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I asked this question on /r/learnmachinelearning, but there was no answer so I'm reposting it here.

I was reading this article on detecting rectangles in an image, here. My doubt is in the part where the model works fine with detecting a single object, but struggles with two rectangles detection.

The author reasons this as follows:

We train our network on the leftmost image in the plot above. Let’s say 
that the expected bounding box of the left rectangle is at position 1 in the 
target vector (x1, y1, w1, h1), and the expected bounding box of the 
right rectangle is at position 2 in the vector (x2, y2, w2, h2). Apparently, 
our optimizer will change the parameters of the network so that the first 
predictor moves to the left, and the second predictor moves to the right. 
Imagine now that a bit later we come across a similar image, but this 
time the positions in the target vector are swapped (i.e. left rectangle at 
position 2, right rectangle at position 1). Now, our optimizer will pull 
predictor 1 to the right and predictor 2 to the left — exactly the opposite 
of the previous update step! In effect, the predicted bounding boxes stay 
in the center.

I don't understand how this reasoning is correct, apart from the fact that when they try to flip the rectangles to mitigate this error, accuracy actually improves (so there's experimental observation, but not much theoretical reasoning).

The reason I think so is because in case of single rectangle also the network has to learn for all differently placed objects just as in the two-rectangle-case, so there too, it should predict boxes in the somewhat the center only. I have to concede I am only a noob in this, so I would love to find out where I am wrong in my reasoning, because experimentally I am wrong (i.e. accuracy does improve when rectangles are flipped).

Thoughts? Also if this is not the correct sub/forum for these type of questions, please feel free to guide me towards those that better suit the content.

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If I understood that post right (I just skimmed through, so it's possible I missed some details), they are using several predictors on the inputs with several rectangles. This basically means separate, not shared, weights to detect each rectangle.

It's fairly likely that these neurons will adjust to certain areas on the input image. As far as the neurons are concerned, they are "punished" if they detect the wrong rectangle, as if the other rectangle is the noise that the network should learn to ignore. As a result, the "left" predictor learns to fire more actively when it detects a rectangle on the left, because there's high chance it's the correct one. Same for the "right" predictor.

When, all of a sudden, the training image swaps the targets, each predictor gets confused. Because now what they used to detect as noise becomes the ground truth and vice versa. It certainly hurts the performance and makes the network be sure the most, when the target is around the center. When the targets are flipped, the dataset becomes more consistent and less confusing for the network, it's no wonder that the accuracy goes up.

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