# MANO: Exploiting Matrix Norm for Unsupervised Accuracy Estimation Under Distribution Shifts

arXiv: https://arxiv.org/abs/2405.18979 · HTML: https://mlsanity.com/paper/2405.18979/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 68 of its 105 references that are in the map.
- First posted on arXiv 29 May 2024.

## Builds on (most cited first, 30 of 68)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [FixMatch: Simplifying Semi-Supervised Learning with Consistency and Confidence](https://mlsanity.com/paper/2001.07685/) (2020)
- [Unsupervised Feature Learning via Non-Parametric Instance-level Discrimination](https://mlsanity.com/paper/1805.01978/) (2018)
- [Do ImageNet Classifiers Generalize to ImageNet?](https://mlsanity.com/paper/1902.10811/) (2019)
- [ImageNet-trained CNNs are biased towards texture; increasing shape bias improves accuracy and robustness](https://mlsanity.com/paper/1811.12231/) (2018)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [Moment Matching for Multi-Source Domain Adaptation](https://mlsanity.com/paper/1812.01754/) (2018)
- [Deep Hashing Network for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1706.07522/) (2017)
- [Deeper, Broader and Artier Domain Generalization](https://mlsanity.com/paper/1710.03077/) (2017)
- [SphereFace: Deep Hypersphere Embedding for Face Recognition](https://mlsanity.com/paper/1704.08063/) (2017)
- [Sharp Minima Can Generalize For Deep Nets](https://mlsanity.com/paper/1703.04933/) (2017)
- [On the Number of Linear Regions of Deep Neural Networks](https://mlsanity.com/paper/1402.1869/) (2014)
- [Entropy-SGD: Biasing Gradient Descent Into Wide Valleys](https://mlsanity.com/paper/1611.01838/) (2016)
- [Minimally distorted Adversarial Examples with a Fast Adaptive Boundary Attack](https://mlsanity.com/paper/1907.02044/) (2019)
- [Identifying and attacking the saddle point problem in high-dimensional non-convex optimization](https://mlsanity.com/paper/1406.2572/) (2014)
- [The Loss Surfaces of Multilayer Networks](https://mlsanity.com/paper/1412.0233/) (2014)
- [Exponential expressivity in deep neural networks through transient chaos](https://mlsanity.com/paper/1606.05340/) (2016)
- [Contrastive Test-Time Adaptation](https://mlsanity.com/paper/2204.10377/) (2022)
- [Mitigating Neural Network Overconfidence with Logit Normalization](https://mlsanity.com/paper/2205.09310/) (2022)
- [NormFace: L2 Hypersphere Embedding for Face Verification](https://mlsanity.com/paper/1704.06369/) (2017)
- [Sparse Sequence-to-Sequence Models](https://mlsanity.com/paper/1905.05702/) (2019)

## Built on by (most cited first, 8 of 8)

- [Optimal Self-Consistency for Efficient Reasoning with Large Language Models](https://mlsanity.com/paper/2511.12309/) (2025)
- [FLOSS: Free Lunch in Open-vocabulary Semantic Segmentation](https://mlsanity.com/paper/2504.10487/) (2025)
- [Layer by layer, module by module: Choose both for optimal OOD probing of ViT](https://mlsanity.com/paper/2603.05280/) (2026)
- [Confidence and Dispersity as Signals: Unsupervised Model Evaluation and Ranking](https://mlsanity.com/paper/2510.02956/) (2025)
- [ODP-Bench: Benchmarking Out-of-Distribution Performance Prediction](https://mlsanity.com/paper/2510.27263/) (2025)
- [TopoGeoScore: A Self-Supervised Source-Only Geometric Framework for OOD Checkpoint Selection](https://mlsanity.com/paper/2605.08870/) (2026)
- [Measuring Pre-training Data Quality without Labels for Time Series Foundation Models](https://mlsanity.com/paper/2412.06368/) (2024)
- [Teacher-Anchored Selection of Post-Training Quantized Models under Domain Shift](https://mlsanity.com/paper/2609.31155/) (2026)

## Abstract (arXiv)

Leveraging the models' outputs, specifically the logits, is a common approach to estimating the test accuracy of a pre-trained neural network on out-of-distribution (OOD) samples without requiring access to the corresponding ground truth labels. Despite their ease of implementation and computational efficiency, current logit-based methods are vulnerable to overconfidence issues, leading to prediction bias, especially under the natural shift. In this work, we first study the relationship between logits and generalization performance from the view of low-density separation assumption. Our findings motivate our proposed method MaNo which (1) applies a data-dependent normalization on the logits to reduce prediction bias, and (2) takes the Lp norm of the matrix of normalized logits as the estimation score. Our theoretical analysis highlights the connection between the provided score and the model's uncertainty. We conduct an extensive empirical study on common unsupervised accuracy estimation benchmarks and demonstrate that MaNo achieves state-of-the-art performance across various architectures in the presence of synthetic, natural, or subpopulation shifts. The code is available at urlhttps://github.com/Renchunzi-Xie/MaNo.