# Self-Certifying Classification by Linearized Deep Assignment

arXiv: https://arxiv.org/abs/2201.11162 · HTML: https://mlsanity.com/paper/2201.11162/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 35 references that are in the map.
- First posted on arXiv 26 Jan 2022.

## Builds on (most cited first, 12 of 12)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [A Primer on PAC-Bayesian Learning](https://mlsanity.com/paper/1901.05353/) (2019)
- [Tighter risk certificates for neural networks](https://mlsanity.com/paper/2007.12911/) (2020)
- [Entropy-SGD optimizes the prior of a PAC-Bayes bound: Generalization properties of Entropy-SGD and data-dependent priors](https://mlsanity.com/paper/1712.09376/) (2017)
- [A Strongly Quasiconvex PAC-Bayesian Bound](https://mlsanity.com/paper/1608.05610/) (2016)
- [Image Labeling by Assignment](https://mlsanity.com/paper/1603.05285/) (2016)
- [Assignment Flows for Data Labeling on Graphs: Convergence and Stability](https://mlsanity.com/paper/2002.11571/) (2020)
- [Continuous-Domain Assignment Flows](https://mlsanity.com/paper/1910.07287/) (2019)

## Built on by (most cited first, 2 of 2)

- [Sigma Flows for Image and Data Labeling and Learning Structured Prediction](https://mlsanity.com/paper/2408.15946/) (2024)
- [On Certified Generalization in Structured Prediction](https://mlsanity.com/paper/2306.09112/) (2023)

## Abstract (arXiv)

We propose a novel class of deep stochastic predictors for classifying metric data on graphs within the PAC-Bayes risk certification paradigm. Classifiers are realized as linearly parametrized deep assignment flows with random initial conditions. Building on the recent PAC-Bayes literature and data-dependent priors, this approach enables (i) to use risk bounds as training objectives for learning posterior distributions on the hypothesis space and (ii) to compute tight out-of-sample risk certificates of randomized classifiers more efficiently than related work. Comparison with empirical test set errors illustrates the performance and practicality of this self-certifying classification method.