Hanwen Zhang

Hanwen Zhang, Vladimir Rokhlin

We present a scheme for finding all roots of an analytic function in a square domain in the complex plane. The scheme can be viewed as a generalization of the classical approach to finding roots of a function on the real line, by first approximating it by a polynomial in the Chebyshev basis, followed by diagonalizing the so-called ''colleague matrices''. Our extension of the classical approach is based on several observations that enable the construction of polynomial bases in compact domains that satisfy three-term recurrences and are reasonably well-conditioned. This class of polynomial bases gives rise to ''generalized colleague matrices'', whose eigenvalues are roots of functions expressed in these bases. In this paper, we also introduce a special-purpose QR algorithm for finding the eigenvalues of generalized colleague matrices, which is a straightforward extension of the recently introduced componentwise stable QR algorithm for the classical cases (See [Serkh]). The performance of the schemes is illustrated with several numerical examples.

Nairen Cao, Vincent Cohen-Addad, Euiwoong Lee et al.

Correlation clustering is a well-studied problem, first proposed by Bansal, Blum, and Chawla [Mach. Learn. '04]. The input is an unweighted, undirected graph. The problem is to cluster the vertices so as to minimize the number of edges between vertices in different clusters and missing edges between vertices inside the same cluster. This problem has a wide application in data mining and machine learning. We introduce a general framework that transforms existing static correlation clustering algorithms into fully-dynamic ones that work against an adaptive adversary. We show how to apply our framework to known efficient correlation clustering algorithms, starting from the classic 3-approximate Pivot algorithm from Ailon, Charikar and Newman [JACM'08]. Applied to the most recent sublinear $1.485$-approximation algorithm from Cao, Cohen-Addad, Lee, Li, Lolck, Newman, Thorup, Vogl, Yan and Zhang [STOC'25], we get a $1.485$-approximation fully-dynamic algorithm that works with worst-case constant update time. The original static algorithm gets its approximation factor with constant probability, and we get the same against an adaptive adversary in the sense that for any given update step, not known to our algorithm, our solution is a $1.485$-approximation with constant probability when we reach this update. Most of previous dynamic algorithms, including the celebrated result from Behnezhad, Charikar, Ma and Tan [FOCS'19], had approximation factors around $3$ in expectation, and they could only handle an oblivious adversary. A recent algorithm by Braverman, Dharangutte, Pai, Shah, and Wang [AISTATS'25] could handle an adaptive adversary, but it has a large unspecified constant approximation ratio. This contrasts with our general transformation, which works with all the best approximation factors known for the static case.

Yufei Ma, Hanwen Zhang, Qiya Yang et al.

In multi-center scenarios, One-Shot Federated Learning (OSFL) has attracted increasing attention due to its low communication overhead, requiring only a single round of transmission. However, existing generative model-based OSFL methods suffer from low training efficiency and potential privacy leakage in the healthcare domain. Additionally, achieving convergence within a single round of model aggregation is challenging under non-Independent and Identically Distributed (non-IID) data. To address these challenges, in this paper a modified OSFL framework is proposed, in which a new Feature-Guided Rectified Flow Model (FG-RF) and Dual-Layer Knowledge Distillation (DLKD) aggregation method are developed. FG-RF on the client side accelerates generative modeling in medical imaging scenarios while preserving privacy by synthesizing feature-level images rather than pixel-level images. To handle non-IID distributions, DLKD enables the global student model to simultaneously mimic the output logits and align the intermediate-layer features of client-side teacher models during aggregation. Experimental results on three non-IID medical imaging datasets show that our new framework and method outperform multi-round federated learning approaches, achieving up to 21.73% improvement, and exceeds the baseline FedISCA by an average of 21.75%. Furthermore, our experiments demonstrate that feature-level synthetic images significantly reduce privacy leakage risks compared to pixel-level synthetic images. The code is available at https://github.com/LMIAPC/one-shot-fl-medical.

Kun Fang, Hanwen Zhang, Ziyu Wang et al.

Piano sustain pedal detection has previously been approached as a binary on/off classification task, limiting its application in real-world piano performance scenarios where pedal depth significantly influences musical expression. This paper presents a novel approach for high-resolution estimation that predicts continuous pedal depth values. We introduce a Transformer-based architecture that not only matches state-of-the-art performance on the traditional binary classification task but also achieves high accuracy in continuous pedal depth estimation. Furthermore, by estimating continuous values, our model provides musically meaningful predictions for sustain pedal usage, whereas baseline models struggle to capture such nuanced expressions with their binary detection approach. Additionally, this paper investigates the influence of room acoustics on sustain pedal estimation using a synthetic dataset that includes varied acoustic conditions. We train our model with different combinations of room settings and test it in an unseen new environment using a "leave-one-out" approach. Our findings show that the two baseline models and ours are not robust to unseen room conditions. Statistical analysis further confirms that reverberation influences model predictions and introduces an overestimation bias.

Rasmus Pagh, Lukas Retschmeier, Hao Wu et al.

We study the problem of privately releasing an approximate minimum spanning tree (MST). Given a graph $G = (V, E, \vec{W})$ where $V$ is a set of $n$ vertices, $E$ is a set of $m$ undirected edges, and $ \vec{W} \in \mathbb{R}^{|E|} $ is an edge-weight vector, our goal is to publish an approximate MST under edge-weight differential privacy, as introduced by Sealfon in PODS 2016, where $V$ and $E$ are considered public and the weight vector is private. Our neighboring relation is $\ell_\infty$-distance on weights: for a sensitivity parameter $Δ_\infty$, graphs $ G = (V, E, \vec{W}) $ and $ G' = (V, E, \vec{W}') $ are neighboring if $\|\vec{W}-\vec{W}'\|_\infty \leq Δ_\infty$. Existing private MST algorithms face a trade-off, sacrificing either computational efficiency or accuracy. We show that it is possible to get the best of both worlds: With a suitable random perturbation of the input that does not suffice to make the weight vector private, the result of any non-private MST algorithm will be private and achieves a state-of-the-art error guarantee. Furthermore, by establishing a connection to Private Top-k Selection [Steinke and Ullman, FOCS '17], we give the first privacy-utility trade-off lower bound for MST under approximate differential privacy, demonstrating that the error magnitude, $\tilde{O}(n^{3/2})$, is optimal up to logarithmic factors. That is, our approach matches the time complexity of any non-private MST algorithm and at the same time achieves optimal error. We complement our theoretical treatment with experiments that confirm the practicality of our approach.