arXiv subjects

Tian-Yi Zhou

Publications and source records attributed to Tian-Yi Zhou.

6 recordsLinked to original sources

arXiv2026

Neural Operators for Nonlinear Functionals on RKHS

Motivated by the abundance of functional data, such as time series and images, we study the approximation and statistical learning of nonlinear functionals defined on reproducing kernel Hilbert spaces (RKHSs) using neural networks. By leveraging interpolating orthogonal projections in RKHSs, we use finitely many point evaluations in place of integration-based basis function expansions. This leads to a simpler and more flexible neural-network architecture that remains applicable even when the data domain or the underlying kernel is not explicitly known. We establish universal approximation results and derive explicit kernel-dependent approximation rates and parameter-complexity bounds for RKHSs induced by inverse multiquadric, Gaussian, and Sobolev kernels. We also apply our results to the regression maps arising in generalized functional linear models. Finally, we analyze the generalization properties of the resulting neural-network classes and establish finite-sample guarantees for learning nonlinear functionals.

stat.ML↗

arXiv2026

Learning to Detect Cyber Attacks: Neural Anomaly Detection for Cybersecurity with Theoretical Insights

In cybersecurity practice, new forms of cyberattacks continuously emerge, deliberately designed to evade defense systems that rely on previously observed behaviors. Motivated by this challenge, we propose a neural network-based method for anomaly detection that does not rely on (1) prior knowledge of anomaly distributions or (2) the availability of real anomalies during training. Our proposed method trains a neural network classifier using only normal samples, combining the supervision from synthetic anomalies, and is particularly suitable when collecting real anomaly samples is expensive or impractical. The trained classifier is proven to attain minimax excess risk, and more importantly, it is guaranteed to learn the boundary of the normal region. Once the normal region is well estimated, the model can detect a wide range of anomalies without requiring explicit modeling of their distributions. Extensive experiments across cybersecurity, industrial, and medical anomaly detection tasks demonstrate that our method is consistently robust and competitive compared to state-of-the-art baselines. Notably, in the context of network intrusion detection, our approach significantly enhances the detection of difficult and previously unseen cyberattacks compared to other baselines.

stat.ML↗

arXiv2026

MindCine: Multimodal EEG-to-Video Reconstruction with Large-Scale Pretrained Models

Reconstructing human dynamic visual perception from electroencephalography (EEG) signals is of great research significance since EEG's non-invasiveness and high temporal resolution. However, EEG-to-video reconstruction remains challenging due to: 1) Single Modality: existing studies solely align EEG signals with the text modality, which ignores other modalities and are prone to suffer from overfitting problems; 2) Data Scarcity: current methods often have difficulty training to converge with limited EEG-video data. To solve the above problems, we propose a novel framework MindCine to achieve high-fidelity video reconstructions on limited data. We employ a multimodal joint learning strategy to incorporate beyond-text modalities in the training stage and leverage a pre-trained large EEG model to relieve the data scarcity issue for decoding semantic information, while a Seq2Seq model with causal attention is specifically designed for decoding perceptual information. Extensive experiments demonstrate that our model outperforms state-of-the-art methods both qualitatively and quantitatively. Additionally, the results underscore the effectiveness of the complementary strengths of different modalities and demonstrate that leveraging a large-scale EEG model can further enhance reconstruction performance by alleviating the challenges associated with limited data.

cs.CV↗

arXiv2025

Bridging Unsupervised and Semi-Supervised Anomaly Detection: A Theoretically-Grounded and Practical Framework with Synthetic Anomalies

Anomaly detection (AD) is a critical task across domains such as cybersecurity and healthcare. In the unsupervised setting, an effective and theoretically-grounded principle is to train classifiers to distinguish normal data from (synthetic) anomalies. We extend this principle to semi-supervised AD, where training data also include a limited labeled subset of anomalies possibly present in test time. We propose a theoretically-grounded and empirically effective framework for semi-supervised AD that combines known and synthetic anomalies during training. To analyze semi-supervised AD, we introduce the first mathematical formulation of semi-supervised AD, which generalizes unsupervised AD. Here, we show that synthetic anomalies enable (i) better anomaly modeling in low-density regions and (ii) optimal convergence guarantees for neural network classifiers -- the first theoretical result for semi-supervised AD. We empirically validate our framework on five diverse benchmarks, observing consistent performance gains. These improvements also extend beyond our theoretical framework to other classification-based AD methods, validating the generalizability of the synthetic anomaly principle in AD.

stat.ML↗

arXiv2023

Learning Ability of Interpolating Deep Convolutional Neural Networks

It is frequently observed that overparameterized neural networks generalize well. Regarding such phenomena, existing theoretical work mainly devotes to linear settings or fully-connected neural networks. This paper studies the learning ability of an important family of deep neural networks, deep convolutional neural networks (DCNNs), under both underparameterized and overparameterized settings. We establish the first learning rates of underparameterized DCNNs without parameter or function variable structure restrictions presented in the literature. We also show that by adding well-defined layers to a non-interpolating DCNN, we can obtain some interpolating DCNNs that maintain the good learning rates of the non-interpolating DCNN. This result is achieved by a novel network deepening scheme designed for DCNNs. Our work provides theoretical verification of how overfitted DCNNs generalize well.

stat.ML↗

arXiv2023

Classification of Data Generated by Gaussian Mixture Models Using Deep ReLU Networks

This paper studies the binary classification of unbounded data from ${\mathbb R}^d$ generated under Gaussian Mixture Models (GMMs) using deep ReLU neural networks. We obtain $\unicode{x2013}$ for the first time $\unicode{x2013}$ non-asymptotic upper bounds and convergence rates of the excess risk (excess misclassification error) for the classification without restrictions on model parameters. The convergence rates we derive do not depend on dimension $d$, demonstrating that deep ReLU networks can overcome the curse of dimensionality in classification. While the majority of existing generalization analysis of classification algorithms relies on a bounded domain, we consider an unbounded domain by leveraging the analyticity and fast decay of Gaussian distributions. To facilitate our analysis, we give a novel approximation error bound for general analytic functions using ReLU networks, which may be of independent interest. Gaussian distributions can be adopted nicely to model data arising in applications, e.g., speeches, images, and texts; our results provide a theoretical verification of the observed efficiency of deep neural networks in practical classification problems.

stat.ML↗