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Theory · Learning Theory

Shinsaku Sakaue, Taira Tsuchiya, Han Bao, Taihei Oki

In online inverse linear optimization, a learner observes time-varying sets of feasible actions and an agent's optimal actions, selected by solving linear optimization over the feasible actions. The learner sequentially makes predictions of the agent's true linear objective function, and their quality is measured by the *regret*, the cumulative gap between optimal objective values and those achieved by following the learner's predictions. A seminal work by Bärmann et al. (2017) obtained a regret bound of $O(\sqrt{T})$, where $T$ is the time horizon. Subsequently, the regret bound has been improved to $O(n^4 \ln T)$ by Besbes et al. (2021, 2025) and to $O(n \ln T)$ by Gollapudi et al. (2021), where $n$ is the dimension of the ambient space of objective vectors. However, these logarithmic-regret methods are highly inefficient when $T$ is large, as they need to maintain regions specified by $O(T)$ constraints, which represent possible locations of the true objective vector. In this paper, we present the first logarithmic-regret method whose per-round complexity is independent of $T$; indeed, it achieves the best-known bound of $O(n \ln T)$. Our method is strikingly simple: it applies the online Newton step (ONS) to appropriate exp-concave loss functions. Moreover, for the case where the agent's actions are possibly suboptimal, we establish a regret bound of $O(n\ln T + \sqrt{\Delta_T n\ln T})$, where $\Delta_T$ is the cumulative suboptimality of the agent's actions. This bound is achieved by using MetaGrad, which runs ONS with $\Theta(\ln T)$ different learning rates in parallel. We also present a lower bound of $\Omega(n)$, showing that the $O(n\ln T)$ bound is tight up to an $O(\ln T)$ factor.

General Machine Learning · Representation Learning

Binh Vu, Jan Kapar, Marvin Wright, David Watson

We propose a principled method for autoencoding with random forests. Our strategy builds on foundational results from nonparametric statistics and spectral graph theory to learn a low-dimensional embedding of the model that optimally represents relationships in the data. We provide exact and approximate solutions to the decoding problem via constrained optimization, split relabeling, and nearest neighbors regression. These methods effectively invert the compression pipeline, establishing a map from the embedding space back to the input space using splits learned by the ensemble's constituent trees. The resulting decoders are universally consistent under common regularity assumptions. The procedure works with supervised or unsupervised models, providing a window into conditional or joint distributions. We demonstrate various applications of this autoencoder, including powerful new tools for visualization, compression, clustering, and denoising. Experiments illustrate the ease and utility of our method in a wide range of settings, including tabular, image, and genomic data.

General Machine Learning · Transfer, Multitask and Meta-learning

Faisal Hamman, Pasan Dissanayake, Yanjun Fu, Sanghamitra Dutta

Knowledge distillation is a promising approach to transfer capabilities from complex teacher models to smaller, resource-efficient student models that can be deployed easily, particularly in task-aware scenarios. However, existing methods of task-aware distillation typically require substantial quantities of data which may be unavailable or expensive to obtain in many practical scenarios. In this paper, we address this challenge by introducing a novel strategy called **Co**unterfactual-explanation-infused **D**istillation CoD for *few-shot task-aware knowledge distillation by systematically infusing counterfactual explanations*. Counterfactual explanations (CFEs) refer to inputs that can flip the output prediction of the teacher model with minimum perturbation. Our strategy CoD leverages these CFEs to precisely map the teacher's decision boundary with significantly fewer samples. We provide theoretical guarantees for motivating the role of CFEs in distillation, from both statistical and geometric perspectives. We mathematically show that CFEs can improve parameter estimation by providing more informative examples near the teacher’s decision boundary. We also derive geometric insights on how CFEs effectively act as knowledge probes, helping the students mimic the teacher's decision boundaries more effectively than standard data. We perform experiments across various datasets and LLMs to show that CoD outperforms standard distillation approaches in few-shot regimes (as low as 8 - 512 samples). Notably, CoD only uses half of the original samples used by the baselines, paired with their corresponding CFEs and still improves performance.

Social Aspects · Privacy-preserving Statistics and Machine Learning

Qiangqiang Zhang, Chenfei Gu, Xinwei Feng, Jinhan Xie, Ting Li

We propose an online conformal prediction framework under local differential privacy to address the emerging challenge of privacy-preserving uncertainty quantification in streaming data environments. Our method constructs dynamic, model-free prediction sets based on randomized binary inquiries, ensuring rigorous privacy protection without requiring access to raw data. Importantly, the proposed algorithm can be conducted in a one-pass online manner, leading to high computational efficiency and minimal storage requirements with $\mathcal{O}(1)$ space complexity, making it particularly suitable for real-time applications. The proposed framework is also broadly applicable to both regression and classification tasks, adapting flexibly to diverse predictive settings. We establish theoretical guarantees for long-run coverage at a target confidence level, ensuring statistical reliability under strict privacy constraints. Extensive empirical evaluations on both simulated and real-world datasets demonstrate that the proposed method delivers accurate, stable, and privacy-preserving predictions across a range of dynamic environments.

Applications · Genetics, Cell Biology, etc

Yuhao Sun, Zhenyi Zhang, Zihan Wang, Tiejun Li, Peijie Zhou

Recovering the dynamics from a few snapshots of a high-dimensional system is a challenging task in statistical physics and machine learning, with important applications in computational biology. Many algorithms have been developed to tackle this problem, based on frameworks such as optimal transport and the Schrödinger bridge. A notable recent framework is Regularized Unbalanced Optimal Transport (RUOT), which integrates both stochastic dynamics and unnormalized distributions. However, since many existing methods do not explicitly enforce optimality conditions, their solutions often struggle to satisfy the principle of least action and meet challenges to converge in a stable and reliable way. To address these issues, we propose Variational RUOT (Var-RUOT), a new framework to solve the RUOT problem. By incorporating the optimal necessary conditions for the RUOT problem into both the parameterization of the search space and the loss function design, Var-RUOT only needs to learn a scalar field to solve the RUOT problem and can search for solutions with lower action. We also examined the challenge of selecting a growth penalty function in the widely used Wasserstein-Fisher-Rao metric and proposed a solution that better aligns with biological priors in Var-RUOT. We validated the effectiveness of Var-RUOT on both simulated data and real single-cell datasets. Compared with existing algorithms, Var-RUOT can find solutions with lower action while exhibiting faster convergence and improved training stability. Our code is available at https://github.com/ZerooVector/VarRUOT.

Social Aspects · Privacy-preserving Statistics and Machine Learning

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

Gaussian sketching, which consists of pre-multiplying the data with a random Gaussian matrix, is a widely used technique in data science and machine learning. Beyond computational benefits, this operation also provides differential privacy guarantees due to its inherent randomness. In this work, we revisit this operation through the lens of \Renyi Differential Privacy (RDP), providing a refined privacy analysis that yields significantly tighter bounds than prior results. We then demonstrate how this improved analysis leads to performance improvement in different linear regression settings, establishing theoretical utility guarantees. Empirically, our methods improve performance across multiple datasets and, in several cases, reduce runtime.

Social Aspects · Privacy-preserving Statistics and Machine Learning

Atefeh Gilani, Naima Tasnim, Lalitha Sankar, Oliver Kosut

Differentially private stochastic gradient descent (DP-SGD) is the most widely used method for training machine learning models with provable privacy guarantees. A key challenge in DP-SGD is setting the per-sample gradient clipping threshold, which significantly affects the trade-off between privacy and utility. While recent adaptive methods improve performance by adjusting this threshold during training, they operate in the standard coordinate system and fail to account for correlations across the coordinates of the gradient. We propose GeoClip, a geometry-aware framework that clips and perturbs gradients in a transformed basis aligned with the geometry of the gradient distribution. GeoClip adaptively estimates this transformation using only previously released noisy gradients, incurring no additional privacy cost. We provide convergence guarantees for GeoClip and derive a closed-form solution for the optimal transformation that minimizes the amount of noise added while keeping the probability of gradient clipping under control. Experiments on both tabular and image datasets demonstrate that GeoClip consistently outperforms existing adaptive clipping methods under the same privacy budget.

Social Aspects · Privacy-preserving Statistics and Machine Learning

Zhao Song, Jianfei Xue, Lichen Zhang

In this paper, we study differentially private mechanisms for functions whose outputs lie in a Euclidean Jordan algebra. Euclidean Jordan algebras capture many important mathematical structures and form the foundation of linear programming, second-order cone programming, and semidefinite programming. Our main contribution is a generic Gaussian mechanism for such functions, with sensitivity measured in $\ell_2$, $\ell_1$, and $\ell_\infty$ norms. Notably, this framework includes the important case where the function outputs are symmetric matrices, and sensitivity is measured in the Frobenius, nuclear, or spectral norm. We further derive private algorithms for solving symmetric cone programs under various settings, using a combination of the multiplicative weights update method and our generic Gaussian mechanism. As an application, we present differentially private algorithms for semidefinite programming, resolving a major open question posed by [Hsu, Roth, Roughgarden, and Ullman, ICALP 2014].

Theory · Everything Else

Yaroslav Mukhin

The influence function (IF) of a statistical functional is the Riesz representer of its derivative, also known as its first variation and Fisher-Rao gradient. It is a key object for numerical optimization over probability measures, semiparametric efficiency theory, standard constructions of efficient estimators, and an arsenal of inference methods for these estimators. Yet, deriving the IF analytically is often an obstruction for practitioners. To automate this task, we develop a novel spectral representation of the IF that lends itself to a low-rank functional estimator in a reproducing kernel Hilbert space (rkHs). Our estimator (i) does not require analytic derivations by the user, (ii) relies on kernel Principal Component Analysis and numerical pathwise derivatives along these components. We present the derivation of the representation and prove consistency of the low-rank rkHs estimator.

Social Aspects · Trustworthy Machine Learning

Andre Kassis, Urs Hengartner, Yaoliang Yu

Diffusion-based purification (DBP) has become a cornerstone defense against adversarial examples (AEs), regarded as robust due to its use of diffusion models (DMs) that project AEs onto the natural data manifold. We refute this core claim, theoretically proving that gradient-based attacks effectively target the DM rather than the classifier, causing DBP's outputs to align with adversarial distributions. This prompts a reassessment of DBP's robustness, accrediting it two critical factors: inaccurate gradients and improper evaluation protocols that test only a single random purification of the AE. We show that when accounting for stochasticity and resubmission risk, DBP collapses. To support this, we introduce DiffBreak, the first reliable toolkit for differentiation through DBP, eliminating gradient mismatches that previously further inflated robustness estimates. We also analyze the current defense scheme used for DBP where classification relies on a single purification, pinpointing its inherent invalidity. We provide a statistically grounded majority-vote (MV) alternative that aggregates predictions across multiple purified copies, showing partial but meaningful robustness gain. We then propose a novel adaptation of an optimization method against deepfake watermarking, crafting systemic perturbations that defeat DBP even under MV, challenging DBP's viability.

General Machine Learning · Causality

William Roy Orchard, Nastaran Okati, Sergio Garrido Mejia, Patrick Blöbaum, Dominik Janzing

The goal of Root Cause Analysis (RCA) is to explain why an anomaly occurred by identifying where the fault originated. Several recent works model the anomalous event as resulting from a change in the causal mechanism at the root cause, i.e., as a soft intervention. RCA is then the task of identifying which causal mechanism changed. In real-world applications, one often has either few or only a single sample from the post-intervention distribution: a severe limitation for most methods, which assume one knows or can estimate the distribution. However, even those that do not are statistically ill-posed due to the need to probe regression models in regions of low probability density. In this paper, we propose simple, efficient methods to overcome both difficulties in the case where there is a single root cause and the causal graph is a polytree. When one knows the causal graph, we give guarantees for a traversal algorithm that requires only marginal anomaly scores and does not depend on specifying an arbitrary anomaly score cut-off. When one does not know the causal graph, we show that the heuristic of identifying root causes as the variables with the highest marginal anomaly scores is causally justified. To this end, we prove that anomalies with small scores are unlikely to cause those with larger scores in polytrees and give upper bounds for the likelihood of causal pathways with non-monotonic anomaly scores.

Data-centric AI · Everything Else

Liuhao Lin, Ke Li, Zihan Xu, Yuchen Shi, Yulei Qin, Yan Zhang, Xing Sun, Rongrong Ji

Current evaluation paradigms for large language models (LLMs) represent a critical blind spot in AI research—relying on opaque numerical metrics that conceal fundamental limitations in spatial reasoning while providing no intuitive understanding of model capabilities. This deficiency creates a dangerous disconnect between reported performance and practical abilities, particularly for applications requiring physical world understanding. We introduce LTD-Bench, a breakthrough benchmark that transforms LLM evaluation from abstract scores to directly observable visual outputs by requiring models to generate drawings through dot matrices or executable code. This approach makes spatial reasoning limitations immediately apparent even to non-experts, bridging the fundamental gap between statistical performance and intuitive assessment. LTD-Bench implements a comprehensive methodology with complementary generation tasks (testing spatial imagination) and recognition tasks (assessing spatial perception) across three progressively challenging difficulty levels, methodically evaluating both directions of the critical language-spatial mapping. Our extensive experiments with state-of-the-art models expose an alarming capability gap: even LLMs achieving impressive results on traditional benchmarks demonstrate profound deficiencies in establishing bidirectional mappings between language and spatial concepts—a fundamental limitation that undermines their potential as genuine world models. Furthermore, LTD-Bench's visual outputs enable powerful diagnostic analysis, offering a potential approach to investigate model similarity. Our dataset and codes are available at https://github.com/walktaster/LTD-Bench.

Theory · Learning Theory

Fares El Khoury, Edouard Pauwels, Samuel Vaiter, Michael Arbel

Bilevel optimization has emerged as a technique for addressing a wide range of machine learning problems that involve an outer objective implicitly determined by the minimizer of an inner problem. While prior works have primarily focused on the parametric setting, a learning-theoretic foundation for bilevel optimization in the nonparametric case remains relatively unexplored. In this paper, we take a first step toward bridging this gap by studying Kernel Bilevel Optimization (KBO), where the inner objective is optimized over a reproducing kernel Hilbert space. This setting enables rich function approximation while providing a foundation for rigorous theoretical analysis. In this context, we derive novel finite-sample generalization bounds for KBO, leveraging tools from empirical process theory. These bounds further allow us to assess the statistical accuracy of gradient-based methods applied to the empirical discretization of KBO. We numerically illustrate our theoretical findings on a synthetic instrumental variable regression task.

Probabilistic Methods

Hongyu Shen, Zhizhen Jane Zhao

Recent advances in false discovery rate (FDR)-controlled feature selection methods have improved reliability by effectively limiting false positives, making them well-suited for complex applications. A popular FDR-controlled framework called data splitting uses the "mirror statistics" to select features. However, we find that the unit variance assumption on mirror statistics could potentially limit the feature selection power. To address this, we generalize the mirror statistics in the Gaussian mirror framework and introduce a new approach called "generalized Gaussian mirror" ($\text{G}^2\text{M}$), which adaptively learns the variance and forms new test statistics. We demonstrate both theoretically and empirically that the proposed test statistics achieve higher power than those of Gaussian mirror and data splitting. Comparisons with other FDR-controlled frameworks on synthetic, semi-synthetic, and real datasets highlight the superior performance of the $\text{G}^2\text{M}$ method in achieving higher power while maintaining FDR control. These findings suggest the potential for the $\text{G}^2\text{M}$ method for practical applications in real-world problems. Code is available in https://github.com/skyve2012/G2M.

Probabilistic Methods · Monte Carlo and Sampling Methods

Kijung Jeon, Michael Muehlebach, Molei Tao

Sampling from constrained statistical distributions is a fundamental task in various fields including Bayesian statistics, computational chemistry, and statistical physics. This article considers the cases where the constrained distribution is described by an unconstrained density, as well as additional equality and/or inequality constraints, which often make the constraint set nonconvex. Existing methods for nonconvex constraint set $\Sigma \subset \mathbb{R}^d$ defined by equality or inequality constraints commonly rely on costly projection steps. Moreover, they cannot handle equality and inequality constraints simultaneously as each method only specialized in one case. In addition, rigorous and quantitative convergence guarantee is often lacking. In this paper, we introduce Overdamped Langevin with LAnding (OLLA), a new framework that can design overdamped Langevin dynamics accommodating both equality and inequality constraints. The proposed dynamics also deterministically corrects trajectories along the normal direction of the constraint surface, thus obviating the need for explicit projections. We show that, under suitable regularity conditions on the target density and $\Sigma$, OLLA converges exponentially fast in $W_2$ distance to the constrained target density $\rho_\Sigma(x) \propto \exp(-f(x))d\sigma_\Sigma$. Lastly, through experiments, we demonstrate the efficiency of OLLA compared to projection-based constrained Langevin algorithms and their slack variable variants, highlighting its favorable computational cost and reasonable empirical mixing.

Social Aspects · Privacy-preserving Statistics and Machine Learning

Yijun Quan, Zushu Li, Giovanni Montana

Growing data privacy demands, driven by regulations like GDPR and CCPA, require machine unlearning methods capable of swiftly removing the influence of specific training points. Although verified approaches like SISA, using data slicing and checkpointing, achieve efficient unlearning for single models by reverting to intermediate states, these methods struggle in teacher-student knowledge distillation settings. Unlearning in the teacher typically forces costly, complete student retraining due to pervasive information propagation during distillation. Our primary contribution is PURGE (Partitioned Unlearning with Retraining Guarantee for Ensembles), a novel framework integrating verified unlearning with distillation. We introduce constituent mapping and an incremental multi-teacher strategy that partitions the distillation process, confines each teacher constituent’s impact to distinct student data subsets, and crucially maintains data isolation. The PURGE framework substantially reduces retraining overhead—requiring only partial student updates—when teacher-side unlearning occurs. We provide both theoretical analysis, quantifying significant speed-ups in the unlearning process, and empirical validation on multiple datasets, demonstrating that PURGE achieves these efficiency gains while maintaining student accuracy comparable to standard baselines.

Theory · Reinforcement Learning and Planning

Imad Aouali

Efficient online decision-making in contextual bandits is challenging, as methods without informative priors often suffer from computational or statistical inefficiencies. In this work, we leverage pre-trained diffusion models as expressive priors to capture complex action dependencies and develop a practical algorithm that efficiently approximates posteriors under such priors, enabling both fast updates and sampling. Empirical results demonstrate the effectiveness and versatility of our approach across diverse contextual bandit settings.

Theory · Learning Theory

Jingqiu Ding, Yiding Hua, Lucas Slot, David Steurer

We investigate implications of the (extended) low-degree conjecture (recently formalized in [moitra et al2023]) in the context of the symmetric stochastic block model. Assuming the conjecture holds, we establish that no polynomial-time algorithm can weakly recover community labels below the Kesten-Stigum (KS) threshold. In particular, we rule out polynomial-time estimators that, with constant probability, achieve $n^{-0.49}$ correlation with the true communities. Whereas, above the KS threshold, polynomial-time algorithms are known to achieve constant correlation with the true communities with high probability [massoulie et al 2014,abbe et al 2015]. To our knowledge, we provide the first rigorous evidence for such sharp transition in recovery rate for polynomial-time algorithms at the KS threshold. Notably, under a stronger version of the low-degree conjecture, our lower bound remains valid even when the number of blocks diverges. Furthermore, our results provide evidence of a computational-to-statistical gap in learning the parameters of stochastic block models. In contrast, prior work either (i) rules out polynomial-time algorithms with $1 - o(1)$ success probability [Hopkins 18, bandeira et al 2021] under the low-degree conjecture, or (ii) degree-$\text{poly}(k)$ polynomials for learning the stochastic block model [Luo et al 2023]. For this, we design a hypothesis test which succeeeds with constant probability under symmetric stochastic block model, and $1-o(1)$ probability under the distribution of \Erdos \Renyi random graphs. Our proof combines low-degree lower bounds from [Hopkins 18, bandeira et al 2021] with graph splitting and cross-validation techniques. In order to rule out general recovery algorithms, we employ the correlation preserving projection method developed in [Hopkins et al 17].

Deep Learning · Algorithms

Sana Ayromlou, David B. Emerson

Federated learning (FL) is an effective and widely used approach to training deep learning models on decentralized datasets held by distinct clients. FL also strengthens both security and privacy protections for training data. Common challenges associated with statistical heterogeneity between distributed datasets have spurred significant interest in personalized FL (pFL) methods, where models combine aspects of global learning with local modeling specific to each client’s unique characteristics. This work investigates the efficacy of theoretically supported, adaptive MMD measures in pFL, primarily focusing on the Ditto framework, a state-of-the-art technique for distributed data heterogeneity. The use of such measures significantly improves model performance across a variety of tasks, especially those with pronounced feature heterogeneity. Additional experiments demonstrate that such measures are directly applicable to other pFL techniques and yield similar improvements across a number of datasets. Finally, the results motivate the use of constraints tailored to the various kinds of heterogeneity expected in FL systems.

Computer Vision · Everything Else

Zenghao Guan, Yucan Zhou, Wu Liu, Xiaoyan Gu

Test-time adaptation (TTA) for Vision-Language Models (VLMs) aims to enhance performance on unseen test data. However, existing methods struggle to achieve robust and continuous knowledge accumulation during test time. To address this, we propose Statistics Caching test-time Adaptation (SCA), a novel cache-based approach. Unlike traditional feature-caching methods prone to forgetting, SCA continuously accumulates task-specific knowledge from all encountered test samples. By formulating the reuse of past features as a least squares problem, SCA avoids storing raw features and instead maintains compact, incrementally updated feature statistics. This design enables efficient online adaptation without the limitations of fixed-size caches, ensuring that the accumulated knowledge grows persistently over time. Furthermore, we introduce adaptive strategies that leverage the VLM's prediction uncertainty to reduce the impact of noisy pseudo-labels and dynamically balance multiple prediction sources, leading to more robust and reliable performance. Extensive experiments demonstrate that SCA achieves compelling performance while maintaining competitive computational efficiency.