Tokenization

An agent that drives an LLM sends the model the same conversation again and again, and each turn adds only a little text at the end. Inference engines reuse the KV cache of the shared prefix, so only the new tokens pass through the model. However, tokenization has no such shortcut. The CPU front end of the serving engine converts every request back into token IDs from its first character, which lengthens the time to first token (TTFT) and consumes CPU on every turn. We present Delta Tokenizer, a CPU tokenization front end that tokenizes only the delta between a request and the previous request of the same session. It retains the earlier token sequence, encodes again only the appended text and the short tail whose tokens the append could affect, and joins the two only at a position the tokenizer's splitting rules themselves cannot move, which keeps the result exact. For long requests with no state to reuse, it cuts the text where practical tokenizers already keep neighboring pieces independent, encodes the pieces on several cores at once, and concatenates the outputs into the reference encoding, exactly. A shared CPU pool schedules these chunks together with the short incremental updates, so an update runs between two chunks rather than behind an entire long job. The incremental path shortens the tokenization of a session turn by roughly 40x relative to the Hugging Face reference tokenizer, and on 16 cores the chunk-parallel path encodes a four-million-character request 8.2x faster than a serial encode and 1.6-2.1x faster than LoPT. Inside SGLang, Delta Tokenizer reduces the median TTFT through the chat interface by 59% at 100K tokens and brings the P99 TTFT of agent sessions down 9.5x under load and 23x when long requests tie up the front end. Every output we checked matches the reference, among them 41.8 billion documents encoded by its fast encoder.

Tokenization is an essential preprocessing step in almost all large language models (LLMs). One of the most popular frameworks is BPE tokenization, which consists of special token segmentation, pretokenization, and byte-pair encoding (BPE). However, existing algorithms are sequential, with each stage only processing complete output from the previous stage. In order to reduce latency and memory footprints, recent works (Jiang and Gong, ICML 2026) (Li, Yang and Mamouras, ASPLOS 2026) (Mamouras, Li and Yang, PLDI 2026) have initiated the study of online algorithms for subroutines such as pretokenization and BPE with a goal of streaming input to output as the input arrives online. However, the search for efficient online tokenization remains open. In this work, we formalize and resolve online tokenization. We introduce the notion of delay for online tokenization which characterizes the extent to which the algorithm output lags behind the (possibly computationally intractable) optimum. We give a near-linear time algorithm with optimal delay (up to constant factors). We complement this algorithm with a conditional lower bound: unless $\mathbf{P} = \mathbf{NP}$, there is no polynomial time algorithm that beats the delay of our algorithm by more than a constant factor. We implement a practical variant for tokenizers from OpenAI's tiktoken and HuggingFace's tokenizers. We obtain a $7.9\times$-$34.8\times$ latency advantage (measured as time to first token) over tiktoken (as well as the recent gigatoken tokenizer) and our implementation maintains approximately constant memory usage independent of input size. Our implementation also achieves a $2.4\times$-$7.0\times$ improvement in throughput over tiktoken and $15.8\times$-$38.1\times$ over tokenizers.

Agentic workloads resend long contexts that barely change between calls. Prefix caching now skips most of their prefill, yet every request must still be tokenized in full before the cache can even be consulted. Tokenization, a CPU stage long treated as negligible, becomes the largest part of time-to-first-token (TTFT), and a frontend that tokenizes for a whole GPU fleet limits how many GPUs it can feed. We present GraphTok, a GPU tokenizer that runs the entire encoding pipeline, from pre-tokenization through byte-pair encoding (BPE) merging to token-ID assembly, as one replayable CUDA graph. GraphTok reproduces the reference token IDs bit-for-bit on GPT-2, Llama 3, Qwen 2.5, DeepSeek-V3, and Gemma 3, hands short inputs to a CPU engine where the GPU cannot win, and plugs into unmodified vLLM and NVIDIA Dynamo. GraphTok encodes one million GPT-2 tokens in 1.7-3.2 ms including data transfers, and on Llama 3 it is 4.7-6.0x faster than gigatoken, the strongest CPU tokenizer. On TokTier's own single-request benchmark, it is 2.6-3.9x faster than gigatoken and up to 18.1x faster than TokTier. In vLLM with a cached prefix, it lowers mean TTFT by 2.1-2.4x. The largest gain is capacity. Within a 2 s P99 target, one Dynamo frontend with GraphTok sustains 518 requests/s of 121k-token traffic, the busiest-hour load of 56 GPUs, against 296 with gigatoken and 18.5 with the default tokenizer. Across 121k to one million tokens, this is 1.75-2.5x the load gigatoken sustains, with a P99 up to 64x lower where gigatoken's tail breaks.

Tokenizers are commonly optimized for compression, but a compact vocabulary does not necessarily distribute its capacity evenly across languages. We introduce the Latent Core Tokenizer (LCT), a language-agnostic approach that separates structural discovery from vocabulary construction. LCT uses Minimum Description Length, entropy-based boundary signals, and morphotactic constraints to identify reusable linguistic units before constructing a shared vocabulary. Across 104 languages with a 200K-token vocabulary, LCT achieves lower fertility and higher MorphScore than BPE, Unigram, and parity-aware BPE, while maintaining comparable cross-lingual disparity in tokenization cost. Across four multilingual downstream benchmarks, LCT improves aggregate score by 1.48, 1.83, and 2.00 points over BPE, Unigram, and parity-aware BPE, respectively. Our findings show that compression alone does not predict representation quality and highlight the importance of morphology-driven structural discovery and how frequency is used to allocate the final vocabulary across languages.

Language models process and generate text sequentially in token units, and the tokenizer determines how much text each inference step covers. Under standard tokenization, a short English phrase such as "On the table." is usually produced as four separate predictions for the preposition (On), article (the), noun (table), and punctuation (.), where each consumes a sequence position and adds inference cost. We introduce CoBPE, a compositional tokenization approach that represents such phrases as a lexical base token (table) attached with a small set of reusable surface modifiers, composed in embedding space at input and predicted jointly at output. In controlled pretraining from scratch at 780M and 1.3B scales, CoBPE shortens sequences by 30% and improves average downstream performance by 1.2 points relative to standard BPE under matched training compute. Our results suggest that part of what is now expressed through token sequences can instead be modeled through structured representations, opening a broad design space for more token-efficient and capable language models.

Conventional tokenizers represent text as characters or statistically derived subwords, overlooking the internal phonological structure of syllables and often requiring large vocabularies. We introduce Phonemic Tokenizer, a linguistically motivated tokenizer for Vietnamese and Chinese that converts each syllable into IPA and factorizes it into three phonological components: onset, rime, and tone. The three components jointly occupy one contextual position, preserving syllable-level sequence length while enabling representation sharing across phonologically related syllables. Non-phonological and unsupported units are handled through character-level fallback. This deterministic design requires no corpus-dependent vocabulary learning and yields vocabularies of only 112 entries for Chinese and 256 for Vietnamese. Intrinsic evaluation shows that the tokenizer achieves substantially higher Rényi efficiency in both languages, represents every entry in a standard Vietnamese syllable dictionary with a Fertility of exactly one, and generally produces shorter Vietnamese sequences than existing pretrained tokenizers. We further instantiate the tokenizer in PhonemicBERT, which combines factorized component embeddings and reconstructs complete masked syllables using three prediction heads. Under a controlled Chinese pretraining setup, PhonemicBERT-Zh is competitive with or outperforms character, subword, and SubChar alternatives across diverse language-understanding tasks. PhonemicBERT-Vi also achieves competitive or superior results to established Vietnamese and multilingual pretrained models. These results establish phonemic factorization as a compact, efficient, and interpretable alternative to atomic and statistically segmented text representations.

Two dominant tokenisation algorithms are used by modern language models: byte-pair encoding (BPE) and UnigramLM. These differ along two orthogonal axes: their optimisation objective (compression vs. log-likelihood) and their search procedure (bottom-up merging vs. top-down pruning). Existing comparisons confound these axes, making it unclear whether their observed differences stem from what is being optimised vs. how it is being optimised. We disentangle the two by introducing two new tokenisation algorithms that complete this 2x2 design space: BottomUpLL, a bottom-up likelihood-based tokeniser, and TopDownComp, a top-down compression-based tokeniser. We train language models with tokenisers produced by each algorithm, varying: model size, vocabulary sizes, and domain (English-only vs. multilingual). Evaluating models on bits-per-byte, we find that the search procedure -- not the objective -- is the dominant factor: bottom-up tokenisers consistently achieve lower bits-per-byte in most settings. Evaluating models on the BLiMP task, however, shows no consistent relationship between design choice and performance. Overall, our results disentangle the effect of tokeniser design choices on language modelling performance, offering concrete guidance for their more principled construction.

Byte-level BPE tokenizers that use the HuggingFace ByteLevel pre-tokenizer inherit GPT-2's word regex, where a word is defined as \p{L}+, one or more Unicode letters. In abugida scripts, vowels are written as combining marks; this pattern therefore splits each word at every vowel sign. Since BPE merges only within a pre-token, those splits persist through training regardless of vocabulary size or corpus composition. We formalise this effect as a training-free lower bound on fertility. Across 26 languages from a parallel corpus, every one of the 17 abugidas is affected, ranging from 1.47x (Tibetan) to 9.02x (Thai), whereas Latin, Cyrillic, Hangul, and Han show exactly 1.00x. For 5 languages, matched tokenizer pairs that differ only in this character class fall within 2.2% of the predicted floor, scoring 4.78 versus 1.58 tokens per word on Nepali. When the Nepali share of the training corpus is swept from 5% to 95%, the broken tokenizer barely shifts at all (1.7%) while the fixed one shifts 33.9%, which separates a structural ceiling from a data shortage without needing to inspect any code. We train three 268M models that differ only in their tokenizer; the fixed variant achieves 4.43% lower held-out Nepali bits per byte at equal compute, and it still leads when given the same bytes with 1.59x the compute. A census of 3,479 HuggingFace repositories finds the letters-only word class present in 63.3% of the most-downloaded text-generation models, accounting for 72.5% of their downloads. GPT-4o's o200k pattern already uses a mark-aware word class, making the repair itself prior art. We quantify its value, show how to recognise its absence from symptoms alone, map which scripts it reaches, measure how widely it is deployed, and release a 65,536-entry Nepali-English tokenizer with a harness that regenerates every number here from public data on a laptop.

Item tokenizer encodes semantic embeddings into token IDs to replace the randomly assigned item IDs used in traditional recommendation models, fundamentally addressing the problems of excessive parameters and cold starts. However, the most common tokenizer, RQ-VAE, suffers from low decoding efficiency due to the inherent dependencies among its codebooks. Meanwhile, efficient independent tokenizers such as optimized product quantization (OPQ) still struggle with dimensional correlations and distribution complexity of semantic embeddings. In this work, we propose a flow-based item Tokenizer (Tlow) to transform raw semantic embeddings into a latent space where embeddings conform to a unified standard normal distribution, achieving dual advantages of dimensional independence and distributional simplicity. Independent tokenization performed on these latent embeddings yields semantically clear token IDs. Additionally, we introduce a novel codebook guidance to align the codebook space with the token embedding space, further aiding the learning of more semantically distinct token embeddings. Offline experiments on four public datasets demonstrate that Tlow's tokenization and codebook guidance significantly improve recommendation performance. The improvement on cross-domain and multi-modal recommendations also proves the effectiveness of item tokenization in a simplified embedding space. Online experiments for a multi-modal retrieval task on China's largest social media platform WeChat validate Tlow's powerful distribution transformation capability. The retrieval model based on token IDs improves user CTR by 10.32% globally and by 11.64% for new items. Our codes are available at https://github.com/wjjln/Tlow.

Standard tokenizers used in large language models produce malformed text when applied to Brahmic scripts. They are a family of abugidas, writing systems whose consonants carry an inherent vowel that dependent marks can modify. They include Devanagari, Telugu, Tamil, Kannada, and others. The underlying issue is that these tokenizers violate orthographic constraints that do not arise in alphabetic scripts like English. We observe that while English orthography forms a semigroup (any two valid tokens can be freely concatenated), Brahmic orthography forms a partial semigroup: not every concatenation yields a valid string. We formalise this distinction in Agda, model valid Brahmic tokens as chains in a transition system, and derive a provably correct fixToken function that extends any candidate token to respect orthographic boundaries. We then show how this formal derivation translates into a practical patch for SentencePiece as well as a standalone Rust-based pre-tokenizer library, eliminating the observed errors across Indic scripts.

Language model tokenizers are typically selected with minimal evaluation, despite the fact that their design choices directly impact model capabilities. This can be partly attributed to a limited understanding of which tokenizer properties affect which aspects of downstream performance. We introduce TokEval, a framework of tokenizer evaluation metrics that goes beyond standard measures like fertility and compression rate to capture linguistically and structurally meaningful properties, e.g., UTF-8 character boundary integrity and digit place-value boundary alignment for mathematics. To validate whether these metrics are predictive of downstream model performance, we conduct controlled language model pretraining experiments, varying solely the tokenizers' training data mixture, pretokenization strategy, and training algorithm. We evaluate the resulting models on bits-per-byte (a tokenizer-agnostic version of perplexity) and several benchmarks, spanning linguistic understanding, mathematical reasoning, and code generation. Our experiments suggest that different intrinsic properties have different impacts on model abilities: information-theoretic metrics predict language modeling abilities (Spearman rho up to 0.80), while structure-sensitive metrics, such as those measuring digit and line-break handling, correlate with task accuracy. We hope TokEval enables more principled tokenizer evaluation, replacing pretraining sweeps with intrinsic measurement wherever the two agree.

GPT-style models have achieved remarkable success with finite vocabularies of reusable tokens, making the token interface a central component of modern sequence modeling. Symbolic music appears naturally compatible with this paradigm: it consists of discrete note events and recurring structures such as chords, motifs, and phrases. However, when tokenization moves beyond language, the interface must be specified for each domain. Existing work offers many effective designs, but no unified criterion for deciding what tokenization should represent and how far it should go. Using predictive codelength as a common criterion, we formulate the Effectiveness--Losslessness Framework to define where tokenization should begin and where it should end. The Fact--Token Boundary marks where observation-determined structure should enter the token interface, through operations such as coordinate construction. Within this interface, the resulting carrier may be reversibly recoded without changing the represented facts. The Token--State Boundary marks where tokenization should stop: relations that depend on context should remain for model-state computation rather than being fixed in advance by the tokenizer. We validate the framework through controlled multi-seed symbolic-music experiments, with an independent-corpus replication of the temporal intervention. Making musical time explicit consistently reduces predictive code and also improves pitch and duration prediction, while tonal-frame canonicalization and pitch factorization provide further gains. Fixed circle-of-fifths pitch coordinates instead increase predictive code, suggesting that imposing a fixed pitch relation before context can burden prediction. Reversible BPE substantially shortens the carrier but increases predictive codelength in every seed, showing that carrier compaction alone does not guarantee predictive gain.

Adaptive latent tokenization maps a fine-grained input to a shorter sequence of continuous representations associated with input-dependent spans. We introduce ReconSpan, which divides text into chunks that a backward decoder can reconstruct from a single contextual prefix code and retains one such code as the latent token for each chunk. The reconstruction criterion is applied when chunks are formed, allowing one trained autoencoder to produce average chunk lengths from 6.5 to 12.2. At matched average length, reconstruction-guided boundaries preserve more text than random boundaries. Readers of the resulting latent sequence recover topic information reliably but struggle to extract exact details.

Subword tokenizers represent many common words twice in space-using writing systems, once with a leading space and once without. The two entries have separate embeddings in models, so occurrences of one word are divided across rows that are trained independently, and the two forms need not even segment the string the same way: " together" may be a single entry while the same word without a preceding space is tokenized as "to|gether". Capitalization divides a word further, into as many as six forms. We introduce an alternative to standard whitespace conventions using an explicit word boundary marker, which prevents such duplication. Words are delimited by the boundary markers, and spaces between words are represented as pairs of such markers. Two shift codes do the same for title case and upper case, allowing one internal representation of a word to be re-used across different settings. Switching to this convention mitigates the duplicate-entry issue, but does not improve tokenization compression: for both vocabulary-learning algorithms, the best marker scheme stays within one percent of the baseline in characters per token, averaged across six languages. It does result in better language modeling performance. Every marker scheme tested downstream reaches lower bits per byte than the baseline, suggesting that duplication carries a cost that compression does not capture.

LLM serving caches prompt KV state, yet most front ends still re-tokenize the full request on every call. Coding agents pay most: sessions repeatedly submit a long transcript after a small append, which can shift token boundaries near the end of the prior sequence. Across 153,951 calls the median append is ~1.4K characters; only 1.0-3.6% of calls start or rebuild a session, yet those carrymulti-million-character contexts. Fleet prompt-cache hit rate is 94.1%, and as it approaches 0.99, tokenization grows from 10% to 64% of time to first token (TTFT) in component measurements. TokTier is a stateful CPU+GPU tokenization service for this two-mode workload, under one contract: emitted token IDs are always identical to full reference tokenization. For session continuations it re-tokenizes a small window around the append and splices only when a per-request check finds a stable pre-tokenization boundary; failed checks widen the window or fall back to full reference tokenization. For calls without a reusable prefix it runs exact GPT-family regex pre-tokenization and BPE on a GPU. A sampled shadow verifier re-checks live traffic. Across 17 production tokenizer families, differential campaigns cover 1.5x10^10 split checks, a 12.4 TB real-text corpus, and 93,000+ replayed agent steps, with zero divergence. Incremental repair takes 0.5-1.1 ms from 100K to 3M characters, up to 437x faster than HF tokenization and 2.1x faster at 1M characters than the strongest cache-based baseline (Gigatoken) fully prewarmed. GPU tokenization encodes a 1M-character request in 0.87 ms, up to 491x below HF and 23.4x below the fastest published CPU method on the same protocol. With vLLM, median TTFT drops 16-34% and P99 TTFT 23% under recorded bursts. Under a 50 ms P99 objective, a four-core repair pool plus one GPU sustains 1,821 requests/s, where a 16-core stateless front end saturates at 40 requests/s.

Multilingual language models rely on shared subword vocabularies to represent multiple languages within a limited number of token units. While such sharing is often useful, it can also create cases in which identical surface forms are treated too uniformly across languages, even when their meanings or usage differ. We investigate this limitation through cross-lingual homographs and false friends, and examine whether introducing language information earlier in the tokenization process can improve their treatment. We propose a simple tokenizer-level intervention based on language cues: language-specific characters replacing initial characters of shared-vocabulary words, reducing common identity during vocabulary construction. In intrinsic analysis, we find through tokenizer-level statistics that BPE and UnigramLM often treat cross-lingual homographs in a largely language agnostic way, whereas the context-sensitive SaGe tokenizer diverges more strongly; our intervention removes this gap. In downstream English-to-X machine translation, our cues yield modest improvements in several settings, especially under BPE, although the effect is not consistent across all languages and evaluation sets. Overall, the findings suggest that adding lightweight language information at the tokenizer level is a promising direction for further exploration.

Language models encode text as subword tokens, raw bytes, or rendered pixels, but these encodings are usually compared under modeling constraints that expose different amounts of linguistic content to models across different languages. We instead ask what each encoding preserves when both the content and the downstream capacity are controlled. Using verified parallel sentences across thirteen languages and five scripts, we compare tokens, bytes, and pixels through a shared bottleneck whose width is swept to trace rate-utility frontiers. This separates three quantities that are often conflated: the number of input positions an encoding creates, the latent capacity available after encoding, and the task-relevant information that survives compression. We evaluate three utilities: surface form preservation, cross-lingual sentence alignment, and topic classification. No encoding dominates across tasks or capacity regimes. Pixels preserve surface form best, bytes preserve cross-lingual alignment best, especially in same-script multilingual settings, and tokens support topic prediction best. These performances are not explained by sequence length alone. Short inputs can discard useful meaning, while long inputs can preserve information that compresses well. Choosing an encoding is therefore not a fixed preference for tokens, bytes, or pixels, but a rate-utility tradeoff that depends on the task, language mix, capacity regime, and compute budget.

The Unigram tokenizer uses an elegant representation which makes it straightforward to edit vocabularies, but its training is comparatively heavy and complex. We introduce MinGram (Minimalist Unigram), which keeps the token-list representation but simplifies training using a BPE-derived seed vocabulary, Hard EM on a minimum-token path, and a single flat score-pruning step. This removes the suffix array, the forward-backward pass, and the iterative prune loop, leaving a procedure that requires little beyond tokenizer inference itself. By making token count the primary objective and using a Unigram score only as a tiebreak, MinGram keeps the compression of pure token-count methods while retaining much of the morphological alignment and downstream quality of probabilistic ones. Across six languages, MinGram compresses better than both BPE and standard Unigram, and a compression-oriented variant matches the strongest token-count compressors while retaining substantially higher morphological alignment. In controlled downstream language-model training, Unigram-family tokenizers, with MinGram among the best, consistently beat BPE in bits-per-byte.

Learning discrete speech representations that preserve similarity across variable-length utterances is central to query-by-example spoken term detection (QbE-STD). While wav2tok introduced CTC-based sequence alignment to enforce token consistency, its tightly coupled clustering and alignment training recipe limits scalability. We propose wav2tok 2.0, a scalable alignment-aware speech tokenizer built on the BEST-STD backbone. wav2tok 2.0 employs staged training, first learning discriminative, speaker-invariant representations via contrastive learning and vector quantization, and then enforcing pairwise token consistency using a CTC alignment loss and a novel DTW-aligned framewise prediction objective with adaptive weighting. Experiments show that wav2tok 2.0 consistently outperforms BEST-STD and general-purpose tokenizers on QbE-STD while remaining efficient and scalable.

Large language models (LLMs) are attractive for context-aware time series forecasting because they can integrate heterogeneous textual signals, yet their discrete, language-oriented tokenization and embedding interfaces are misaligned with continuous numerical values, often harming numerical ordering and forecasting reliability. We propose TempoWave, a plug-and-play temporal wavelet digit interface that maps each scalar observation into digit-wise embeddings constructed from multi-wavelet, multi-scale coefficients. By directly overriding standard token representations, TempoWave seamlessly exposes both fine-grained local fluctuations and macro global structures in a transformer-compatible form, ensuring that precise numerical formatting, distinct digit identity, and robustness to common normalization operations are maintained throughout the LLM pipeline. Experiments across five context-enriched forecasting benchmarks demonstrate that TempoWave consistently improves LLM-based forecasters over standard numeric tokenization and alternative embedding interfaces, achieving a new state-of-the-art. These results highlight the numeric interface as a key bottleneck and suggest that principled multi-resolution embeddings can better couple LLMs' contextual reasoning with precise forecasting. Our code is available at https://github.com/DC-research/TempoWAVE and our model can be accessed at https://huggingface.co/Melady/TempoWAVE.

Language-specific tokenizers improve tokenization quality and the downstream performance of models on those languages. However, using such a tokenizer comes at a cost: either a new model must be trained from scratch, or the vocabulary of an existing pretrained model must be adapted. We propose Language-adaptive Maximum a Posteriori (LangMAP) Tokenization, a tokenization scheme that extends the UnigramLM algorithm to the multilingual setting, producing language-specific tokenization from a single shared vocabulary. Notably, LangMAP can be used when training a multilingual language model from scratch or to adapt a pretrained model's tokenizer to individual languages without changing its vocabulary. While language labels are required at training time, a key feature of the algorithm is that it then performs language-specific tokenization at inference without knowledge of the input's language. Across 14 open-source tokenizers, 9 natural languages, and 9 programming languages, LangMAP improves morphological boundary alignment and, for all coding languages tested, alignment with abstract syntax tree (AST) leaf boundaries. In fine-tuning experiments, results are mixed: LangMAP improves target-language grammatical acceptability (MultiBLiMP) on the languages tested; its benefits are less consistent on knowledge-related tasks (Global-PIQA, Belebele).

Generative recommendation is an emerging paradigm that has shown promise in industrial recommendation systems, aiming to predict users' next interactions from their historical behaviors. At the core of generative recommendation lies item tokenization, which bridges item semantics and recommendation models. However, existing methods often struggle to effectively organize and inject complex user-behavioral and item-semantic contexts into recommendation models simultaneously. On the one hand, existing graph-based integration methods, such as graph serialization and graph neural networks, either suffer from scalability issues or exploit only local graph information. On the other hand, existing semantic tokenization methods typically rely on heuristics and lack explicit supervision signals, which may lead to inaccurate or suboptimal semantic representations. To address these limitations in user interest context modeling, we propose G2Rec, a scalable framework that unifies holistic graph-based user co-engagement modeling with semantic tokenization for industrial-scale generative recommendation. Overall, G2Rec enables recommendation models to capture holistic and semantically grounded user interest prototypes without requiring ground-truth user interests, thereby providing more comprehensive and accurate modeling of user behavior contexts in industrial sequential recommendation. Online deployment across product surfaces and extensive experiments on public datasets demonstrate the superiority of G2Rec over existing methods.

Turkish is agglutinative: meaning is carried by morphemes, yet the subword tokenizers that drive modern language models split words by corpus statistics, fragmenting semantically loaded suffixes and -- in the case of WordPiece and rule-based analyzers -- failing to decode their output back to the original text. This paper presents Morpheus, a neural morpheme-boundary model for Turkish that is at once a lossless, morphology-aware tokenizer and a word-embedding producer. A differentiable Poisson-binomial dynamic program turns per-character boundary probabilities into soft morpheme memberships during training and exact segments at inference, with no string normalization, so $\mathrm{decode}(\mathrm{encode}(w)) = w$ holds by construction. Because the model is neural, the same forward pass that tokenizes also emits a structured word embedding. Among reversible tokenizers -- the only ones valid for generation -- Morpheus attains the lowest bits-per-character ($1.425$), roughly doubles the gold morphological alignment of the subword family (MorphScore macro-F1 $0.61$ vs.\ ${\sim}0.32$), and uses ${\sim}19\%$ less GPU memory than 64K-vocabulary subword tokenizers. As an embedder, frozen Morpheus vectors lead on lexical retrieval (root-family MAP $0.85$) and same-root verification (ROC-AUC $1.00$), surpassing the multilingual retriever BGE-M3 and BERTurk; on context- and inflection-dependent tasks (NER, case/number probing) the heavier contextual encoders remain ahead -- a trade-off we attribute to Morpheus's root-centric geometry. Code: https://github.com/lonewolf-rd/TurkishMorpheus; model: https://huggingface.co/lonewolflab/Morpheus-TR-50K; interactive demo: https://huggingface.co/spaces/lonewolflab/morpheus-tr-demo.

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

We present BrahmicTokenizer-131K, a 131,072-vocabulary byte-level BPE tokenizer that closes the Brahmic compression gap at the 131K-vocabulary class while preserving the English, EU-language, and code compression of OpenAI's o200k_base. We construct it through a two-stage retrofit: (1) a script-prune crop that reduces 200,019 tokens to 131,072 by removing nine out-of-scope writing systems, and (2) a surgical retrofit of 2,372 corpus-dead vocabulary slots determined by linear-programming allocation across nine Brahmic Unicode blocks. The pre-tokenizer, decoder, and inherited merge rules are unchanged from o200k_base, making BrahmicTokenizer-131K a drop-in replacement at the tokenizer interface. On 27 million documents of public Indic pretraining text (2.84 billion words, 46.21 GB), BrahmicTokenizer-131K produces 26.7% fewer tokens than Mistral-Nemo Tekken / Sarvam-m at the same vocabulary budget, with per-language savings of 15.79% (Tamil) to 76.79% (Odia, a 4.31x compression ratio). The Odia advantage is mechanistically explained by Tekken/Sarvam-m containing zero Oriya-block tokens; our surgery added 725. On non-Indic content, BrahmicTokenizer-131K matches o200k_base's English fertility (1.235 vs 1.232 tokens/word) and beats Tekken/Sarvam-m by 4.0-14.2% on HumanEval, MBPP, and GSM8K. Across our 14-tokenizer benchmark, it is the only tokenizer simultaneously competitive on Brahmic, English, EU, code, and math at the 131K budget. Specialist tokenizers at other vocab classes (Sarvam-30B, Sarvam-1, MUTANT-Indic) achieve better Indic compression at the cost of non-Indic performance: Sarvam-1's English fertility is 15.9% worse and its code/math compression 26-33% worse than ours. We release the artifact under Apache 2.0 at https://huggingface.co/theschoolofai/BrahmicTokenizer-131K.

Tokenizer fertility the number of tokens per word imposes a hidden cost on non-English NLP. We measure fertility for ten foundation models across 25 European languages on parallel text, producing the first controlled tokenizer tax map for the continent. The tax spans 2.5x from English (1.2 tokens/word) to Greek/Maltese (~3.1), following a clear hierarchy: Romance (1.5-1.7), Germanic (1.7-1.9), Slavic (2.2-2.5), Uralic/Baltic (2.7-3.0). Ukrainian (2.7) pays 15-18% more than cognate Slavic languages, reflecting underrepresentation in pre-training data. Fertility rankings are domain-invariant across three text registers (rho > 0.97). A subword analysis reveals that high-fertility tokenizers fragment morphological boundaries rather than preserving them. Cross-lingual few-shot evaluation on four Slavic languages shows that few-shot effects are model-intrinsic, not language-dependent. We release all measurements as a public dataset.

Tokenisation is an integral part of the current NLP pipeline. Current tokenisation algorithms such as BPE and Unigram are greedy algorithms -- they make locally optimal decisions without considering the resulting vocabulary as a whole. We instead formulate tokeniser construction as a linear program and solve it using convex optimisation tools, yielding a new algorithm we call ConvexTok. We find ConvexTok consistently improves intrinsic tokenisation metrics and the bits-per-byte (BpB) achieved by language models; it also improves downstream task performance, but less consistently. Furthermore, ConvexTok allows the user to certify how far their tokeniser is from optimal, with respect to a certain objective, via a lower bound, and we empirically find it to be within 1% of optimal at common vocabulary sizes.

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.

Transformers predict over a representation of a sequence. The same data can be written as bytes, characters, or subword tokens, and these representations may be lossless. Yet, under a fixed context window, they need not expose the same information to the model. This raises a basic question: how does the choice of representation change what a finite-context predictor can achieve? We study this question on Markov sources and uncover two complementary phenomena. First, we observe that moving to smaller representation units can hurt prediction even when the context window is enlarged to cover the relevant source history. To explain this, we introduce fragmentation: a lossless recoding that replaces each source symbol by several smaller units. We prove that fragmentation can strictly increase the optimal finite-context log-loss, showing that the gap is not merely an optimization or capacity issue, but can be intrinsic to the representation. This gives a theoretical account of the finite-context gap observed in byte- and character-level models such as ByT5 and CANINE relative to subword-tokenized models. Second, we study the opposite direction: greedy tokenization -- BPE, WordPiece, and related methods -- which groups source symbols into larger units. We show that tokenization can make a short token window behave like a longer source-context window, and we give a loss guarantee describing when this is achievable. The guarantee depends on how reliably token windows span the needed source history, together with the compression rate of the tokenizer. This also yields a simple diagnostic for real tokenizers: measuring how much source context a fixed token window reliably contains. Together, the two directions establish a finite-context information-theoretic framework for reasoning about representation choices in Transformers.

The diachronic evolution from Latin to the Romance languages involved a restructuring of the grammatical gender system from a tripartite configuration (masculine, feminine, neuter) to a bipartite one (masculine, feminine) in most Romance languages. In this work, we introduce an interpretable deep learning framework to investigate this phenomenon at both lexical and contextual levels. First, we show that conventional tokenization strategies are insufficiently robust for this low-resource historical setting, and that our proposed tokenizer improves performance over these baselines. At the lexical level, we evaluate the contribution of morphological features to gender prediction. At the contextual level, we quantify the contributions of different part-of-speech categories to grammatical gender prediction. Together, these analyses characterize the distribution of gender information between the lemma and its sentential context. We make our codebase, datasets, and results publicly available at https://github.com/ahan-2000/Lost-in-Translation-.