# Understanding Open-Set Recognition by Jacobian Norm and Inter-Class Separation

arXiv: https://arxiv.org/abs/2209.11436 · HTML: https://mlsanity.com/paper/2209.11436/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 49 references that are in the map.
- First posted on arXiv 23 Sep 2022.

## Builds on (most cited first, 30 of 34)

- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Generalized Out-of-Distribution Detection: A Survey](https://mlsanity.com/paper/2110.11334/) (2021)
- [Towards Open Set Deep Networks](https://mlsanity.com/paper/1511.06233/) (2015)
- [Using Self-Supervised Learning Can Improve Model Robustness and Uncertainty](https://mlsanity.com/paper/1906.12340/) (2019)
- [Open-Set Recognition: a Good Closed-Set Classifier is All You Need?](https://mlsanity.com/paper/2110.06207/) (2021)
- [Recent Advances in Open Set Recognition: A Survey](https://mlsanity.com/paper/1811.08581/) (2018)
- [Deep Anomaly Detection Using Geometric Transformations](https://mlsanity.com/paper/1805.10917/) (2018)
- [Sensitivity and Generalization in Neural Networks: an Empirical Study](https://mlsanity.com/paper/1802.08760/) (2018)
- [Reducing Network Agnostophobia](https://mlsanity.com/paper/1811.04110/) (2018)
- [Adversarial Reciprocal Points Learning for Open Set Recognition](https://mlsanity.com/paper/2103.00953/) (2021)
- [Classification-Reconstruction Learning for Open-Set Recognition](https://mlsanity.com/paper/1812.04246/) (2018)
- [Robust Learning with Jacobian Regularization](https://mlsanity.com/paper/1908.02729/) (2019)
- [Learning Placeholders for Open-Set Recognition](https://mlsanity.com/paper/2103.15086/) (2021)
- [Robust Large Margin Deep Neural Networks](https://mlsanity.com/paper/1605.08254/) (2016)
- [Learning Open Set Network with Discriminative Reciprocal Points](https://mlsanity.com/paper/2011.00178/) (2020)
- [Three Mechanisms of Weight Decay Regularization](https://mlsanity.com/paper/1810.12281/) (2018)
- [DOC: Deep Open Classification of Text Documents](https://mlsanity.com/paper/1709.08716/) (2017)
- [Improving DNN Robustness to Adversarial Attacks using Jacobian Regularization](https://mlsanity.com/paper/1803.08680/) (2018)
- [Towards neural networks that provably know when they don't know](https://mlsanity.com/paper/1909.12180/) (2019)
- [Open Category Detection with PAC Guarantees](https://mlsanity.com/paper/1808.00529/) (2018)
- [The Familiarity Hypothesis: Explaining the Behavior of Deep Open Set Methods](https://mlsanity.com/paper/2203.02486/) (2022)
- [Class-Specific Semantic Reconstruction for Open Set Recognition](https://mlsanity.com/paper/2207.02158/) (2022)
- [Learning Bounds for Open-Set Learning](https://mlsanity.com/paper/2106.15792/) (2021)
- [Gradient Regularization Improves Accuracy of Discriminative Models](https://mlsanity.com/paper/1712.09936/) (2017)

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

- [Modular Foundation Models for Time-Series Perception in Digital Twins](https://mlsanity.com/paper/2607.03585/) (2026)
- [Dynamics to decision: A mathematical theory of Lyapunov spectra and decision boundaries in deep classifiers](https://mlsanity.com/paper/2609.39190/) (2026)

## Abstract (arXiv)

The findings on open-set recognition (OSR) show that models trained on classification datasets are capable of detecting unknown classes not encountered during the training process. Specifically, after training, the learned representations of known classes dissociate from the representations of the unknown class, facilitating OSR. In this paper, we investigate this emergent phenomenon by examining the relationship between the Jacobian norm of representations and the inter/intra-class learning dynamics. We provide a theoretical analysis, demonstrating that intra-class learning reduces the Jacobian norm for known class samples, while inter-class learning increases the Jacobian norm for unknown samples, even in the absence of direct exposure to any unknown sample. Overall, the discrepancy in the Jacobian norm between the known and unknown classes enables OSR. Based on this insight, which highlights the pivotal role of inter-class learning, we devise a marginal one-vs-rest (m-OvR) loss function that promotes strong inter-class separation. To further improve OSR performance, we integrate the m-OvR loss with additional strategies that maximize the Jacobian norm disparity. We present comprehensive experimental results that support our theoretical observations and demonstrate the efficacy of our proposed OSR approach.