Tokenization in Language Models

Autoregressive foundation language models predominantly target high-resource Indo-European languages, imposing computational and morphological penalties on under-represented African languages. Generic multilingual tokenizers routinely exceed fertility rates of 3.2 tokens per word on agglutinative Bantu languages, degrading context efficiency and inflating latency. We present Pearl-Chat, an 8,473,122-parameter ($\sim$8.5M) causal decoder-only transformer engineered for Luganda (Oluganda, ISO 639-2: lg), a low-resource Niger-Congo Bantu language spoken by over 10 million people in East Africa. Built from first mathematical principles in JAX and Flax NNX, Pearl-Chat uses explicit functional state decomposition (nnx.split and nnx.merge), deterministic resumable data streaming via Google Grain, and SPMD tensor parallelism using jax.sharding.Mesh. We introduce a byte-level byte-pair encoding (BPE) subword tokenizer trained from scratch on curated Luganda corpora ($V = 8,192$), achieving 4.88 characters per token compression and 1.60 tokens per word fertility, a two-fold compression improvement over LLaMA-3 (128K) and Gemma (256K). The model is trained with a two-stage curriculum: Stage 1 pre-training on 59,501 sequences across parallel, biblical, encyclopedic, and journalistic corpora, and Stage 2 instruction fine-tuning on 510 dialogues with assistant-only loss masking. Across 4,000 optimization steps, validation cross-entropy loss drops monotonically from 9.4695 (perplexity: 12,958.98) to 0.1818 (perplexity: 1.20), a decrease of 9.2877 nats. On a three-tier held-out diagnostic benchmark, Pearl-Chat achieves 0.9792 ROUGE-L and 0.9405 BLEU while maintaining concordial agreement across Bantu noun classes. We provide a Python Server-Sent Events (SSE) streaming runtime and open-source all weights, tokenizers, and code.

Many hierarchical byte-level language models group bytes into patches using a learned boundary predictor whose view of the next codepoint depends on encoding and lookahead. In UTF-8, codepoints of many scripts take three bytes: 8 of 24 bits mark length and continuation, and the first byte carries only 4 high codepoint bits. After the same left context, a mark extending a grapheme cluster and a letter starting the next can thus share their first byte. Universal Byte-Level Encoding (UBE) keeps one- and two-byte UTF-8 encodings but writes these codepoints as two UTF-16 bytes, low byte first, so its first symbol carries 8 low codepoint bits that can distinguish such continuations. We train small causal predictors on matched FineWeb-2 text and evaluate on FLORES-200 under UTF-8, UBE, and UBE's same-length big-endian variant. At one-symbol lookahead, balanced grapheme-boundary error at codepoint boundaries across 17 languages in 13 Brahmic scripts is 8.76% with UTF-8, 8.62% with the big-endian variant, and 0.06% with UBE. When the target instead retains a parent tokenizer's subword cuts at grapheme boundaries, UBE lowers the mean error relative to UTF-8 at the same lookahead by 72.91% in Korean, 35.29% in Chinese, and 67.32-99.55% in eight more scripts. In the seven of them whose main Unicode block fits on one 256-codepoint page, the big-endian variant stays within 3.0% of UTF-8, so the gain follows byte order, not length. In Korean and Chinese, UBE's mean error falls below UTF-8's final mean error after only 25% and 37.5% of training. Which byte comes first thus affects how much lookahead a byte-level boundary predictor needs.

Tokenization is a critical component of the language modeling pipeline, but it is poorly understood. Tokenizers can impact downstream performance, but there is currently mixed evidence about which tokenizer features predict a better language model without requiring a full training run. In this paper, we analyze approximately 200 language models trained on nine different languages. We evaluate both models and their tokenizers and test whether there is a relationship between any proposed intrinsic tokenizer evaluations and model performance, as measured by a wide variety of benchmarks. Despite the quantity and variety of proposed intrinsic tokenizer metrics, we find that none consistently predicts downstream performance across model families, tasks, and languages. This motivates the need for novel tokenizer evaluation metrics and approaches. We propose novel linguistically grounded metric introduced in this work shows that new metrics can capture aspects of tokenizer quality that existing metrics miss, though their predictive power is likely to vary across model families, languages, and tasks.

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.

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.

Tokenizer-free language models remove the inductive bias of fixed tokenizers by modeling text directly as bytes, but the resulting longer sequences substantially increase computation and eliminate explicit text abstractions. We ask whether this additional computation can be useful, and whether standard Transformers can learn the abstractions that tokenization provides. We study these questions on Transformers without specialized tokenization-related architectures. With token-superposition training and hash embeddings, byte Transformers consistently outperform subword Transformers as model size scales. We further find that byte Transformers build local text abstractions as external tokenizers: a set of segmentation-like positions are used to collect local context representations, and restricting up to $25\%$ of intermediate layers to these local representations preserves downstream performance. Finally, these learned structures induce highly non-uniform generation difficulty, with uncertainty concentrated near local structure boundaries; exploiting them for speculative decoding yields $3.4\times$ more accepted tokens than in subword Transformers.

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.

Large language models are increasingly used where small syntactic errors matter, yet character-level reasoning is still evaluated mostly through isolated probes and aggregate accuracy. We introduce SyntaxBench, a diagnostic benchmark and statistical evaluation framework for character-level reasoning. It contains five core tasks, character counting, letter containment, palindrome detection, edit distance, and longest-string selection, plus index_to_span, a harder substring-extraction stress test. The five core tasks use paired English and character-length-matched random-string inputs. index_to_span documents share a 200-500 word band and are not character-length matched. All six tasks use zero-, one-, and four-shot prompts. We evaluate eight open-weight models from 2B to 32B parameters across 11 reasoning-mode configurations. The framework reports exact-match and relaxed accuracy, Cohen's kappa, paired McNemar tests with odds ratios, bootstrap confidence intervals, Kendall's tau, class-conditional metrics, tokenization analysis, and multiple-comparison-corrected tests. Three findings stand out. First, tokenization shapes accuracy: random strings are more character-visible than English strings (1.892 vs. 3.169 characters per token), and character-counting accuracy falls as English words occupy more tokens. Second, reasoning mode is not uniformly helpful: Gemma4-31B is nearly unchanged across modes on the near-saturated tasks, while Qwen3.6-27B is worse with thinking on palindrome detection (0.952 non-thinking vs. 0.886 thinking at four-shot). Third, index_to_span remains largely unsolved; the best four-shot exact-match accuracy is 6.75%. Character-level evaluation needs controlled inputs, paired tests, and analyses of tokenization and reasoning mode rather than aggregate accuracy alone.

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.

Open-weight language models publish the strings their chat templates use to mark turns, roles and tool results, which the tokenizer maps back to the reserved identifiers the model obeys. Anyone who controls text in a prompt can therefore write a turn boundary indistinguishable from one the serving stack wrote. We audit 256 deployed chat tokenizers. All are forgeable, and the flag usually recommended as a fix leaves 56.6% forgeable because it misses the tool and reasoning markers agent systems rely on. We propose nameless tokenization, which leaves the control entries with a reserved identifier and no surface string, so the content encoder cannot emit one and message content reaches the model unaltered. Across five tokenizer families it reproduces the standard token stream exactly on attack-free data and lifts accuracy on a probe of delimiter-bearing text from 8.5% to 59.9%, where sanitizers lose it. Separating a delimiter's appearance from its identifier shows the identifier matters little against a bare task instruction, but carries most of a forged tool result and most of any forged turn once the system message tells the model to treat user content as data.

Tokenization in language models is treated by default as an input preprocessing decision. We argue that this framing is incomplete: in autoregressive models, tokenizer granularity determines what the model must resolve in a single forward pass, and therefore the supervision signal it receives. This affects both the difficulty of the learning problem and the representations that emerge inside the model. We test this in a controlled experiment on numeric reasoning with a novel decoupling of input and output tokenization. As the output supervision view predicts, differences in task performance, training dynamics, and model internals are induced by output tokenization and largely invariant to input tokenization. This may matter in practice, because models with different tokenization strategies differ not only in input representation but in the task they were trained on. Comparisons between models may thus partly reflect task definition rather than ability. A survey of 120 recent *CL papers on numeric reasoning confirms that this is rarely acknowledged: only about 10% report the numeric tokenization of the models they evaluate, while 69% compare across tokenization, and thus supervision, regimes without reporting it. While prior work documents that tokenization consistently affects model performance, there is no principled account of why. We argue that framing tokenization as output supervision provides that account.

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.

The performance of textual neural models often degrades when their inputs are corrupted by noise such as typos, OCR errors, or dropped words. We study the degradation rate across neural models, both sentence embeddings and decoder-only LLMs, and find that how consistent it is depends on the scale of the noise: under word-level noise, models with very different architectures decline along nearly the same curve, while under character-level noise they separate. We further identify the determining factor to be the training objective, not the architecture: eight encoders spanning six pretraining paradigms are scattered initially, and collapse onto a common curve after a short contrastive training recipe. We trace the word/character split to tokenization: a single character edit forces the tokenizer to re-segment the surrounding word, disturbing the token sequence far more than dropping a whole word does. This finding and its underlying mechanism provide a practical means to predict a model's robustness to noise without any noisy evaluation, and to install robustness at a chosen noise scale through noise-augmented training.

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.

Artificial intelligence tools for education and language support are increasingly framed as scalable responses to access gaps in under-resourced communities. Yet the infrastructure underlying these tools, including training corpora, tokenization schemes, evaluation benchmarks, and deployment architectures, can systematically disadvantage speakers of underrepresented languages before a model is trained. This paper examines these structural barriers through Bengali, one of the world's most widely spoken languages, focusing on AI-assisted education in low-connectivity environments. We identify four interlocking failures: a severe web presence gap, with Bengali accounting for less than 0.5% of global web content despite representing nearly 4% of the global population; a 67:1 training-token deficit between English and Bengali in major multilingual corpora; a tokenization penalty associated with Bengali's alphasyllabary script that compounds the data deficit through higher token fertility; and connectivity exclusion, with individual internet penetration at 36.5% in rural areas compared with 71.4% in urban areas. These failures reflect longstanding resource-allocation decisions, institutional priorities, and design defaults that did not center underrepresented languages in mainstream AI development. We argue that dataset scarcity should be understood as a structural barrier rather than an isolated technical limitation, and that offline-first design should be treated as an equity-oriented infrastructure strategy. We conclude with directions for linguistics and AI research aimed at reducing these structural inequalities.

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.

Byte-level language models are usually argued for on the grounds of robustness, multilingual fairness, and character-level skills. We point to a different, structural advantage: because they read and write bytes, any two of them share an output space, so knowledge transfer between them is exact and independent of how either was originally tokenized. We hypothesize that the two distributions a byte-level model produces, one over the next byte, one over where its patch boundaries fall, can be disentangled and changed almost independently. A model could absorb a teacher's capability while keeping its own boundaries, or change how it places those boundaries while keeping its capabilities. We lay out the two experiments that would settle the hypothesis, alongside preliminary measurements of the properties they rest on. We argue that the community should move toward a byte-level interface as a shared standard: if the hypothesis holds, then once byte-level models are the norm, transferring capabilities and reshaping boundaries between them become cheap and routine, free of the per-model tokenizer that blocks them today.

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.

Despite the existence of exponentially many valid tokenizations for a given string, language models operate on a single canonical sequence deterministically produced by the tokenizer, leaving the broader tokenization space largely uncharacterized. In this paper, we investigate this overlooked space by studying the behavior of language models under non-canonical tokenizations across diverse languages. For English, prior work shows that models are largely invariant to alternative tokenizations that represent the same underlying string. We ask whether this invariance generalizes to other languages beyond English. We conduct a multilingual study across 27 languages spanning diverse scripts and evaluate LLM behavior under alternative tokenizations across six downstream tasks. We find that tokenization invariance does not generalize: model behavior varies substantially across languages with instruction-tuned models exhibiting an average relative performance drop of 23.7% for Llama-3.1-8B, 11.4% for Qwen3-8B, and 9.9% for Gemma-3-12B. The variation of tokenization invariance is systematic across languages. Languages that exhibit higher token fragmentation show significantly greater sensitivity to non-canonical tokenizations. Our study of tokenization robustness serves as a diagnostic of how tightly a model is coupled to its tokenizer. These results demonstrate that tokenization robustness is not a universal property of language models, but depends strongly on the language and its interaction with the tokenizer. We also show that LoRA fine-tuning with multi-tokenization training data provides an effective mitigation for tokenization sensitivity. Fine-tuning on English alone improves tokenization robustness across languages, while systematically sampling diverse non-canonical tokenizations achieves the strongest overall performance.

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.

Modern language models generally represent text as sequences of discrete token embeddings, an assumption deeply rooted in current practice but rarely questioned. We challenge this representation, especially for Chinese, by replacing index-based token embeddings entirely with a single rasterized image of the character sequence, processed by a vision encoder composed of a shared ResNet and a shallow Vision Transformer. To isolate the role of input representation, we construct a dual-branch controlled framework in which both a Vision-based model and an index-based baseline share an identical decoder backbone, training objective, optimizer, and data curriculum. Any performance difference is therefore attributable to the input modality only. Across all tested decoder backbones, the Vision-based model consistently outperforms the baseline, reaching a peak accuracy of 0.429 versus 0.355 for the index-based baseline,that is, a 21% relative improvement, while converging in about half the number of training epochs. The advantage emerges especially within the first five epochs (under 21% of total data) and persists under moderate character corruption: the corrupted Vision model matches the clean index-based baseline. Ablation studies reveal that the advantage requires both spatially coherent input and a ViT encoder with 2D positional encodings. A cross-script comparison on English shows the advantage does not transfer directly to alphabetic writing systems, suggesting that the uniform visual density and radical structure of Chinese characters are enabling conditions. These findings suggest that transformers are more modality-agnostic than commonly assumed, and that discrete tokenization is not a fundamental requirement for Chinese language modeling.

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).

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.

Tokenization introduces representational redundancy: under a fixed token vocabulary, every byte string admits many valid token encodings, or segmentations, that decode to the same surface string. However, given a prompt, most language model tokenizers break this representational symmetry by returning a canonical segmentation. Training only on canonical segmentations should influence inference behavior, and there is little reason to expect models to respect segmentation symmetry on downstream tasks. We find that this symmetry partially emerges during training. Here, we probe this emergent symmetry through experiments testing token compositional understanding, representation diversity, and task focused benchmark performance. We primarily use retokenization -- replacing a prompt's canonical tokenization with an alternative segmentation while preserving its bytes exactly. Relative to other prompt perturbations, retokenization is unusually clean because it isolates segmentation effects without changing syntax, semantics or surface form. We use retokenization to study sensitivity and robustness to semantically identical input representations across pretraining and post-training. Moreover, this partial retokenization symmetry suggests a distinct inference-time sampling axis. While temperature sampling generates diverse outputs from the model using its next-token probability distribution, retokenization generates diversity from the model's internal computations through semantically equivalent input representations. We find that while this retokenization sampling strategy can hurt performance on easy problems, it can also recover solutions that conventional sampling does not find. Overall, our work presents retokenization as a simple yet powerful probe of large language models, shedding light on compositional understanding and prompt sensitivity, and offering a novel sampling strategy.

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

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.

Tokenization is a foundational step in the text process of Large Language Models (LLMs). Texts must be first tokenized into token IDs, which are then input to LLMs. Inefficient tokenization results in long token-ID sequences and will slow down the training and inference of LLMs. The fine-grained knowledge transfer between LLMs, like token-level distillation, is also impeded by the mismatch in vocabulary. To bridge this gap, we introduce a method named TokAlign++ to improve vocabulary adaptation performance by learning better token alignment lexicon. The source and target vocabularies are taken as two different languages, and the bilingual token alignment lexicon is learned from monolingual token representations. Model parameters are rearranged following this bilingual lexicon for new vocabulary, and progressively fine-tuned for adaptation. Experimental results on 15 languages show that our method boosts the multilingual text compression rates and preserves most of the multilingual ability of vanilla models. It costs as few as 1k steps to restore the performance of the vanilla model. After unifying vocabularies between vanilla models, token-level distillation remarkably improves the base model with only 235M tokens.

Tokenization is the first step in every language model (LM), yet it never takes the sounds of words into account. We investigate how tokenization influences text-only LMs' ability to represent phonological knowledge. Through a series of probing experiments, we show that subword-based tokenization systematically weakens the encoding of both local (e.g., rhyme) and global (e.g., syllabification) phonological features. To quantify this effect, we introduce the syllabification-tokenization alignment distance (STAD), a metric that measures the misalignment between a model's tokenization and the natural syllable boundaries of words, and find that higher misalignment correlates with poorer phonological representations, providing a simple diagnostic for phonology-aware tokenization. To address these limitations, we propose a lightweight IPA-based fine-tuning method that infuses phonological awareness into LMs, leading to consistent improvements across three phonology-related tasks while largely preserving math and general reasoning ability, with 1.1% and 0.9% drops on GSM8K and MMLU, respectively.

All languages are equal; when it comes to tokenization, some are more equal than others. Tokens are the hidden currency that dictate the cost and latency of access to contemporary LLMs. However, many languages written in non-Latin scripts observe a poor exchange rate: LLMs take several multiples of tokens to encode the same information in many languages as they do for English. Our analysis reveals that this issue, known as 'token over-fragmentation', persists in modern open-weight LLMs. The standard remedy is vocabulary expansion that adds target language items missing from the model's vocabulary. In this work, we comprehensively study and advance interpretability-based vocabulary expansion, a new research direction. We focus on two core decisions in the vocabulary expansion process: What items should we add? and How should we initialize their corresponding input and output embeddings? First, we question the conventional use of frequency-based methods to choose candidate vocabulary items to add (a decision long treated as settled), and show that interpretability-based methods offer a superior performance-token efficiency trade-off. Next, we strengthen the case for interpretability-based embedding initialization by showing large gains (~20 pts) over baseline initialization methods for several languages written in non-Latin scripts. We identify the phenomenon of "subword detokenization" where models progressively merge fragmented subword tokens into larger subwords across layers. Grounded in our analysis of this phenomenon, we propose FragMend to further push the efficiency ceiling of interpretability-based expansion. We validate the effectiveness of FragMend through comparison against strong baselines and we present extensive analysis of its design choices.