# Understanding Parameter Saliency via Extreme Value Theory

arXiv: https://arxiv.org/abs/2310.17951 · HTML: https://mlsanity.com/paper/2310.17951/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 35 references that are in the map.
- First posted on arXiv 27 Oct 2023.

## Builds on (most cited first, 24 of 24)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Sanity Checks for Saliency Maps](https://mlsanity.com/paper/1810.03292/) (2018)
- [Pruning Filters for Efficient ConvNets](https://mlsanity.com/paper/1608.08710/) (2016)
- [Deeper, Broader and Artier Domain Generalization](https://mlsanity.com/paper/1710.03077/) (2017)
- [RISE: Randomized Input Sampling for Explanation of Black-box Models](https://mlsanity.com/paper/1806.07421/) (2018)
- [Network Dissection: Quantifying Interpretability of Deep Visual Representations](https://mlsanity.com/paper/1704.05796/) (2017)
- [Interpretable Explanations of Black Boxes by Meaningful Perturbation](https://mlsanity.com/paper/1704.03296/) (2017)
- [Learning Structured Sparsity in Deep Neural Networks](https://mlsanity.com/paper/1608.03665/) (2016)
- [Evaluating the visualization of what a Deep Neural Network has learned](https://mlsanity.com/paper/1509.06321/) (2015)
- [Last Layer Re-Training is Sufficient for Robustness to Spurious Correlations](https://mlsanity.com/paper/2204.02937/) (2022)
- [Distilling a Neural Network Into a Soft Decision Tree](https://mlsanity.com/paper/1711.09784/) (2017)
- [NISP: Pruning Networks using Neuron Importance Score Propagation](https://mlsanity.com/paper/1711.05908/) (2017)
- [Counterfactual Explanations and Algorithmic Recourses for Machine Learning: A Review](https://mlsanity.com/paper/2010.10596/) (2020)
- [Identifying and Controlling Important Neurons in Neural Machine Translation](https://mlsanity.com/paper/1811.01157/) (2018)
- [Evaluating Saliency Map Explanations for Convolutional Neural Networks: A User Study](https://mlsanity.com/paper/2002.00772/) (2020)
- [meProp: Sparsified Back Propagation for Accelerated Deep Learning with Reduced Overfitting](https://mlsanity.com/paper/1706.06197/) (2017)
- [Where do Models go Wrong? Parameter-Space Saliency Maps for Explainability](https://mlsanity.com/paper/2108.01335/) (2021)

## Abstract (arXiv)

Deep neural networks are being increasingly implemented throughout society in recent years. It is useful to identify which parameters trigger misclassification in diagnosing undesirable model behaviors. The concept of parameter saliency is proposed and used to diagnose convolutional neural networks (CNNs) by ranking convolution filters that may have caused misclassification on the basis of parameter saliency. It is also shown that fine-tuning the top ranking salient filters efficiently corrects misidentification on ImageNet. However, there is still a knowledge gap in terms of understanding why parameter saliency ranking can find the filters inducing misidentification. In this work, we attempt to bridge the gap by analyzing parameter saliency ranking from a statistical viewpoint, namely, extreme value theory. We first show that the existing work implicitly assumes that the gradient norm computed for each filter follows a normal distribution. Then, we clarify the relationship between parameter saliency and the score based on the peaks-over-threshold (POT) method, which is often used to model extreme values. Finally, we reformulate parameter saliency in terms of the POT method, where this reformulation is regarded as statistical anomaly detection and does not require the implicit assumptions of the existing parameter-saliency formulation. Our experimental results demonstrate that our reformulation can detect malicious filters as well. Furthermore, we show that the existing parameter saliency method exhibits a bias against the depth of layers in deep neural networks. In particular, this bias has the potential to inhibit the discovery of filters that cause misidentification in situations where domain shift occurs. In contrast, parameter saliency based on POT shows less of this bias.