Norm-Based Capacity Control in Neural Networks
arXiv:1503.00036
Abstract
We investigate the capacity, convexity and characterization of a general family of norm-constrained feed-forward networks.
29 pages
Cited by in corpus (122)
- Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges
- Benign Overfitting in Linear Regression
- Robust Large Margin Deep Neural Networks
- Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data
- Generalization in Deep Learning
- Towards Understanding the Role of Over-Parametrization in Generalization of Neural Networks
- Toward Deeper Understanding of Neural Networks: The Power of Initialization and a Dual View on Expressivity
- Generalization Bounds of Stochastic Gradient Descent for Wide and Deep Neural Networks
- When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization?
- The Modern Mathematics of Deep Learning
- A Theoretical Analysis of Deep Q-Learning
- Fisher-Rao Metric, Geometry, and Complexity of Neural Networks
- A Priori Estimates of the Population Risk for Two-layer Neural Networks
- Deep learning generalizes because the parameter-function map is biased towards simple functions
- What Can Neural Networks Reason About?
- The no-free-lunch theorems of supervised learning
- Stronger generalization bounds for deep nets via a compression approach
- Predicting trends in the quality of state-of-the-art neural networks without access to training or testing data
- Layer-adaptive sparsity for the Magnitude-based Pruning
- Analyzing Upper Bounds on Mean Absolute Errors for Deep Neural Network Based Vector-to-Vector Regression
- Fast Convergence of Natural Gradient Descent for Overparameterized Neural Networks
- Generalization Error Bounds of Gradient Descent for Learning Over-parameterized Deep ReLU Networks
- An analytic theory of generalization dynamics and transfer learning in deep linear networks
- Pruning Neural Networks at Initialization: Why are We Missing the Mark?
- On Interpretability of Artificial Neural Networks: A Survey
- Universal Statistics of Fisher Information in Deep Neural Networks: Mean Field Approach
- Approximation and Estimation for High-Dimensional Deep Learning Networks
- What Kinds of Functions do Deep Neural Networks Learn? Insights from Variational Spline Theory
- Predicting Neural Network Accuracy from Weights
- Explicit Regularisation in Gaussian Noise Injections
- Lipschitz Continuity in Model-based Reinforcement Learning
- On Generalization Error Bounds of Noisy Gradient Methods for Non-Convex Learning
- A Generalized Neural Tangent Kernel Analysis for Two-layer Neural Networks
- What Do Neural Networks Learn When Trained With Random Labels?
- Improved Sample Complexities for Deep Networks and Robust Classification via an All-Layer Margin
- How Much Over-parameterization Is Sufficient to Learn Deep ReLU Networks?
- Understanding Generalization through Visualizations
- Foundations of Sequence-to-Sequence Modeling for Time Series
- Gradient Descent Quantizes ReLU Network Features
- Reducing Communication for Split Learning by Randomized Top-k Sparsification
- Hausdorff Dimension, Heavy Tails, and Generalization in Neural Networks
- How Does Mixup Help With Robustness and Generalization?
- How does Weight Correlation Affect the Generalisation Ability of Deep Neural Networks
- Learning Halfspaces and Neural Networks with Random Initialization
- Learning Optimal Representations with the Decodable Information Bottleneck
- Network size and weights size for memorization with two-layers neural networks
- Effects of quantum resources on the statistical complexity of quantum circuits
- Adversarial Training Versus Weight Decay
- The Deep Bootstrap Framework: Good Online Learners are Good Offline Generalizers
- Inductive Biases and Variable Creation in Self-Attention Mechanisms
- Exploring Memorization in Adversarial Training
- LocalDrop: A Hybrid Regularization for Deep Neural Networks
- Dropout: Explicit Forms and Capacity Control
- Understanding Generalization in Deep Learning via Tensor Methods
- Generative Modeling with Denoising Auto-Encoders and Langevin Sampling
- How Many Samples are Needed to Estimate a Convolutional or Recurrent Neural Network?
- Compression based bound for non-compressed network: unified generalization error analysis of large compressible deep neural network
- Deep Learning is Singular, and That's Good
- Inductive Bias of Gradient Descent based Adversarial Training on Separable Data
- Stationary Points of Shallow Neural Networks with Quadratic Activation Function
- Deep Neural Networks for Choice Analysis: A Statistical Learning Theory Perspective
- Information-Theoretic Generalization Bounds for Stochastic Gradient Descent
- CNNs Avoid Curse of Dimensionality by Learning on Patches
- On the Depth of Deep Neural Networks: A Theoretical View
- Statistically Meaningful Approximation: a Case Study on Approximating Turing Machines with Transformers
- Formalizing Generalization and Robustness of Neural Networks to Weight Perturbations
- Model Complexity of Deep Learning: A Survey
- Distance-Based Regularisation of Deep Networks for Fine-Tuning
- The Role of Information Complexity and Randomization in Representation Learning
- Spectral Pruning: Compressing Deep Neural Networks via Spectral Analysis and its Generalization Error
- Neural Complexity Measures
- Deep Neural Networks for Choice Analysis: Extracting Complete Economic Information for Interpretation
- On generalization bounds for deep networks based on loss surface implicit regularization
- Are deep ResNets provably better than linear predictors?
- Deep Online Convex Optimization with Gated Games
- Function Norms and Regularization in Deep Networks
- Information-Theoretic Local Minima Characterization and Regularization
- Learning with Gradient Descent and Weakly Convex Losses
- Improved Generalization Bounds of Group Invariant / Equivariant Deep Networks via Quotient Feature Spaces
- An Embedding of ReLU Networks and an Analysis of their Identifiability
- Norm-based generalisation bounds for multi-class convolutional neural networks
- In Search of Robust Measures of Generalization
- Data-Dependent Path Normalization in Neural Networks
- De-randomized PAC-Bayes Margin Bounds: Applications to Non-convex and Non-smooth Predictors
- A Deep Conditioning Treatment of Neural Networks
- Functional Gradient Boosting based on Residual Network Perception
- Self-Regularity of Non-Negative Output Weights for Overparameterized Two-Layer Neural Networks
- Stochasticity of Deterministic Gradient Descent: Large Learning Rate for Multiscale Objective Function
- Hyperplane Arrangements of Trained ConvNets Are Biased
- On a Sparse Shortcut Topology of Artificial Neural Networks
- Improve Generalization and Robustness of Neural Networks via Weight Scale Shifting Invariant Regularizations
- Subspace Embeddings Under Nonlinear Transformations
- Post-mortem on a deep learning contest: a Simpson's paradox and the complementary roles of scale metrics versus shape metrics
- The Rate of Convergence of Variation-Constrained Deep Neural Networks
- On the Robustness and Generalization of Deep Learning Driven Full Waveform Inversion
- An ETF view of Dropout regularization
- Extreme Memorization via Scale of Initialization
- GraphConnect: A Regularization Framework for Neural Networks
- Ridge Regression with Over-Parametrized Two-Layer Networks Converge to Ridgelet Spectrum
- Why Mixup Improves the Model Performance
- RATT: Leveraging Unlabeled Data to Guarantee Generalization
- Relative Deviation Margin Bounds
- Stable Rank Normalization for Improved Generalization in Neural Networks and GANs
- Deep Semi-Random Features for Nonlinear Function Approximation
- Bounds for Vector-Valued Function Estimation
- On the Generalization of Models Trained with SGD: Information-Theoretic Bounds and Implications
- Surprising properties of dropout in deep networks
- Why Do Better Loss Functions Lead to Less Transferable Features?
- Fast generalization error bound of deep learning without scale invariance of activation functions
- Revisiting minimum description length complexity in overparameterized models
- Non-linear, Sparse Dimensionality Reduction via Path Lasso Penalized Autoencoders
- The role of invariance in spectral complexity-based generalization bounds
- Uniform Convergence, Adversarial Spheres and a Simple Remedy
- Semantically Robust Unpaired Image Translation for Data with Unmatched Semantics Statistics
- Embedding Inequalities for Barron-type Spaces
- Deep Neural Networks for Choice Analysis: Architectural Design with Alternative-Specific Utility Functions
- Deep Networks as Logical Circuits: Generalization and Interpretation
- A Functional Perspective on Learning Symmetric Functions with Neural Networks
- Information Theoretic Lower Bounds for Feed-Forward Fully-Connected Deep Networks
- Relative Flatness and Generalization
- Ghosts in Neural Networks: Existence, Structure and Role of Infinite-Dimensional Null Space
- The duality structure gradient descent algorithm: analysis and applications to neural networks