The performance of the proposed algorithm isevaluated on awide variety of machine learning tasks.

We adopt the natural assumption that the empirical NTK develops a block structure aligned with the class labels, i.e., samples within the same class have stronger

Adaptability has been regarded as a central feature in the foundation models, enabling them to effectively acclimate to unseen downstream tasks. Parameter-efficient fine-tuning methods such as celebrated LoRA facilitate efficient adaptation of large foundation models using labeled, high-quality and generally scarce task data. To mitigate data scarcity in fine-tuning of foundation models, we propose to leverage task similarity across multiple downstream users. Intuitively, users with similar tasks must be able to assist each other in boosting the effective fine-tuning data size. We propose Collaborative Low-Rank Adaptation, or CoLoRA, which exploits task similarity to collaboratively and efficiently fine-tune personalized foundation models. The main idea in CoLoRA is to train one shared adapter capturing underlying task similarities across all tasks, and personalized adapters tailored to user-specific tasks. We theoretically study CoLoRA on heterogeneous linear regression and provide provable guarantees for ground truth recovery. We also conduct several natural language experiments with varying task similarity, which further demonstrate that when trained together with similar tasks, individual performances are significantly boosted.

Decision tree ensembles are widely used in critical domains, making robustness and sensitivity analysis essential to their trustworthiness. We study the feature sensitivity problem, which asks whether an ensemble is sensitive to a specified subset of features -- such as protected attributes -- whose manipulation can alter model predictions. Existing approaches often yield examples of sensitivity that lie far from the training distribution, limiting their interpretability and practical value. We propose a data-aware sensitivity framework that constrains the sensitive examples to remain close to the dataset, thereby producing realistic and interpretable evidence of model weaknesses. To this end, we develop novel techniques for data-aware search using a combination of mixed-integer linear programming (MILP) and satisfiability modulo theories (SMT) encodings. Our contributions are fourfold. First, we strengthen the NP-hardness result for sensitivity verification, showing it holds even for trees of depth 1. Second, we develop MILP-optimizations that significantly speed up sensitivity verification for single ensembles and for the first time can also handle multiclass tree ensembles. Third, we introduce a data-aware framework generating realistic examples close to the training distribution. Finally, we conduct an extensive experimental evaluation on large tree ensembles, demonstrating scalability to ensembles with up to 800 trees of depth 8, achieving substantial improvements over the state of the art. This framework provides a practical foundation for analyzing the reliability and fairness of tree-based models in high-stakes applications.

We study the problem of offline changepoint localization in a distribution-free setting. One observes a vector of data with a single changepoint, assuming that the data before and after the changepoint are iid (or more generally exchangeable) from arbitrary and unknown distributions. The goal is to produce a finite-sample confidence set for the index at which the change occurs without making any other assumptions. Existing methods often rely on parametric assumptions, tail conditions, or asymptotic approximations, or only produce point estimates. In contrast, our distribution-free algorithm, CONformal CHangepoint localization (CONCH), only leverages exchangeability arguments to construct confidence sets with finite sample coverage. By proving a conformal Neyman-Pearson lemma, we derive principled score functions that yield informative (small) sets. Moreover, with such score functions, the normalized length of the confidence set shrinks to zero under weak assumptions. We also establish a universality result showing that any distribution-free changepoint localization method must be an instance of CONCH. Experiments suggest that CONCH delivers precise confidence sets even in challenging settings involving images or text.

The dynamics of gradient-based training in neural networks often exhibit nontrivial structures; hence, understanding them remains a central challenge in theoretical machine learning. In particular, a concept of feature unlearning, in which a neural network progressively loses previously learned features over long training, has gained attention. In this study, we consider the infinite-width limit of a two-layer neural network updated with a large-batch stochastic gradient, then derive differential equations with different time scales, revealing the mechanism and conditions for feature unlearning to occur. Specifically, we utilize the fast-slow dynamics: while an alignment of first-layer weights develops rapidly, the second-layer weights develop slowly. The direction of a flow on a critical manifold, determined by the slow dynamics, decides whether feature unlearning occurs. We give numerical validation of the result, and derive theoretical grounding and scaling laws of the feature unlearning. Our results yield the following insights: (i) the strength of the primary nonlinear term in data induces the feature unlearning, and (ii) an initial scale of the second-layer weights mitigates the feature unlearning.

Two-sample testing, where we aim to determine whether two distributions are equal or not equal based on samples from each one, is challenging if we cannot place assumptions on the properties of the two distributions. In particular, certifying equality of distributions, or even providing a tight upper bound on the total variation (TV) distance between the distributions, is impossible to achieve in a distribution-free regime. In this work, we examine the blurred TV distance, a relaxation of TV distance that enables us to perform inference without assumptions on the distributions. We provide theoretical guarantees for distribution-free upper and lower bounds on the blurred TV distance, and examine its properties in high dimensions.