A Formal Perspective on Byte-Pair Encoding

Code

• github.com/zouharvi/formal-bpe
  Officialnone★ 2

Abstract

Byte-Pair Encoding (BPE) is a popular algorithm used for tokenizing data in NLP, despite being devised initially as a compression method. BPE appears to be a greedy algorithm at face value, but the underlying optimization problem that BPE seeks to solve has not yet been laid down. We formalize BPE as a combinatorial optimization problem. Via submodular functions, we prove that the iterative greedy version is a 1(^)(1-e^-(^))-approximation of an optimal merge sequence, where (^) is the total backward curvature with respect to the optimal merge sequence ^. Empirically the lower bound of the approximation is 0.37. We provide a faster implementation of BPE which improves the runtime complexity from O(N M) to O(N M), where N is the sequence length and M is the merge count. Finally, we optimize the brute-force algorithm for optimal BPE using memoization.

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