Frequency-Ordered Tokenization for Better Text Compression

Dynamic vocabularies built on-the-fly via Lempel-Ziv-Welch (LZW) compression let a language model represent the same text in fewer tokens, but prior work shows that this efficiency comes at a cost to reasoning and perplexity. We show that this quality gap is not a fundamental price of compression but can be substantially closed through targeted improvements to the compression layer and LZW codec, without modifying the underlying pretrained language model. Our analysis reveals four key issues: (1) LZW's compression algorithm creates an implicit conflict between the input embedding and the output embedding, a tension that a single shared embedding cannot resolve; (2) naively applying RoPE to LZW-compressed sequences ignores that merged tokens can span multiple tokens; (3) merging certain tokens (notably digits) disproportionately hurts downstream accuracy; and (4) dynamic vocabularies introduce an inherent segmentation ambiguity that confounds standard evaluation. We address these through decoupled input/output dynamic embedding layer, size-aware RoPE positioning, and a modified LZW codec supporting selective merges and multi-view segmentations. Across four models, our recipe improves perplexity on every corpus we evaluated as well as mathematical reasoning accuracy, closing roughly half the quality gap between zip2zip and the uncompressed baseline at a similar compression ratio on general text. This represents a significant step toward lossless adaptive-vocabulary compression for language models.

Traditional lossless text compression preserves every byte, but its gains on natural language are often modest in realistic operating regimes. We study lossy semantic text compression, where the encoder strategically deletes parts of the text and a large language model (LLM) reconstructs the original content from the retained skeleton. We benchmark a progression of deletion strategies, including uniform step deletion, word-length-guided deletion (WordLen), word-frequency-guided deletion (WordFreq), LP-optimized deletion (Opt), entropy-based deletion using GPT-2 surprisal, and hybrid methods that combine frequency and surprisal signals. Evaluation on the BBC News dataset across retention rates \r_{keep} \in [0.1,0.9] shows three main findings. First, WordFreq is a strong low-cost baseline: despite using only a static frequency lookup, it remains competitive with much more expensive semantic methods while being far faster at the encoder. Second, semantic and hybrid methods provide their clearest gains at mild-to-moderate compression, whereas word-frequency deletion is often more robust at the lowest retention rates. Third, QLoRA fine-tuning yields a strong local decoder that is competitive with Gemini 2.0 Flash and is often strongest in decoder-only comparisons. Additional English and Chinese experiments show that the overall framework transfers across domains, while the best deletion rule remains dataset-dependent.

We introduce Tokenization with Split Trees (ToaST), a subword tokenization method that directly optimizes compression under a new recursive inference procedure. ToaST greedily splits each pretoken into a full binary tree using precomputed byte n-gram counts, independent of any vocabulary. Given a vocabulary, inference recursively descends each split tree and emits the first in-vocabulary node reached on each path. Vocabulary selection is formulated as an Integer Program (IP) that minimizes the total token count over all split trees under this inference procedure. The Linear Programming (LP) relaxation is near-integral in practice, yielding provably near-optimal vocabularies, with training time empirically scaling quadratically in the number of split trees. On English text, ToaST reduces token counts by more than 11% compared to BPE, WordPiece, and UnigramLM at vocabulary sizes of 40,960 and above, reducing the number of inference tokens for models using this tokenizer, thus extending the effective context length. ToaST also uses common single-byte tokens less frequently than these baselines, leading to a substantial improvement in Renyi efficiency. In experiments training 1.5B parameter language models, ToaST achieves the highest CORE score, outperforming baselines by 2.6%--7.6%, with significance for two of three, and scoring best on 13 of 22 individual tasks.