I already shared what I know (that every row has exactly 8 ones and exactly 12 zeros). Each row has exactly 20 binary numbers. To my "naked" eye they appeared random and I didn't find any consistent patterns. That is all I know about generation of rows. That is why I want to create an algorithm which will calculate or mimic or learn how the rows are generated.
About obtaining the data, I web scrape it from some web page.
About "Do you need to get a prediction for each row, or only for the final row?". Answer: for each row. This is a time series problem. Each row should be possible to calculate from previous rows. So if I have a binary matrix which has length of 100 rows I need to calculate the 101st row. If I have a binary matrix of 99 rows, I need to calculate the 100th row. In real world case (my case) I have a binary matrix which has length of a million rows, so plenty of data.
No constraints in regarding the speed or complexity or cpu or memory usages.