grammar

content/post/2024-02-23-magnitude-constrained-featurevis.md

@@ -17,7 +17,7 @@ Unlike shallow models like VGG etc, running featurevis on deeper models yield hi
 
 This proves that featurevis images contain a a much larger amount of high frequency components. The solution to this problem would be to constrain the power spectrum to lower frequency components only.
 
-Apart from constraining high frequencies, the method is also motivated by psychophysics experiments [1, 2] that have shown that  when viewing images, humans are more sensitive to differences in phase than in magnitude. The authors build an analogous mathematical constraint for featurevis which optimizes only the phase of the image and not the magnitudes of the frequency components. 
+Apart from constraining high frequencies, the method is also motivated by psychophysics experiments [1, 2] that have shown that  when viewing images, humans are more sensitive to differences in phase than in magnitude. The authors build an analogous mathematical constraint for featurevis which optimizes only the phase of each frequency component (wave) and not the magnitudes of the frequency components. 
 
 # Method
 

posts/2024-02-23-magnitude-constrained-featurevis.html

@@ -31,7 +31,7 @@ <h1 class="title">MaCo - feature visualization for deeper networks</h1>
 <p>Unlike shallow models like VGG etc, running featurevis on deeper models yield higher frequency components which are impossible to interpret by humans. To illustrate this, they ran featurevis on the logits of a ViT trained on imagenet and compared it’s mean power spectrum (left) with that of the Imagenet dataset’s power spectrum (right).</p>
 <p><img src = "https://github.com/Mayukhdeb/notes/assets/53133634/c2c0133f-4e60-4eea-ace6-cad344176aaf" width = "80%"></p>
 <p>This proves that featurevis images contain a a much larger amount of high frequency components. The solution to this problem would be to constrain the power spectrum to lower frequency components only.</p>
-<p>Apart from constraining high frequencies, the method is also motivated by psychophysics experiments [1, 2] that have shown that when viewing images, humans are more sensitive to differences in phase than in magnitude. The authors build an analogous mathematical constraint for featurevis which optimizes only the phase of the image and not the magnitudes of the frequency components.</p>
+<p>Apart from constraining high frequencies, the method is also motivated by psychophysics experiments [1, 2] that have shown that when viewing images, humans are more sensitive to differences in phase than in magnitude. The authors build an analogous mathematical constraint for featurevis which optimizes only the phase of each frequency component (wave) and not the magnitudes of the frequency components.</p>
 <h1 id="method">Method</h1>
 <p>The first thing that they do is that they break down the fourier spectrum into magnitude and <a href="https://mayukhdeb.github.io/notes/posts/2024-02-24-phase-spectrum.html">phase spectrum</a>. They optimize the phase spectrum of the image while keeping the magnitude spectrum to a constant at an average value computed over a set of natural images.</p>
 <p><img src = "https://github.com/Mayukhdeb/notes/assets/53133634/4419c6be-da5a-474d-95ae-9aaa9a6b82ab" width = "100%"></p>