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Probabilistic Methods · Bayesian Models and Methods

Xiaoxian Zhu, Yingmeng Li, Shuangge Ma, Mengyun Wu

In modern applications such as ECG monitoring, neuroimaging, wearable sensing, and industrial equipment diagnostics, complex and continuously structured data are ubiquitous, presenting both challenges and opportunities for functional data analysis. However, existing methods face a critical trade-off: conventional functional models are limited by linearity, whereas deep learning approaches lack interpretable region selection for sparse effects. To bridge these gaps, we propose a sparse Bayesian functional deep neural network (sBayFDNN). It learns adaptive functional embeddings through a deep Bayesian architecture to capture complex nonlinear relationships, while a structured prior enables interpretable, region-wise selection of influential domains with quantified uncertainty. Theoretically, we establish rigorous approximation error bounds, posterior consistency, and region selection consistency. These results provide the first theoretical guarantees for a Bayesian deep functional model, ensuring its reliability and statistical rigor. Empirically, comprehensive simulations and real‑world studies confirm the effectiveness and superiority of sBayFDNN. Crucially, sBayFDNN excels in recognizing intricate dependencies for accurate predictions and more precisely identifies functionally meaningful regions, capabilities fundamentally beyond existing approaches.

Social Aspects · Privacy

Omri Lev, Moshe Shenfeld, Vishwak Srinivasan, Katrina Ligett, Ashia Wilson

We study differentially private ordinary least squares (DP-OLS) with bounded data $(X,Y)$ via sketching-based mechanisms. While Gaussian sketching approaches have been explored for DP-OLS \citep{sheffet2017differentially}, they are typically viewed as less competitive than the Adaptive Sufficient Statistics Perturbation (AdaSSP) method \citep{wang_adassp}, which directly perturbs the sufficient statistics $(X^{\top}X, X^{\top}Y)$ and is information theoretically optimal while also exhibiting strong empirical performance. In this work, we propose the \emph{Iterative Hessian Mixing} (IHM), an algorithm that builds on Gaussian sketching approaches to DP-OLS and is inspired by the Iterative Hessian Sketch of \citet{pilanci_hessiansketch}. We prove that IHM is differentially private and provide utility guarantees in the form of excess empirical risk bounds. These bounds improve upon those of AdaSSP by removing a multiplicative factor that can be as large as the square root of the data dimension. The design of the IHM is based on new accuracy guarantees that we present for prior Gaussian sketching approaches for DP-OLS, which clarify when these methods are expected to perform well and how IHM circumvents their inherent limitations. We also conduct a rigorous empirical evaluation on a large suite of datasets, demonstrating that IHM consistently outperforms prior baselines, including AdaSSP.

Augustinos Saravanos, Oswin So, H M Sabbir Ahmad, Chuchu Fan

We introduce *FlowOptimizer*, a deep unfolded, flow-based framework for learned iterative optimization. Motivated by the expressiveness of flow models, we represent each optimization iteration via a velocity field that operates on a population of candidate solutions, i.e., a set of parallel iterates, conditioned on contextual information including their objective values and gradients, as well as population-level statistics. The velocity field is initially trained in a simulation-free manner by matching displacements from source populations to improved target ones obtained through sampling the objective. Subsequently, we unfold this velocity field as the internal iteration of an optimization sequence, and fine-tune it in an end-to-end manner by directly optimizing objective values over a targeted class of problems. Notably, FlowOptimizer is a self-supervised framework whose training relies solely on objective evaluations without requiring knowledge of solutions. We evaluate our approach on a series of tasks from standard non-convex optimization benchmarks to real-world problems from supply chain, robotics and power grid applications. FlowOptimizer consistently outperforms well-established sampling-based/gradient-based traditional optimization and learning-to-optimize methods, often by orders of magnitude in terms of solution quality. We further highlight its ability to be trained on low-dimensional problems and successfully generalize to substantially higher-dimensional $(\times 10)$ ones.

Social Aspects · Privacy

Shuyan Zou, Shaowei Wang, Zhanxing Zhu, Jin Li, Changyu Dong, Vladimiro Sassone, Han Wu

Differentially private stochastic gradient descent (DP-SGD) achieves privacy by clipping per-sample gradients and injecting Gaussian noise, but its utility is highly sensitive to the choice of the clipping threshold $C$. A fixed $C$ often degrades performance and necessitates repeated empirical calibration. Existing adaptive clipping methods either modify the gradient update in vanilla DP-SGD, causing additional tuning or optimization overhead, or introduce separate query mechanisms to monitor gradient statistics. In contrast, we leverage the *slack* information induced by the standard clipping operation, an overlooked signal in prior work, and show that it provides an effective indication for adapting $C$. In light of this, we propose *SlaClip*, a privacy-preserving adaptive clipping strategy using a post-hoc *Slack Indicator*. Under the same training configuration, both *SlaClip*-DP-SGD and vanilla DP-SGD instantiate the identical Gaussian mechanism, and therefore incur equivalent privacy cost. Moreover, it requires minimal task-specific hyperparameter tuning and exhibits robust performance improvement across diverse datasets and model architectures.

Probabilistic Methods · Variational Inference

Bohan Wu, David Blei

Variational inference (VI) has emerged as a popular method for approximate inference for high-dimensional Bayesian models. In this paper, we propose a novel VI method that extends the naive mean field via entropic regularization, referred to as $\Xi$-variational inference ($\Xi$-VI). $\Xi$-VI has a close connection to the entropic optimal transport problem and benefits from the computationally efficient Sinkhorn algorithm. We show that $\Xi$-variational posteriors effectively recover the true posterior dependency, where the likelihood function is downweighted by a regularization parameter. We analyze the role of dimensionality of the parameter space on the accuracy of $\Xi$-variational approximation and the computational complexity of computing the approximate distribution, providing a rough characterization of the statistical-computational trade-off in $\Xi$-VI, where higher statistical accuracy requires greater computational effort. We also investigate the frequentist properties of $\Xi$-VI and establish results on consistency, asymptotic normality, high-dimensional asymptotics, and algorithmic stability. We provide sufficient criteria for our algorithm to achieve polynomial-time convergence. Finally, we show the inferential benefits of using $\Xi$-VI over mean-field VI and other competing methods, such as normalizing flow, on simulated and real datasets.

Deep Learning · Everything Else

Bin Hu, Xiancong Pan, Dongjin Yu, Tianyi Hu

Artificial intelligence has achieved remarkable breakthroughs in fields such as text, image, and video analysis, with deep learning serving as the mainstream paradigm widely adopted across applications. Trained deep learning models can be integrated into various applications either through fine-tuning or without any modification. While this practice promotes the advancement of artificial intelligence, it also raises concerns regarding intellectual property protection and information security risks. Therefore, it is necessary to propose relevant methods to measure the similarity between models. Existing code clone detection techniques are insufficient to address this issue. In this paper, we formalize deep learning models as weighted graph objects defined by both computational structure and parameter distribution. Drawing inspiration from code clone analysis, we provide the first definition of model cloning and design a method for model similarity detection. The framework characterizes model topology at the structural level based on normalized computational graphs, and at the weight level, it employs a method that does not require explicit parameter alignment to measure the statistical similarity of weight parameters. Experiments on a synthetic model clone benchmark dataset and real-world open-source models demonstrate that the proposed method can accurately detect similar models. The experimental analysis results align with the expected similarity changes during model fine-tuning and derivation processes. This method provides a unified and extensible quantitative foundation for model lineage analysis, model retrieval, and intellectual property protection of models.

Applications · Chemistry, Physics, and Earth Sciences

Zishuo Lan, Junjie Li, Lei Wang, Jincheng Wang

Autoregressive learning of time-stepping operators offers an effective approach to data-driven PDE simulation on grids. For conservation laws, however, long-horizon rollouts are often destabilized when learned updates violate global conservation and, in many applications, additional state bounds—such as nonnegative mass and densities or concentrations constrained to [0,1]. Enforcing these coupled constraints via direct next-state regression remains difficult. We introduce a framework for learning conservative transport operators on regular grids, inspired by lattice Boltzmann–style discrete-velocity transport representations. Instead of predicting the next state, the model outputs local transport operators that update cells through neighborhood exchanges, guaranteeing discrete conservation by construction. For bounded quantities, we parameterize transport within a capacity-constrained feasible set, enforcing bounds structurally rather than by post-hoc clipping. We validate FluxNet on convection-diffusion, shallow water equations, traffic flow, and spinodal decomposition. Experiments on shallow-water equations and traffic flow show improved rollout stability and physical consistency over strong baselines. On phase-field spinodal decomposition, the method enables large time-steps with long-range transport, accelerating simulation while preserving microstructure evolution in both pointwise and statistical measures.

Social Aspects · Accountability, Transparency, and Interpretability

Ariel Fargion, Lahav Dabah, Tom Tirer

Conformal Prediction (CP) has emerged as a powerful statistical framework for reliable classification, which generates a prediction set, guaranteed to include the true label with a pre-specified probability. The performance of CP methods is typically assessed by their average prediction set size. In setups where the classes can be partitioned into semantic groups, e.g., based on shared downstream actions or more interpretable coarse labels, users can benefit from prediction sets that are not only small but also contain a limited number of groups. This paper begins by addressing this problem and ultimately offers a widely applicable tool for boosting any CP method on any dataset. First, given a class partition, we propose augmenting the CP score function with a term that penalizes predictions with "out-of-group" errors. We theoretically analyze this strategy and prove its advantages for group-related metrics. Surprisingly, we show mathematically that, for common class partitions, it can also reduce the average set size of any CP score function. Our analysis reveals the class similarity factors behind this improvement and motivates us to propose a model-specific variant, which does not require any human semantic partition and can further reduce the prediction set size. Finally, we present an extensive empirical study, encompassing prominent CP methods, multiple models, and several datasets, which demonstrates that our class-similarity-based approach consistently enhances CP methods.

General Machine Learning · Evaluation

Magda Dubois, Harry Coppock, Mario Giulianelli, Ole Jorgensen, Timo Flesch, Lennart Luettgau, Cozmin Ududec

The evaluation of large language models (LLMs) is increasingly performed by other LLMs, a setup commonly known as "LLM-as-a-judge", or autograders. While autograders offer a scalable alternative to human evaluation, they are not free from biases (e.g., favouring longer outputs or generations from their own model family). Here we propose a statistical framework based on Bayesian generalised linear models (GLMs) that enables researchers to address their primary research questions (e.g., LLM capability or risk assessment), while simultaneously identifying, quantifying and mitigating various biases in their autograders. Our approach can be applied to various evaluation formats (e.g., absolute scores or pairwise preferences) and augments traditional metrics (e.g., inter-rater agreement) by providing precise uncertainty estimates and clarifying sources of disagreement between graders. This framework also enables efficient counterfactual simulations without costly re-evaluation (e.g., assessing agreement after removing systematic biases). We demonstrate these capabilities through simulated examples, with all methods available in an open-source software package. Overall, we introduce a novel framework for autograder evaluation which allows researchers to detect, quantify and correct for various biases in a systematic way.

General Machine Learning · Kernel methods

Nathan Doumèche, Francis Bach, Gérard Biau, Claire Boyer

Kernel methods are powerful tools in statistical learning, but their cubic complexity in the sample size $n$ limits their use on large-scale datasets. In this work, we introduce a scalable framework for kernel regression with complexity $O(n \log n)$, fully leveraging GPU acceleration. The approach is based on a Fourier representation of kernels combined with non-uniform fast Fourier transforms (NUFFT), enabling exact, fast, and memory-efficient computations. We instantiate our framework in three settings: Sobolev kernel regression, physics-informed regression, and additive models. When known, the proposed estimators are shown to achieve minimax convergence rates, consistent with classical kernel theory. Empirical results demonstrate that our methods can process up to tens of billions of samples within minutes, providing both statistical accuracy and computational scalability. These contributions establish a flexible approach, paving the way for the routine application of kernel methods in large-scale learning tasks, whenever the kernel norm can be efficiently expressed in the Fourier space and the ambient dimension $d$ is small.

Deep Learning · Large Language Models

Lizhang Chen, Jonathan Li, Qi Wang, Runlong Liao, Shuozhe Li, Chen Liang, Ni Lao, qiang liu

Mixture-of-Experts (MoE) models rely on balanced expert utilization to fully realize their scalability. However, existing load-balancing methods are largely heuristic and operate on mini-batch assignment statistics, introducing bias relative to population-level objectives. We propose $\phi$-balancing, a principled framework that directly targets population-level expert balance by minimizing a Schur-convex potential of the expected routing distribution. Using convex duality, we derive an equivalent min-max formulation and obtain a simple online algorithm via mirror descent, yielding an efficient EMA-based routing adjustment with negligible overhead. Across large-scale pretraining and downstream fine-tuning, $\phi$-balancing consistently outperforms prior Switch-style and loss-free baselines, demonstrating more stable and effective expert utilization.

Deep Learning · Generative Models and Autoencoders

Chengyao Yu, Hao Zeng, Youxin Zhu, Jianguo Huang, Huajun Zeng, Bingyi Jing

Large Reasoning Models (LRMs) have demonstrated remarkable performance on complex tasks but suffer from high computational costs and latency. While selective thinking strategies improve efficiency by routing easy queries to non-thinking models, existing approaches often incur uncontrollable errors, especially in online settings where the performance loss of a non-thinking model is only partially observed and data are non-stationary. To address this, we propose *Betting Probably Approximately Correct* (B-PAC) *reasoning*, a principled method that enables anytime safe and efficient online reasoning under partial feedback. Specifically, we utilize inverse propensity scoring estimators to construct test supermartingales for candidate thresholds, and then dynamically adjust the routing threshold based on the accumulated statistical evidence of safety. Theoretically, we establish the anytime-valid performance loss control and the efficiency of B-PAC reasoning. Extensive experiments demonstrate that B-PAC reasoning significantly reduces computational overhead, decreasing thinking model usage by up to 81.01\%, while controlling the performance loss below the user-specified level.

Deep Learning · Generative Models and Autoencoders

Kairan Zhao, Eleni Triantafillou, Peter Triantafillou

Generative models have been shown to "memorize" certain training data, leading to verbatim or near-verbatim generating images, which may cause privacy concerns or copyright infringement. We introduce Guidance Using Attractive-Repulsive Dynamics (GUARD), a novel framework for memorization mitigation in text-to-image diffusion models. GUARD adjusts the image denoising process to guide the generation away from an original training image and towards one that is distinct from training data while remaining aligned with the prompt, guarding against reproducing training data, without hurting image generation quality. We propose a concrete instantiation of this framework, where the positive target that we steer towards is given by a novel method for (cross) attention attenuation based on (i) a novel statistical mechanism that automatically identifies the prompt positions where cross attention must be attenuated and (ii) attenuating cross-attention in these per-prompt locations. The resulting GUARD offers a surgical, dynamic per-prompt inference-time approach that, we find, is by far the most robust method in terms of consistently producing state-of-the-art results for memorization mitigation across two architectures and for both verbatim and template memorization, while also improving upon or yielding comparable results in terms of image quality.

Reinforcement Learning · Batch/Offline

Imad AOUALI, Otmane Sakhi

Off-policy evaluation (OPE) and off-policy learning (OPL) are foundational for decision-making in offline contextual bandits. Recent advances in OPL primarily optimize OPE estimators with improved statistical properties, assuming that better estimators inherently yield superior policies. Although theoretically justified, this estimator-centric approach neglects a critical practical obstacle: challenging optimization landscapes. In this paper, we provide theoretical insights and empirical evidence showing that current OPL methods encounter severe optimization issues, particularly as the action space grows. We show that estimator-aware policy parametrization can mitigate, but not fully resolve, optimization challenges. Building on this, we explore simpler weighted log-likelihood objectives and demonstrate that they enjoy substantially better optimization properties and still recover competitive, often superior, learned policies. Our findings emphasize the necessity of explicitly addressing optimization considerations in the development of OPL algorithms for large action spaces.

Deep Learning · Large Language Models

Dawei Zhu, Rui Meng, Yale Song, Xiyu Wei, Sujian Li, Tomas Pfister, Jinsung Yoon

Despite rapid advances in autonomous AI scientists powered by language models, generating publication-ready illustrations remains a labor-intensive bottleneck in the research workflow. To lift this burden, we introduce PaperBanana, an agentic framework for automated generation of publication-ready academic illustrations. Powered by state-of-the-art VLMs and image generation models, PaperBanana orchestrates specialized agents to retrieve references, plan content and style, render images, and iteratively refine via self-critique. To rigorously evaluate our framework, we introduce PaperBananaBench, comprising 292 test cases for methodology diagrams curated from NeurIPS 2025 publications, covering diverse research domains and illustration styles. Comprehensive experiments demonstrate that PaperBanana consistently outperforms leading baselines in faithfulness, conciseness, readability, and aesthetics. We further show that our method effectively extends to the generation of high-quality statistical plots. Collectively, PaperBanana paves the way for the automated generation of publication-ready illustrations.

Probabilistic Methods · Everything Else

Meshi Bashari, Yonghoon Lee, Roy Lotan, Edgar Dobriban, Yaniv Romano

The rapid proliferation of high-quality synthetic data---generated by advanced AI models or collected as auxiliary data from related tasks---presents both opportunities and challenges for statistical inference. This paper introduces a GEneral Synthetic-Powered Inference (GESPI) framework that wraps around any statistical inference procedure to safely enhance sample efficiency by combining synthetic and real data. Our framework leverages high-quality synthetic data to boost statistical power, yet adaptively defaults to the standard method using only real data when synthetic data are of low quality. The error rate of our method remains below a user-specified bound without any distributional assumptions on the synthetic data, and decreases as the quality of the synthetic data improves. This flexibility enables seamless integration with conformal prediction, risk control, hypothesis testing, and multiple testing procedures, all without modifying the base inference method. We demonstrate the benefits of our method on challenging tasks with limited labeled data, including AlphaFold protein structure prediction, and comparing large reasoning models on complex math problems.

General Machine Learning · Unsupervised and Semi-supervised Learning

Zelei Wu, Kun Zhou, xulun ye, Jie Hong, Jieyu Zhao, Yifan Mei

In real-world Few-Shot Learning (FSL), support sets are quickly constructed and inevitably contain noisy samples. With limited examples per class, even a single noisy instance can distort class distributions, cause prototype drift, and reduce generalization. Existing methods mostly assume clean data or require large-scale statistics, which are impractical in FSL’s data-scarce setting. We find that clean samples in semantic feature space lie in low-rank subspaces, while noisy samples cause rank anomalies disrupting this structure. To address this, we propose a differentiable low-rank approximation that estimates the intrinsic rank of the support set and detects anomalous noisy samples. Building on this, a rank-guided diffusion process generates high-quality replacements under low-rank constraints, reconstructing a clean, consistent support set for improved robustness.This low-rank guided approach effectively mitigates prototype drift and significantly reduces errors under noise levels up to 40% across MiniImageNet, TieredImageNet, and other noisy benchmarks, demonstrating the power of low-rank geometry for noise detection and correction in FSL.

General Machine Learning · Kernel methods

Zhijian Zhou, Liuhua Peng, Xunye Tian, Mingming Gong, Feng Liu

Are two distributions close to each other with statistical significance? Distribution closeness testing (DCT) formalizes this question by testing whether the distance between a distribution pair is at least $\epsilon$-far. Existing DCT methods mainly measure discrepancies between a distribution pair defined on discrete spaces (e.g., using total variation), which limits their applications to complex data (e.g., images). To extend DCT to more types of data, a natural idea is to introduce maximum mean discrepancy (MMD), a powerful measurement of the distributional discrepancy between two complex distributions, into DCT scenarios. However, we find that MMD's value can be the same for many pairs of distributions that have different norms in the same reproducing kernel Hilbert space (RKHS), which potentially have different closeness levels, making MMD less informative when assessing the closeness of multiple distribution pairs. To mitigate the issue, we design a new measurement of distributional discrepancy, norm-adaptive MMD (NAMMD), which scales MMD's value using the RKHS norms of distributions. Based on the asymptotic distribution of NAMMD, we finally propose the NAMMD-based DCT to assess the closeness level of a distribution pair. Theoretically, we prove that NAMMD-based DCT has higher test power compared to MMD-based DCT, with bounded type-I error, which is also validated by extensive experiments on many types of data (e.g., synthetic noise, real images).

Deep Learning · Robustness

Ziteng Hong, Bingzhi Chen, Yishu Liu, Sudong Cai, Guangming Lu

Real-world multimodal systems inevitably face partial observability due to sensor dropout and degradation. Standard robustness methods can improve average performance, but they often remain unreliable in rare, adverse long-tail conditions. Under a locked same-support contract, we uncover a same-support tail failure where two runs with matched average performance still diverge on worst-case and shift-reweighted metrics computed on the same observable support. We attribute this instability to conditional interaction where environment coverage does not guarantee parameter exposure. Information is routed through different parameter groups, leaving some groups rarely updated even when environment coverage is complete, and tail-focused aggregation amplifies errors from these high-leverage but underexposed groups. This mismatch is auditable from gating logs, and we summarize it with TailPressure, an exposure-normalized statistic of tail-leveraged interaction. Guided by this diagnosis, we propose Heterogeneity-aware Closed-loop Exposure Stabilizer (H-CES), a controller that regulates per-group pressure via deterministic increment-branch gating and group-wise decoupled weight decay, without changing the task loss or adding inference branches. Experiments across diverse multimodal settings and backbones show that H-CES improves tail reliability under the same-support contract while preserving clean performance.

Deep Learning · Large Language Models

Guanghui Min, Tianhao Huang, Ke Wan, Chen Chen

Targeted data selection has emerged as a crucial paradigm for efficient instruction tuning, aiming to identify a small yet influential subset of training examples for a specific target task. In practice, influence is often measured through the effect of an example on parameter updates. To make selection scalable, many approaches leverage optimizer statistics (e.g., Adam states) as an axis-aligned surrogate for update geometry (i.e., diagonal precondition), implicitly treating parameters as coordinate-wise independent. We show that this assumption breaks down in parameter-efficient fine-tuning (PEFT) methods such as LoRA. In this setting, the induced optimization geometry exhibits strong cross-parameter coupling with non-trivial off-diagonal interactions, while the task-relevant update directions are confined to a low-dimensional subspace. Motivated by this mismatch, we propose **GIST** (Gradient Isometric Subspace Transformation), a simple yet principled alternative that replaces axis-aligned scaling with robust subspace alignment. **GIST** recovers a task-specific subspace from validation gradients via spectral filtering (SVD), projects training gradients into this coupled subspace, and scores examples by their alignment with target directions. Extensive experiments have demonstrated that **GIST** matches or outperforms the state-of-the-art baseline with only 0.29% of the storage and 25% of the computational time under the same selection budget. Our code is available at https://anonymous.4open.science/r/GIST-1464.