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 and byte-pair-encoding (BPE)%2C induce a sampling bias that cannot be mitigated with more training or data. To counter this universal problem%2C for each encoding scheme above%2C we propose a novel algorithm to obtain unbiased estimates from any language model trained on tokenized data. Our methods do not require finetuning the model%2C and the complexity%2C defined as the number of model runs%2C scales linearly with the sequence length in the case of MPE. As a result%2C we show that one can simulate token-free behavior from a tokenized language model. We empirically verify the correctness of our method through a Markov-chain setup%2C where it accurately recovers the transition probabilities%2C as opposed to the conventional method of directly prompting tokens into the language model.?quality=80&w=800)
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