ICASSP 2017 Tutorial on Methods for Interpreting and Understanding Deep Neural Networks G. Montavon, W. Samek, K.-R. Müller Part 2: Making Deep Neural Networks Transparent 5 March 2017
Making Deep Neural Nets Transparent DNN transparency interpreting models explaining decisions activation data sensitivity decomposition maximization generation analysis - Berkes 2006 - Hinton 2006 - Khan 2001 - Poulin 2006 - Erhan 2010 - Goodfellow 2014 - Gevrey 2003 - Landecker 2013 - Simonyan 2013 - v. den Oord 2016 - Baehrens 2010 - Bach 2015 - Nguyen 2015/16 - Nguyen 2016 - Simonyan 2013 - Montavon 2017 focus on model focus on data ICASSP 2017 Tutorial — G. Montavon, W. Samek, K.-R. Müller 2/44
Making Deep Neural Nets Transparent model analysis decision analysis - visualizing fi lters - include distribution - sensitivity analysis - max. class activation (RBM, DGN, etc.) - decomposition ICASSP 2017 Tutorial — G. Montavon, W. Samek, K.-R. Müller 3/44
Interpreting Classes and Outputs Image classification: GoogleNet "motorbike" Question: How does a “motorbike” typically look like? Quantum chemical calculations: GDB-7 high Question: How to interpret “ α high” in terms of molecular geometry? ICASSP 2017 Tutorial — G. Montavon, W. Samek, K.-R. Müller 4/44
The Activation Maximization (AM) Method Let us interpret a concept predicted by a deep neural net (e.g. a class, or a real-valued quantity): Examples: ◮ Creating a class prototype: max x ∈X log p ( ω c | x ) . ◮ Synthesizing an extreme case: max x ∈X f ( x ) . ICASSP 2017 Tutorial — G. Montavon, W. Samek, K.-R. Müller 5/44
Interpreting a Handwritten Digits Classifier converged solutions x ⋆ initial solutions → → optimizing max x p ( ω c | x ) → → ICASSP 2017 Tutorial — G. Montavon, W. Samek, K.-R. Müller 6/44
Interpreting a DNN Image Classifier goose ostrich Images from Simonyan et al. 2013 “Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps” Observations: ◮ AM builds typical patterns for these classes (e.g. beaks, legs). ◮ Unrelated background objects are not present in the image. ICASSP 2017 Tutorial — G. Montavon, W. Samek, K.-R. Müller 7/44
Improving Activation Maximization Activation-maximization produces class-related patterns, but they are not resembling true data points. This can lower the quality of the interpretation for the predicted class ω c . Idea: ◮ Force the interpretation x ⋆ to match the data more closely. This can be achieved by redefining the optimization problem: Find the input pattern that → Find the most likely input maximizes class probability. pattern for a given class. ICASSP 2017 Tutorial — G. Montavon, W. Samek, K.-R. Müller 8/44
Improving Activation Maximization Find the input pattern that Find the most likely input → maximizes class probability. pattern for a given class. x * x 0 x 0 x * ICASSP 2017 Tutorial — G. Montavon, W. Samek, K.-R. Müller 9/44
Improving Activation Maximization Find the input pattern that Find the most likely input → maximizes class probability. pattern for a given class. Nguyen et al. 2016 introduced several enhancements for activation maximization: ◮ Multiplying the objective by an expert p ( x ) : p ( x | ω c ) ∝ p ( ω c | x ) · p ( x ) � �� � old ◮ Optimization in code space: x ⋆ = g ( z ⋆ ) ) + λ � z � 2 z ∈Z p ( ω c | g ( z ) max ���� x These two techniques require an unsupervised model of the data, either a density model p ( x ) or a generator g ( z ) . ICASSP 2017 Tutorial — G. Montavon, W. Samek, K.-R. Müller 10/44
discriminative model log p ( ω c | x ) interpre- 0 1 2 3 4 5 6 7 8 9 AM + density neural 10 tation network - optimum has for ω c clear meaning log p ( x | ω c ) 784 + - objective can be + const. hard to optimize x 900 1 log p ( x ) discriminative model density model x =g ( z ) z AM + generator log p ( ω c | x ) neural - more straightforward 900 784 100 10 network to optimize - not optimizing log p( x | ω c ) 0 1 2 3 4 5 6 7 8 9 generative model ICASSP 2017 Tutorial — G. Montavon, W. Samek, K.-R. Müller 11/44
Comparison of Activation Maximization Variants simple AM AM-density AM-gen simple AM (init. to (init. to (init. to (initialized class class class to mean) means) means) means) Observation: Connecting to the data leads to sharper prototypes. ICASSP 2017 Tutorial — G. Montavon, W. Samek, K.-R. Müller 12/44
Enhanced AM on Natural Images Images from Nguyen et al. 2016. “Synthesizing the preferred inputs for neurons in neural networks via deep generator networks” Observation: Connecting AM to the data distribution leads to more realistic and more interpretable images. ICASSP 2017 Tutorial — G. Montavon, W. Samek, K.-R. Müller 13/44
Summary ◮ Deep neural networks can be interpreted by finding input patterns that maximize a certain output quantity (e.g. class probability). ◮ Connecting to the data (e.g. by adding a generative or density model) improves the interpretability of the solution. x * x 0 x 0 x * ICASSP 2017 Tutorial — G. Montavon, W. Samek, K.-R. Müller 14/44
Limitations of Global Interpretations Question: Below are some images of motorbikes. What would be the best prototype to interpret the class “motorbike”? Observations: ◮ Summarizing a concept or category like “motorbike” into a single image can be difficult (e.g. different views or colors). ◮ A good interpretation would grow as large as the diversity of the concept to interpret. ICASSP 2017 Tutorial — G. Montavon, W. Samek, K.-R. Müller 15/44
From Prototypes to Individual Explanations Finding a prototype: GoogleNet "motorbike" Question: How does a “motorbike” typically look like? Individual explanation: GoogleNet "motorbike" Question: Why is this example classified as a motorbike? ICASSP 2017 Tutorial — G. Montavon, W. Samek, K.-R. Müller 16/44
From Prototypes to Individual Explanations Finding a prototype: GDB-7 high Question: How to interpret “ α high” in terms of molecular geometry? Individual explanation: GDB-7 = ... Question: Why α has a certain value for this molecule? ICASSP 2017 Tutorial — G. Montavon, W. Samek, K.-R. Müller 17/44
From Prototypes to Individual Explanations Other examples where individual explanations are preferable to global interpretations: ◮ Brain-computer interfaces: Analyze input data for a given user at a given time in a given environment. ◮ Personalized medicine: Extracting the relevant information about a medical condition for a given patient at a given time. Each case is unique and needs its own explanation. ICASSP 2017 Tutorial — G. Montavon, W. Samek, K.-R. Müller 18/44
From Prototypes to Individual Explanations model analysis decision analysis - visualizing fi lters - include distribution - sensitivity analysis - max. class activation (RBM, DGN, etc.) - decomposition ICASSP 2017 Tutorial — G. Montavon, W. Samek, K.-R. Müller 19/44
Explaining Decisions Goal: Determine the relevance of each input variable for a given decision f ( x 1 , x 2 , . . . , x d ) , by assigning to these variables relevance scores R 1 , R 2 , . . . , R d . f ( x ) R 1 R 2 x 2 f ( x ') R 1 R 2 x 1 ICASSP 2017 Tutorial — G. Montavon, W. Samek, K.-R. Müller 20/44
Basic Technique: Sensitivity Analysis Consider a function f , a data point x = ( x 1 , . . . , x d ) , and the prediction f ( x 1 , . . . , x d ) . Sensitivity analysis measures the local variation of the function along each input dimension � � ∂ f � 2 � R i = � ∂ x i x = x Remarks: ◮ Easy to implement (we only need access to the gradient of the decision function). ◮ But does it really explain the prediction? ICASSP 2017 Tutorial — G. Montavon, W. Samek, K.-R. Müller 21/44
Explaining by Decomposing R 3 R 2 R 4 aggregate R 1 f ( x ) = quantity � i R i = f ( x ) decomposition Examples: ◮ Economic activity (e.g. petroleum, cars, medicaments, ...) ◮ Energy production (e.g. coal, nuclear, hydraulic, ...) ◮ Evidence for object in an image (e.g. pixel 1, pixel 2, pixel 3, ...) ◮ Evidence for meaning in a text (e.g. word 1, word 2, word 3, ...) ICASSP 2017 Tutorial — G. Montavon, W. Samek, K.-R. Müller 22/44
What Does Sensitivity Analysis Decompose? Sensitivity analysis � ∂ f � � 2 � R i = � ∂ x i x = x is a decomposition of the gradient norm �∇ x f � 2 . � i R i = �∇ x f � 2 Proof: Sensitivity analysis explains a variation of the function, not the function value itself. ICASSP 2017 Tutorial — G. Montavon, W. Samek, K.-R. Müller 23/44
What Does Sensitivity Analysis Decompose? Example: Sensitivity for class “car” input image sensitivity ◮ Relevant pixels are found both on cars and on the background. ◮ Explains what reduces/increases the evidence for cars rather what is the evidence for cars. ICASSP 2017 Tutorial — G. Montavon, W. Samek, K.-R. Müller 24/44
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