Quantifying the generalization error in deep learning in terms of data distribution and neural network smoothness
Explore this paper's citation graph
Summary
The cover complexity (CC) is introduced to measure the difficulty of learning a data set and the inverse of the modulus of continuity to quantify neural network smoothness and a quantitative bound for expected accuracy/error is derived by considering both the CC and neural network Smoothness.
- Type
- preprint
- Published
- 2019-05-27
- Cited by
- 70
- References
- 63
- Access
- Open access
- OpenAlex
- https://openalex.org/W2947664235
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:263796258
Keywords
Smoothness, Artificial neural network, Generalization, Computer science, Algorithm
References
- Balls in Rk do not cut all subsets of k + 2 points
- Columbia Object Image Library (COIL100)
- Path-SGD: Path-Normalized Optimization in Deep Neural Networks
- The Elements of Statistical Learning: Data Mining, Inference, and Prediction
- The Elements of Statistical Learning
- Approximation by superpositions of a sigmoidal function
- Gradient-based learning applied to document recognition
- In Search of the Real Inductive Bias: On the Role of Implicit Regularization in Deep Learning
- Multilayer feedforward networks are universal approximators
- ImageNet classification with deep convolutional neural networks
- Mastering the game of Go with deep neural networks and tree search
- Gradient Descent Converges to Minimizers
- Reading Digits in Natural Images with Unsupervised Feature Learning
- On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima
- Robust Large Margin Deep Neural Networks
- Understanding deep learning requires rethinking generalization
- Fast Rates for Empirical Risk Minimization of Strict Saddle Problems
- Opening the Black Box of Deep Neural Networks via Information
- Theory II: Landscape of the Empirical Risk in Deep Learning
- Data-Dependent Stability of Stochastic Gradient Descent
Cited by
- DeepXDE: A Deep Learning Library for Solving Differential Equations
- Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators
- Variational Physics-Informed Neural Networks For Solving Partial Differential Equations
- Deep learning architectures for nonlinear operator functions and nonlinear inverse problems
- Symplectic networks: Intrinsic structure-preserving networks for identifying Hamiltonian systems
- Deep Hamiltonian networks based on symplectic integrators
- A machine-learning-based surrogate model of Mars’ thermal evolution
- SympNets: Intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems
- Adaptive Checkpoint Adjoint Method for Gradient Estimation in Neural ODE
- Inverse modified differential equations for discovery of dynamics
- Relative Flatness and Generalization in the Interpolation Regime.
- Quantitative analysis of the generalization ability of deep feedforward neural networks
- Physics-informed neural networks with hard constraints for inverse design
- Research on Classification of Watermelon Ripeness Based on Neural Network Pattern Recognition
- Approximation capabilities of measure-preserving neural networks
- European Union–Ukraine Association Agreement: Challenges and Prospects for Cooperation
- Mosaic flows: A transferable deep learning framework for solving PDEs on unseen domains
- An Contract Theory based Federated Learning Aggregation Algorithm in IoT Network
- Embedding Principle: a hierarchical structure of loss landscape of deep neural networks
- The mnemonic basis of subjective experience
Related papers
- Neural Tangent Kernel Eigenvalues Accurately Predict Generalization
- Generalization error of deep neural networks: Role of classification margin and data structure
- A Spectral Approach to Generalization and Optimization in Neural Networks
- A Fourier-Based Approach to Generalization and Optimization in Deep Learning
- Generalization in fully-connected neural networks for time series forecasting
- On the modeling of error functions as high dimensional landscapes for weight initialization in learning networks
- Trainability and Accuracy of Artificial Neural Networks: An Interacting Particle System Approach