# H2ST: Hierarchical Two-Sample Tests for Continual Out-of-Distribution Detection

arXiv: https://arxiv.org/abs/2503.14832 · HTML: https://mlsanity.com/paper/2503.14832/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 57 references that are in the map.
- First posted on arXiv 19 Mar 2025.

## Builds on (most cited first, 30 of 36)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Matching Networks for One Shot Learning](https://mlsanity.com/paper/1606.04080/) (2016)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [Memory Aware Synapses: Learning what (not) to forget](https://mlsanity.com/paper/1711.09601/) (2017)
- [Experience Replay for Continual Learning](https://mlsanity.com/paper/1811.11682/) (2018)
- [A Comprehensive Survey of Continual Learning: Theory, Method and Application](https://mlsanity.com/paper/2302.00487/) (2023)
- [Generalized Out-of-Distribution Detection: A Survey](https://mlsanity.com/paper/2110.11334/) (2021)
- [Overcoming catastrophic forgetting with hard attention to the task](https://mlsanity.com/paper/1801.01423/) (2018)
- [ReAct: Out-of-distribution Detection With Rectified Activations](https://mlsanity.com/paper/2111.12797/) (2021)
- [Scaling Out-of-Distribution Detection for Real-World Settings](https://mlsanity.com/paper/1911.11132/) (2019)
- [Expert Gate: Lifelong Learning with a Network of Experts](https://mlsanity.com/paper/1611.06194/) (2016)
- [On the Importance of Gradients for Detecting Distributional Shifts in the Wild](https://mlsanity.com/paper/2110.00218/) (2021)
- [CORe50: a New Dataset and Benchmark for Continuous Object Recognition](https://mlsanity.com/paper/1705.03550/) (2017)
- [Rainbow Memory: Continual Learning with a Memory of Diverse Samples](https://mlsanity.com/paper/2103.17230/) (2021)
- [Revisiting Classifier Two-Sample Tests](https://mlsanity.com/paper/1610.06545/) (2016)
- [Online Structured Laplace Approximations For Overcoming Catastrophic Forgetting](https://mlsanity.com/paper/1805.07810/) (2018)
- [DICE: Leveraging Sparsification for Out-of-Distribution Detection](https://mlsanity.com/paper/2111.09805/) (2021)
- [FeTrIL: Feature Translation for Exemplar-Free Class-Incremental Learning](https://mlsanity.com/paper/2211.13131/) (2022)
- [How catastrophic can catastrophic forgetting be in linear regression?](https://mlsanity.com/paper/2205.09588/) (2022)
- [A Theoretical Study on Solving Continual Learning](https://mlsanity.com/paper/2211.02633/) (2022)
- [Provable Guarantees for Understanding Out-of-distribution Detection](https://mlsanity.com/paper/2112.00787/) (2021)
- [Neural Mean Discrepancy for Efficient Out-of-Distribution Detection](https://mlsanity.com/paper/2104.11408/) (2021)
- [Block Selection Method for Using Feature Norm in Out-of-distribution Detection](https://mlsanity.com/paper/2212.02295/) (2022)
- [A Multi-Head Model for Continual Learning via Out-of-Distribution Replay](https://mlsanity.com/paper/2208.09734/) (2022)
- [Open-World Continual Learning: Unifying Novelty Detection and Continual Learning](https://mlsanity.com/paper/2304.10038/) (2023)
- [Continual Evidential Deep Learning for Out-of-Distribution Detection](https://mlsanity.com/paper/2309.02995/) (2023)

## Built on by (most cited first, 4 of 4)

- [Out-of-Distribution Detection for Continual Learning: Design Principles and Benchmarking](https://mlsanity.com/paper/2512.19725/) (2025)
- [Mitigating the ID-OOD Tradeoff in Open-Set Test-Time Adaptation](https://mlsanity.com/paper/2604.01589/) (2026)
- [LOTTERY: Learning from Reference-Only Samples in Two-Sample Testing under Size Asymmetry](https://mlsanity.com/paper/2606.08460/) (2026)
- [CURE-OOD: Benchmarking Out-of-Distribution Detection for Survival Prediction](https://mlsanity.com/paper/2605.00350/) (2026)

## Abstract (arXiv)

Task Incremental Learning (TIL) is a specialized form of Continual Learning (CL) in which a model incrementally learns from non-stationary data streams. Existing TIL methodologies operate under the closed-world assumption, presuming that incoming data remains in-distribution (ID). However, in an open-world setting, incoming samples may originate from out-of-distribution (OOD) sources, with their task identities inherently unknown. Continually detecting OOD samples presents several challenges for current OOD detection methods: reliance on model outputs leads to excessive dependence on model performance, selecting suitable thresholds is difficult, hindering real-world deployment, and binary ID/OOD classification fails to provide task-level identification. To address these issues, we propose a novel continual OOD detection method called the Hierarchical Two-sample Tests (H2ST). H2ST eliminates the need for threshold selection through hypothesis testing and utilizes feature maps to better exploit model capabilities without excessive dependence on model performance. The proposed hierarchical architecture enables task-level detection with superior performance and lower overhead compared to non-hierarchical classifier two-sample tests. Extensive experiments and analysis validate the effectiveness of H2ST in open-world TIL scenarios and its superiority to the existing methods. Code is available at hrefhttps://github.com/YuhangLiuu/H2SThttps://github.com/YuhangLiuu/H2ST.