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The last argument is the number of feature maps produced, i.e. you have 64 feature maps of size 16x16. Each feature map is still smaller than your input image. The number of feature maps produced depends on the number of filters set in the convolutional layer.

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The formula which you posted in your question refers to binary_crossentropy, not categorical_crossentropy. The former is used when you have only one class. The latter refers to a situation when you have multiple classes and its formula looks like below: $$J(\textbf{w}) = -\sum_{i=1}^{N} y_i \text{log}(\hat{y}_i).$$ This loss works as skadaver mentioned on ...

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In general, if you don't have a dataset that contains those 7 classes, you wouldn't be able to get a neural network which performs your task of semantic segmentation. My understanding of your question is the following: you own a dataset, each image labelled with a single class label you are able to train a CNN or similar structure with these images you want ...

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If there is no padding, then we could only slide the filter to the right until its right edge touches the right boundary of the image. So, the filter first spans columns [1,5], then [2,6] and so on until [96,100]. So, the filter is multiplied with image patches 96 times for a single row. Similarly, we’ll have 76 rows in the output image. For a single ...

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This book mentions this in page 61. The author interprets this as: $t$ is the $t$th training example, and $\lambda$ is an additional hyperparameter

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