Using regression discontinuity, the paper shows that adding a subword to a tokenizer's vocabulary can raise the model's probability for that string by up to about 17 times in small models.
Tokenisation is NP-Complete
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abstract
In this work, we prove the NP-completeness of two variants of tokenisation, defined as the problem of compressing a dataset to at most $\delta$ symbols by either finding a vocabulary directly (direct tokenisation), or selecting a sequence of merge operations (bottom-up tokenisation).
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Causal Estimation of Tokenisation Bias
Using regression discontinuity, the paper shows that adding a subword to a tokenizer's vocabulary can raise the model's probability for that string by up to about 17 times in small models.