# Revisiting Discriminative vs. Generative Classifiers: Theory and Implications

arXiv: https://arxiv.org/abs/2302.02334 · HTML: https://mlsanity.com/paper/2302.02334/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 46 references that are in the map.
- First posted on arXiv 5 Feb 2023.

## Builds on (most cited first, 20 of 20)

- [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)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Improved Baselines with Momentum Contrastive Learning](https://mlsanity.com/paper/2003.04297/) (2020)
- [Big Self-Supervised Models are Strong Semi-Supervised Learners](https://mlsanity.com/paper/2006.10029/) (2020)
- [SimMIM: A Simple Framework for Masked Image Modeling](https://mlsanity.com/paper/2111.09886/) (2021)
- [A Theoretical Analysis of Contrastive Unsupervised Representation Learning](https://mlsanity.com/paper/1902.09229/) (2019)
- [Provable Guarantees for Self-Supervised Deep Learning with Spectral Contrastive Loss](https://mlsanity.com/paper/2106.04156/) (2021)
- [Predicting What You Already Know Helps: Provable Self-Supervised Learning](https://mlsanity.com/paper/2008.01064/) (2020)
- [Contrastive learning, multi-view redundancy, and linear models](https://mlsanity.com/paper/2008.10150/) (2020)
- [A vector-contraction inequality for Rademacher complexities](https://mlsanity.com/paper/1605.00251/) (2016)

## Built on by (most cited first, 29 of 29)

- [Cross-Entropy Loss Functions: Theoretical Analysis and Applications](https://mlsanity.com/paper/2304.07288/) (2023)
- [Predictor-Rejector Multi-Class Abstention: Theoretical Analysis and Algorithms](https://mlsanity.com/paper/2310.14772/) (2023)
- [Advancements in Generative AI: A Comprehensive Review of GANs, GPT, Autoencoders, Diffusion Model, and Transformers](https://mlsanity.com/paper/2311.10242/) (2023)
- [Theoretically Grounded Loss Functions and Algorithms for Score-Based Multi-Class Abstention](https://mlsanity.com/paper/2310.14770/) (2023)
- [Regression with Multi-Expert Deferral](https://mlsanity.com/paper/2403.19494/) (2024)
- [Ranking with Abstention](https://mlsanity.com/paper/2307.02035/) (2023)
- [Realizable H-Consistent and Bayes-Consistent Loss Functions for Learning to Defer](https://mlsanity.com/paper/2407.13732/) (2024)
- [Toward Understanding Generative Data Augmentation](https://mlsanity.com/paper/2305.17476/) (2023)
- [ChatGLM-RLHF: Practices of Aligning Large Language Models with Human Feedback](https://mlsanity.com/paper/2404.00934/) (2024)
- [Cardinality-Aware Set Prediction and Top-k Classification](https://mlsanity.com/paper/2407.07140/) (2024)
- [H-Consistency Guarantees for Regression](https://mlsanity.com/paper/2403.19480/) (2024)
- [Enhanced H-Consistency Bounds](https://mlsanity.com/paper/2407.13722/) (2024)
- [Mastering Multiple-Expert Routing: Realizable H-Consistency and Strong Guarantees for Learning to Defer](https://mlsanity.com/paper/2506.20650/) (2025)
- [Balancing the Scales: A Theoretical and Algorithmic Framework for Learning from Imbalanced Data](https://mlsanity.com/paper/2502.10381/) (2025)
- [Do we really have to filter out random noise in pre-training data for language models?](https://mlsanity.com/paper/2502.06604/) (2025)
- [Multiscale Flow for Robust and Optimal Cosmological Analysis](https://mlsanity.com/paper/2306.04689/) (2023)
- [Unified Classification and Rejection: A One-versus-All Framework](https://mlsanity.com/paper/2311.13355/) (2023)
- [Generative Classifiers Avoid Shortcut Solutions](https://mlsanity.com/paper/2512.25034/) (2025)
- [Scaling Diffusion Transformers Efficiently via μP](https://mlsanity.com/paper/2505.15270/) (2025)
- [Principled Algorithms for Optimizing Generalized Metrics in Binary Classification](https://mlsanity.com/paper/2512.23133/) (2025)
- [Top-k Classification and Cardinality-Aware Prediction](https://mlsanity.com/paper/2403.19625/) (2024)
- [On Mesa-Optimization in Autoregressively Trained Transformers: Emergence and Capability](https://mlsanity.com/paper/2405.16845/) (2024)
- [Generative vs. Discriminative modeling under the lens of uncertainty quantification](https://mlsanity.com/paper/2406.09172/) (2024)
- [Risk-based Calibration for Generative Classifiers](https://mlsanity.com/paper/2409.03542/) (2024)
- [Exploring Structured Semantic Priors Underlying Diffusion Score for Test-time Adaptation](https://mlsanity.com/paper/2501.00873/) (2025)
- [The Hidden Cost of Modeling P(X): Vulnerability to Membership Inference Attacks in Generative Text Classifiers](https://mlsanity.com/paper/2510.16122/) (2025)
- [Causal Interpretability for Adversarial Robustness: A Hybrid Generative Classification Approach](https://mlsanity.com/paper/2412.20025/) (2024)
- [Generative Classifier for Domain Generalization](https://mlsanity.com/paper/2504.02272/) (2025)
- [Generative Cross-Entropy: A Strictly Proper Loss for Data-Efficient Classification](https://mlsanity.com/paper/2604.06689/) (2026)

## Abstract (arXiv)

A large-scale deep model pre-trained on massive labeled or unlabeled data transfers well to downstream tasks. Linear evaluation freezes parameters in the pre-trained model and trains a linear classifier separately, which is efficient and attractive for transfer. However, little work has investigated the classifier in linear evaluation except for the default logistic regression. Inspired by the statistical efficiency of naive Bayes, the paper revisits the classical topic on discriminative vs. generative classifiers. Theoretically, the paper considers the surrogate loss instead of the zero-one loss in analyses and generalizes the classical results from binary cases to multiclass ones. We show that, under mild assumptions, multiclass naive Bayes requires O(log n) samples to approach its asymptotic error while the corresponding multiclass logistic regression requires O(n) samples, where n is the feature dimension. To establish it, we present a multiclass H-consistency bound framework and an explicit bound for logistic loss, which are of independent interests. Simulation results on a mixture of Gaussian validate our theoretical findings. Experiments on various pre-trained deep vision models show that naive Bayes consistently converges faster as the number of data increases. Besides, naive Bayes shows promise in few-shot cases and we observe the "two regimes" phenomenon in pre-trained supervised models. Our code is available at https://github.com/ML-GSAI/Revisiting-Dis-vs-Gen-Classifiers.