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Theory · Online Learning and Bandits

Gabriel Sargent, Wei Sun, Zhengwu Zhang, Yufeng Liu

In adaptive experiments, statistical inference is essential for reliable decision-making and scientific discovery. Often in these settings, collecting labeled data is expensive, but decision-makers have access to large unlabeled datasets and strong pretrained AI models that can generate outcome predictions. Effectively leveraging these predictions in online experiments poses fundamental challenges for statistical inference: AI models may be misspecified, and data collected under adaptive policies are inherently non-i.i.d., invalidating classical inference techniques. To address these challenges, we propose a Prediction-Powered Adaptive Inference (PPAI) estimator that integrates unlabeled data, predicted labels, and adaptively collected labeled data through a single estimating equation. We establish asymptotic normality of the PPAI estimator under mild conditions on the data-collection policy, enabling valid confidence intervals and hypothesis tests for a broad class of Z-functionals. The method incorporates a data-driven tuning mechanism that adaptively weights AI predictions according to their informativeness, guaranteeing that the resulting asymptotic variance is no worse than that of the labeled-only baseline, and is strictly smaller when predictions are informative. Numerical experiments further support the theory, illustrating efficiency gains with informative AI predictions and robust performance when predictions are inaccurate.

Deep Learning · Large Language Models

Haechan Kim, Soohyun Ryu, Gyouk Chu, Doohyuk Jang, Eunho Yang

Reinforcement learning with verifiable rewards (RLVR) has emerged as an effective post-training paradigm for improving the reasoning capabilities of large language models. However, existing group-based RLVR methods often suffer from severe sample inefficiency. This inefficiency stems from reliance on point estimation of rewards from a small number of rollouts, leading to high estimation variance, variance collapse, and ineffective utilization of generated responses. In this work, we reformulate RLVR from a statistical estimation perspective by modeling rewards as samples drawn from a policy-induced distribution and casting advantage computation as the problem of estimating the reward distribution from finite data. Building on this view, we propose **D**iscounted **B**eta-**B**ernoulli (**DBB**) reward estimation, which leverages historical reward statistics for the non-stationary distribution. Although biased, the resulting estimator exhibits reduced and stable variance, theoretically avoids estimated variance collapse, and achieves lower mean squared error than standard point estimation. Extensive experiments across six in-distribution and three out-of-distribution reasoning benchmarks demonstrate that GRPO with DBB consistently outperforms naive GRPO, achieving average Acc@8 improvements of 3.22/2.42 points in-distribution and 12.49/6.92 points out-of-distribution on the 1.7B and 8B models, respectively, without additional computational cost or memory usage.

Yanhao Jin, Krishna Balasubramanian, Debashis Paul

Meta-learning involves training models on a variety of training tasks in a way that enables them to generalize well on new, unseen test tasks. In this work, we consider meta-learning within the framework of high-dimensional multivariate random-effects linear models and study generalized ridge-regression based predictions. The statistical intuition of using generalized ridge regression in this setting is that the covariance structure of the random regression coefficients could be leveraged to make better predictions on new tasks. Accordingly, we first characterize the precise asymptotic behavior of the predictive risk for a new test task when the data dimension grows proportionally to the number of samples per task. We next show that this predictive risk is optimal when the weight matrix in generalized ridge regression is chosen to be the inverse of the covariance matrix of random coefficients. Finally, we propose and analyze an estimator of the inverse covariance matrix of random regression coefficients based on data from the training tasks. As opposed to intractable MLE-type estimators, the proposed estimators could be computed efficiently as they could be obtained by solving (global) geodesically-convex optimization problems. Our analysis and methodology use tools from random matrix theory and Riemannian optimization. Simulation results demonstrate the improved generalization performance of the proposed method on new unseen test tasks within the considered framework.

Theory · Probabilistic Methods

Yang Yang, Duo Zheng, Sandeep Jain, Kai Zhang, Ping-Shou Zhong

This paper introduces a new family of adaptive, distribution-free independence tests for multivariate random vectors based on binary expansion coefficients, supported by a tractable asymptotic theory. Our first key contribution establishes a general equivalence between independence testing and testing cross-covariances among exponentially many binary expansion interaction coefficients, applicable to broad sample spaces and not limited to kernel-induced representations. While this exponential interaction structure makes naive construction and computation infeasible, we overcome this challenge by reformulating the proposed tests as a class of U-statistics and deriving an explicit kernel representation that enables scalable and efficient computation. Exploiting the multiscale nature of binary expansions, the proposed framework automatically adapts to unknown dependence structures by selectively truncating higher-order interactions, yielding both strong power and clear interpretability. To further enhance power and computational efficiency, we introduce an adaptive weighted aggregation procedure, termed wa-dCoBET, which combines a baseline Covariance Binary Expansion Test (CoBET) with a distance-measure–based CoBET. Extensive simulations and a real-data application demonstrate that wa-dCoBET consistently matches or outperforms HSIC and distance covariance, particularly in higher-dimensional and non-monotone settings, while maintaining accurate type I error control.

Theory · Deep Learning

Hang Zhou, Ju-Sheng Hong, Xiucai Ding, Jane-Ling Wang

Regression with functional covariates poses fundamental challenges due to the infinite-dimensional nature of functional data, and its theoretical properties have been studied under specialized frameworks in classical nonparametric statistics. While deep neural networks (DNNs) have demonstrated remarkable empirical success in high-dimensional regression, their theoretical behavior in settings involving infinite-dimensional covariates remains largely unexplored. In this work, we study the theoretical performance of DNN-based estimators for regression problems with functional covariates. We extend existing theoretical techniques, which are developed for finite-dimensional covariates supported on compact sets, to the infinite-dimensional and non-compact functional data setting. Under mild conditions, we show that DNN estimators attain minimax-optimal polynomial rates of convergence for both functional linear models and functional generalized linear models. For fully nonparametric regression with functional covariates, we establish a lower bound on the prediction error, and further discuss the fundamental obstacles inherent to this problem and their connections to existing state-of-the-art methods in the literature.

Deep Learning · Large Language Models

Siyuan Li, Youyuan Zhang, Fangming Liu, Jing Li

Online model editing for multimodal large language models (MLLMs) requires assimilating a stream of corrections under tight compute and memory budgets. Yet editors developed for text-only LLMs often degrade on MLLMs: visually dominant activations skew the statistics that shape updates, causing *cross-modal conflict*, while sequential writes become entangled in a shared edit space and amplify long-horizon interference, causing *inter-edit interference*. To address these, we propose **M-ORE**, a modality-decoupled online recursive editor for lifelong MLLM adaptation. M-ORE is derived from a unified proximal-projection formulation and admits a closed-form update with a Sherman-Morrison recursion, yielding constant per-edit overhead. It maintains module-wise locality statistics for the text stack and the visual projector to avoid visually dominated update shaping and performs continual updates in a fixed orthogonal low-rank edit subspace via a Sherman-Morrison recursion to mitigate long-horizon interference. Experiments on multiple MLLM backbones and online editing benchmarks show that our M-ORE method consistently improves reliability, generality, and locality over strong baselines, while achieving favorable quality-efficiency scaling.

Shenshen Li, Kaiyuan Deng, RuoHuai Xie, Xing Xu, Heng Tao Shen, Yazhou Yao, Fumin Shen

Egocentric reasoning fundamentally differs from third-person understanding in LVLMs. Third-person settings offer wide and stable contexts with consistent global regularities, allowing models to utilize broad statistical correlations. In contrast, egocentric scenes are highly dynamic and heterogeneous, where decisive cues are localized and atypical. Therefore, robust egocentric reasoning requires models to focus on ''what is seen now'', i.e., the immediate visual input. However, existing methods tend to exhibit "inertial thinking'', relying excessively on language priors and global context. To address this limitation, we propose a novel three-stage Ego3S framework to ground models' reasoning in interaction evidence. Specifically, before training, we first utilize the counterfactual-based paradigm to select high-value samples that effectively activate multimodal reasoning, thus mitigating the over-reliance on language priors and global context. Moreover, we introduce an interaction-centric reward for reinforcement learning that strengthens the model’s sensitivity to localized interaction cues. Finally, during training, we employ a variance-aware learning schedule that monitors reward distributions to dynamically synchronize data selection with the evolving model competence. Experiments on five datasets show that our Ego3S consistently achieves superior performance using only 26.5% of the training data, while reducing computational costs by over 46%. Code is available at https://anonymous.4open.science/r/Ego3S-70A2.

General Machine Learning · Sequential, Network, and Time Series Modeling

Wenlong Shang, Shihao Tian, Xutong Wan, Peng Chang

Reconstruction-based methods are a dominant paradigm in time series anomaly detection (TSAD), however, their near-universal reliance on Mean Squared Error (MSE) loss results in statistically flawed reconstruction residuals. This fundamental weakness leads to noisy, unstable anomaly scores, hindering reliable detection. To address this, we propose Constrained Gaussian-Noise Optimization and Smoothing (COGNOS), a universal, model-agnostic enhancement framework that tackles this issue at its source. COGNOS introduces a novel Gaussian-White Noise Regularization strategy during training, which directly constrains the model's output residuals to conform to a Gaussian white noise distribution. This engineered statistical property creates the ideal precondition for our second contribution: Adaptive Residual Kalman Smoother that provably operates as a statistically robust estimator to denoise the raw anomaly scores. Extensive experiments on multiple benchmarks demonstrate that COGNOS consistently enhances the performance of state-of-the-art backbones significantly, validating the efficacy of coupling statistical regularization with adaptive filtering.

Theory · Probabilistic Methods

Laura Lützow, Michael Eichelbeck, Mykel Kochenderfer, Matthias Althoff

Conformal prediction is a popular uncertainty quantification method that augments a base predictor to return sets of predictions with statistically valid coverage guarantees. However, current methods are often computationally expensive and data-intensive, as they require constructing an uncertainty model before calibration. Moreover, existing approaches typically represent the prediction sets with intervals, which limits their ability to capture dependencies in multi-dimensional outputs. We address these limitations by introducing zono-conformal prediction, a novel approach inspired by interval predictor models and reachset-conformant identification that constructs prediction zonotopes with assured coverage. By placing zonotopic uncertainty sets directly into the model of the base predictor, zono-conformal predictors can be identified via a single, data-efficient linear program. While we can apply zono-conformal prediction to arbitrary nonlinear base predictors, we focus on feed-forward neural networks in this work. Aside from regression tasks, we also construct optimal zono-conformal predictors in classification settings where the output of an uncertain predictor is a set of possible classes. We provide probabilistic coverage guarantees and present methods for detecting outliers in the identification data. In extensive numerical experiments, we show that zono-conformal predictors are less conservative than interval predictor models and standard conformal prediction methods, while achieving a similar coverage over the test data.

Deep Learning · Algorithms

Xinpei Gao, Xin Luo, Ming Liu, Chunjiang Wang, S Kevin Zhou

High-resolution visual encoders in multimodal large language models (MLLMs) substantially improve fine-grained perception, yet incur prohibitive computational costs.Existing token pruning methods are effective on natural images but struggle with spatially sparse structured inputs (e.g., charts), where critical high-frequency information is sparse, localized, and structurally essential. To address this challenge, we propose Adaptive Dual-Branch Token Sparsification (AD-BTS), a density-aware framework that dynamically allocates computation according to input signal characteristics. Specifically, AD-BTS introduces a Gradient-based Routing Gate (GRG) that uses lightweight pixel-level gradient statistics to estimate structural flatness and guide routing. Then, AD-BTS activates either a Redundancy Selection Branch (RSB) for aggressive token pruning with a frozen encoder, or a Structural Fusion Branch (SFB) with conditional LoRA and context fusion to preserve sparse structural information.Extensive experiments on Qwen2.5-VL demonstrate that AD-BTS establishes a new Pareto frontier between efficiency and accuracy. Under extreme compression (20% token retention), AD-BTS outperforms the strongest baseline by 12.1% on ChartQA while achieving a 1.8× prefill speedup, effectively reconciling computational efficiency with structural robustness.

Social Aspects · Fairness

Xiaoyi MAI, Jean-Michel Loubes

Bias mitigation is particularly challenging for overparameterized machine learning (ML) models. Overfitting of training points not only amplifies data bias induced by spurious correlations, but also causes the failure of usual bias mitigation methods. To provide actionable insights to address this challenge, we propose a precise analysis of fair empirical risk minimization (ERM) in the overparameterized regime. Importantly, we show that even though conventional fair ERM fails on overparameterized models, this approach can be corrected by modifying the equality fairness constraint to allow for bias overcompensation. Moreover, our analysis presents an empirical criterion for strong equalized odds: balanced group-conditional means of representer coefficients, indicating equal average contribution from each sensitive group. Motivated by this result, we provide an estimable search interval that localizes the required overcompensation level for balanced coefficients. Despite the asymptotic nature of our findings, they closely capture the statistical behavior of moderately large ML models.

Applications · Health / Medicine

Ana Sanchez Fernandez, Thomas Pinetz, Werner Zellinger, Günter Klambauer

Biomedical imaging data presents enormous potential for deep learning models to predict invaluable properties, such as diseases and drug effects. However, unavoidable alterations of the technical conditions cause *batch effects*: variations between groups of samples that are not due to any biological signal of interest. Batch effects greatly hinder the generalization abilities of deep learning models, preventing their practical use in the real world. Unsupervised Domain Adaptation (UDA) methods have been proposed to mitigate batch effects, but they usually assume that the data is comprised of only one source domain and one target domain, whereas biological datasets are comprised of multiple domains, both at training and at inference time. While Batch Normalization–based test-time and meta-learning adaptation methods offer a promising mechanism for domain alignment, we show that existing approaches exhibit degraded performance under the usual inference scenarios of small target batch sizes and label shift. We address these limitations by leveraging negative control samples, which are consistently present in every experimental batch in biological datasets, as stable context for adaptation. We propose CS-ARM-BN, a meta-learning BN adaptation method that uses controls both during training and inference to stabilize domain statistics. We perform a suite of experiments of Mechanism-Of-Action (MoA) classification, a crucial task for drug discovery, on the large JUMP-CP imaging dataset. Our experiments show that CS-ARM-BN substantially improves robustness to batch size and class distribution shifts, enabling practical use of deep learning models for biomedical images.

General Machine Learning · Representation Learning

Daniil Karzanov, Marcin Detyniecki

Deep neural networks for image classification often exhibit overconfidence on out-of-distribution (OOD) samples. To address this, we introduce Geometrically Constrained Outlier Synthesis (GCOS), a training-time regularization framework aimed at improving OOD robustness during inference. GCOS addresses a limitation of prior synthesis methods by generating virtual outliers in the hidden feature space that respect the learned manifold structure of in-distribution (ID) data. The synthesis proceeds in two stages: (i) a dominant-variance subspace extracted from the training features identifies geometrically informed, off-manifold directions; (ii) a conformally-inspired shell, defined by the empirical quantiles of a nonconformity score from a calibration set, adaptively controls the synthesis magnitude to produce boundary samples. The shell ensures that generated outliers are neither trivially detectable nor indistinguishable from in-distribution data, facilitating smoother learning of robust features. This is combined with a contrastive regularization objective that promotes separability of ID and OOD samples in a chosen score space, such as Mahalanobis or energy-based. Experiments demonstrate that GCOS outperforms state-of-the-art methods using standard energy-based inference on near-OOD benchmarks, defined as tasks where outliers share the same semantic domain as in-distribution data. As an exploratory extension, the framework naturally transitions to conformal OOD inference, which translates uncertainty scores into statistically valid p-values and enables thresholds with formal error guarantees, providing a pathway toward more predictable and reliable OOD detection.

Probabilistic Methods · Everything Else

Yingyan Zeng, Zipan Huang, Xiaoyu Chen

Existing online change-point detection (CPD) methods rely on fixed-dimensional Euclidean summaries, implicitly assuming that distributional changes are well captured by moment-based or feature-based representations. They can obscure important changes in distributional shape or geometry. We propose a geometry-aware CPD framework that treats streaming batch data as a stochastic process on the 2-Wasserstein space. Our method detects changes in the law of this process by mapping each empirical distribution to a tangent space relative to a pre-change Fréchet barycenter, yielding a reference-centered local linearization of 2-Wasserstein space. This representation enables sequential detectors by adapting classical multivariate monitoring statistics to tangent fields. We provide theoretical guarantees and demonstrate, via synthetic and real-world experiments, that our approach detects complex distributional shifts with reduced detection delay at matched $\mathrm{ARL}_0$ compared with moments-based and model-free baselines.

General Machine Learning · Kernel methods

Rustem Takhanov, Zhenisbek Assylbekov

Conditionally positive definite (CPD) kernels are defined with respect to a function class $\mathcal{F}$. It is well known that such a kernel $K$ is associated with its native space (defined analogously to an RKHS), which in turn gives rise to a learning method --- called conditional kernel ridge regression (conditional KRR) due to its analogy with KRR --- where the estimated regression function is penalized by the square of its native space norm. This method is of interest because it can be viewed as classical linear regression, with features specified by $\mathcal{F}$, followed by the application of standard KRR to the residual (unexplained) component of the target variable. Methods of this type have recently attracted increasing attention. We study the statistical properties of this method by reducing its behavior to that of KRR with another fixed kernel, called the residual kernel. Our main theoretical result shows that such a reduction is indeed possible, at the cost of an additional term in the expected test risk, bounded by $\mathcal{O}(1/\sqrt{N})$, where $N$ is the sample size and the hidden constant depends on the class $\mathcal{F}$ and the input distribution. This reduction enables us to analyze conditional KRR in the case where $K$ is positive definite and $\mathcal{F}$ is given by the first $k$ principal eigenfunctions in the Mercer decomposition of $K$. We also consider the setting where $\mathcal{F}$ consists of $k$ random features from a random feature representation of $K$. It turns out that these two settings are closely related. Both our theoretical analysis and experiments confirm that conditional KRR outperforms standard KRR in these cases whenever the $\mathcal{F}$-component of the regression function is more pronounced than the residual part.

Deep Learning · Generative Models and Autoencoders

Ziang Gan, Qi Zhu, Libao Zhang

Diffusion models serve as generative priors for dataset distillation, yet existing pipelines rely on per-sample update rules that evolve each synthetic image independently, limiting their ability to optimize collective set-level objectives. We propose Set-Coupled Guidance (SCG), a plug-and-play auxiliary controller that shifts from per-image to group (IPC-at-once) sampling by injecting set-symmetric feedback at each diffusion step. SCG combines spectral set-point regulation, which aligns set-level statistics to real data via empirical characteristic function matching, with cooperative kernel coupling that stabilizes joint trajectories under noisy feedback. All computations operate on lightweight descriptors extracted from predicted clean latents, adding low overhead to the base method. We provide theoretical analysis including Lyapunov descent and input-to-state stability for distributional tracking. Experiments on ImageNette, ImageWoof, ImageNet-100 and ImageNet-1K show consistent accuracy gains across multiple diffusion-based baselines.

Deep Learning · Large Language Models

Hoyoon Byun, Youngjun Choi, Taero Kim, Sungrae Park, Kyungwoo Song

Pre-Layer Normalization (Pre-LN) is the de facto choice for large language models (LLMs) and is crucial for stable pretraining and effective transfer learning. However, Pre-LN is inefficient due to repeated statistical calculations and suffers from the curse of depth. As layers grow, the magnitude and variance of the hidden state escalate, destabilizing training. Efficiency-oriented normalization-free methods such as Dynamic Tanh (DyT) improve speed but remain fragile at depth. To jointly address stability and efficiency, we propose Bounded Hyperbolic Tanh (BHyT), a drop-in replacement for Pre-LN. BHyT couples a tanh nonlinearity with explicit, data-driven input bounding to keep activations within a non-saturating range. It prevents depth-wise growth in activation magnitude and variance and comes with a theoretical stability guarantee. For efficiency, BHyT computes exact statistics once per block and replaces a second normalization with a lightweight variance approximation, enhancing efficiency. Empirically, BHyT demonstrates improved stability and efficiency during pretraining, achieving an average of 15.8\% faster training and an average of 4.2\% higher token generation throughput compared to RMSNorm., while matching or surpassing its inference performance and robustness across language understanding and reasoning benchmarks. Our code is available at: \url{https://anonymous.4open.science/r/BHyT}

General Machine Learning · Evaluation

Sailendra Akash Bonagiri, Gerard Anderias, Saee Patil, Angelina Lai, Devang Borkar, Gezheng Kang, Ishant Gandhi, Setareh Rafatirad, Houman Homayoun

Human evaluation remains the primary standard for assessing modern AI systems, yet annotator disagreement, bias, and variability make system rankings fragile under standard majority vote aggregation. Majority vote discards annotator reliability and item-level ambiguity, often yielding unstable comparisons across annotator subsets. We introduce STABLEVAL, a disagreement-aware evaluation framework that models latent item correctness and annotator-specific confusion patterns to produce posterior expected item credit and calibrated agent-level scores. Unlike label-denoising approaches such as Dawid–Skene, STABLEVAL is explicitly designed for stable and uncertainty-aware system evaluation rather than hard label recovery. We formalize ranking stability as a first-class evaluation objective and analyze how aggregation methods preserve or distort underlying annotator behavior. Across controlled synthetic experiments and multiple real-world human-annotated benchmarks, majority vote exhibits increasing score error and ranking instability under annotator heterogeneity and adversarial noise, while STABLEVAL yields more stable and statistically grounded system rankings. These results demonstrate that modeling disagreement is essential for robust and reproducible AI evaluation.

Deep Learning · Large Language Models

Ibne Farabi Shihab, SANJEDA AKTER, Anuj Sharma

Large language models increasingly generate structured outputs, including citation-grounded summaries, multi-step reasoning chains, and tool-augmented responses, where correctness is inherently compositional: a single flawed claim can invalidate an otherwise accurate response. Existing certification methods treat outputs as atomic units, forcing a binary choice between unsafe acceptance and wasteful rejection. We introduce \textbf{Claim Graph Risk Control (CGRiC)}, a framework that decomposes responses into dependency graphs of verifiable claims and assigns calibrated per-claim risk bounds via information-lift statistics. By composing these bounds, CGRiC provides explicit guarantees on the probability that any incorrect claim passes verification undetected. When this composed risk exceeds a target threshold, the system triggers localized repairs rather than full abstention, preserving correct content while fixing problematic claims. Our approach explicitly models extraction noise and verifier imperfection, and exploits conditional independence structure for tighter certificates when validated. Empirically, CGRiC achieves target risk levels while reducing abstention by 31\% compared to atomic baselines across QA, summarization, and reasoning tasks.

Qiru Li, Ao Zhou, Zhiwei Jiang, Zifeng Cheng, Cong Wang, Yafeng Yin, Qing Gu

Vision--language models such as CLIP have shown strong zero-shot performance, but their reliability degrades in realistic multi-label settings under distribution shift. Standard test-time adaptation (TTA) methods either rely on costly gradient-based updates or adopt lightweight statistical schemes that implicitly assume label independence. The latter is particularly harmful in multi-label scenarios, where visually dominant classes suppress semantically correlated yet weaker labels, leading to severe recall loss. We revisit multi-label TTA from a Bayesian perspective and propose Bayesian Conditional Priors~(BCP) estimation, a backpropagation-free framework that injects label dependencies into CLIP's zero-shot predictions. Treating the zero-shot scores as approximate marginal posteriors, BCP derives an anchor-conditioned Bayesian refinement in which each logit is corrected by a term determined solely by the conditional prior $P(c_i=1 \mid c_a=1)$. These conditional priors are estimated online via second-order co-occurrence statistics over the test stream and instantiated as closed-form, monotonic logit transformations, without backpropagation or architectural changes. Experiments on multi-label benchmarks show that this structure-aware adaptation consistently improves mean average precision over entropy-based and retrieval-augmented TTA baselines, while incurring negligible computational overhead.