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Pytorch iAlgebra

Document|Paper|References

Pytorch iAlgebra is an interactive interpretation library for deep learning on Pytorch.

Pytorch iAlgebra provides an interactive frame for interpreting a group of deep leanring models using a set of interpretation methods.

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iAlgebra Operations

Operators

Identity

$$ [\phi(x)]{i}=\frac{1}{d} \sum{k=0}^{d-1} \mathbb{E}{I{k}}\left[f\left(x_{I_{k} \cup{i}}\right)-f\left(x_{I_{k}}\right)\right] $$

Projection

$$ \left[\Pi_{w}(x)\right]{i}=\left{\begin{array}{cc}{\frac{1}{|w|} \sum{k=0}^{|w|-1} \mathbb{E}{I{k}}\left[f\left(x_{I_{k} \cup{i}}\right)-f\left(x_{I_{k}}\right)\right]} & {i \in w} \ {0} & {i \notin w}\end{array}\right. $$

Selection $$ \left[\sigma_{l}(x)\right]{i}=\left[\phi\left(x ; \bar{x}, f{l}\right)\right]_{i} $$

Join

$$ \left[x \bowtie x^{\prime}\right]{i}=\frac{1}{2}\left([\phi(x ; \bar{x}, f)]{i}+\left[\phi\left(x^{\prime} ; \bar{x}, f\right)\right]_{i}\right) $$

Anti-Join

$$ \left[x \diamond x^{\prime}\right]{i}=\left(\left[\phi\left(x ; x^{\prime}, f\right)\right]{i},\left[\phi\left(x^{\prime} ; x, f\right)\right]_{i}\right) $$

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Supportive DNN and Interpretation Models

DNN Models

Model Performance on dataset Mnist

Dataset	Models
Mnist	LeNet-L1	LeNet-L2
Accuracy	98.866%	99.020%

Model Performance on dataset Cifar10

Dataset	Models
Cifar10	Vgg19 -L1	Vgg19-L2
Accuracy	98.866%	99.020%

Interpretation Methods

In detail, we implement the following interpretation methods as the identity in Pytorch-iAlgebra.

• GradSaliency from Simonyan et al.:Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps (CVPR 2013)

• SmoothGrad from Smilkov et al.:SmoothGrad: removing noise by adding noise

• Mask from Fong et al.:Interpretable Explanations of Black Boxes by Meaningful Perturbation (ICCV 2017)

• GradCam from Selvaraju et al.: Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization (ICCV 2017)

• GuidedBackpropGrad from Springenberg et al.:Striving for Simplicity: The All Convolutional Net (ICLR 2015)

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Installation

Library dependencies for the Pytorch-iAlgebra. Before installation, you need to install these with

$ pip install -r requirements.txt

Then Pytorch-iAlgebra can be installed by:

$ pip install pytorch-ialgebra