and inference dynamics are treated together.

Open World Object Detection (OWOD) requires a detector to recognize known categories, detect unknown objects, and incrementally learn new classes. Recent work such as OW-OVD adapts a pre-trained Vision-Language Object Detector (VLOD) to OWOD through fine-tuning. However, this approach demands costly backpropagation and often degrades the detector's own zero-shot performance on known categories, calling into question whether training is necessary. In this paper, we propose CAVE (Clustering in Attribute-Visual Embedding space), a training-free framework that adapts a VLOD to OWOD without any parameter updates. From a single forward pass, CAVE collects per-class visual and attribute statistics via von Mises-Fisher-based clustering, along with attribute co-occurrence patterns, without any gradient computation. At inference, CAVE fuses the original VLOD's text-based scores with MAS (Mixture-Aggregate Score) derived from the collected statistics for known-class detection, while unknown objects are identified by AOS (Attribute Objectness Score) that combines superclass responses with attribute co-occurrence patterns. Experiments on M-OWODB show that CAVE outperforms OW-OVD by +16.2 known-class mAP (Task 4) and +28.0 average unknown recall, while surpassing the zero-shot VLOD across all incremental tasks.

Diffusion models generate samples by denoising along the score of a perturbed target distribution. In practice, one trains a neural diffusion model, which is computationally expensive. Recent work suggests that score matching implicitly smooths the empirical score, and that this smoothing bias promotes generalization by capturing low-dimensional data geometry. We propose moment-matched score-smoothed overdamped Langevin dynamics (MM-SOLD), a training-free interacting particle sampler that enforces the target moments throughout the sampling trajectory. We prove that, in the large-particle limit, the empirical particle density converges to a deterministic limit whose one-particle stationary marginal is a Gibbs--Boltzmann density obtained by exponentially tilting a naive score-smoothed diffusion target. The mean and covariance of this distribution agree with the empirical moments of the training data. Experiments on 2D distributions and latent-space image generation show that MM-SOLD enables fast, robust, training-free sampling on CPUs, with sample fidelity and diversity competitive with neural diffusion baselines.

Choosing where to place entangling gates is a central design choice in quantum machine learning circuits, yet entanglers are still typically chosen from fixed templates or by expensive search procedures requiring training or pairwise kernel evaluations. We propose the \emph{HSD-Lipschitz principle}, a training-free geometric criterion built on a simple intuition: a useful entangler should keep encoded states stable across the dataset while separating different classes. We formalise this through a two-sided bound on local light-cone subsystems. Under a light-cone locality assumption, dataset-level gradient variance is upper-bounded by reduced-state spread; under random initialisation, the expected between-class gradient signal is lower-bounded by class-conditional reduced-state distance. The resulting algorithm, HSD-greedy, adaptively grows an entanglement structure using only single-state reduced moments, estimable via classical shadows, and avoids the $\mathcal{O}(N^2)$ pairwise kernel evaluations of kernel-target alignment proxies. Empirically, both bounds hold without violation across $110$ topologies and $440$ parameter rows, and extend to $180$ additional configurations. HSD-greedy attains the strongest average AUC among training-free entangler selectors on synthetic and real-world benchmarks, at roughly $60\times$ lower selection cost than the strongest baseline in 13-qubit simulation. End-to-end execution on a 20-qubit IBM Eagle subchain substantially outperforms a fixed 19-CNOT Linear chain and matches or exceeds a matched-budget Random baseline while using far fewer two-qubit gates than the Linear chain.

Large Language Models (LLMs) have achieved remarkable performance on a wide range of specialized tasks, exhibiting strong problem-solving capabilities. However, training these models is prohibitively expensive, and they often lack domain-specific expertise because they rely on general knowledge datasets. Expertise finetuning can address this issue; however, it often leads to overspecialization, and developing a single multi-domain expert remains difficult due to diverging objectives. Furthermore, multitask training is challenging due to interference and catastrophic forgetting. Existing work proposes combining the expertise of dense models within a Mixture of Experts (MoE) architecture, although this approach still requires multitask finetuning. To address these issues, we introduce Dynamic Upcycling MoE (DUME), a novel approach that reuses dense experts trained on different domains to construct a unified MoE model. Our method builds a single multitask model that preserves the capabilities of the original dense experts without requiring additional training. DUME is both cost-efficient and scalable: by leveraging the closed-form solution of ridge regression, it eliminates the need for further optimization and enables experts to be added or removed dynamically. Our extensive experiments on different tasks (on causal language modeling and reasoning settings) with several model sizes (between 115M and 9B parameters) and architectures demonstrate that DUME consistently outperforms baseline approaches. In particular, in a reasoning setting, DUME can also surpass the dense expert model's performance in its domain, achieving 109.9\% of the dense expert's performance on average. Finally, we also show that the DUME model can be fine-tuned to further improve performance in complex reasoning scenarios. Our code is available at this anonymous link: https://anonymous.4open.science/r/DUME-NeurIPS-D551.

Large language models are increasingly deployed in decisions that require culture-dependent moral judgements, yet they answer as if the whole world thinks with a Western mindset. The Moral Machine experiment showed this is wrong at scale: 40 million judgments across 233 countries reveal that moral preferences are systematically structured by culture, and a model that ignores this variation does not merely underperform, but also imposes one society's intuitions on all others. Existing fixes do not scale to global deployment, as fine-tuning needs per-country preference data and GPU budgets, reward-guided decoding needs per-country reward models, and activation steering needs access to model internals that black-box APIs do not expose. In this work, we focus on this realistic inference-time regime, with no weight updates, no training data, and no internal access. The key observation is that within-country demographic disagreement, not consensus, is the steering signal. When culturally grounded personas agree, the base model is already calibrated. But when they disagree, the spread tells us what to fix and how. We propose DISCA (Disagreement-Informed Steering for Cultural Alignment), which instantiates each country as a panel of four World-Values-Survey-grounded persona agents, converts their disagreement into a bounded, loss-averse correction whose magnitude is set by the panel's variance, and shrinks the correction toward zero when the estimate is unreliable. Across 20 countries and 7 open-weight backbones (2B–70B) from five model families, DISCA reduces cultural misalignment on MultiTP by 10–24% on binary moral dilemmas and 2–7% on open-ended scenarios. Furthermore, a smaller 14B backbone with DISCA reaches lower absolute misalignment than a vanilla 70B model.

Modifying 3D assets requires enacting targeted structural transformations while strictly preserving the geometric identity of unedited regions. While recent probability flow models enable training-free editing, bounding these modifications within a high-dimensional latent space presents severe mathematical challenges. Current inversion-free trajectories rely on global velocity updates, which consistently result in spatial bleed into preserved structures and induce trajectory under-commitment, causing edits to stall mid-path. To resolve these dual failures, we introduce FocusFlow, a segmentation-free framework that structures the integration trajectory into two disjoint phases. During early coarse structure formation, FocusFlow applies Feature-Divergence Localization (FDL) to spatially gate the velocity field using intrinsic cross-attention. During late-stage fine-detail refinement, Reference-Guided Generation (RGG) drives topological convergence by pulling the trajectory toward an explicit clean-latent target. Evaluated on the joint Google Scanned Objects and PartObjaverse-Tiny benchmarks, FocusFlow breaks the traditional preservation-modification trade-off. It achieves superior structural preservation while maximizing edit magnitude. By providing stable, localized geometric control without manual spatial annotations, this phase-scheduled approach removes significant technical barriers to the precise modification of synthetic 3D media.

To defend against backdoor attacks on neural networks, the defender must identify the verifier function that determines whether an input is a trigger, rather than rejecting individual triggers in isolation, since an attacker can generate new triggers satisfying the same verifier, against which trigger-by-trigger blocking cannot keep up. If a backdoor verifier could be installed with the same kind of asymmetry as a cryptographic authentication scheme, in which only the attacker can produce trigger inputs while the defender cannot reverse-engineer the verifier from observations, learning-based defense would face a principled impossibility. We show that no such asymmetry can arise for any backdoor installed by training into a model. We establish two complementary impossibility results. First, any verifier installable by training a polynomial-size neural network is reconstructible by the defender with sample complexity matching the attacker's up to polynomial factors. Second, any cryptographic secret the attacker might supply to the model at inference is necessarily observable to a white-box defender. Together, these results rule out any way of giving a self-contained backdoor cryptographic asymmetry. We confirm both routes empirically on pretrained large language models, demonstrating that no configuration yields a backdoor simultaneously effective for the attacker and irrecoverable by the defender.

Inference-time harnesses substantially improve large language models on complex reasoning tasks. However, the intrinsic capabilities of the underlying model remain unchanged by the addition of these external workflows. To bridge this gap, we introduce \emph{On-Policy Harness Self-Distillation} (OPHSD), which employs the harness-augmented current model as a teacher for self-distillation, thereby introducing extra supervisory signals from the harness beyond training data. OPHSD internalizes task-specific harness capabilities into the student model, yielding robust generalizability and strong standalone performance across diverse reasoning tasks. Evaluated across draft--verify harness for text classification and plan--solve for mathematical reasoning tasks, OPHSD consistently outperforms strong baselines (e.g., +10.83\% over OPSD on HMMT25). Our analysis further indicates that reattaching the harness during inference yields no additional benefits and can even degrade performance, suggesting that complex harnesses need not always be permanent fixtures; instead, they can serve as temporary training scaffolds whose benefits are permanently fed back into the base model. Our code and training data are available at \url{https://anonymous.4open.science/r/OPHSD-On-Policy-Harness-Self-Distillation-99F7}.