# Confidence Dimension for Deep Learning based on Hoeffding Inequality and Relative Evaluation

arXiv: https://arxiv.org/abs/2203.09082 · HTML: https://mlsanity.com/paper/2203.09082/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 60 references that are in the map.
- First posted on arXiv 17 Mar 2022.

## Builds on (most cited first, 30 of 32)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [Rich feature hierarchies for accurate object detection and semantic segmentation](https://mlsanity.com/paper/1311.2524/) (2013)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [Neural Architecture Search with Reinforcement Learning](https://mlsanity.com/paper/1611.01578/) (2016)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks](https://mlsanity.com/paper/1603.05279/) (2016)
- [Exploring Generalization in Deep Learning](https://mlsanity.com/paper/1706.08947/) (2017)
- [Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data](https://mlsanity.com/paper/1703.11008/) (2017)
- [Fantastic Generalization Measures and Where to Find Them](https://mlsanity.com/paper/1912.02178/) (2019)
- [Sharp Minima Can Generalize For Deep Nets](https://mlsanity.com/paper/1703.04933/) (2017)
- [Stronger generalization bounds for deep nets via a compression approach](https://mlsanity.com/paper/1802.05296/) (2018)
- [Bi-Real Net: Enhancing the Performance of 1-bit CNNs With Improved Representational Capability and Advanced Training Algorithm](https://mlsanity.com/paper/1808.00278/) (2018)
- [Understanding Straight-Through Estimator in Training Activation Quantized Neural Nets](https://mlsanity.com/paper/1903.05662/) (2019)
- [Uniform convergence may be unable to explain generalization in deep learning](https://mlsanity.com/paper/1902.04742/) (2019)
- [ReActNet: Towards Precise Binary Neural Network with Generalized Activation Functions](https://mlsanity.com/paper/2003.03488/) (2020)
- [Deep learning generalizes because the parameter-function map is biased towards simple functions](https://mlsanity.com/paper/1805.08522/) (2018)
- [Towards Understanding the Role of Over-Parametrization in Generalization of Neural Networks](https://mlsanity.com/paper/1805.12076/) (2018)
- [Training and Inference with Integers in Deep Neural Networks](https://mlsanity.com/paper/1802.04680/) (2018)
- [In Search of Robust Measures of Generalization](https://mlsanity.com/paper/2010.11924/) (2020)
- [Oriented Response Networks](https://mlsanity.com/paper/1701.01833/) (2017)
- [Latent Weights Do Not Exist: Rethinking Binarized Neural Network Optimization](https://mlsanity.com/paper/1906.02107/) (2019)
- [On Generalization Error Bounds of Noisy Gradient Methods for Non-Convex Learning](https://mlsanity.com/paper/1902.00621/) (2019)
- [Stiffness: A New Perspective on Generalization in Neural Networks](https://mlsanity.com/paper/1901.09491/) (2019)
- [Understanding Why Neural Networks Generalize Well Through GSNR of Parameters](https://mlsanity.com/paper/2001.07384/) (2020)

## Built on by (most cited first, 1 of 1)

- [Reliability and Interpretability in Science and Deep Learning](https://mlsanity.com/paper/2401.07359/) (2024)

## Abstract (arXiv)

Research on the generalization ability of deep neural networks (DNNs) has recently attracted a great deal of attention. However, due to their complex architectures and large numbers of parameters, measuring the generalization ability of specific DNN models remains an open challenge. In this paper, we propose to use multiple factors to measure and rank the relative generalization of DNNs based on a new concept of confidence dimension (CD). Furthermore, we provide a feasible framework in our CD to theoretically calculate the upper bound of generalization based on the conventional Vapnik-Chervonenk dimension (VC-dimension) and Hoeffding's inequality. Experimental results on image classification and object detection demonstrate that our CD can reflect the relative generalization ability for different DNNs. In addition to full-precision DNNs, we also analyze the generalization ability of binary neural networks (BNNs), whose generalization ability remains an unsolved problem. Our CD yields a consistent and reliable measure and ranking for both full-precision DNNs and BNNs on all the tasks.