Dynamic-Programming-Guided Hierarchical BPE and Empirical Analysis of Vocabulary Pruning

Byte Pair Encoding (BPE) is widely used for subword tokenization, but standard BPE exposes every learned merge token to the downstream model, including tokens that mainly serve as intermediate construction units and rarely appear in the final encoded corpus. This paper proposes Pruned BPE, a post-training visibility-pruning and token-reallocation method that separates merge construction from model-visible vocabulary selection. After standard BPE training, tokens are evaluated by final exposure. Low-exposure tokens are retained as internal-only merge nodes, while their visible vocabulary slots are reassigned to better-exposed candidates learned through resumed training. During encoding, internal-only tokens are recursively expanded into visible descendants while the original BPE merge order is preserved. Experiments on two non-overlapping English- and Chinese-dominated corpora and their combination show that Pruned BPE consistently reduces encoded length relative to Standard BPE at the same training corpus, evaluation corpus, and model-visible vocabulary size. At a 40% exposure threshold, the reduction is approximately 0.27%--0.36% on same-corpus evaluations. In a vocabulary-only evaluation using a shared exact minimum-token dynamic-programming encoder, Pruned BPE retains an advantage of approximately 0.23%--0.31%, indicating that the improvement arises from a more efficient visible vocabulary. These gains represent a meaningful fraction of the approximately 1.5%--3.8% marginal reduction that would otherwise require adding another 2K Standard BPE tokens. Qualitative analysis shows that internal-only tokens include reusable English fragments, Chinese components, partial UTF-8 byte sequences, and structured-text fragments. The results indicate that post-training visibility pruning can improve BPE vocabulary efficiency without increasing the vocabulary exposed to the language model.

Recent work has shown that subword vocabularies can be trained to optimize compression for a specific inference rule rather than relying on greedy heuristics such as Byte Pair Encoding (BPE). We extend this approach to greedy left-to-right longest-match decoding, the fast and widely used inference rule underlying WordPiece. We introduce Joint Optimization for Greedy Longest-Match Tokenization (JOLT), which formulates vocabulary learning as an integer program over vocabulary-selection and segmentation-choice variables. Greedy-consistency constraints ensure that each optimized segmentation exactly matches the segmentation produced by longest-match decoding under the selected vocabulary, aligning the training objective with deployment-time tokenization. To scale the optimization, we solve a linear programming relaxation and selectively introduce higher-order segmentations only for unresolved pretokens. The resulting relaxation is nearly integral: rounded solutions fall within 0.008 - 0.176 % of the LP lower bound on the training scope. The bound also shows that BPE is already within 1 - 2 % of the best achievable compression under greedy longest-match decoding, while JOLT closes 89.6 - 99.4 % of the remaining gap. On held-out validation data across four training scopes and vocabulary sizes of 32,000 and 64,000, JOLT produces up to 0.78 % fewer tokens than BPE, with improvements generally increasing as the training scope grows. These results demonstrate that inference-aligned vocabulary optimization can recover most of the limited compression headroom left by BPE while providing a certificate of near-optimality.

Subword tokenization methods such as Byte-Pair Encoding (BPE) are a core component of modern language models; yet, tokenizer capacity remains typically determined by a fixed merge budget, chosen heuristically. Since larger vocabularies increase memory usage and computational cost, selecting compact and effective token inventories is essential for efficient language modeling. We study the optimization of a BPE merge budget as a statistical model selection problem and investigate information-theoretic criteria for computing optimal merge sets directly from corpus statistics. To further improve the merge selection in limited data conditions, we augment the BPE training corpora with synthetic texts generated from the original data, providing estimates for the unigram and bigram distributions. Experiments across multiple corpora and downstream tasks show that using a principled vocabulary selection technique reduces model size, with little degradation in performance. We further observe that synthetic data can yield better tokenizers, especially in low-resource settings.