NeurIPS 2026 Papers

Context-based offline meta-reinforcement learning (COMRL) aims to learn adaptable policies entirely from static datasets by inferring latent task representations from small contexts. Most COMRL methods rely on immediate, per-step reward signals. This can be generalized by aggregating rewards into ``bags'' and being delivered after a sequence of actions (where bag size $n=1$ is the per-step case). We formally prove that under Bagged Rewards, existing per-transition COMRL methods suffer an information-theoretic collapse ($\mathcal{O}(1/n)$), causing their task inference to degrade to behavior cloning. To solve this, we introduce SpectralMeta, an algorithm that fully decouples dynamics representation from task inference. By pre-training an energy-based spectral representation on reward-free transitions, we recast task identification as a closed-form Bayesian linear regression over bagged rewards. SpectralMeta comes with finite-sample bounds on reward recovery and policy sub-optimality. In continuous-control meta-RL benchmarks, SpectralMeta maintains robust task inference and competitive returns even when rewards are reduced to a single episode-level scalar, a regime where existing baselines fail to recover task-relevant structure.

Implicit neural representations (INRs) model signals as continuous functions from coordinates to values, but their performance depends strongly on how spectral capacity is allocated. Yet most Quantum INR (QINR) architectures treat spectral components as independent outputs of separate quantum blocks. We introduce the Spectral Quantum Memory Model (SQMM), a memory coupled quantum INR in which sequential hybrid data reuploading layers (bands) communicate through a shared coherent quantum memory register. The construction gives a controlled way to share spectral information across quantum modules while preserving the finite Fourier structure of a band. When memory read and write layers are input independent, we prove that the memory state forms an operator valued Fourier series whose support grows by Minkowski summation of local band spectra. Downstream bands then condition their Fourier coefficients on the spectral content stored by earlier bands. This theory motivates a spectral memory alignment loss that encourages memory to encode the spectrum expressed by the deployed prefix of the model. Across audio and image reconstruction benchmarks, SQMM improves over QINR and INR baselines, achieving state of the art results.

Multi-output regression can be approached either by fitting one joint vector-valued predictor or by training separate univariate predictors for each target coordinate. This holistic-versus-separate choice is classical in the largely non-neural multi-output regression literature, but is less characterized analytically for neural networks, where joint prediction arises naturally through shared features and vector-valued output layers. Because neural networks are highly non-linear and high-dimensional, exact analysis is notoriously difficult. We study two questions using the Unconstrained Feature Model (UFM) as a tractable surrogate for exact analysis: $\textbf{(1)}$ how does joint-output regression compare with independent coordinate-wise regression under regularization? $\textbf{(2)}$ when can target whitening or normalization improve original-scale MSE? Under UFM, the minimal training MSE depends only on the regularization product and the spectrum of the target covariance. This yields two theoretical results: joint-output regression has no larger training MSE than independent coordinate-wise regression under matched regularization, and whitening or normalizing targets can help or hurt original-scale MSE depending on the average target variance. Experiments on neural networks trained with standard weight decay across robotic imitation-learning and autonomous-driving datasets support these theoretical results, with test-MSE trends following the same qualitative pattern. Our results show that simplified analytical surrogates can provide useful guidance for neural multi-output regression.

Modular networks pursue specialization through learned routers, gates, and load-balancing losses. However, at matched total-parameter budgets, learned routers can underperform equal-weight No-Routing baselines. Is the bottleneck the routing algorithm, or the alignment between training-signal granularity and the target categories? We show that when each training and inference unit carries one coarse category tag, a fixed parameter-free routing scheme (SpecDrop) induces branch-category specialization and matches or exceeds the learned-routing baselines we evaluate at matched parameter budget; when this alignment breaks, the scheme matches the multi-branch No-Routing baseline. SpecDrop assigns each of $K$ branches weight $p_{\mathrm{a}}$ for its category and a small leakage $p_{\mathrm{i}}{>}0$ otherwise, merged through a category-independent fixed denominator that calibrates merged-branch magnitude to single-branch scale, with no learnable routing parameters or auxiliary losses. Category labels are required at inference, drawn from dataset metadata. On vision tasks where each image has one superclass label, SpecDrop reaches $\mathbf{79.23\%}$ on CIFAR-100 with ResNet-110, outperforming dense by $+4.75$, and $\mathbf{79.89\%}$ on ImageNet-1K with Vision Transformer ViT-S/16, outperforming the matched-supervision No-Routing baseline with a shared expert by $+6.53$. SpecDrop reaches the highest top-1 among the multi-branch routing baselines we evaluate at this parameter budget (Soft MoE and Mod-Squad on ImageNet). On NLP tasks where training units span multiple categories, SpecDrop matches the multi-branch No-Routing baseline on both SlimPajama-6B language modeling with a 30M Transformer and SuperNI instruction tuning over Llama-3.2-1B with LoRA. Furthermore, SpecDrop matches or outperforms multi-branch routing baselines including Demix and LoRAMoE, and is statistically tied with HydraLoRA. Per-branch pruning sensitivity reveals four specialization regimes ranked by category clarity: strongest on ImageNet-1K, strong on CIFAR-100, weakening on SlimPajama, and anti-aligned on SuperNI LoRA. Granularity alignment, not algorithm choice, localizes when routing helps. Code: https://anonymous.4open.science/r/C30862.

A central limitation of modern machine learning systems is the lack of formal certificates guaranteeing their behavior beyond empirical, sample-based evaluation. Sum-of-squares (SOS) methods provide such guarantees by certifying polynomial inequalities over continuous domains via semidefinite programming (SDP). While prior work has introduced SDP layers as differentiable components in neural networks, their scalability is limited by two key bottlenecks, that we are fixing in this paper: (i) failure to preserve sparsity from the forward SOS program in the backward pass, leading to inefficient training, and (ii) loss of certificate structure during differentiation, preventing its use in learning. We propose a differentiable sparse SOS layer whose backward pass mirrors the sparse structure of the forward solve, reusing local blocks, overlaps, and sparse constraints. The method avoids building dense certificates for scalar losses and computes gradients using the same sparse structure when certificate details are required. Experiments show that this enables practical SOS-based layers within learning systems, reducing backward computation time by one to three orders of magnitude while preserving certification quality. We evaluate on sparse polynomial certification, pendulum control, combinatorial relaxations, robotics projection, oscillator chains, and pose graph synchronization. Results demonstrate that sparse certificate objectives can be effectively integrated into learning pipelines when the backward pass respects the verifier's structure.

Language models are increasingly used in text generation, decision support, and automated interaction, where their behavior must be controlled in a localized, reversible, and selective way. Existing methods either update shared parameters or constrain generation through external interfaces, leaving open whether frozen models contain compact internal control. We introduce sparse internal control, a framework for steering target behavior by applying inference-time interventions to a small set of internal model nodes. The framework formulates control through local target controllability, where candidate site–direction pairs are characterized by their behavioral effects under target, preservation, and energy constraints. This yields two complementary selectors: Driver-OMP, which selects nodes that sparsely reconstruct a desired behavioral displacement, and Coverage-Driver, which favors nodes whose effects cover prompts stably. We further propose a six-axis control-evaluation protocol measuring reachability, signed reversal, dose response, feedback controllability, off-target preservation, and held-out reuse. Across IOI, MMLU MCQA, and sentiment steering on models from GPT-2 small to Qwen3-4B, sparse driver sets act as executable actuators: they steer target behavior, respond monotonically to dose, support closed-loop control, and preserve unrelated next-token behavior. On refusal steering, the same protocol exposes a boundary case that passes all evaluated axes except strict reachability. Held-out reuse separates prompt-specific controls requiring refitted strengths from population-level controls that transfer as frozen interventions. These results show that model control can move beyond output-side steering: mechanistic internal variables can be selected, certified, and reused as localized control handles for frozen language models.

Sparse attention improves LLM inference efficiency by selecting a subset of key–value (KV) entries, but at the cost of potential accuracy degradation. In particular, omitting critical KV entries can induce substantial errors in model outputs. Existing methods typically operate under fixed or adaptive token budgets and provide empirical robustness or partial theoretical guarantees, yet they do not ensure zero false negatives across decoding steps, particularly since the set of relevant tokens is both query- and step-dependent. Our empirical observations confirm that missing even one critical key can lead to sharp error spikes, especially in long-output reasoning tasks where the set of important tokens varies throughout decoding. This observation motivates the need for indexing methods that dynamically adapt to these variations across decoding steps while guaranteeing a full recall of the relevant keys above a certain threshold. We address this challenge by reformulating sparse attention as the computational geometry problem of halfspace range searching. However, existing range searching data structures are not suitable for modern LLM inference due to their computational and implementation overheads. To overcome this, we introduce Louver, a novel index structure tailored for efficient KV cache retrieval. Louver (i) guarantees zero false negatives with respect to a specified threshold in both theory and practice, (ii) is lightweight to integrate into existing LLM inference pipelines, and (iii) incorporates hardware-aware optimizations for both CPU and GPU executions. Our experiments demonstrate that Louver outperforms prior sparse attention methods in both accuracy and runtime, and is faster than highly optimized dense implementations such as FlashAttention. These results highlight that recall guarantees are a critical and overlooked dimension of sparse attention, and open a new direction for building theoretically grounded, efficient KV cache indices.

Despite remarkable progress in text-to-image generation, current Diffusion Transformers (DiTs) inherently struggle with learning intricate visual content, such as accurate multilingual scene text rendering and novel visual concepts. This limitation stems from the inherent contradiction between vague semantic guidance provided by text and the objects of accurate reconstruction during diffusion training. To address this bottleneck, we propose SpaG-DiT, a novel spatial grounding training framework. SpaG-DiT directly injects explicit spatial priors into the DiTs before the attention module via Contextual Diagonal Position Encoding (CDPE), which dynamically modulates spatial coordinates without destroying the inherent sequential structure of the linguistic input. Furthermore, we introduce VLM Grounding Guidance (VLM-GG) as an automated pipeline to extract implicit spatial priors from pre-trained Vision-Language Models, eliminating human annotation costs. To evaluate the grounding ability, we establish two new datasets: SpaG-DiT-MultiLingual for non-Latin/Chinese text rendering and SpaG-DiT-Creature for new concept learning. Extensive experiments demonstrate that SpaG-DiT achieves superior training efficiency and significantly outperforms vanilla self-finetuning on the above two tasks and the widely adopted GenEval benchmark. These results validate the plug-and-play nature of SpaG-DiT and its potential to enhance DiT training processes. Code, model, and data will be released.

PDE foundation models (PDE-FMs) promise general-purpose surrogate simulation, yet deploying a pretrained model to a new physical regime inevitably introduces distribution mismatch, demanding task-specific post-training. The dominant approach, supervised fine-tuning (SFT), is fundamentally off-policy: the model trains on pre-generated states but is evaluated autoregressively on its own. In chaotic regimes, this mismatch is catastrophic as per-step errors compound exponentially along the Lyapunov spectrum, and exact pointwise trajectory matching beyond the predictability horizon becomes an ill-posed training signal. To resolve this, we introduce **Solver-as-Teacher (SaT)**, an on-policy post-training framework for PDE-FMs. During training, the student rolls out autoregressively; a numerical solver branches multi-step correction targets from each student-visited state; and the student is updated against these solver corrections, learning to correct its own rollout dynamics. We instantiate SaT in a unified post-training suite with SFT, physics-informed temporal alignment, and learned-teacher on-policy distillation. Across seven 2D/3D PDE benchmarks and six pretrained PDE-FMs, SaT variants achieve the lowest 50-step rollout RMSE in 23 of 24 in-distribution model--task pairs. The best SaT variant reduces RMSE over SFT up to 90.0\%, and SaT gives the lowest RMSE on all seven OOD parameter-shift benchmarks.

Decomposition-based Programming-by-example (PBE) scales performance by splitting tasks into subtasks that a learned synthesizer solves: a decomposer predicts intermediate subgoals, and a synthesizer generates programs conditioned on them. Current approaches train the decomposer to imitate ground-truth (GT) subgoals, implicitly treating decomposition quality as intrinsic to the task. We challenge this assumption: for bounded solvers with fixed inductive biases, GT decompositions reflect the annotator’s factorization choices – not the solver’s search dynamics. A decomposer trained to match GT decompositions may therefore propose subgoals that are logically valid yet intractable for the solver. We propose Solver-Aware Decomposition (SAD), a training framework that retains supervised training on GT subgoals as a structural scaffold, while additionally optimizing the decomposer via direct feedback from a frozen synthesizer. Subgoals are rewarded based on the synthesizer’s loss on the target program – a signal of subtask difficulty that encourages decompositions the solver can act on. Our experiments reveal an accuracy paradox: higher agreement with GT decompositions does not improve synthesis success – even though the synthesizer was trained on the very same GT data the decomposer is optimized to mimic. SAD instead learns decompositions that trade GT alignment for solver tractability, yielding consistent gains in synthesis and end-to-end task accuracy across two PBE domains. Moreover, SAD solves tasks that a GT decomposition oracle fails – empirical evidence that GT decompositions are not universally optimal for bounded solvers, and that decomposition quality is solver-relative, not intrinsic.

Electrolyte conductivity is not a property of isolated molecules, but a response over a formulation landscape defined by solvents, salts, composition, salt mole ratio, and temperature. The same molecular component can play different effective roles as its amount and operating conditions change, while the underlying formulation state is observed only through macroscopic conductivity measurements. This makes conductivity prediction a distinctive mixture learning problem: a model must learn how molecular identities become formulation-specific states, rather than merely how molecules are represented. We introduce SolvMix, a framework for learning formulation-state landscapes for electrolyte conductivity prediction. SolvMix constructs component tokens for solvent and salt molecules, calibrates them into amount-aware component states before mixture interaction, and predicts conductivity through a temperature-formatted readout. We evaluate SolvMix on three curated electrolyte conductivity benchmarks, CALiSol-23, DiffMix, and Bamboo-mixer, covering diverse solvents, salts, compositions, salt mole ratios, and temperatures. Across standard splits on all three benchmarks and binned out-of-distribution (OOD) splits on Bamboo-mixer, SolvMix outperforms strong molecular-representation, mixture-aggregation, and geometric-interaction baselines under the reported protocols. Ablations show that the best-performing formulation-state construction combines amount-and-type-aware component tokens, multiplicative amount calibration, token-level interaction followed by mean pooling, and late-concat temperature formatting. OOD results further show clear gains under formulation-level shifts, where static component descriptors and local interaction patterns are least aligned with the required generalization. These results suggest that electrolyte conductivity prediction benefits from treating formulation-state construction as a first-class modeling problem, beyond molecular representation learning or explicit local interaction modeling.

In recent years, Large Language Models (LLMs) have demonstrated remarkable performance in tasks such as mathematical reasoning and code generation. However, as LLMs are increasingly deployed as autonomous agents, their reasoning capabilities in dynamic, human-like social interactions remain largely unexplored. To bridge this gap, we propose the benchmark SoDeArena—Social Deduction Arena, designed to evaluate the socially-situated reasoning capabilities of LLMs through a diverse set of interactive games. Through large-scale multi-agent simulations and human interaction experiments, we have identified three key insights for improving current LLMs: (1) the overall proficiency of models in social deduction is fundamentally bottlenecked by model scale and reasoning capabilities; (2) models lack proactive intent management, defaulting instead to strategic passivity and output conformity during multi-agent interactions; and (3) LLMs exhibit dual behavioral biases, manifesting as a rigid safety alignment in adversarial roles and a pathological reliance on shallow positional patterns over robust reasoning processes. These findings point to potential directions for the future development of AI systems with robust socially-situated reasoning capabilities.

Deploying deep learning models across heterogeneous hardware requires each model to jointly satisfy a bundle of coupled constraints on accuracy, latency, memory, and energy. Maintaining a specialist for every deployment scenario is operationally prohibitive, so practitioners need a small portfolio of $K$ models that collectively covers many deployment profiles. Existing hardware-aware NAS and Pareto-based approaches target marginal objectives and do not directly address this downstream decision. We formalize it as Deployment Portfolio Selection over a fixed pre-measured archive, where a profile is covered only when a single retained model simultaneously satisfies its entire constraint bundle. The induced objective is weighted maximum coverage, which is NP-hard but monotone submodular, so greedy selection inherits a $(1-1/e)$ guarantee, and sample-then-optimize admits a finite-sample bound. Across an 18-family sweep on HW-NAS-Bench, direct bundled-coverage optimization is most valuable in the small-portfolio, low-coverability regime: gains concentrate on the hardest profiles, are most robust at $K = 3$, and persist under three non-uniform demand models. Complementary analyses of remeasurement noise, runtime, and compact feasibility storage clarify when bundled coverage is preferable to scalarized or Pareto-based alternatives.

Adapting language agents often means teaching them domain procedures: where to look, which tools to call, how to verify intermediate results, and how to format outputs for a grader. Existing context-level adaptation usually either hand-writes such procedures, generates them once, or lets skill artifacts grow through loosely controlled self-revision. We ask whether a skill can instead be trained as the compact external state of a frozen agent. SkillOpt is a harness-agnostic text-space optimizer for a single natural-language skill document. It runs the frozen target model on scored rollout batches, uses a separate optimizer model to reflect over success and failure minibatches, proposes structured add/delete/replace edits, ranks them under a textual learning-rate budget, and accepts a candidate only if it improves held-out selection performance. Rejected-update memory, slow cross-epoch guidance, and optimizer-side meta skill make the editing loop behave like bounded training while leaving deployment as a single best_skill.md. Across six direct-chat benchmarks covering QA, spreadsheets, documents, math, and embodied decision making, \ourmethod{} improves GPT--5.5 over no skill by 21.5 points on average, with positive gains on every task and the best measured result on five of six. Codex- and Claude-Code-style harness runs show that the same artifact remains useful in tool-backed execution. Ablations and transfer studies identify validation-gated, bounded edits and update memory as key to stable, portable skill learning.

Inferring cellular dynamics from unpaired single-cell snapshots requires modeling both state transitions and population growth or death. Unbalanced dynamic optimal transport (UDOT) addresses this by penalizing growth along transport paths, making the choice of growth penalty a key way to encode biological priors on proliferation and apoptosis. However, existing UDOT solvers either rely on computationally expensive NeuralODE simulations or depend on analytical solutions of conditional paths, restricting their efficiency solely to quadratic penalties, i.e. Wasserstein-Fisher-Rao (WFR) geodesics. To enable an efficient UDOT solver for general growth penalties, we first show that concave growth penalties lead to degenerate solutions where growth and transport are separated. We then introduce **S**imulation-free **U**nbalanced **D**ynamic **O**ptimal transport (SUDO), a simulation-free framework for UDOT with general non-quadratic convex growth penalties. SUDO learns the conditional paths and transport costs, solves the induced semi-coupling problem, and subsequently leverages unbalanced flow matching to achieve a simulation-free solution. On WFR benchmarks, SUDO matches the accuracy of efficient, analytical solution-driven algorithms while outperforming simulation-based methods in computational speed. Beyond WFR, SUDO supports asymmetric penalties that encode proliferation-dominant priors and produce more plausible trajectories and growth estimates on synthetic and single-cell datasets.

Reinforcement Learning (RL) algorithms often rely on data collected from a target environment, which can be expensive and noisy. Although simulators can generate large amounts of additional data, standard simulation mixing approaches—which directly combine simulated and real experience—can degrade performance due to simulator inaccuracies, especially when they bias the solution away from the optimal policy. We propose a conservative simulation-aided learning method based on control variates, where simulated data is used solely to reduce variance in the learning process rather than directly shaping the learning target. We develop our approach for Policy-Evaluation, which is a fundamental building block of RL algorithms. Then we combine it within the actor-critic framework towards policy improvement, as well as extend it towards offline RL scenarios. Experiments on multiple MuJoCo benchmark tasks demonstrate improvements over standard simulation mixing approaches, highlighting control variates as an effective tool for simulation-aided reinforcement learning.

Machine learning models for answering logical queries on knowledge graphs estimate the likelihood of answers that are not reachable via direct traversal. Recent work has proposed extending such queries with \emph{soft entity constraints}, which require the \emph{target variable} to be similar or dissimilar to specified sets of entities. We study a more general formulation where similarity constraints are specified on an arbitrary variable in a query, and introduce SCORE: a computationally efficient and interpretable method for incorporating similarity constraints on an arbitrary variable of a query. SCORE is based on a lightweight and interpretable score adjustment function that only requires tuning two hyperparameters on a validation set. Our experiments show that SCORE effectively incorporates preferences while maintaining strong query answering performance. It significantly improves ranking quality when constraints apply to the target variable and performs effectively in the more general case involving constraints on intermediate variables.

Modern LLM workflows increasingly move coordinate-indexed objects across checkpoints: steering vectors, sparse autoencoders, top-$k$ neuron sets, attribution lists, and merge alignments. This is only well posed after fixing the model's residual-stream gauge. We show that the native discrete gauge is architecture-dependent: LayerNorm residual charts have permutation gauge $S_d$, up to a global sign flip, while RMSNorm residual charts with generic per-channel gain have signed-permutation gauge $B_d = S_d \ltimes \{\pm 1\}^d$. Thus permutation-only alignment is symmetry-incomplete for RMSNorm models. We introduce sign-marginalized Hungarian matching and prove a sharp population failure mode: with decorrelated source coordinates, raw signed-correlation matching has a structural permutation-accuracy ceiling equal to the fraction of positive signs in the true gauge up to $O(d \cdot 2^{-d})$, whereas sign-marginalized matching removes this obstruction. We then make coordinate-preserving transport, rather than function-level merging, the primary object: composing saved-checkpoint local $B_d$ gauges along same-base fine-tuning trajectories recovers 91.1% of cross-run coordinates at 1500 steps versus 60.3% for endpoint matching, and the gain is not explained by merely routing through the base. The recovered gauge transfers tools that permutation-only alignment breaks: TinyLlama SAE reconstruction has NMSE $0.004$ under $B_d$ recovery versus $1.08$ under $S_d$; Qwen sentiment steering preserves 95.8% of its effect versus 17.2%; refusal steering reverses sign under $S_d$. Coordinate-preserving merge tests show the same mechanism. The same covariance governs stateful training: signed transport of AdamW state preserves the resumed trajectory, while permutation-only state transport starts from a functionally identical checkpoint but follows a different trajectory. Finally, we give gauge-sweep audits for index-level interpretability claims: coordinate names are reproducible only relative to an explicit gauge.

Modern classifiers remain sensitive to small input perturbations, while strong model-agnostic robustness certificates such as randomized smoothing are often too expensive for deployment, requiring an extensive number (e.g. 2000) of model forward passes per input. We propose a framework that delegates certification to a cheap proxy function while statistically controlling its deviation from the original sound certificate. Given an exchangeable unlabeled calibration set, we tune the proxy via robust conformal risk control to guarantee a bounded marginal false-approval rate: the probability that the proxy accepts an input whose prediction is flipped due to perturbation. The resulting proxy certificate can be used either as a standalone marginal certificate or as a fallback mechanism that invokes the expensive certificate only when the proxy rejects. We provide both single-sample and sample-heavy calibration recipes. Empirically, our method substantially reduces test-time certification cost (to a single model forward) while retaining much of the certified performance of randomized smoothing, enabling cheap yet effective robustness guarantees for larger architectures such as vision transformers and language models.