The model must be autoregressive. It receives a token sequence as input and predicts the next token. Output digits are generated one at a time, with each new token fed back as input for predicting the next. The carry propagation must emerge from this autoregressive process — not from explicit state variables passed between steps in Python.
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All of the examples demonstrating ordered dithering so far have been produced using a specific type of threshold matrix commonly known as a Bayer matrix. In theory however any matrix could be used and a number of alternatives are available depending on your qualitative preference. Matrices also don’t have to be square or even rectangular; polyomino-based dithering matrices have been explored as well[6].