Faster Superword Tokenization

We propose a novel algorithm for incremental Byte Pair Encoding (BPE) tokenization. The algorithm processes each input byte in worst-case $\mathcal{O}(\log^2 t)$ time, leading to an overall complexity of $\mathcal{O}(n \log^2 t)$, where $n$ is the input length and $t$ is the maximum token length. The algorithm incrementally maintains BPE tokenization results for every prefix of the input text, implementing the standard BPE merge procedure defined by a fixed set of merge rules. This enables efficient partial tokenization in streaming settings. Functioning as a drop-in replacement for standard BPE, our approach achieves a speedup of up to ${\sim}3\times$ over Hugging Face's tokenizers, and demonstrates significant latency reductions over OpenAI's tiktoken on pathological inputs. We further introduce an eager output algorithm that enables streaming output, emitting tokens as soon as token boundaries are determined during incremental tokenization. Overall, our results demonstrate that BPE tokenization can be performed incrementally with strong worst-case guarantees, while providing practical latency benefits in modern large language model pipelines. Code: https://github.com/ModelTC/mtc-inc-bpe

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.

Pre-training of Large Language Models is often prohibitively expensive and inefficient at scale, requiring complex and invasive modifications in order to achieve high data throughput. In this work, we present Token-Superposition Training (TST), a simple drop-in method that significantly improves the data throughput per FLOPs during pre-training without modifying the parallelism, optimizer, tokenizer, data, or model architecture. TST is done in two phases: (i) A highly efficient superposition phase where we combine many contiguous tokens into one bag and train using a multi-hot cross-entropy (MCE) objective, and (ii) a recovery phase where we revert back to standard training. We extensively evaluate TST on the scale of 270M and 600M parameters and validate on 3B and a 10B A1B mixture of experts model, demonstrating that it is highly robust in different settings. Ultimately, TST consistently outperforms baseline loss and downstream evaluations, and under equal-loss settings, TST yields up to a 2.5x reduction in total pre-training time at the 10B A1B scale.