# TULiP: Test-time Uncertainty Estimation via Linearization and Weight Perturbation

arXiv: https://arxiv.org/abs/2505.16923 · HTML: https://mlsanity.com/paper/2505.16923/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 57 references that are in the map.
- First posted on arXiv 22 May 2025.

## Builds on (most cited first, 30 of 39)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [The Many Faces of Robustness: A Critical Analysis of Out-of-Distribution Generalization](https://mlsanity.com/paper/2006.16241/) (2020)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [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)
- [Generalized Out-of-Distribution Detection: A Survey](https://mlsanity.com/paper/2110.11334/) (2021)
- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [Deep Neural Networks as Gaussian Processes](https://mlsanity.com/paper/1711.00165/) (2017)
- [Gradient Descent Finds Global Minima of Deep Neural Networks](https://mlsanity.com/paper/1811.03804/) (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)
- [ViM: Out-Of-Distribution with Virtual-logit Matching](https://mlsanity.com/paper/2203.10807/) (2022)
- [Laplace Redux -- Effortless Bayesian Deep Learning](https://mlsanity.com/paper/2106.14806/) (2021)
- [Open-Set Recognition: a Good Closed-Set Classifier is All You Need?](https://mlsanity.com/paper/2110.06207/) (2021)
- [On the Importance of Gradients for Detecting Distributional Shifts in the Wild](https://mlsanity.com/paper/2110.00218/) (2021)
- [OpenOOD: Benchmarking Generalized Out-of-Distribution Detection](https://mlsanity.com/paper/2210.07242/) (2022)
- [Learning Confidence for Out-of-Distribution Detection in Neural Networks](https://mlsanity.com/paper/1802.04865/) (2018)
- [MOS: Towards Scaling Out-of-distribution Detection for Large Semantic Space](https://mlsanity.com/paper/2105.01879/) (2021)
- [Extremely Simple Activation Shaping for Out-of-Distribution Detection](https://mlsanity.com/paper/2209.09858/) (2022)
- [Deep learning versus kernel learning: an empirical study of loss landscape geometry and the time evolution of the Neural Tangent Kernel](https://mlsanity.com/paper/2010.15110/) (2020)

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

- [DCAC: Dynamic Class-Aware Cache Creates Stronger Out-of-Distribution Detectors](https://mlsanity.com/paper/2601.12468/) (2026)
- [DynProto: Dynamic Prototype Evolution for Out-of-Distribution Detection](https://mlsanity.com/paper/2604.23729/) (2026)

## Abstract (arXiv)

A reliable uncertainty estimation method is the foundation of many modern out-of-distribution (OOD) detectors, which are critical for safe deployments of deep learning models in the open world. In this work, we propose TULiP, a theoretically-driven post-hoc uncertainty estimator for OOD detection. Our approach considers a hypothetical perturbation applied to the network before convergence. Based on linearized training dynamics, we bound the effect of such perturbation, resulting in an uncertainty score computable by perturbing model parameters. Ultimately, our approach computes uncertainty from a set of sampled predictions. We visualize our bound on synthetic regression and classification datasets. Furthermore, we demonstrate the effectiveness of TULiP using large-scale OOD detection benchmarks for image classification. Our method exhibits state-of-the-art performance, particularly for near-distribution samples.