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@@ -113,7 +113,7 @@ $$
 
 [Comp NN Patches]
 
-As written, the above procedure is inefficient because features are interpolated (to pixel resolution) before they are matched to the patch database. Instead, it is natural to match features at their native resolution, and then interpolate the matches. This results in significant speed ups. For example, the bottleneck layer has an activation map of size $1 \times 1 \times 5 1 2$ . Matching to bottleneck features in the re y refers to pixels of set S (m⇤) from the nth training image.training set is quite fast because it acts as a compact global descriptor for matching entire images. j   The downside is that the matches are not compositional. By matching to convolutional embeddings rse-to-fine nearest-neighbor search: An important special case is the bottleneck feature, whichextracted from later layers, one can compute progressively more compositional matches, that are omputed from an activation map of size 1 ⇥ 1 ⇥ 512. In this case, we posit that the corresponding512initially global, then patch-based, and finally pixel-based (see Fig. 4). In our experiments, we found ure ij (x) 2 R is a good global descriptor of image x. In our experiments, we found thatthat such patch embeddings could be used to prune the NN pixel search, significantly speeding up run-time performance (e.g., we first prune the training database to a shortlist of images with similar bottleneck features, and then search through these images for similar patches, and then search through those patches for similar pixels).
+As written, the above procedure is inefficient because features are interpolated (to pixel resolution) before they are matched to the patch database. Instead, it is natural to match features at their native resolution, and then interpolate the matches. This results in significant speed ups. For example, the bottleneck layer has an activation map of size $1 \times 1 \times 5 1 2$ . Matching to bottleneck features in the re y refers to pixels of set S (m⇤) from the nth training image.training set is quite fast because it acts as a compact global descriptor for matching entire images. j   The downside is that the matches are not compositional. By matching to convolutional embeddings rse-to-fine nearest-neighbor search: An important special case is the bottleneck feature, whichextracted from later layers, one can compute progressively more compositional matches, that are omputed from an activation map of size 1 ⇥ 1 ⇥ 512. In this case, we posit that the corresponding512initially global, then patch-based, and finally pixel-based (see Fig. 4). In our experiments, we found ure ij (x) 2 R is a good global descriptor of image x. In our experiments, we found thatthat such patch embeddings could be used to prune the NN pixel search, significantly speeding up run-time performance (e.g., we first prune the training database to a shortlist of images with similar bottleneck features, and then search through these images for similar patches, and then search through those patches for similar pixels).
 
 ![](images/0c1372504d35f1c2317feb5577039d1e3798a26a4860ffdf287db12a4dec58b1.jpg)  
 Comp-NN in different embedding space: [Deva: Add the input label image on theFigure 4: Adding composition by matching to later layers: We apply compositional nearestneighbor matching to features extracted from different layers, starting with the bottleneck layer 6  2     and progressing to the penultimate deconv2 layer. We match local neighborhoods of convolutional embeddings, which naturally allows for more composition as we use later laters.
@@ -121,7 +121,7 @@ Comp-NN in different embedding space: [Deva: Add the input label image on theFig
 ![](images/2f69f8c3f1a1c1a94d612af578ad3b9b81228e2ebe646b107d6af265738d00e4.jpg)  
 ixels to apply a linear projection. For correctness, considering feature positions i in decoder4Figure 5: Original labels v.s. self-supervised labels: Given the label input on the left, we show reh a shape of 32 ⇤ 32 ⇤ 256, we can rewrite i as (x, y) where x = i/32, y = i%32. Thus, eachsults of Pix2Pix in the Convolutional Neural Networks column, and non-parametric matching to the ure is corresponding to a 8 ⇤ 8 image patch on final output with a shape of 256 ⇤ 256 ⇤ 3. Hence,training set using the original labels and the predicted “self-supervised” labels of the Pix2Pix netj      ⇤    ⇤  ⇤    ⇤work. Generating images with the predicted labels looks smoother, though the qualitative behavior ...3]. Thus, one can generate output results by constructing a dataset of training patches withof the network is still explained by the original training labels. We quantify this in our experimental ij n     n,Sj (i)         results, and include additional qualitative visualizations of the original and self-supervised labels in Figs. 13 and 14.
 
-Bias modification: Finally, our results suggest that the matching database from Eq.(2) serves as mory by changing the dataset of training images x , labels y , or both. We experimentan explicit “associative memory” of a network (Carpenter, 1989). We can explicitly modify the various modifications in our experimental results. Onememory by changing the dataset of training images $\ { \bar { \{ \{ x } }   _ { n } \}$ cation th, labels $\left\{ y _ { n } \right\}$ sistently produced, or both. We experiment other visual results was to refine the training labels to those predicted by a network:with various modifications in our experimental results. One modification that consistently produced     smoother visual results was to refine the training labels to those predicted by a network:
+Bias modification: Finally, our results suggest that the matching database from Eq.(2) serves as mory by changing the dataset of training images x , labels y , or both. We experimentan explicit “associative memory” of a network (Carpenter, 1989). We can explicitly modify the various modifications in our experimental results. Onememory by changing the dataset of training images $\ { \bar { \{ \{ x } }   _ { n } \}$ cation th, labels $\left\{ y _ { n } \right\}$ sistently produced, or both. We experiment other visual results was to refine the training labels to those predicted by a network:with various modifications in our experimental results. One modification that consistently produced     smoother visual results was to refine the training labels to those predicted by a network:
 
 $$
 \{ \left( x _ { n } , y _ { n } \right) \} \Rightarrow \{ \left( x _ { n } , C N N ( x _ { n } ) \right) \} .