%20and%20byte-pair-encoding%20(BPE)%2C%20induce%20a%20sampling%20bias%20that%20cannot%20be%20mitigated%20with%20more%20training%20or%20data.%20To%20counter%20this%20universal%20problem%2C%20for%20each%20encoding%20scheme%20above%2C%20we%20propose%20a%20novel%20algorithm%20to%20obtain%20unbiased%20estimates%20from%20any%20language%20model%20trained%20on%20tokenized%20data.%20Our%20methods%20do%20not%20require%20finetuning%20the%20model%2C%20and%20the%20complexity%2C%20defined%20as%20the%20number%20of%20model%20runs%2C%20scales%20linearly%20with%20the%20sequence%20length%20in%20the%20case%20of%20MPE.%20As%20a%20result%2C%20we%20show%20that%20one%20can%20simulate%20token-free%20behavior%20from%20a%20tokenized%20language%20model.%20We%20empirically%20verify%20the%20correctness%20of%20our%20method%20through%20a%20Markov-chain%20setup%2C%20where%20it%20accurately%20recovers%20the%20transition%20probabilities%2C%20as%20opposed%20to%20the%20conventional%20method%20of%20directly%20prompting%20tokens%20into%20the%20language%20model.)
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