Contrary to common belief, we show that gradient ascent-based unconstrained optimization methods frequently fail to perform machine unlearning, a phenomenon we attribute to the inherent statistical dependence between the forget and retain data sets. This dependence, which can manifest itself even as simple correlations, undermines the misconception that these sets can be independently manipulated during unlearning. We provide empirical and theoretical evidence showing these methods often fail precisely due to this overlooked relationship. For random forget sets, this dependence means that degrading forget set metrics (which, for a retrained model, should mirror test set metrics) inevitably harms overall test performance. Going beyond random sets, we consider logistic regression as an instructive example where a critical failure mode emerges: inter-set dependence causes gradient descent-ascent iterations to progressively diverge from the ideal retrained model. Strikingly, these methods can converge to solutions that are not only far from the retrained ideal but are potentially even further from it than the original model itself, rendering the unlearning process actively detrimental. A toy example further illustrates how this dependence can trap models in inferior local minima, inescapable via finetuning. Our findings highlight that the presence of such statistical dependencies, even when manifest only as correlations, can be sufficient for ascent-based unlearning to fail. Our theoretical insights are corroborated by experiments on complex neural networks, demonstrating that these methods do not perform as expected in practice due to this unaddressed statistical interplay.

Abstract--In mixed-traffic environments, where autonomous vehicles (A Vs) must interact with diverse human-driven vehicles (HVs), the unpredictability of human intentions and heterogeneous driving behaviors poses significant challenges to safe and efficient lane change maneuvers. Existing methods often oversimplify these interactions by assuming uniform or fixed behavioral patterns. T o address this limitation, we propose an intention-driven lane change framework that integrates driving-style recognition with cooperation-aware decision-making and motion-planning. First, a deep learning-based classifier is developed to identify distinct human driving styles from the NGSIM dataset in real time. Second, we introduce a cooperation score composed of intrinsic and interactive components, which estimates surrounding drivers' intentions and quantifies their willingness to cooperate with the ego vehicle's lane change. Third, a decision-making module is designed by combining behavior cloning (BC) with inverse reinforcement learning (IRL) to determine whether a lane change should be initiated under current conditions. Finally, a coordinated motion-planning architecture is established, integrating IRL-based intention inference with model predictive control (MPC) to generate collision-free and socially compliant trajectories. Extensive experiments demonstrate that the proposed intention-driven BC-IRL model achieves superior performance, reaching 94.2% accuracy and 94.3% F1-score, and outperforming multiple rule-based and learning-based baselines. In particular, it improves lane change recognition by 4-15% in F1-score, highlighting the benefit of modeling inter-driver heterogeneity via intrinsic and interactive cooperation scores.

Heart rate prediction is vital for personalized health monitoring and fitness, while it frequently faces a critical challenge when deploying in real-world: data heterogeneity. We classify it in two key dimensions: source heterogeneity from fragmented device markets with varying feature sets, and user heterogeneity reflecting distinct physiological patterns across individuals and activities. Existing methods either discard device-specific information, or fail to model user-specific differences, limiting their real-world performance. To address this, we propose a framework that learns latent representations agnostic to both heterogeneity, enabling downstream predictors to work consistently under heterogeneous data patterns. Specifically, we introduce a random feature dropout strategy to handle source heterogeneity, making the model robust to various feature sets. To manage user heterogeneity, we employ a time-aware attention module to capture long-term physiological traits and use a contrastive learning objective to build a discriminative representation space. To reflect the heterogeneous nature of real-world data, we created and publicly released a new benchmark dataset, ParroTao. Evaluations on both ParroTao and the public FitRec dataset show that our model significantly outperforms existing baselines by 17% and 15%, respectively. Furthermore, analysis of the learned representations demonstrates their strong discriminative power, and one downstream application task confirm the practical value of our model.

As rich sources of history, maps provide crucial insights into historical changes, yet their diverse visual representations and limited annotated data pose significant challenges for automated processing. We propose a simple yet effective approach for few-shot segmentation of historical maps, leveraging the rich semantic embeddings of large vision foundation models combined with parameter-efficient fine-tuning. Our method outperforms the state-of-the-art on the Siegfried benchmark dataset in vineyard and railway segmentation, achieving +5% and +13% relative improvements in mIoU in 10-shot scenarios and around +20% in the more challenging 5-shot setting. Additionally, it demonstrates strong performance on the ICDAR 2021 competition dataset, attaining a mean PQ of 67.3% for building block segmentation, despite not being optimized for this shape-sensitive metric, underscoring its generalizability. Notably, our approach maintains high performance even in extremely low-data regimes (10- & 5-shot), while requiring only 689k trainable parameters - just 0.21% of the total model size. Our approach enables precise segmentation of diverse historical maps while drastically reducing the need for manual annotations, advancing automated processing and analysis in the field.

Conformal inference [Vovk et al., 2005] provides a general procedure for constructing prediction sets with guaranteed coverage, under the assumption that the data are exchangeable. This assumption, however, is often too restrictive: it typically fails in sequential or time-dependent settings such as time series forecasting, where the distribution of observations may shift over time. To address this issue, Gibbs and Cand` es [2021] introduced Adaptive Conformal Inference (ACI), which extends Conformal Prediction (CP) to adversarial environments. ACI adapts to distribution shifts by updating prediction intervals in response to observed outcomes, ensuring that the empirical coverage converges to the desired level. While effective in maintaining coverage, ACI and its extensions generally lack efficiency guarantees-for instance, there is no control over the average length of prediction intervals in adversarial regimes. In this work, we study sequential conformal inference as a repeated two-player finite game and invoke Blackwell's theory of approachability to characterize feasible objectives. Building on this perspective, we design a calibration-based algorithm that ensures asymptotic validity while achieving asymptotic efficiency under mild assumptions. Our approach relies on the notion of opportunistic approachability [Bernstein et al., 2014], which allows the learner to exploit potential restrictions in the opponent's play. We argue that such assumptions better fit the typical use cases of ACI-such as distributional drift or regime switching-than the fully adversarial setting.

Open world Machine Learning (OWML) aims to develop intelligent systems capable of recognizing known categories, rejecting unknown samples, and continually learning from novel information. Despite significant progress in open set recognition, novelty detection, and continual learning, the field still lacks a unified theoretical foundation that can quantify uncertainty, characterize information transfer, and explain learning adaptability in dynamic, nonstationary environments. This paper presents a comprehensive review of information theoretic approaches in open world machine learning, emphasizing how core concepts such as entropy, mutual information, and Kullback Leibler divergence provide a mathematical language for describing knowledge acquisition, uncertainty suppression, and risk control under open world conditions. We synthesize recent studies into three major research axes: information theoretic open set recognition enabling safe rejection of unknowns, information driven novelty discovery guiding new concept formation, and information retentive continual learning ensuring stable long term adaptation. Furthermore, we discuss theoretical connections between information theory and provable learning frameworks, including PAC Bayes bounds, open-space risk theory, and causal information flow, to establish a pathway toward provable and trustworthy open world intelligence. Finally, the review identifies key open problems and future research directions, such as the quantification of information risk, development of dynamic mutual information bounds, multimodal information fusion, and integration of information theory with causal reasoning and world model learning.

Kernel ridge regression (KRR) is a foundational tool in machine learning, with recent work emphasizing its connections to neural networks. However, existing theory primarily addresses the i.i.d. setting, while real-world data often exhibits structured dependencies - particularly in applications like denoising score learning where multiple noisy observations derive from shared underlying signals. We present the first systematic study of KRR generalization for non-i.i.d. data with signal-noise causal structure, where observations represent different noisy views of common signals. By developing a novel blockwise decomposition method that enables precise concentration analysis for dependent data, we derive excess risk bounds for KRR that explicitly depend on: (1) the kernel spectrum, (2) causal structure parameters, and (3) sampling mechanisms (including relative sample sizes for signals and noises). We further apply our results to denoising score learning, establishing generalization guarantees and providing principled guidance for sampling noisy data points. This work advances KRR theory while providing practical tools for analyzing dependent data in modern machine learning applications.

Transfer learning is a key component of modern machine learning, enhancing the performance of target tasks by leveraging diverse data sources. Simultaneously, overparameterized models such as the minimum-$\ell_2$-norm interpolator (MNI) in high-dimensional linear regression have garnered significant attention for their remarkable generalization capabilities, a property known as benign overfitting. Despite their individual importance, the intersection of transfer learning and MNI remains largely unexplored. Our research bridges this gap by proposing a novel two-step Transfer MNI approach and analyzing its trade-offs. We characterize its non-asymptotic excess risk and identify conditions under which it outperforms the target-only MNI. Our analysis reveals free-lunch covariate shift regimes, where leveraging heterogeneous data yields the benefit of knowledge transfer at limited cost. To operationalize our findings, we develop a data-driven procedure to detect informative sources and introduce an ensemble method incorporating multiple informative Transfer MNIs. Finite-sample experiments demonstrate the robustness of our methods to model and data heterogeneity, confirming their advantage.

We study nonparametric estimation of a probability mass function (PMF) on a large discrete support, where the PMF is multi-modal and heavy-tailed. The core idea is to treat the empirical PMF as a signal on a line graph and apply a data-dependent low-pass filter. Concretely, we form a symmetric tri-diagonal operator, the path graph Laplacian perturbed with a diagonal matrix built from the empirical PMF, then compute the eigenvectors, corresponding to the smallest feq eigenvalues. Projecting the empirical PMF onto this low dimensional subspace produces a smooth, multi-modal estimate that preserves coarse structure while suppressing noise. A light post-processing step of clipping and re-normalizing yields a valid PMF. Because we compute the eigenpairs of a symmetric tridiagonal matrix, the computation is reliable and runs time and memory proportional to the support times the dimension of the desired low-dimensional supspace. We also provide a practical, data-driven rule for selecting the dimension based on an orthogonal-series risk estimate, so the method "just works" with minimal tuning. On synthetic and real heavy-tailed examples, the approach preserves coarse structure while suppressing sampling noise, compares favorably to logspline and Gaussian-KDE baselines in the intended regimes. However, it has known failure modes (e.g., abrupt discontinuities). The method is short to implement, robust across sample sizes, and suitable for automated pipelines and exploratory analysis at scale because of its reliability and speed.

Kernel Stein discrepancies (KSDs) have emerged as a powerful tool for quantifying goodness-of-fit over the last decade, featuring numerous successful applications. To the best of our knowledge, all existing KSD estimators with known rate achieve $\sqrt n$-convergence. In this work, we present two complementary results (with different proof strategies), establishing that the minimax lower bound of KSD estimation is $n^{-1/2}$ and settling the optimality of these estimators. Our first result focuses on KSD estimation on $\mathbb R^d$ with the Langevin-Stein operator; our explicit constant for the Gaussian kernel indicates that the difficulty of KSD estimation may increase exponentially with the dimensionality $d$. Our second result settles the minimax lower bound for KSD estimation on general domains.