arXiv subjects

Jiahao Tan

Publications and source records attributed to Jiahao Tan.

3 recordsLinked to original sources

arXiv2026

Maximal estimates for perturbations of the Schr\"odinger operator on $\mathbb{T}^d$

We study $L^p_x L^\infty_t$ maximal estimates for exponential sums associated to $C^2$ graph hypersurfaces, motivated by Schr\"odinger maximal estimates on $\mathbb{T}^d$. We show that the conjectured maximal estimate for the periodic Schr\"odinger equation fails when one allows small perturbations of the paraboloid, which can be viewed as a higher-dimensional extension of the phenomenon proved by Fu, Ren, and Wang. Our approach uses new lower bounds for incidence estimates originally proven by Cairo and Zhang, for which we provide an alternative proof based on homogeneous dynamics. Moreover the estimates are essentially sharp at the decoupling endpoint for the paraboloid $p = \frac{2(d+2)}{d}$.

math.CA↗

arXiv2025

NABench: Large-Scale Benchmarks of Nucleotide Foundation Models for Fitness Prediction

Nucleotide sequence variation can induce significant shifts in functional fitness. Recent nucleotide foundation models promise to predict such fitness effects directly from sequence, yet heterogeneous datasets and inconsistent preprocessing make it difficult to compare methods fairly across DNA and RNA families. Here we introduce NABench, a large-scale, systematic benchmark for nucleic acid fitness prediction. NABench aggregates 162 high-throughput assays and curates 2.6 million mutated sequences spanning diverse DNA and RNA families, with standardized splits and rich metadata. We show that NABench surpasses prior nucleotide fitness benchmarks in scale, diversity, and data quality. Under a unified evaluation suite, we rigorously assess 29 representative foundation models across zero-shot, few-shot prediction, transfer learning, and supervised settings. The results quantify performance heterogeneity across tasks and nucleic-acid types, demonstrating clear strengths and failure modes for different modeling choices and establishing strong, reproducible baselines. We release NABench to advance nucleic acid modeling, supporting downstream applications in RNA/DNA design, synthetic biology, and biochemistry. Our code is available at https://github.com/mrzzmrzz/NABench.

q-bio.GN↗

arXiv2023

pFedSim: Similarity-Aware Model Aggregation Towards Personalized Federated Learning

The federated learning (FL) paradigm emerges to preserve data privacy during model training by only exposing clients' model parameters rather than original data. One of the biggest challenges in FL lies in the non-IID (not identical and independently distributed) data (a.k.a., data heterogeneity) distributed on clients. To address this challenge, various personalized FL (pFL) methods are proposed such as similarity-based aggregation and model decoupling. The former one aggregates models from clients of a similar data distribution. The later one decouples a neural network (NN) model into a feature extractor and a classifier. Personalization is captured by classifiers which are obtained by local training. To advance pFL, we propose a novel pFedSim (pFL based on model similarity) algorithm in this work by combining these two kinds of methods. More specifically, we decouple a NN model into a personalized feature extractor, obtained by aggregating models from similar clients, and a classifier, which is obtained by local training and used to estimate client similarity. Compared with the state-of-the-art baselines, the advantages of pFedSim include: 1) significantly improved model accuracy; 2) low communication and computation overhead; 3) a low risk of privacy leakage; 4) no requirement for any external public information. To demonstrate the superiority of pFedSim, extensive experiments are conducted on real datasets. The results validate the superb performance of our algorithm which can significantly outperform baselines under various heterogeneous data settings.

cs.LG↗