Interpretability


CSE 891: Deep Learning

Vishnu Boddeti

Today

  • Visualization
  • Adversarial Examples
  • Style Transfer

Looking Inside a Neural Network

What are the intermediate features looking for?

Weights

Interpreting Weights: First Layer

AlexNet
ResNet-18
ResNet-101
DenseNet

Interpreting Weights: Higher Layer

ConvNetJS

Features

Interpreting Features

  • Last Layer:
    • 4096-dimensional feature vector for an image
      • layer immediately before the classifier
    • Run the network on many images and collect the feature vectors

Nearest Neighbors

$L_2$ Nearest Neighbors in feature space.

Dimensionality Reduction

  • Visualize the space of feature vectors via dimensionality reduction to 2 dimensions.
  • Dimensionality Reduction:
    • Principal Component Analysis (PCA)
    • More Complex: t-SNE
    • Even more complex: DeepMDS
  • Van der Maaten and Hinton "Visualizing Data using t-SNE" JMLR 2008
  • Gong et.al. "On the Intrinsic Dimensionality of Image Representations" CVPR 2019

Dimensionality Reduction

521-D Features
10-D Features

Activations

Visualizing Activations

  • conv5 feature map is $128\times 13\times 13$; visualize as 128 $13\times 13$ grayscale images.

Maximally Activating Patches

  • Pick a layer and a channel; e.g. conv5 is $128\times 13\times 13$, pick channel 17/128
  • Run many images through the network, record values of chosen channel
  • Visualize image patches that correspond to maximal activations
  • Springenberg et.al. "Striving for Simplicity: The All Convolutional Net" ICLR Workshop 2015

Which Pixels Matter?

  • Saliency via Occlusion
    • Mask part of the image before feeding to CNN, check how much predicted probabilities change
  • Zeiler et.al. "Visualizing and Understanding Convolutional Networks" ECCV 2014

Which Pixels Matter?

  • Saliency via Backpropagation
    • Forward pass: Compute probabilities
  • Compute gradient of (unnormalized) class score with respect to image pixels, take absolute value and max over RGB channels
  • Simonyan et.al. "Deep Inside Convolutional Networks: Visualizing Image Classification Models and Saliency Maps" ICLR Workshop 2014

Saliency via Backprop

  • Simonyan et.al. "Deep Inside Convolutional Networks: Visualizing Image Classification Models and Saliency Maps" ICLR Workshop 2014

Segmentation from Saliency Maps

Using GrabCut on saliency map

Guided Backpropagation

  • Guided backprop is a total hack, but useful.
  • Do the backward pass as normal, but apply the ReLU nonlinearity to all the activation error signals.
    • $$ \begin{equation} y = \mbox{ReLU}(z) \quad z' = \begin{cases} y' & \quad \text{if } z > 0 \mbox{ and } y' > 0 \\ 0 & \quad \text{otherwise}\end{cases} \end{equation} $$
  • Note: this isn’t really the gradient of anything!
  • We want to visualize what excites a given unit, not what suppresses it.
Backprop
Guided Backprop

Guided Backpropagation Examples

Class Activation Mapping (CAM)

$$F_k = \frac{1}{HW}\sum_{h,w} f_{h,w,k}$$
$$S_c = \sum_{k} w_{k,c} F_{k}$$
  • Zhou et al, “Learning Deep Features for Discriminative Localization”, CVPR 2016

Class Activation Mapping Examples

Class activation maps of top 5 predictions
Problem: can only apply to last convolutional layer

Gradient Weighted Class Activation Mapping (Grad-CAM)

    • Pick any layer, with activations $\mathbf{A} \in \mathbb{R}^{H\times W\times K}$
    • Compute gradient of class score $\mathbf{S}_c$ with respect to $\mathbf{A}$
      • $$\frac{\partial \mathbf{S}_c}{\partial \mathbf{A}} \in \mathbb{R}^{H \times W \times K}$$
    • Global average pool of the gradients to get weights $\alpha \in \mathbb{R}^K$:
      • $$\alpha_k = \frac{1}{HW}\sum_{h,w} \frac{\partial \mathbf{S}_c}{\partial A_{h,w,k}}$$
    • Compute activation map $\mathbf{M}^c \in \mathbb{R}^{H,W}$:
      • $$M^c_{h,w} = ReLU(\sum_{k}\alpha_kA_{h,w,k})$$
  • Selvaraju et al, "Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization", CVPR 2017

Grad-CAM Examples

  • Selvaraju et al, "Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization", CVPR 2017

Grad-CAM Examples

  • Can be applied to other tasks like image captioning, dense prediction etc.
  • Selvaraju et al, "Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization", CVPR 2017

Visualizing CNN Features

Guided Backprop: Find part of the image a neuron responds to
$$\mathbf{I}^* = \underset{\mathbf{I}}{\operatorname{arg max}} \color{cyan}{f(\mathbf{I})} + \color{yellow}{R(\mathbf{I})}$$
  • $\color{cyan}{f(\mathbf{I})}$: Neuron Value
  • $\color{yellow}{R(\mathbf{I})}$: Natural Image Regularizer

Gradient Ascent

  • Initialize image to zeros
  • Repeat:
    • Forward image to compute current scores
    • Backprop to get gradient of neuron value with respect to image pixels
    • Make a small update to the image

Gradient Ascent

$$\underset{\mathbf{I}}{\operatorname{arg max}} S_c(\mathbf{I}) -\lambda\color{red}{\|\mathbf{I}\|_2^2}$$
  • Simple Regularizer: Penalize $L_2$ norm of generated image

Gradient Ascent

$$\underset{\mathbf{I}}{\operatorname{arg max}} S_c(\mathbf{I}) -\lambda\|\mathbf{I}\|_2^2$$
  • Better Regularizer: Penalize $L_2$ norm of image; also during optimization periodically
    • Gaussian blur image
    • Clip pixels with small values to 0
    • Clip pixels with small gradients to 0
  • Yosinski et.al. "Understanding Neural Networks through Deep Visualization" ICML DL Workshop 2014

Gradient Ascent

Use the same approach to visualize intermediate features

Gradient Ascent

  • Adding "multi-faceted" visualization gives even nicer results along with more careful regularization, center-bias.
  • Nguyen et.al. "Multifaceted Feature Visualization: Uncovering the Different Types of Features Learned By Each Neuron in Deep Neural Networks" ICML Visualization for DL Workshop 2016

Gradient Ascent

  • Nguyen et.al. "Synthesizing the preferred inputs for neurons in neural networks via deep generator networks" NeurIPS 2016

Adversarial Examples

What are Adversarial Examples?

  • One of the most surprising findings about neural nets has been the existence of adversarial inputs, i.e. inputs optimized to fool an algorithm.
  • Given an image for one category (e.g. "cat"), compute the image gradient to maximize the network’s output unit for a different category (e.g. "dog")
    • Perturb the image slightly in this direction, and chances are, the network will think it is a dog.
    • A faster alternative is to take the sign of the entries in the gradient; this is called the fast gradient sign method.

Adversarial Examples: Recipe

    • Start from an arbitrary image
    • Pick an arbitrary category
    • Modify image to maximize the class score (typically via SGD)
    • Stop when the network is fooled
  • Szegedy et.al. "Intriguing properties of neural networks" ICLR 2014

Adversarial Examples

African Elephant
Koala
Difference
$10\times$ Difference
Schooner
Schooner
Difference
$10\times$ Difference

Adversarial Examples

  • 2013: this is cute
    • The paper which introduced adversarial examples was titled "Intriguing Properties of Neural Networks."
  • 2018: serious security threat
    • No reliable methods yet to defend against them.
      • 7 of 8 proposed defenses accepted to ICLR 2018 were cracked within days.
    • Adversarial examples transfer to different networks trained on a totally separate training set!
    • You don’t need access to the original network; you can train up a new network to match its predictions, and then construct adversarial examples for that.
      • Attack carried out against proprietary classification networks accessed using prediction APIs (MetaMind, Amazon, Google)

Physical Attacks

Adversarial T-Shirts

Style Transfer

Feature Inversion

  • Given a CNN activation for an image, find a new image that:
    • Matches the given activation map
    • "looks natural" (image prior regularization)
$$ \begin{eqnarray} \mathbf{x}^* &=& \underset{\mathbf{x} \in \mathbb{R}^{H\times W\times C}}{\operatorname{arg min}} \mathcal{L}\left(\Phi(\mathbf{x}), \Phi_0)\right) + \lambda\mathcal{R}(\mathbf{x}) \\ \mathcal{L}\left(\Phi(\mathbf{x}), \Phi_0)\right) &=& \|\Phi(\mathbf{x})-\Phi_0\|_2^2 \\ \mathcal{R}_{\beta}(\mathbf{x}) &=& \underbrace{\sum_{i,j}\left((x_{i,j+1}-x_{ij})^2+(x_{i+1,j}-x_{ij})^2\right)^{\frac{\beta}{2}}}_{\mbox{Total Variation (encourages spatial smoothness)}} \end{eqnarray} $$

Feature Inversion

Reconstructing from different layers of VGG-16

DeepDream: Feature Amplification

  • Rather than synthesizing an image to maximize a specific neuron, instead try to amplify the neuron activations at some layer in the network
  • Choose an image and a layer in a CNN; repeat:
      • Forward: compute activations at chosen layer
      • Set gradient of chosen layer equal to its activation
      • Backward: Compute gradient on image
      • Update Image

What is Texture Synthesis

  • Given a sample patch of some texture, can we generate a bigger image of the same texture?
  • Generate pixels one at a time in scanline order;form neighborhood of already generated pixels and copy nearest neighbor from input.

Texture Synthesis: Nearest Neighbor

Texture Synthesis: Neural Networks

  • Each layer of CNN gives $C \times H \times W$ tensor of features; $H \times W$ grid of $C$-dimensional vectors
  • Outer product of two C-dimensional vectors gives $C \times C$ matrix of element wise products
  • Average over all HW pairs gives Gram Matrix of shape $C \times C$ giving unnormalized covariance
  • Efficient to compute; reshape features from $C\times H\times W$ to $\mathbf{F}=C\times HW$, the compute $\mathbf{G}=\mathbf{FF}^T$

Neural Texture Synthesis

  • Pretrain a CNN on ImageNet (VGG-19)
  • Run input texture forward through CNN, record activations on every layer; layer $i$ gives feature map of shape $C_i \times H_i \times W_i$
  • At each layer compute the Gram matrix giving outer product of features: $G_{ij}^l = \sum_{k}F_{ik}^lF_{jk}^l$
  • Initialize generated image from random noise
  • Pass generated image through CNN, compute Gram matrix on each layer

Neural Texture Synthesis

  • Reconstructing texture from higher layers recovers larger features from the input texture

Neural Style Transfer

  • Feature Reconstruction + Gram Reconstruction
  • Johnson et al, "Perceptual Losses for Real-Time Style Transfer and Super-Resolution", ECCV 2016

Neural Style Transfer

  • Gatys et al, "Image Style transfer using convolutional neural networks", CVPR 2016

Neural Style Transfer

Neural Style Transfer

Recall Normalization Methods?

Fast Neural Style Transfer

  • Replacing Batch Normalization with Instance Normalization improves results.
  • Ulyanov et al, "Texture Networks: Feed-forward Synthesis of Textures and Stylized Images", ICML 2016
  • Ulyanov et al, "Instance Normalization: The Missing Ingredient for Fast Stylization", Arxiv 2016

One Network, Many Styles

  • Dumoulin et al, "A Learned Representation for Artistic Style", ICLR 2017

One Network, Many Styles

  • Use the same network for multiple styles using conditional instance normalization: learn separate scale and shift parameters per style
  • Dumoulin et al, "A Learned Representation for Artistic Style", ICLR 2017

Summary

  • Many methods for interpreting CNNs
    • Activations: Nearest Neighbors, Dimensionality Reduction, Maximal Patches, Occlusion
    • Gradients: Grad-CAM, Saliency Maps, Class Visualization, Adversarial Images, Feature Inversion
    • Fun Applications: DeepDream, Style Transfer