## 3 Attempts at Model Interpretation
### Reasons for Model Interpretation Failure  
The examples we reviewed, as well as other interpretation models for implicit non-linear stochastic models, are very elegant attempts to reduce the stunning dimensionality of the dNN domain and range spaces to dimensions that can be understood by human users. However, these approaches merely provide the user with a narrative that enables a superficial, partial understanding of what is going on inside the dNN, and no causal explanation of _how it works_. This understanding may help some skeptics to develop a kind of emotional trust in the function of dNNs. It can certainly help to understand their limitations. But it can provide no explanation of a sort that would work reliably from one input to the next. Deep learning models cannot be _explained_, because deep learning induces model parameterizations with millions or billions of parameters to master classification or regression tasks. dNNs solve these tasks in a manner that differs completely from the way humans interpret text, language, sounds, images, or smell or somatosensory input.  
Some authors think that neural networks are modeled in a way that mimics the structure of human neural systems and that the inspection of the artificial networks can teach us something about the way the nervous system works [32]. Though it is true that convolutional neural networks, for example, were designed by using basic models of the mammalian visual system, the details of the natural and artificial systems are radically different. Consider that one single neuron in the visual cortex (which is supposed to be modeled by one node of a convolutional neural network in its upper layers) contains millions of functionally relevant molecules and interacts directly and indirectly with billions of other neurons, each again endowed with millions of functional molecules, to contribute to the conscious experience of vision. For more details see [33; 34] (Ch. 2-3)).  
In this context, the results of [PERSON] et al. are very relevant. They showed that neural network image classifiers can be nudged into a complete misclassification of images when the input material is mixed with small and universal perturbation vectors [24] generated using an iterative parsimonious perturbation search algorithm. When the image data are perturbed using this universal vector, drastic misclassification occurs. For example, a sock is classified as an elephant or a whale as a bird. [PERSON] and [PERSON] [25] hypothesized that these perturbations are possible because convolutional neural networks (a CNN is a neural network that can take matrices (image data) as input by using convolutional filter matrices on the input data to map their matrix structure to the nodes of the neural network). use different features of the input space to perform their classifications than humans do--features which they call'surface statistical regularities'--and that the perturbations alter these features to bring about the mentioned drastic effects.  
They used Fourier transformations to construct datasets that share with the original images exactly identical high-level abstractions but differ with regard to surface regularities. For example, a portrait was transformed into an image that preserves the feature contours but uses different colors, with the result that the transformed result maintains the features of the face but presents it in unnatural colors (like the Marylin Monroe series by [PERSON]).  
They found that the dNNs tend to model the 'Fourier image statistics of the training dataset, sometimes exhibiting up to a 28% generalization gap across the various test sets.' This confirms their hypothesis and explains why dNN-image classification can be perturbed so easily. It also provides insight into the way in which these models achieve their results namely--and in contrast to humans--without using any semantics. This provides yet another reason why dNNs are non-explainable.