# Instance-wise Linearization of Neural Network for Model Interpretation

arXiv: https://arxiv.org/abs/2310.16295 · HTML: https://mlsanity.com/paper/2310.16295/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 41 references that are in the map.
- First posted on arXiv 25 Oct 2023.

## Builds on (most cited first, 29 of 29)

- [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)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [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)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["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)
- [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)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [SmoothGrad: removing noise by adding noise](https://mlsanity.com/paper/1706.03825/) (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)
- [Weight Normalization: A Simple Reparameterization to Accelerate Training of Deep Neural Networks](https://mlsanity.com/paper/1602.07868/) (2016)
- [On the Number of Linear Regions of Deep Neural Networks](https://mlsanity.com/paper/1402.1869/) (2014)
- [High-Performance Large-Scale Image Recognition Without Normalization](https://mlsanity.com/paper/2102.06171/) (2021)
- [On the Expressive Power of Deep Neural Networks](https://mlsanity.com/paper/1606.05336/) (2016)
- [Understanding Deep Networks via Extremal Perturbations and Smooth Masks](https://mlsanity.com/paper/1910.08485/) (2019)
- [Sensitivity and Generalization in Neural Networks: an Empirical Study](https://mlsanity.com/paper/1802.08760/) (2018)
- [Object Detectors Emerge in Deep Scene CNNs](https://mlsanity.com/paper/1412.6856/) (2014)
- [Complexity of Linear Regions in Deep Networks](https://mlsanity.com/paper/1901.09021/) (2019)
- [Bounding and Counting Linear Regions of Deep Neural Networks](https://mlsanity.com/paper/1711.02114/) (2017)
- [Do Feature Attribution Methods Correctly Attribute Features?](https://mlsanity.com/paper/2104.14403/) (2021)
- [Demystifying the Draft EU Artificial Intelligence Act](https://mlsanity.com/paper/2107.03721/) (2021)
- [Empirical Bounds on Linear Regions of Deep Rectifier Networks](https://mlsanity.com/paper/1810.03370/) (2018)
- [Towards Robust, Locally Linear Deep Networks](https://mlsanity.com/paper/1907.03207/) (2019)
- [Dissecting Deep Neural Networks](https://mlsanity.com/paper/1910.03879/) (2019)

## Abstract (arXiv)

Neural network have achieved remarkable successes in many scientific fields. However, the interpretability of the neural network model is still a major bottlenecks to deploy such technique into our daily life. The challenge can dive into the non-linear behavior of the neural network, which rises a critical question that how a model use input feature to make a decision. The classical approach to address this challenge is feature attribution, which assigns an important score to each input feature and reveal its importance of current prediction. However, current feature attribution approaches often indicate the importance of each input feature without detail of how they are actually processed by a model internally. These attribution approaches often raise a concern that whether they highlight correct features for a model prediction. For a neural network model, the non-linear behavior is often caused by non-linear activation units of a model. However, the computation behavior of a prediction from a neural network model is locally linear, because one prediction has only one activation pattern. Base on the observation, we propose an instance-wise linearization approach to reformulates the forward computation process of a neural network prediction. This approach reformulates different layers of convolution neural networks into linear matrix multiplication. Aggregating all layers' computation, a prediction complex convolution neural network operations can be described as a linear matrix multiplication F(x) = W · x + b. This equation can not only provides a feature attribution map that highlights the important of the input features but also tells how each input feature contributes to a prediction exactly. Furthermore, we discuss the application of this technique in both supervise classification and unsupervised neural network learning parametric t-SNE dimension reduction.