# What Does Softmax Probability Tell Us about Classifiers Ranking Across Diverse Test Conditions?

arXiv: https://arxiv.org/abs/2406.09908 · HTML: https://mlsanity.com/paper/2406.09908/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 90 of its 106 references that are in the map.
- First posted on arXiv 14 Jun 2024.

## Builds on (most cited first, 30 of 90)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [BLIP-2: Bootstrapping Language-Image Pre-training with Frozen Image Encoders and Large Language Models](https://mlsanity.com/paper/2301.12597/) (2023)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [BLIP: Bootstrapping Language-Image Pre-training for Unified Vision-Language Understanding and Generation](https://mlsanity.com/paper/2201.12086/) (2022)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [Sigmoid Loss for Language Image Pre-Training](https://mlsanity.com/paper/2303.15343/) (2023)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [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)
- [The Many Faces of Robustness: A Critical Analysis of Out-of-Distribution Generalization](https://mlsanity.com/paper/2006.16241/) (2020)
- [Do ImageNet Classifiers Generalize to ImageNet?](https://mlsanity.com/paper/1902.10811/) (2019)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [Natural Adversarial Examples](https://mlsanity.com/paper/1907.07174/) (2019)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Moment Matching for Multi-Source Domain Adaptation](https://mlsanity.com/paper/1812.01754/) (2018)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [Deep CORAL: Correlation Alignment for Deep Domain Adaptation](https://mlsanity.com/paper/1607.01719/) (2016)
- [In Search of Lost Domain Generalization](https://mlsanity.com/paper/2007.01434/) (2020)
- [Learning Robust Global Representations by Penalizing Local Predictive Power](https://mlsanity.com/paper/1905.13549/) (2019)
- [Domain Generalization: A Survey](https://mlsanity.com/paper/2103.02503/) (2021)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)

## Built on by (most cited first, 6 of 6)

- [Ranked from Within: Ranking Large Multimodal Models Without Labels](https://mlsanity.com/paper/2412.06461/) (2024)
- [Model-agnostic Selective Labeling with Provable Statistical Guarantees](https://mlsanity.com/paper/2510.14581/) (2025)
- [Confidence and Dispersity as Signals: Unsupervised Model Evaluation and Ranking](https://mlsanity.com/paper/2510.02956/) (2025)
- [Noise reduction in BERT NER models for clinical entity extraction](https://mlsanity.com/paper/2603.00022/) (2026)
- [CIAR: Interval-based Collaborative Decoding for Image Generation Acceleration](https://mlsanity.com/paper/2603.25463/) (2026)
- [Teacher-Anchored Selection of Post-Training Quantized Models under Domain Shift](https://mlsanity.com/paper/2609.31155/) (2026)

## Abstract (arXiv)

This work aims to develop a measure that can accurately rank the performance of various classifiers when they are tested on unlabeled data from out-of-distribution (OOD) distributions. We commence by demonstrating that conventional uncertainty metrics, notably the maximum Softmax prediction probability, possess inherent utility in forecasting model generalization across certain OOD contexts. Building on this insight, we introduce a new measure called Softmax Correlation (SoftmaxCorr). It calculates the cosine similarity between a class-class correlation matrix, constructed from Softmax output vectors across an unlabeled test dataset, and a predefined reference matrix that embodies ideal class correlations. A high resemblance of predictions to the reference matrix signals that the model delivers confident and uniform predictions across all categories, reflecting minimal uncertainty and confusion. Through rigorous evaluation across a suite of datasets, including ImageNet, CIFAR-10, and WILDS, we affirm the predictive validity of SoftmaxCorr in accurately forecasting model performance within both in-distribution (ID) and OOD settings. Furthermore, we discuss the limitations of our proposed measure and suggest avenues for future research.