# Probing the Purview of Neural Networks via Gradient Analysis

arXiv: https://arxiv.org/abs/2304.02834 · HTML: https://mlsanity.com/paper/2304.02834/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 69 references that are in the map.
- First posted on arXiv 6 Apr 2023.

## Builds on (most cited first, 30 of 46)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features](https://mlsanity.com/paper/1905.04899/) (2019)
- [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)
- [Adversarial examples in the physical world](https://mlsanity.com/paper/1607.02533/) (2016)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks](https://mlsanity.com/paper/2003.01690/) (2020)
- [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)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [A Closer Look at Memorization in Deep Networks](https://mlsanity.com/paper/1706.05394/) (2017)
- [Grad-CAM++: Improved Visual Explanations for Deep Convolutional Networks](https://mlsanity.com/paper/1710.11063/) (2017)
- [CSI: Novelty Detection via Contrastive Learning on Distributionally Shifted Instances](https://mlsanity.com/paper/2007.08176/) (2020)
- [On the Number of Linear Regions of Deep Neural Networks](https://mlsanity.com/paper/1402.1869/) (2014)
- [Measuring the Intrinsic Dimension of Objective Landscapes](https://mlsanity.com/paper/1804.08838/) (2018)
- [In Search of the Real Inductive Bias: On the Role of Implicit Regularization in Deep Learning](https://mlsanity.com/paper/1412.6614/) (2014)
- [On the Importance of Gradients for Detecting Distributional Shifts in the Wild](https://mlsanity.com/paper/2110.00218/) (2021)
- [Adversarially Robust Generalization Requires More Data](https://mlsanity.com/paper/1804.11285/) (2018)
- [Characterizing Adversarial Subspaces Using Local Intrinsic Dimensionality](https://mlsanity.com/paper/1801.02613/) (2018)
- [Intrinsic dimension of data representations in deep neural networks](https://mlsanity.com/paper/1905.12784/) (2019)
- [Learning Confidence for Out-of-Distribution Detection in Neural Networks](https://mlsanity.com/paper/1802.04865/) (2018)
- [Learning a Deep ConvNet for Multi-label Classification with Partial Labels](https://mlsanity.com/paper/1902.09720/) (2019)
- [Gradients as a Measure of Uncertainty in Neural Networks](https://mlsanity.com/paper/2008.08030/) (2020)

## Built on by (most cited first, 9 of 9)

- [Pursuing Feature Separation based on Neural Collapse for Out-of-Distribution Detection](https://mlsanity.com/paper/2405.17816/) (2024)
- [Controlling Neural Collapse Enhances Out-of-Distribution Detection and Transfer Learning](https://mlsanity.com/paper/2502.10691/) (2025)
- [Low-Dimensional Gradient Helps Out-of-Distribution Detection](https://mlsanity.com/paper/2310.17163/) (2023)
- [Transitional Uncertainty with Layered Intermediate Predictions](https://mlsanity.com/paper/2405.17494/) (2024)
- [Intelligent Multi-View Test Time Augmentation](https://mlsanity.com/paper/2406.08593/) (2024)
- [VOICE: Variance of Induced Contrastive Explanations to quantify Uncertainty in Neural Network Interpretability](https://mlsanity.com/paper/2406.00573/) (2024)
- [Counterfactual Gradients-based Quantification of Prediction Trust in Neural Networks](https://mlsanity.com/paper/2405.13758/) (2024)
- [Are Objective Explanatory Evaluation metrics Trustworthy? An Adversarial Analysis](https://mlsanity.com/paper/2406.07820/) (2024)
- [A unified framework for evaluating the robustness of machine-learning interpretability for prospect risking](https://mlsanity.com/paper/2602.14430/) (2026)

## Abstract (arXiv)

We analyze the data-dependent capacity of neural networks and assess anomalies in inputs from the perspective of networks during inference. The notion of data-dependent capacity allows for analyzing the knowledge base of a model populated by learned features from training data. We define purview as the additional capacity necessary to characterize inference samples that differ from the training data. To probe the purview of a network, we utilize gradients to measure the amount of change required for the model to characterize the given inputs more accurately. To eliminate the dependency on ground-truth labels in generating gradients, we introduce confounding labels that are formulated by combining multiple categorical labels. We demonstrate that our gradient-based approach can effectively differentiate inputs that cannot be accurately represented with learned features. We utilize our approach in applications of detecting anomalous inputs, including out-of-distribution, adversarial, and corrupted samples. Our approach requires no hyperparameter tuning or additional data processing and outperforms state-of-the-art methods by up to 2.7%, 19.8%, and 35.6% of AUROC scores, respectively.