A Photo Read Like a Sentence

A Vision Transformer never slides a filter across an image. It cuts the image into fixed squares and treats each square as a token, exactly the way a language model treats a word. Before any attention can happen, something has to do the cutting.

Task: write patchify(image, p) that turns an image into its list of patch tokens.

• image[r][c] is the pixel at row r, column c, given as a list of channel values. A colour pixel might be [red, green, blue]; a grayscale pixel is a list holding one number.
• Each patch is a $p \times p$ square. Patches are taken in reading order: left to right across the top band of rows, then left to right across the next band down, and so on.
• Each token is its patch flattened into one list: the patch's top row first, left to right, then its next row, and so on, with each pixel contributing all of its channel values in order. A patch of a $C$-channel image therefore becomes a list of $p \times p \times C$ numbers.
• If the height or width isn't a multiple of $p$, the leftover rows at the bottom or columns at the right can't fill a whole patch and are dropped.

Return the list of tokens.

For example, in a 4×4 grayscale image whose pixel at row $r$, column $c$ holds $10r + c$, the first token for $p = 2$ is [0, 1, 10, 11].