# Mutual Information Learned Classifiers: an Information-theoretic Viewpoint of Training Deep Learning Classification Systems

arXiv: https://arxiv.org/abs/2210.01000 · HTML: https://mlsanity.com/paper/2210.01000/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 41 of its 61 references that are in the map.
- First posted on arXiv 3 Oct 2022.

## Builds on (most cited first, 30 of 41)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Inception-v4, Inception-ResNet and the Impact of Residual Connections on Learning](https://mlsanity.com/paper/1602.07261/) (2016)
- [Rethinking Semantic Segmentation from a Sequence-to-Sequence Perspective with Transformers](https://mlsanity.com/paper/2012.15840/) (2020)
- [ShuffleNet V2: Practical Guidelines for Efficient CNN Architecture Design](https://mlsanity.com/paper/1807.11164/) (2018)
- [Distillation as a Defense to Adversarial Perturbations against Deep Neural Networks](https://mlsanity.com/paper/1511.04508/) (2015)
- [Regularizing Neural Networks by Penalizing Confident Output Distributions](https://mlsanity.com/paper/1701.06548/) (2017)
- [Diffusion Autoencoders: Toward a Meaningful and Decodable Representation](https://mlsanity.com/paper/2111.15640/) (2021)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [Information-theoretic analysis of generalization capability of learning algorithms](https://mlsanity.com/paper/1705.07809/) (2017)
- [Adversarial Attacks and Defenses in Images, Graphs and Text: A Review](https://mlsanity.com/paper/1909.08072/) (2019)
- [Formal Limitations on the Measurement of Mutual Information](https://mlsanity.com/paper/1811.04251/) (2018)
- [Rethinking Semantic Segmentation: A Prototype View](https://mlsanity.com/paper/2203.15102/) (2022)
- [Nonlinear Information Bottleneck](https://mlsanity.com/paper/1705.02436/) (2017)
- [InfinityGAN: Towards Infinite-Pixel Image Synthesis](https://mlsanity.com/paper/2104.03963/) (2021)
- [Closing the Generalization Gap of Cross-silo Federated Medical Image Segmentation](https://mlsanity.com/paper/2203.10144/) (2022)
- [Generalized Entropy Regularization or: There's Nothing Special about Label Smoothing](https://mlsanity.com/paper/2005.00820/) (2020)
- [ProSelfLC: Progressive Self Label Correction for Training Robust Deep Neural Networks](https://mlsanity.com/paper/2005.03788/) (2020)
- [Towards Robust Pattern Recognition: A Review](https://mlsanity.com/paper/2006.06976/) (2020)

## Abstract (arXiv)

Deep learning systems have been reported to acheive state-of-the-art performances in many applications, and one of the keys for achieving this is the existence of well trained classifiers on benchmark datasets which can be used as backbone feature extractors in downstream tasks. As a main-stream loss function for training deep neural network (DNN) classifiers, the cross entropy loss can easily lead us to find models which demonstrate severe overfitting behavior when no other techniques are used for alleviating it such as data augmentation. In this paper, we prove that the existing cross entropy loss minimization for training DNN classifiers essentially learns the conditional entropy of the underlying data distribution of the dataset, i.e., the information or uncertainty remained in the labels after revealing the input. In this paper, we propose a mutual information learning framework where we train DNN classifiers via learning the mutual information between the label and input. Theoretically, we give the population error probability lower bound in terms of the mutual information. In addition, we derive the mutual information lower and upper bounds for a concrete binary classification data model in mbRn, and also the error probability lower bound in this scenario. Besides, we establish the sample complexity for accurately learning the mutual information from empirical data samples drawn from the underlying data distribution. Empirically, we conduct extensive experiments on several benchmark datasets to support our theory. Without whistles and bells, the proposed mutual information learned classifiers (MILCs) acheive far better generalization performances than the state-of-the-art classifiers with an improvement which can exceed more than 10% in testing accuracy.