Search Results for author:
Found 26 papers, 6 papers with code
Structure and Gradient Dynamics Near Global Minima of Two-layer Neural Networks
Under mild assumptions, we investigate the structure of loss landscape of two-layer neural networks near global minima, determine the set of parameters which give perfect generalization, and fully characterize the gradient flows around it.
Optimistic Estimate Uncovers the Potential of Nonlinear Models
We propose an optimistic estimate to evaluate the best possible fitting performance of nonlinear models.
Linear Stability Hypothesis and Rank Stratification for Nonlinear Models
By these results, model rank of a target function predicts a minimal training data size for its successful recovery.
Embedding Principle in Depth for the Loss Landscape Analysis of Deep Neural Networks
Regarding the easy training of deep networks, we show that local minimum of an NN can be lifted to strict saddle points of a deeper NN.
Empirical Phase Diagram for Three-layer Neural Networks with Infinite Width
Through experiments under three-layer condition, our phase diagram suggests a complicated dynamical regimes consisting of three possible regimes, together with their mixture, for deep NNs and provides a guidance for studying deep NNs in different initialization regimes, which reveals the possibility of completely different dynamics emerging within a deep NN for its different layers.
Limitation of Characterizing Implicit Regularization by Data-independent Functions
In recent years, understanding the implicit regularization of neural networks (NNs) has become a central task in deep learning theory.
Overview frequency principle/spectral bias in deep learning
This low-frequency implicit bias reveals the strength of neural network in learning low-frequency functions as well as its deficiency in learning high-frequency functions.
A multi-scale sampling method for accurate and robust deep neural network to predict combustion chemical kinetics
The current work aims to understand two basic questions regarding the deep neural network (DNN) method: what data the DNN needs and how general the DNN method can be.
A deep learning-based model reduction (DeePMR) method for simplifying chemical kinetics
The mechanism reduction is modeled as an optimization problem on Boolean space, where a Boolean vector, each entry corresponding to a species, represents a reduced mechanism.
Embedding Principle: a hierarchical structure of loss landscape of deep neural networks
We prove a general Embedding Principle of loss landscape of deep neural networks (NNs) that unravels a hierarchical structure of the loss landscape of NNs, i. e., loss landscape of an NN contains all critical points of all the narrower NNs.
Data-informed Deep Optimization
Complex design problems are common in the scientific and industrial fields.
MOD-Net: A Machine Learning Approach via Model-Operator-Data Network for Solving PDEs
In this paper, we propose a a machine learning approach via model-operator-data network (MOD-Net) for solving PDEs.
Embedding Principle of Loss Landscape of Deep Neural Networks
Understanding the structure of loss landscape of deep neural networks (DNNs)is obviously important.
An Upper Limit of Decaying Rate with Respect to Frequency in Deep Neural Network
frequency in DNN training.
Towards Understanding the Condensation of Neural Networks at Initial Training
Our theoretical analysis confirms experiments for two cases, one is for the activation function of multiplicity one with arbitrary dimension input, which contains many common activation functions, and the other is for the layer with one-dimensional input and arbitrary multiplicity.
Linear Frequency Principle Model to Understand the Absence of Overfitting in Neural Networks
Why heavily parameterized neural networks (NNs) do not overfit the data is an important long standing open question.
Fourier-domain Variational Formulation and Its Well-posedness for Supervised Learning
A supervised learning problem is to find a function in a hypothesis function space given values on isolated data points.
A deep learning-based ODE solver for chemical kinetics
Besides, the ignition delay time differences are within 1%.
On the exact computation of linear frequency principle dynamics and its generalization
Recent works show an intriguing phenomenon of Frequency Principle (F-Principle) that deep neural networks (DNNs) fit the target function from low to high frequency during the training, which provides insight into the training and generalization behavior of DNNs in complex tasks.
Phase diagram for two-layer ReLU neural networks at infinite-width limit
In this work, inspired by the phase diagram in statistical mechanics, we draw the phase diagram for the two-layer ReLU neural network at the infinite-width limit for a complete characterization of its dynamical regimes and their dependence on hyperparameters related to initialization.
A priori generalization error for two-layer ReLU neural network through minimum norm solution
We first estimate \emph{a priori} generalization error of finite-width two-layer ReLU NN with constraint of minimal norm solution, which is proved by \cite{zhang2019type} to be an equivalent solution of a linearized (w. r. t.
Theory of the Frequency Principle for General Deep Neural Networks
Along with fruitful applications of Deep Neural Networks (DNNs) to realistic problems, recently, some empirical studies of DNNs reported a universal phenomenon of Frequency Principle (F-Principle): a DNN tends to learn a target function from low to high frequencies during the training.
Explicitizing an Implicit Bias of the Frequency Principle in Two-layer Neural Networks
It remains a puzzle that why deep neural networks (DNNs), with more parameters than samples, often generalize well.
A type of generalization error induced by initialization in deep neural networks
Overall, our work serves as a baseline for the further investigation of the impact of initialization and loss function on the generalization of DNNs, which can potentially guide and improve the training of DNNs in practice.
Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks
We study the training process of Deep Neural Networks (DNNs) from the Fourier analysis perspective.
Training behavior of deep neural network in frequency domain
Why deep neural networks (DNNs) capable of overfitting often generalize well in practice is a mystery [#zhang2016understanding].
