Yiwen Kou

Yiwen Kou, Zixiang Chen, Yuanzhou Chen et al.

Modern deep learning models with great expressive power can be trained to overfit the training data but still generalize well. This phenomenon is referred to as \textit{benign overfitting}. Recently, a few studies have attempted to theoretically understand benign overfitting in neural networks. However, these works are either limited to neural networks with smooth activation functions or to the neural tangent kernel regime. How and when benign overfitting can occur in ReLU neural networks remains an open problem. In this work, we seek to answer this question by establishing algorithm-dependent risk bounds for learning two-layer ReLU convolutional neural networks with label-flipping noise. We show that, under mild conditions, the neural network trained by gradient descent can achieve near-zero training loss and Bayes optimal test risk. Our result also reveals a sharp transition between benign and harmful overfitting under different conditions on data distribution in terms of test risk. Experiments on synthetic data back up our theory.

Zixiang Chen, Junkai Zhang, Yiwen Kou et al.

The challenge of overfitting, in which the model memorizes the training data and fails to generalize to test data, has become increasingly significant in the training of large neural networks. To tackle this challenge, Sharpness-Aware Minimization (SAM) has emerged as a promising training method, which can improve the generalization of neural networks even in the presence of label noise. However, a deep understanding of how SAM works, especially in the setting of nonlinear neural networks and classification tasks, remains largely missing. This paper fills this gap by demonstrating why SAM generalizes better than Stochastic Gradient Descent (SGD) for a certain data model and two-layer convolutional ReLU networks. The loss landscape of our studied problem is nonsmooth, thus current explanations for the success of SAM based on the Hessian information are insufficient. Our result explains the benefits of SAM, particularly its ability to prevent noise learning in the early stages, thereby facilitating more effective learning of features. Experiments on both synthetic and real data corroborate our theory.

Yiwen Kou, Zixiang Chen, Quanquan Gu

The implicit bias towards solutions with favorable properties is believed to be a key reason why neural networks trained by gradient-based optimization can generalize well. While the implicit bias of gradient flow has been widely studied for homogeneous neural networks (including ReLU and leaky ReLU networks), the implicit bias of gradient descent is currently only understood for smooth neural networks. Therefore, implicit bias in non-smooth neural networks trained by gradient descent remains an open question. In this paper, we aim to answer this question by studying the implicit bias of gradient descent for training two-layer fully connected (leaky) ReLU neural networks. We showed that when the training data are nearly-orthogonal, for leaky ReLU activation function, gradient descent will find a network with a stable rank that converges to $1$, whereas for ReLU activation function, gradient descent will find a neural network with a stable rank that is upper bounded by a constant. Additionally, we show that gradient descent will find a neural network such that all the training data points have the same normalized margin asymptotically. Experiments on both synthetic and real data backup our theoretical findings.

Zixiang Chen, Huizhuo Yuan, Yongqian Li et al.

Discrete diffusion models have emerged as powerful tools for high-quality data generation. Despite their success in discrete spaces, such as text generation tasks, the acceleration of discrete diffusion models remains under-explored. In this paper, we propose discrete non-Markov diffusion models (DNDM), which naturally induce the predetermined transition time set. This enables a training-free sampling algorithm that significantly reduces the number of function evaluations (i.e., calls to the neural network), making the sampling process much faster. Furthermore, we study the transition from finite to infinite step sampling, offering new insights into bridging the gap between discrete and continuous-time processes for discrete diffusion models. Extensive experiments on natural language generation and machine translation tasks demonstrate the superior performance of our method in terms of both generation speed and sample quality compared to existing methods for discrete diffusion models.

Jun Han, Zixiang Chen, Yongqian Li et al.

Electronic health records (EHRs) are a pivotal data source that enables numerous applications in computational medicine, e.g., disease progression prediction, clinical trial design, and health economics and outcomes research. Despite wide usability, their sensitive nature raises privacy and confidentially concerns, which limit potential use cases. To tackle these challenges, we explore the use of generative models to synthesize artificial, yet realistic EHRs. While diffusion-based methods have recently demonstrated state-of-the-art performance in generating other data modalities and overcome the training instability and mode collapse issues that plague previous GAN-based approaches, their applications in EHR generation remain underexplored. The discrete nature of tabular medical code data in EHRs poses challenges for high-quality data generation, especially for continuous diffusion models. To this end, we introduce a novel tabular EHR generation method, EHR-D3PM, which enables both unconditional and conditional generation using the discrete diffusion model. Our experiments demonstrate that EHR-D3PM significantly outperforms existing generative baselines on comprehensive fidelity and utility metrics while maintaining less attribute and membership vulnerability risks. Furthermore, we show EHR-D3PM is effective as a data augmentation method and enhances performance on downstream tasks when combined with real data.

Yiwen Kou, Zixiang Chen, Quanquan Gu et al.

The $k$-sparse parity problem is a classical problem in computational complexity and algorithmic theory, serving as a key benchmark for understanding computational classes. In this paper, we solve the $k$-sparse parity problem with sign stochastic gradient descent, a variant of stochastic gradient descent (SGD) on two-layer fully-connected neural networks. We demonstrate that this approach can efficiently solve the $k$-sparse parity problem on a $d$-dimensional hypercube ($k\leq O(\sqrt{d})$) with a sample complexity of $\tilde{O}(d^{k-1})$ using $2^{Θ(k)}$ neurons, matching the established $Ω(d^{k})$ lower bounds of Statistical Query (SQ) models. Our theoretical analysis begins by constructing a good neural network capable of correctly solving the $k$-parity problem. We then demonstrate how a trained neural network with sign SGD can effectively approximate this good network, solving the $k$-parity problem with small statistical errors. To the best of our knowledge, this is the first result that matches the SQ lower bound for solving $k$-sparse parity problem using gradient-based methods.

Yiwen Kou, Raghu Meka

Agnostic learning of Boolean halfspaces is a fundamental problem in computational learning theory, but it is known to be computationally hard even for weak learning. Recent work [CKKMK24] proposed smoothed analysis as a way to bypass such hardness, but existing frameworks rely on additive Gaussian perturbations, making them unsuitable for discrete domains. We introduce a new smoothed agnostic learning framework for Boolean inputs, where perturbations are modeled via random bit flips. This defines a natural discrete analogue of smoothed optimality generalizing the Gaussian case. Under strictly subexponential assumptions on the input distribution, we give an efficient algorithm for learning halfspaces in this model, with runtime and sample complexity approximately n raised to a poly(1/(sigma * epsilon)) factor. Previously, such algorithms were known only with strong structural assumptions for the discrete hypercube, for example, independent coordinates or symmetric distributions. Our result provides the first computationally efficient guarantee for smoothed agnostic learning of halfspaces over the Boolean hypercube, bridging the gap between worst-case intractability and practical learnability in discrete settings.