Adaptive Frequency Threshold Byte Pair Encoding for Mixed Natural Language and Structured Symbolic Corpora

Tokenization is the first -- and often least scrutinized -- step of most NLP pipelines. Standard algorithms for learning tokenizers rely on frequency-based objectives, which favor languages dominant in the training data and consequently leave lower-resource languages with tokenizations that are disproportionately longer, morphologically implausible, or even riddled with $<UNK>$ placeholders. This phenomenon ultimately amplifies computational and financial inequalities between users from different language backgrounds. To remedy this, we introduce Parity-aware Byte Pair Encoding (BPE), a variant of the widely-used BPE algorithm. At every merge step, Parity-aware BPE applies a fair-max rule that maximizes the compression gain of the currently worst-compressed language, trading a small amount of global compression for cross-lingual parity. We find empirically that Parity-aware BPE reduces tokenization inequality -- operationalized by the Gini coefficient of per-language token costs -- by up to 89% relative to Classical BPE. This comes with negligible impact on global compression rate and no evidence of systematic degradation in downstream LM performance.

Byte-Pair Encoding (BPE) constructs subword vocabularies through greedy pair merging, but conventional BPE requires the number of merges or target vocabulary size to be specified externally. Significance-Gain Pair Encoding (SG-BPE) replaces frequency-only selection with a statistical criterion based on how strongly an observed pair exceeds its expected co-occurrence under an independence model. This paper introduces MDL-Calibrated Significance-Gain Pair Encoding (MDL-SG), a three-stage procedure separating discovery, replication, and utility. Candidate pairs are ranked by Significance-Gain on a discovery partition, tested for replication on a separate partition using an exact one-sided hypergeometric test with per-iteration Benjamini-Hochberg correction, and then evaluated on a utility partition using a Minimum Description Length (MDL) criterion. Merging stops automatically when no replicated candidate yields positive held-out MDL gain. On WikiText-103, MDL-SG stops at 209, 433, and 847 merges for 120K, 250K, and 500K-character tokenizer-training samples, respectively. At 500K characters, it selects a stored vocabulary of 1,017 tokens without prescribing the vocabulary size in advance. In a compute-matched TinyGPT experiment with identical 2,024,448-parameter models and 500 optimizer updates per language model, MDL-SG achieves validation/test BPC of 3.2612/3.2436, compared with test BPC of 3.2894 for SG-BPE and 3.3493 for frequency BPE. Frequency BPE achieves stronger raw compression, while MDL-SG achieves lower BPC, showing that compression-oriented merge selection and language-model utility need not coincide.

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.