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NeurIPS 2026

On the Complexity of Preference-Based Bandits

Ahmed Ben Yahmed, Marc Abeille, Clement Calauzenes

We study preference-based bandits with general reward function classes, where a learner sequentially selects pairs of arms and observes binary preference feedback governed by the Bradley-Terry model. This setting naturally arises in applications such as recommender systems, tournament ranking, and learning from human feedback, where relative preferences are easier to elicit than absolute rewards. The observation model inherits the logistic bandit challenge of handling the problem-dependent constant $\kappa$, which accounts for the non-linearity of the link function and can grow arbitrarily large. Moreover, prior work has predominantly focused on linear or kernelized reward models, precluding the use of richer function classes. To address these limitations, we consider general reward function classes and introduce the *locally sensitive eluder dimension*, a novel complexity measure tailored to the logistic structure of preference feedback that yields fine-grained regret guarantees without unfavorable dependence on $\kappa$. Building on this notion, we propose **GINOP** (**G**eneric **IN**formative **OP**timism), an algorithm that constructs log-loss confidence sets and jointly selects arm pairs to balance optimism and informative exploration. We establish a first-order regret bound that, in contrast with what previous results suggest, demonstrates that learning with preference feedback is as statistically efficient as learning from direct reward observation. Finally, we corroborate our theoretical findings with empirical evaluations against competitive baselines.

NeurIPS 2026

On the Complexity of Offline Reinforcement Learning with Q*-Approximation and Partial Coverage

Haolin Liu, Braham Snyder, Chen-Yu Wei

We study offline reinforcement learning under $Q^\star$-approximation and partial coverage, a setting that motivates practical algorithms such as Conservative $Q$-Learning (CQL) [KZTL20] but has received limited theoretical attention. Our work is inspired by the following open question: \emph{Are $Q^\star$-realizability and Bellman completeness sufficient for sample-efficient offline RL under partial coverage?} We answer this question in the negative through an information-theoretic lower bound. To identify additional structure that enables sample-efficient offline RL under partial coverage, we introduce a general decision-estimation framework, inspired by model-free decision-estimation coefficients (DEC) for online RL [FGO$^+$23, LWZ25b]. Our framework decomposes the complexity of offline RL into two parts: the \emph{decision complexity} and the \emph{value estimation error}. This decomposition allows us to study the two sub-problems in a modular way. Our result not only unifies existing results in the $Q^\star$-approximation and partial coverage regime [CJ22, UKLS23], but further improves and generalizes them. On the decision complexity side, our improvement includes: the first $\epsilon^{-2}$ sample complexity bound for soft $Q$-learning under partial coverage that improves [UKLS23]'s $\epsilon^{-4}$ bound, the removal of the need for additional online interaction in the gap-dependent setting of [CJ22], and new learnable settings beyond the above two cases. On the value estimation side, we provide the first characterization of offline learnability for general low-Bellman-rank MDPs [JKA$^+$17, DKL$^+$21, JLM21], a canonical online RL setting that has remained unexplored in offline RL outside special cases. As a side contribution, our techniques give the first analysis of CQL in the function approximation setting.

NeurIPS 2026

On the Complexity of Discounted Robust MDPs with $L_p$ Uncertainty Sets

Ali Asadi, Krishnendu Chatterjee, Alipasha Montaseri, Ali Shafiee

A basic model in sequential decision making is the Markov decision process (MDP), which is extended to Robust MDPs (RMDPs) by allowing uncertainty in transition probabilities and optimizing against the worst-case transition probabilities from the uncertainty sets. The class of $(s,a)$-rectangular RMDPs with $L_p$ uncertainty sets provides a flexible and expressive model for such problems. We study this class of RMDPs with discounted-sum objectives and a constant discount factor. The existence of an efficient algorithm for this class is a fundamental theoretical question in optimization and sequential decision making. Previous results only establish a strongly polynomial-time algorithm for $L_\infty$ uncertainty sets. In this work, our main results are as follows: (a) we show that for any compact uncertainty set, the policy iteration algorithm for RMDPs is strongly polynomial with oracle access to solutions of Robust Markov chains (RMCs); (b) we present strongly polynomial-time bounds on the policy iteration algorithm for RMCs with $L_1$ and $L_\infty$ uncertainty sets; and (c) we establish hardness results for RMCs with $L_p$ uncertainty sets for integer $p$ satisfying $1<p<\infty$. Finally, motivated by our theoretical bounds, we present experimental results showing the practical efficiency of policy iteration for RMDPs with $L_1, L_\infty$ uncertainty sets.

NeurIPS 2026

On the Burden of Achieving Fairness in Conformal Prediction

Ziang Gao, Pengqi Liu, Archer Yang, Mouloud Belbahri, Jesse Cresswell, Masoud Asgharian

Conformal prediction is often calibrated with a single pooled threshold, but this can hide cross-group heterogeneity in score distributions and distort group-wise coverage. We study this phenomenon through the population score distributions underlying split conformal calibration. First, we derive a conservation law and lower bound showing that pooled calibration incurs irreducible group-wise coverage distortion at a scale set by cross-group quantile heterogeneity. Second, we demonstrate that the two leading fairness definitions for conformal prediction, Equalized Coverage and Equalized Set Size, are fundamentally in tension. Third, we quantify the cost of moving between policies which treat groups separately or pool them. Experiments on synthetic and real data confirm the same bidirectional trade-off after finite-sample calibration. Our results show that, for the policy families studied here, calibration choice does not remove cross-group heterogeneity; it determines whether the resulting distortion appears in the coverage or size dimension, providing a principled lens for analyzing fairness-oriented calibration choices in practice.

NeurIPS 2026

On objective mismatch in molecular retrieval from tandem mass spectrometry

Gaetan De Waele, Marek Wydmuch, Krzysztof Dembczynski, Wojciech Kotlowski, Willem Waegeman

Identifying molecular structures from LC-MS/MS spectra is a central problem in computational metabolomics, often approached by predicting molecular fingerprints and retrieving candidates via similarity search. Despite widespread use, the relationship between training objectives for fingerprint prediction and downstream retrieval performance remains poorly understood. In this work, we show that these objectives are fundamentally misaligned. Adopting a decision-theoretic perspective, we derive novel regret bounds that characterize when Bayes-optimal predictors for fingerprint similarity diverge from those for molecular retrieval. Our analysis reveals that optimizing standard similarity-based losses can provably degrade retrieval performance, and that the extent of this mismatch depends on the similarity structure of candidate sets. Empirically, we validate our theory on the MassSpecGym benchmark, demonstrating a Pareto frontier between fingerprint accuracy and retrieval metrics across commonly used loss functions. These results expose an inherent trade-off in fingerprint-based molecular identification and provide principled guidance for the design of learning objectives in computational mass spectrometry.

NeurIPS 2026

On approximation and estimation of Schrödinger potentials without the curse of dimensionality

Artsiom Patarusau, Nikita Puchkin, Konstantin Yakovlev

We examine generative modelling approaches based on the construction of Schrödinger bridges between Gaussian noise and a target distribution. It is known that the solution of the dynamic Schrödinger problem is a diffusion process with a drift associated with Doob's h-transform of a Schrödinger potential. Although its accurate restoration from finite samples is crucial for reliable, high-quality data generation, the existing literature lacks theoretical guarantees regarding this question. In our work, we establish theoretical upper bounds on the complexity of Schrödinger potential approximation and estimation via neural networks. These bounds are determined by the effective dimension of the target distribution. To our knowledge, this is the first result demonstrating that generative modelling methods based on Schrödinger bridges and stochastic optimal control can escape the curse of dimensionality.

NeurIPS 2026

On Worst-Case Guarantees for Graph-Based Nearest-Neighbor Search

Majid Daliri, Mohammadreza Daneshvaramoli, Purna Dutta, Edo Liberty, Cameron Musco, Christopher Musco, Torsten Suel

Graph-based nearest neighbor search algorithms like HNSW, DiskANN, NSG, and others have surged in popularity in recent years due to their excellent empirical performance in comparison to previously successful ``space partitioning'' methods like IVF data structures and Locality Sensitive Hashing (LSH). However, in contrast to LSH and related methods, obtaining strong worst-case theoretical guarantees for graph-based search has remained a challenging open problem. In this paper, we prove a strong lower bound that helps explain the lack of progress towards such guarantees. In particular, we show that no standard graph-based method (i.e., any method that runs a variant of greedy search on a flat or hierarchical search graph) can achieve sublinear query time for approximate nearest neighbor search in Euclidean space, even for an arbitrarily large approximation factor. On the other hand, we prove that sublinear query time \emph{is possible} if we allow for the use of \emph{Steiner points} in the search graph. We obtain bounds comparable to LSH, showing e.g., that graph-based search with Steiner points can solve $c$-approximate nearest neighbor search in Euclidean space with query time $\tilde{O}\left(n^{1/c}\right)$. We complement this result with initial experiments exploring how Steiner points can be incorporated into practical graph-based methods, showing modest but meaningful improvements in recall versus query-time tradeoffs.

NeurIPS 2026

On Reparameterizing the Score Function

Mohammad Hossein Amani, Leonardo Bocchieri, Maxime Peyrard, Clement Hongler, Robert West

Policy gradients for autoregressive sequence models differentiate each token's log-probability while holding the conditioning history fixed. This discards information about how earlier decisions shape later conditional distributions, creating a credit-assignment bottleneck when rewards are sparse. We introduce History-Reparameterized (HR) policy gradients, which replace the frozen prefix in the score function with a differentiable reparameterized or relaxed history, allowing gradients of downstream log-probabilities to propagate backward through the generated trajectory. The resulting history-pathwise term is generally biased when added directly, so we derive Optimal HR (OHR), a centered control-variate estimator with a closed-form coefficient that minimizes the trace of the gradient variance at the population level. The variance reduction is governed by temporal structure in the policy dynamics: random or weakly structured policies provide little benefit, while policies with learned sequential dependencies yield informative history-pathwise corrections. For discrete tokens, the choice of relaxation is crucial: embedding-level relaxation yields substantial variance reduction that grows with horizon, whereas straight-through Gumbel-Softmax yields essentially none in our diagnostics. We validate the method on a Gaussian linear Markov model, a sparse-reward T-maze with a recurrent policy, and an autoregressive Transformer model for small Traveling Salesman Problem (TSP) instances.

NeurIPS 2026

On Neural Scaling Laws for Weather Emulation through Continual Training

Shashank Subramanian, Alexander Kiefer, Arnur Nigmetov, Amir Gholami, Dmitriy Morozov, Michael Mahoney

Neural scaling laws, which in some domains can predict the performance of large neural networks as a function of model, data, and compute scale, are the cornerstone of building foundation models in Natural Language Processing and Computer Vision. We study neural scaling in Scientific Machine Learning, focusing on models for weather forecasting. To analyze scaling behavior in as simple a setting as possible, we adopt a minimal, scalable, general-purpose Swin Transformer architecture, and we use continual training with constant learning rates and periodic cooldowns as an efficient training strategy. We show that models trained in this minimalist way follow predictable scaling trends and outperform standard cosine learning rate schedules. Cooldown phases can be re-purposed to improve downstream performance, e.g., enabling accurate multi-step rollouts over longer forecast horizons or sharper predictions through spectral loss adjustments. We also systematically explore a wide range of model and dataset sizes under various compute budgets to construct IsoFLOP curves, and we identify compute-optimal training regimes. Extrapolating these trends to larger scales highlights potential performance limits, demonstrating that neural scaling can serve as an important diagnostic for efficient resource allocation. We open-source our code for reproducibility.

NeurIPS 2026

On Nash Equilibria in Participatory Budgeting with Donations and Beyond

Grzegorz Lisowski, Georgios Papasotiropoulos, Grzegorz Pierczyński, Krzysztof Rogowski

This work proposes a framework for public decision processes with a monetary component, where voters can pledge donations to support preferred projects and influence the allocation of public funds. It captures a range of real-world scenarios, including participatory budgeting, blockchain-based funding platforms, charitable programs, and crowdfunding campaigns. Through both theoretical and experimental evaluation, our study addresses questions concerning the existence, structure, number, computation, and quality of Nash equilibria.

NeurIPS 2026

On Minimizing Regret in Fixed-Confidence $\varepsilon$-Best Arm Identification

Tianyuan Jin, Junwen Yang, Vincent TAN

This paper studies the $\varepsilon$-best arm identification problem ($\varepsilon$-BAI) for $K$-armed bandits under the fixed-confidence setting. Departing from the usual objective of identifying the best arm with minimal sample complexity, we focus on minimizing the cumulative regret of identifying an $\varepsilon$-best arm. We consider the usual asymptotic regime in which the error probability $\delta$ of identifying an $\varepsilon$-best arm vanishes. In this setting, we show a novel instance dependent lower bound. In particular, we show that any family of $(\varepsilon,\delta)$-PAC algorithms must incur an expected cumulative regret up to the stopping time that scales as $\log(1/\delta)$, with an instance-dependent constant $C(\mu)$. This is proved using a novel regret-aware change-of-measure technique that allocates information given a budget on the regret. To achieve this lower bound, we devise an algorithm, \algname, that achieves the same scaling in $\delta$, i.e., $\log (1/\delta)$, but with a different constant, which we call $C^\*(\mu)$. KL-UCB+Greedy has two main benefits: (i) it is computationally efficient as $C^\*(\mu)$ admits a closed-form expression; (ii) in broad classes of reward distributions such as Gaussian distributions, $C^\*( \mu) = C( \mu)$, demonstrating asymptotic optimality of KL-UCB+Greedy within these classes. As auxiliary results, we also derive lower bounds on the sample complexity of any family of $(\varepsilon,\delta)$-algorithms as $\delta$ vanishes and show that the sample complexity of KL-UCB+Greedy closely matches that of the lower bound on the sample complexity.

NeurIPS 2026

On Making $SE(2)$-Invariant Networks Optimal

Tomas Karella, Emily Shinkle, Alice Allen, Pieter J Swart, Nicholas Lubbers, Roxana Bujack

Respecting a-priori known symmetries of underlying data is a key principle in designing efficient neural architectures. Convolutional Neural Networks (CNNs) are a canonical example, encoding translation equivariance. Extending this inductive bias to richer symmetry groups such as $\mathrm{SE}(2)$ in the most effective way possible is an ongoing architectural and computational challenge. Building on classical invariant theory, we derive invariant feature maps that are provably optimal: minimal and information-preserving with respect to the symmetry group. Our construction is designed to integrate seamlessly into standard architectures, requiring no modification to nonlinearities or normalization layers. As a concrete implementation, we introduce a plug-and-play module for CNNs that enforces $\mathrm{SE}(2)$ invariance, capturing both translations and rotations within standard architectures. The resulting models are both efficient and expressive. Experiments show competitive or improved accuracy compared to state-of-the-art equivariant methods at significantly lower computational cost. Finally, we provide a theoretical and empirical analysis of the relationship between equivariance and invariance, offering insight into their roles in controlling robustness and flexibility.

NeurIPS 2026

On Lipschitz Explosion in Deep Neural Networks with Normalization: Consequences for Optimization and Robustness

Ashkan Soleymani, Reyhaneh Hosseinpourkhoshkbari, Hadi Daneshmand, Patrick Jaillet

The Lipschitz constant of a neural network is a basic stability quantity appearing in optimization guarantees, generalization bounds, and robustness certificates. Deep networks naturally admit two such notions, \emph{input Lipschitzness}, measuring sensitivity to data perturbations, and \emph{parameter Lipschitzness}, measuring sensitivity to weight perturbations. We prove that, for deep networks with normalization layers, with batch normalization as the canonical example, \emph{both} Lipschitz constants can grow exponentially with depth and hence with parameter dimension, even under strong per-layer norm control such as $\\|W_\ell\\|_2\le 1$, and already for linear activations. Thus, a mechanism widely used to stabilize training can create severe worst-case instabilities that are invisible from layerwise norm bounds alone. Parameter-Lipschitz explosion turns Lipschitz-dependent nonsmooth optimization guarantees into exponential-in-dimension bounds for deep normalized networks, while input-Lipschitz explosion makes worst-case Lipschitz-based generalization and robustness certificates vacuous. The latter also yields a concrete rank-separation mechanism for adversarial vulnerability. The theory predicts that perturbations introducing new singular directions should be amplified much more strongly than equal-energy perturbations that remain within the input's original singular subspace. Experiments on MNIST, Fashion-MNIST, and CIFAR-10 support this prediction, showing that rank-creating perturbations cause substantially sharper drops in accuracy, confidence, and margins than same-subspace perturbations.

NeurIPS 2026

On Length Bias in EEG-to-Text Decoding

Iakovos Tenedios, Yashar Moshfeghi

Sentence-level EEG-to-text decoding models typically pad variable-duration neural signals to a fixed-length window, creating a structural confound where segment duration correlates with sentence identity independently of neural content, a problem we term length bias. Despite being acknowledged in prior work, the prevalence, magnitude, and architectural dependence of this effect have never been systematically quantified. We introduce length-matched noise baselines that isolate this confound by replacing only the true signal region with Gaussian noise while preserving zero-padding, and apply them across three English listening EEG datasets under a strict subject-held-out protocol. Evaluating ten sentence classifiers and three generation models based on the current state-of-the-art, we show that reported decoding scores are substantially inflated by length cues across datasets, with the degree of inflation varying markedly by architecture. Among classifiers, BIOT alone is unaffected by length-matched noise. A systematic decomposition of its components identifies Short-Fourier-Transform (STFT) tokenisation as the bigger source of this invariance. We transfer this finding into two new generation variants that largely eliminate encoder-side length bias, enabling a controlled analysis of where residual bias originates. A classification-to-generation evaluation further reveals that leading generation models operate largely as sentence retrieval systems, with a linear classifier recovering nearly all of their reported BLEU-4 scores. Together, these results establish that length bias is a pervasive and previously unquantified failure mode in EEG-to-text evaluation, and provide both diagnostic tools and architectural directions for future work.

NeurIPS 2026

On JEPA Isotropy

Thomas YL Lin, Han Liu, Jerry Yao-Chieh Hu

We study the empirical risk minimization (ERM) of linear Joint Embedding Predictive Architecture (JEPA) and establish its key conditions for optimality. By casting the embedding bottleneck as a rank constraint, we formulate JEPA as a reduced-rank regression problem. This induces a risk decomposition into an irreducible error and an excess-risk bound. Within the irreducible term, we find the rank of the optimal predictor grows with target heterogeneity and saturates at the bottleneck. Within the excess-risk bound, we find spectral conditioning of the whitened end-to-end predictor governs minimization. Together, these conditions prescribe an isotropic regularizer. Under this regularization, we show such JEPA isotropy subsumes canonical JEPA isotropic embedding designs and hence justifies their empirical successes via ERM. Numerical experiments corroborate our theory.

NeurIPS 2026

On Inherent Privacy of Posterior Sampling: A Unified R\'enyi-Divergence Framework

Ruyu Zhou, Fang Liu

Differential Privacy (DP) provides a rigorous framework for quantifying privacy guarantees. While most methods achieve DP by injecting calibrated random noise, the intrinsic randomness of certain procedures such as sampling can yield DP guarantees ``for free''. In this work, we develop a unified R\'enyi divergence framework to characterize the inherent DP guarantees of sampling from a Bayesian posterior distribution. We show that the privacy loss incurred by One-Posterior-Sampling (OPS) is governed by posterior exponential moments of the single-record log-likelihood ratio, and establish explicit DP guarantees under uniformly bounded, sub-Gaussian, or sub-exponential tail regimes. We apply the framework to representative Bayesian models, including categorical likelihoods with arbitrary priors, Gaussian-Gaussian conjugate pair, generalized linear models from the exponential family and linear regression with Gaussian likelihood, both with Gaussian priors on the regression coefficients. Our results elucidate sample size, model structure, neighboring relations in DP (bounded or unbounded), and how prior if applicable, jointly determine the inherent DP guarantees of OPS. Furthermore, our results recover the existing DP guarantees for OPS as special cases -- often with tighter privacy loss bounds -- and substantially broaden the class of Bayesian models for which the inherent DP guarantees of OPS can be rigorously characterized.

NeurIPS 2026

On Differentially Private Mechanisms for Linear Regression

Bardiya Aryanfard, Monika Henzinger, Farhood Rostamkhani

We study the classic least-squares linear regression problem under differential privacy (DP) in the continual observation setting. In this setting, the mechanism receives a stream of $n$ data points $(x_i,y_i)$ ($x_i\in\mathbb{R}^d$ and $y_i\in\mathbb{R}$) and must output an estimate of the optimal parameters at each time step $i$. Although differentially private linear regression has been extensively studied in the batch setting, the problem remains underexplored for the continual setting, with prior work being restricted to constrained linear regression and update time polynomial in $n$. In this work, we introduce ContinualAdaSSP, the first mechanism for unconstrained linear regression under continual differential privacy. Our mechanism's suboptimality gap is proportional to $\sqrt{d}\operatorname{polylog}(n)$. It requires $O(d^2\log{n})$ space and $O(d^2\log{n}+d^{\omega})$ ($\omega$ is the matrix multiplication exponent.) update time, where $d$ is the dimension of the input space. This matches the suboptimality gap of the continual mechanism for the constrained version. We also study fundamental limits of differentially private linear regression by showing the first lower bounds for the box-constrained least-squares linear regression problem. Our lower bounds are proportional to $\min(n,\frac{\sqrt{d}}{\log^{1.5}d})$ for $(1,O(\frac{1}{n}))$-DP, and $\min(n,\frac{d}{\varepsilon})$ for $\varepsilon$-DP, and are derived using a reduction from a fingerprinting code problem from [Peter et al, 2024], providing new insights into the inherent hardness of this canonical task. Our experimental evaluation on real-world datasets shows that the accuracy of our mechanism clearly outperforms any other known differentially private mechanism for this problem such as rerunning the batch algorithm at each time step.

NeurIPS 2026

On Differential Private $\ell_1$, $\ell_2$ and $\ell_p^p$ Distance Queries

Erzhi Liu, Jerry Yao-Chieh Hu, Alex Reneau, Zhao Song, Han Liu

We introduce a refined differentially private (DP) data structure for kernel density estimation (KDE) with $\ell_1$, $\ell_2$ and $\ell_p^p$ kernels. This new DP data structure offers not only improved privacy-utility tradeoff but also better query efficiency over prior results. Specifically, we study the mathematical problem: given a similarity function $f$ (or DP KDE) and a private dataset $X \subset \mathbb{R}^d$, our goal is to preprocess $X$ so that for any query $y \in \mathbb{R}^d$, we approximate $\sum_{x \in X} f(x, y)$ in a differentially private fashion. The best previous algorithm for $f(x, y) = |x - y|_1$ is the node-contaminated balanced binary tree by [Backurs, Lin, Mahabadi, Silwal, and Tarnawski, ICLR 2024]. Their algorithm requires $O(nd)$ space and time for preprocessing with $n = |X|$. For any query point, the query time is $\alpha^{-1} d \log^2 n$, with an error guarantee of $(1+\alpha)$-approximation and $\varepsilon^{-1} \alpha^{-0.5} d^{1.5} R \log^{1.5} n$. In this paper, we use the same space and pre-processing time, improve the best previous result [Backurs, Lin, Mahabadi, Silwal, and Tarnawski, ICLR 2024] in three aspects - We reduce query time by $\alpha^{-1} \log n$ factor - We improve the approximation ratio from $\alpha$ to $1$ - We reduce the error dependence by a factor of $\alpha^{-0.5}$ From a technical perspective, our method of constructing the search tree differs from previous work [Backurs, Lin, Mahabadi, Silwal, and Tarnawski, ICLR 2024]. In prior work, for each query, the answer is split into $\alpha^{-1} \log n$ numbers, each derived from the summation of $\log n$ values in interval tree countings. In contrast, we construct the tree differently, splitting the answer into $\log n$ numbers, where each is a smart combination of two distance values, two counting values, and $y$ itself. We believe our tree structure may be of independent interest.

NeurIPS 2026

On Data Engineering for Scaling LLM Terminal Capabilities

Renjie Pi, Grace Lam, Mohammad Shoeybi, Pooya Jannaty, Bryan Catanzaro, Wei Ping

Despite rapid recent progress in the terminal capabilities of large language models, the training data strategies behind state-of-the-art terminal agents remain largely undisclosed. We address this gap through a systematic study of data engineering practices for terminal agents, making two key contributions: (1) Terminal-Task-Gen, a lightweight synthetic task generation pipeline that supports seed-based and skill-based task construction, and (2) a comprehensive analysis of data and training strategies, including filtering, curriculum learning, long context training, and scaling behavior. Our pipeline yields Terminal-Corpus, a large-scale open-source dataset for terminal tasks. Using this dataset, we train Nemotron-Terminal, a family of models initialized from Qwen3 (8B, 14B, 32B) that achieve substantial gains on Terminal-Bench 2.0: Nemotron-Terminal-8B improves from 2.5% to 13.0%, Nemotron-Terminal-14B improves from 4.0% to 20.2%, and Nemotron-Terminal-32B improves from 3.4% to 27.4%, matching the performance of significantly larger models. We release Nemotron-Terminal checkpoints and Terminal-Corpus through the Nemotron-Terminal Hugging Face collection.

NeurIPS 2026

On Concentration Inequalities for Sampling without Replacement

Shaojie Li, Bowei Zhu, Yong Liu

This paper studies concentration inequalities for sampling without replacement. We introduce a general inequality that provides simple guidelines for proving concentration inequalities, offers a degree of unification of existing results, and is strong enough to yield sharper bounds. As applications, we revisit several standard statistics and either recover classical inequalities through streamlined proofs or strengthen them to tighter bounds, with rates optimal up to constants.

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