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Generalization and Memorization: The Bias Potential Model
Hongkang Yang, Weinan E
Models for learning probability distributions such as generative models and density estimators behave quite differently from models for learning functions. One example is found in…
A priori estimates for classification problems using neural networks
Weinan E, Stephan Wojtowytsch
We consider binary and multi-class classification problems using hypothesis classes of neural networks. For a given hypothesis class, we use Rademacher complexity estimates and dir…
On the Banach spaces associated with multi-layer ReLU networks: Function representation, approximation theory and gradient descent dynamics
Weinan E, Stephan Wojtowytsch
We develop Banach spaces for ReLU neural networks of finite depth and infinite width. The spaces contain all finite fully connected -layer networks and their -limiting…
The Generalization Error of the Minimum-norm Solutions for Over-parameterized Neural Networks
Weinan E, Chao Ma, Lei Wu
We study the generalization properties of minimum-norm solutions for three over-parametrized machine learning models including the random feature model, the two-layer neural networ…
Understanding and Enhancing the Transferability of Adversarial Examples
Lei Wu, Zhanxing Zhu, Cheng Tai +1
State-of-the-art deep neural networks are known to be vulnerable to adversarial examples, formed by applying small but malicious perturbations to the original inputs. Moreover, the…
Functional Frank-Wolfe Boosting for General Loss Functions
Chu Wang, Yingfei Wang, Weinan E +1
Boosting is a generic learning method for classification and regression. Yet, as the number of base hypotheses becomes larger, boosting can lead to a deterioration of test performa…