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Context: We investigated the following four regularizations. All are designed to overcome different pathologies commonly encountered by gradient descent without regularization. Gaussian blur: Producing images via gradient ascent tends to produce examples with high frequency information (see Supplementary Section S1 for a possible reason). While these images cause high activations, they are neither realistic nor interpretable (Nguyen et al., 2014). A useful regularization is thus to penalize high frequency information. We implement this as a Gaussian blur step r_{\theta}(\mathbf{x})=\mathrm{GaussianBlur}(\mathbf{x},\theta_{\mathrm{b\_width}}). Convolving with a blur kernel is more computationally expensive than the other regularization methods, so we added another hyperparameter \theta_{\mathrm{b\_every}} to allow, for example, blurring every several optimization steps instead of every step. Blurring an image multiple times with a small width Gaussian kernel is equivalent to blurring once with a larger width kernel, and the effect will be similar even if the image changes slightly during the optimization process. This technique thus lowers computational costs without limiting the expressiveness of the regularization. Mahendran & Vedaldi (2014) used a penalty with a similar effect to blurring, called total variation, in their work reconstructing images from layer codes. The second tool — new regularizations that enable improved, interpretable, optimized visualizations of learned features — will help researchers and practitioners understand, debug, and improve their models. The visualizations also reveal a new twist in an ongoing story. Previous studieshave shown that discriminative networks can easily be fooled or hacked by the addition of certain structurednoise in image space (Szegedy et al., 2013; Nguyen et al., 2014).An oft-cited reason for this property is that discriminative training leads networksto ignore non-discriminative information in their input, e.g. learning to detect jaguars by matching the unique spots on their fur while ignoring the fact that they have four legs. For this reason it has been seen as a hopeless endeavor to create a generative model in which one randomly samples an x from a broad distribution on the space of all possible imagesand then iteratively transforms x into a recognizable image by moving it to a region that satisfies both a prior p(x) and posterior p(y|x) for some class label y.Past attempts have largely supported this view by producing unrealistic images using this method (Nguyen et al., 2014; Simonyan et al., 2013). Paragraph 10 : L2 decay: A common regularization, L2 decay penalizes large values and is implemented as rθ (x) = (1−θdecay)·x. L2 decay tends to prevent a small number of extreme pixel values from dominating the example image. Such extreme single-pixel values neither occur naturally with great frequency nor are useful for visualization. Paragraph 11 :Clipping pixels with small norm: The first two regularizations suppress high amplitude and high frequency information, so after applying both, we are left with an x∗ that contains somewhat small, somewhat smooth values. However, x∗ will still tend to contain non-zero pixel values everywhere. Even if some pixels in x∗ show the primary object or type of input causing the unit under consideration to activate, the gradient with respect to all other pixels in x∗ will still generally be non-zero, so these pixels will also shift to show some pattern as well, contributing in whatever small way they can to ultimately raise the chosen unit’s activation. We wish to bias the search away from such behavior and instead show only the main object, letting other regions be exactly zero if they are not needed. Paragraph 12 : Clipping pixels with small contribution: Instead of clipping pixels with small norms, we can try something slightly smarter and clip pixels with small contributions to the activation.

Question: Why did the authors choose the four particular regularizations instead of others?
Authors mainly introduce four different and newly used regularizations that would help researchers in visualizing responses from different layers. These regularizations are designed to overcome different pathologies commonly encountered by gradient descent without regularization : L2 decay to penalize large pixel values which do not naturally occur, Gaussian blur:a useful regularization to iteratively penalize high frequency information associated with generated images via gradient ascent through each optimization step, Clipping pixels with small norm or Clipping pixels with small contribution.