Daily Papers

We present a training-free method to transplant tokenizers in pretrained large language models (LLMs) by reconstructing unseen token embeddings via Orthogonal Matching Pursuit (OMP). Specifically, we approximate each out-of-vocabulary token as a sparse linear combination of shared tokens, in two phases: first, compute each new token's representation in the donor embedding space with a small dictionary of shared anchor tokens, then transfer these same sparse coefficients back into the base model's embedding space. On two challenging cross-tokenizer tasks--LlamatoMistral NeMo (12B) and QwentoLlama (1B)--we show that OMP achieves best zero-shot preservation of the base model's performance across multiple benchmarks, while other zero-shot approaches degrade significantly. Compared to baselines (zero-init, mean-init, and existing approaches like WECHSEL, FOCUS, ZETT), OMP consistently achieves the best overall performance, effectively bridging large tokenizer discrepancies without gradient updates. Our analysis further identifies mismatched numerical tokenization schemes as a critical challenge for preserving mathematical reasoning capabilities. This technique enables direct reuse of pretrained model weights with new tokenizers, facilitating cross-tokenizer knowledge distillation, speculative decoding, ensembling, merging, and domain-specific vocabulary adaptations. We integrate our method into the open-source mergekit-tokensurgeon tool for post hoc vocabulary realignment.

While language models have exceptional capabilities at text generation, they lack a natural inductive bias for emitting numbers and thus struggle in tasks involving reasoning over quantities, especially arithmetics. This has particular relevance in scientific datasets where combinations of text and numerical data are abundant. One fundamental limitation is the nature of the CE loss, which assumes a nominal (categorical) scale and thus cannot convey proximity between generated number tokens. As a remedy, we here present two versions of a number token loss. The first is based on an L_p loss between the ground truth token value and the weighted sum of the predicted class probabilities. The second loss minimizes the Wasserstein-1 distance between the distribution of the predicted output probabilities and the ground truth distribution. These regression-like losses can easily be added to any language model and extend the CE objective during training. We compare the proposed schemes on a mathematics dataset against existing tokenization, encoding, and decoding schemes for improving number representation in language models. Our results reveal a significant improvement in numerical accuracy when equipping a standard T5 model with the proposed loss schemes.

Tokenization, the division of input text into input tokens, is an often overlooked aspect of the large language model (LLM) pipeline and could be the source of useful or harmful inductive biases. Historically, LLMs have relied on byte pair encoding, without care to specific input domains. With the increased use of LLMs for reasoning, various number-specific tokenization schemes have been adopted, with popular models like LLaMa and PaLM opting for single-digit tokenization while GPT-3.5 and GPT-4 have separate tokens for each 1-, 2-, and 3-digit numbers. In this work, we study the effect this choice has on numerical reasoning through the use of arithmetic tasks. We consider left-to-right and right-to-left tokenization for GPT-3.5 and -4, finding that right-to-left tokenization (enforced by comma separating numbers at inference time) leads to largely improved performance. Furthermore, we find that model errors when using standard left-to-right tokenization follow stereotyped error patterns, suggesting that model computations are systematic rather than approximate. We show that the model is able to convert between tokenizations easily, thus allowing chain-of-thought-inspired approaches to recover performance on left-to-right tokenized inputs. We also find the gap between tokenization directions decreases when models are scaled, possibly indicating that larger models are better able to override this tokenization-dependent inductive bias. In summary, our work performs the first study of how number tokenization choices lead to differences in model performance on arithmetic tasks, accompanied by a thorough analysis of error patterns. We hope this work inspires practitioners to more carefully ablate number tokenization-related choices when working towards general models of numerical reasoning.

Though Large Language Models (LLMs) have shown remarkable abilities in mathematics reasoning, they are still struggling with performing numeric operations accurately, such as addition and multiplication. Numbers can be tokenized into tokens in various ways by different LLMs and affect the numeric operations performance. Currently, there are two representatives: 1) Tokenize into 1-digit, and 2) Tokenize into 1sim 3 digit. The difference is roughly equivalent to using different numeral systems (namely base 10 or base 10^{3}). In light of this, we study the scaling behavior of different numeral systems in the context of transformer-based large language models. We empirically show that a base 10 system is consistently more data-efficient than a base 10^{2} or 10^{3} system across training data scale, model sizes under from-scratch training settings, while different number systems have very similar fine-tuning performances. We attribute this to higher token frequencies of a base 10 system. Additionally, we reveal extrapolation behavior patterns on addition and multiplication. We identify that base 100 and base 1000 systems struggle on token-level discernment and token-level operations. We also sheds light on the mechanism learnt by the models.

Language models typically tokenize text into subwords, using a deterministic, hand-engineered heuristic of combining characters into longer surface-level strings such as 'ing' or whole words. Recent literature has repeatedly shown the limitations of such a tokenization strategy, particularly for documents not written in English and for representing numbers. On the other extreme, byte/character-level language models are much less restricted but suffer from increased sequence description lengths and a subsequent quadratic expansion in self-attention computation. Recent attempts to compress and limit these context lengths with fixed size convolutions is helpful but completely ignores the word boundary. This paper considers an alternative 'learn your tokens' scheme which utilizes the word boundary to pool bytes/characters into word representations, which are fed to the primary language model, before again decoding individual characters/bytes per word in parallel. We find that our moderately expressive and moderately fast end-to-end tokenizer outperform by over 300% both subwords and byte/character models over the intrinsic language modeling metric of next-word prediction across datasets. It particularly outshines on rare words, outperforming by a factor of 30! We extensively study the language modeling setup for all three categories of tokenizers and theoretically analyze how our end-to-end models can also be a strong trade-off in efficiency and robustness.

The ability to understand and work with numbers (numeracy) is critical for many complex reasoning tasks. Currently, most NLP models treat numbers in text in the same way as other tokens---they embed them as distributed vectors. Is this enough to capture numeracy? We begin by investigating the numerical reasoning capabilities of a state-of-the-art question answering model on the DROP dataset. We find this model excels on questions that require numerical reasoning, i.e., it already captures numeracy. To understand how this capability emerges, we probe token embedding methods (e.g., BERT, GloVe) on synthetic list maximum, number decoding, and addition tasks. A surprising degree of numeracy is naturally present in standard embeddings. For example, GloVe and word2vec accurately encode magnitude for numbers up to 1,000. Furthermore, character-level embeddings are even more precise---ELMo captures numeracy the best for all pre-trained methods---but BERT, which uses sub-word units, is less exact.

The relationship between language model tokenization and performance is an open area of research. Here, we investigate how different tokenization schemes impact number agreement in Spanish plurals. We find that morphologically-aligned tokenization performs similarly to other tokenization schemes, even when induced artificially for words that would not be tokenized that way during training. We then present exploratory analyses demonstrating that language model embeddings for different plural tokenizations have similar distributions along the embedding space axis that maximally distinguishes singular and plural nouns. Our results suggest that morphologically-aligned tokenization is a viable tokenization approach, and existing models already generalize some morphological patterns to new items. However, our results indicate that morphological tokenization is not strictly required for performance.

Subword tokenization schemes are the dominant technique used in current NLP models. However, such schemes can be rigid and tokenizers built on one corpus do not adapt well to other parallel corpora. It has also been observed that in multilingual corpora, subword tokenization schemes over-segment low-resource languages leading to a drop in translation performance. A simple alternative to subword tokenizers is byte-based methods i.e. tokenization into byte sequences using encoding schemes such as UTF-8. Byte tokens often represent inputs at a sub-character granularity i.e. one character can be represented by a sequence of multiple byte tokens. This results in byte sequences that are significantly longer than character sequences. Enforcing aggregation of local information in the lower layers can guide the model to build higher-level semantic information. We propose a Local Byte Fusion (LOBEF) method for byte-based machine translation -- utilizing byte n-gram and word boundaries -- to aggregate local semantic information. Extensive experiments on multilingual translation, zero-shot cross-lingual transfer, and domain adaptation reveal a consistent improvement over traditional byte-based models and even over subword techniques. Further analysis also indicates that our byte-based models are parameter-efficient and can be trained faster than subword models.

Large language models (LLMs) have achieved impressive performance across various domains. However, the substantial hardware resources required for their training present a significant barrier to efficiency and scalability. To mitigate this challenge, low-precision training techniques have been widely adopted, leading to notable advancements in training efficiency. Despite these gains, low-precision training involves several componentsx2013such as weights, activations, and gradientsx2013each of which can be represented in different numerical formats. The resulting diversity has created a fragmented landscape in low-precision training research, making it difficult for researchers to gain a unified overview of the field. This survey provides a comprehensive review of existing low-precision training methods. To systematically organize these approaches, we categorize them into three primary groups based on their underlying numerical formats, which is a key factor influencing hardware compatibility, computational efficiency, and ease of reference for readers. The categories are: (1) fixed-point and integer-based methods, (2) floating-point-based methods, and (3) customized format-based methods. Additionally, we discuss quantization-aware training approaches, which share key similarities with low-precision training during forward propagation. Finally, we highlight several promising research directions to advance this field. A collection of papers discussed in this survey is provided in https://github.com/Hao840/Awesome-Low-Precision-Training.

Large Language Models (LLMs) have demonstrated remarkable generalization across diverse tasks, leading individuals to increasingly use them as personal assistants and universal computing engines. Nevertheless, a notable obstacle emerges when feeding numerical/temporal data into these models, such as data sourced from wearables or electronic health records. LLMs employ tokenizers in their input that break down text into smaller units. However, tokenizers are not designed to represent numerical values and might struggle to understand repetitive patterns and context, treating consecutive values as separate tokens and disregarding their temporal relationships. Here, we discuss recent works that employ LLMs for human-centric tasks such as in mobile health sensing and present a case study showing that popular LLMs tokenize temporal data incorrectly. To address that, we highlight potential solutions such as prompt tuning with lightweight embedding layers as well as multimodal adapters, that can help bridge this "modality gap". While the capability of language models to generalize to other modalities with minimal or no finetuning is exciting, this paper underscores the fact that their outputs cannot be meaningful if they stumble over input nuances.

Tokenization is a fundamental component of language models for code. It involves breaking down the input into units that are later passed to the language model stack to learn high-dimensional representations used in various contexts, from classification to generation. However, the output of these tokenizers is often longer than that traditionally used in compilers and interpreters. This could result in undesirable effects, such as increased computational overhead. In this work, we investigate the effect of merging the hidden representations of subtokens that belong to the same semantic unit, such as subtokens that form a single identifier. We propose two strategies: one based on averaging the representations and another that leverages a learning-based approach. Both methods can be seamlessly integrated with existing language models for code. We conduct experiments using six language models for code: CodeBERT, GraphCodeBERT, UniXCoder, CdoeT5, CodeT5+ (220M), and CodeT5+ (770M), across three software engineering tasks: vulnerability detection, code classification, and code translation. Results show that these strategies can reduce the number of floating-point operations by 1% to 19%. Regarding downstream performance, the most significant degradation was observed in the vulnerability detection task, where the F1 score decreased by 1.82 points compared to the baseline. In contrast, for code translation, we observed an improvement of 2.47 points in CodeBLEU. This work contributes to the broader effort of improving language models for code across multiple dimensions, including both computational efficiency and downstream performance.

In recent years, language models have become increasingly larger and more complex. However, the input representations for these models continue to rely on simple and greedy subword tokenization methods. In this paper, we propose a novel tokenization method that factorizes subwords onto discrete triplets using a VQ-VAE model. The effectiveness of the proposed tokenization method, referred to as the Factorizer, is evaluated on language modeling and morpho-syntactic tasks for 7 diverse languages. Results indicate that this method is more appropriate and robust for morphological tasks than the commonly used byte-pair encoding (BPE) tokenization algorithm.

One of the most striking findings in modern research on large language models (LLMs) is that scaling up compute during training leads to better results. However, less attention has been given to the benefits of scaling compute during inference. This survey focuses on these inference-time approaches. We explore three areas under a unified mathematical formalism: token-level generation algorithms, meta-generation algorithms, and efficient generation. Token-level generation algorithms, often called decoding algorithms, operate by sampling a single token at a time or constructing a token-level search space and then selecting an output. These methods typically assume access to a language model's logits, next-token distributions, or probability scores. Meta-generation algorithms work on partial or full sequences, incorporating domain knowledge, enabling backtracking, and integrating external information. Efficient generation methods aim to reduce token costs and improve the speed of generation. Our survey unifies perspectives from three research communities: traditional natural language processing, modern LLMs, and machine learning systems.

What are the units of text that we want to model? From bytes to multi-word expressions, text can be analyzed and generated at many granularities. Until recently, most natural language processing (NLP) models operated over words, treating those as discrete and atomic tokens, but starting with byte-pair encoding (BPE), subword-based approaches have become dominant in many areas, enabling small vocabularies while still allowing for fast inference. Is the end of the road character-level model or byte-level processing? In this survey, we connect several lines of work from the pre-neural and neural era, by showing how hybrid approaches of words and characters as well as subword-based approaches based on learned segmentation have been proposed and evaluated. We conclude that there is and likely will never be a silver bullet singular solution for all applications and that thinking seriously about tokenization remains important for many applications.

Large Language Models (LLMs) have demonstrated impressive capabilities in natural language processing tasks, such as text generation and semantic understanding. However, their performance on numerical reasoning tasks, such as basic arithmetic, numerical retrieval, and magnitude comparison, remains surprisingly poor. This gap arises from their reliance on surface-level statistical patterns rather than understanding numbers as continuous magnitudes. Existing benchmarks primarily focus on either linguistic competence or structured mathematical problem-solving, neglecting fundamental numerical reasoning required in real-world scenarios. To bridge this gap, we propose NumericBench, a comprehensive benchmark to evaluate six fundamental numerical capabilities: number recognition, arithmetic operations, contextual retrieval, comparison, summary, and logical reasoning. NumericBench includes datasets ranging from synthetic number lists to the crawled real-world data, addressing challenges like long contexts, noise, and multi-step reasoning. Extensive experiments on state-of-the-art LLMs, including GPT-4 and DeepSeek, reveal persistent weaknesses in numerical reasoning, highlighting the urgent need to improve numerically-aware language modeling. The benchmark is released in: https://github.com/TreeAI-Lab/NumericBench.

Tokenization is the first - and often underappreciated - layer of computation in language models. While Chain-of-Thought (CoT) prompting enables transformer models to approximate recurrent computation by externalizing intermediate steps, we show that the success of such reasoning is fundamentally bounded by the structure of tokenized inputs. This work presents a theoretical and empirical investigation into how tokenization schemes, particularly subword-based methods like byte-pair encoding (BPE), impede symbolic computation by merging or obscuring atomic reasoning units. We introduce the notion of Token Awareness to formalize how poor token granularity disrupts logical alignment and prevents models from generalizing symbolic procedures. Through systematic evaluation on arithmetic and symbolic tasks, we demonstrate that token structure dramatically affect reasoning performance, causing failure even with CoT, while atomically-aligned formats unlock strong generalization, allowing small models (e.g., GPT-4o-mini) to outperform larger systems (e.g., o1) in structured reasoning. Our findings reveal that symbolic reasoning ability in LLMs is not purely architectural, but deeply conditioned on token-level representations.

Tokenization is an understudied and often neglected component of modern LLMs. Most published works use a single tokenizer for all experiments, often borrowed from another model, without performing ablations or analysis to optimize tokenization. Moreover, the tokenizer is generally kept unchanged when fine-tuning a base model. In this paper, we show that the size, pre-tokenization regular expression, and training data of a tokenizer can significantly impact the model's generation speed, effective context size, memory usage, and downstream performance. We train specialized Byte-Pair Encoding code tokenizers, and conduct extensive ablations on the impact of tokenizer design on the performance of LLMs for code generation tasks such as HumanEval and MBPP, and provide recommendations for tokenizer hyper-parameters selection and switching the tokenizer in a pre-trained LLM. We perform our experiments on models trained from scratch and from pre-trained models, verifying their applicability to a wide range of use-cases. We find that when fine-tuning on more than 50 billion tokens, we can specialize the tokenizer of a pre-trained LLM to obtain large gains in generation speed and effective context size.

Discrete audio tokens are compact representations that aim to preserve perceptual quality, phonetic content, and speaker characteristics while enabling efficient storage and inference, as well as competitive performance across diverse downstream tasks.They provide a practical alternative to continuous features, enabling the integration of speech and audio into modern large language models (LLMs). As interest in token-based audio processing grows, various tokenization methods have emerged, and several surveys have reviewed the latest progress in the field. However, existing studies often focus on specific domains or tasks and lack a unified comparison across various benchmarks. This paper presents a systematic review and benchmark of discrete audio tokenizers, covering three domains: speech, music, and general audio. We propose a taxonomy of tokenization approaches based on encoder-decoder, quantization techniques, training paradigm, streamability, and application domains. We evaluate tokenizers on multiple benchmarks for reconstruction, downstream performance, and acoustic language modeling, and analyze trade-offs through controlled ablation studies. Our findings highlight key limitations, practical considerations, and open challenges, providing insight and guidance for future research in this rapidly evolving area. For more information, including our main results and tokenizer database, please refer to our website: https://poonehmousavi.github.io/dates-website/.

Typically, tokenization is the very first step in most text processing works. As a token serves as an atomic unit that embeds the contextual information of text, how to define a token plays a decisive role in the performance of a model.Even though Byte Pair Encoding (BPE) has been considered the de facto standard tokenization method due to its simplicity and universality, it still remains unclear whether BPE works best across all languages and tasks. In this paper, we test several tokenization strategies in order to answer our primary research question, that is, "What is the best tokenization strategy for Korean NLP tasks?" Experimental results demonstrate that a hybrid approach of morphological segmentation followed by BPE works best in Korean to/from English machine translation and natural language understanding tasks such as KorNLI, KorSTS, NSMC, and PAWS-X. As an exception, for KorQuAD, the Korean extension of SQuAD, BPE segmentation turns out to be the most effective.

Large language models (LLMs) can solve an increasing number of complex reasoning tasks while making surprising mistakes in basic numerical understanding and processing (such as 9.11 > 9.9). The latter ability is essential for tackling complex arithmetic and mathematical problems and serves as a foundation for most reasoning tasks, but previous work paid little attention to it or only discussed several restricted tasks (like integer addition). In this paper, we comprehensively investigate the numerical understanding and processing ability (NUPA) of LLMs. Firstly, we introduce a benchmark covering four common numerical representations and 17 distinct numerical tasks in four major categories, resulting in 41 meaningful combinations in total. These tasks are derived from primary and secondary education curricula, encompassing nearly all everyday numerical understanding and processing scenarios, and the rules of these tasks are very simple and clear. Through the benchmark, we find that current LLMs fail frequently in many of the tasks. To study the problem, we train small models with existing and potential techniques for enhancing NUPA (such as tokenizers, PEs, and number formats), comprehensively evaluating their effectiveness using our testbed. We also finetune practical-scale LLMs on our proposed NUPA tasks and find that 1) naive finetuning can improve NUPA a lot on many but not all tasks, and 2) surprisingly, techniques designed to enhance NUPA prove ineffective for finetuning pretrained models. We further explore the impact of chain-of-thought techniques on NUPA. Our work provides a more detailed and comprehensive understanding of NUPA in LLMs. Our benchmark and code are released at https://github.com/GraphPKU/number_cookbook.

Tokenization is a fundamental preprocessing step in Natural Language Processing (NLP), significantly impacting the capability of large language models (LLMs) to capture linguistic and semantic nuances. This study introduces a novel evaluation framework addressing tokenization challenges specific to morphologically-rich and low-resource languages such as Turkish. Utilizing the Turkish MMLU (TR-MMLU) dataset, comprising 6,200 multiple-choice questions from the Turkish education system, we assessed tokenizers based on vocabulary size, token count, processing time, language-specific token percentages (\%TR), and token purity (\%Pure). These newly proposed metrics measure how effectively tokenizers preserve linguistic structures. Our analysis reveals that language-specific token percentages exhibit a stronger correlation with downstream performance (e.g., MMLU scores) than token purity. Furthermore, increasing model parameters alone does not necessarily enhance linguistic performance, underscoring the importance of tailored, language-specific tokenization methods. The proposed framework establishes robust and practical tokenization standards for morphologically complex languages.

We present the KL3M tokenizers, a family of specialized tokenizers for legal, financial, and governmental text. Despite established work on tokenization, specialized tokenizers for professional domains remain understudied. Our paper offers two main contributions to this area. First, we introduce domain-specific BPE tokenizers for legal, financial, and governmental text. Our kl3m-004-128k-cased tokenizer uses 9-17% fewer tokens than GPT-4o and Llama3 for domain-specific documents, despite having a smaller vocabulary. For specialized terminology, our cased tokenizer is even more efficient, using up to 83% fewer tokens for legal terms and 39% fewer tokens for financial terms. Second, we develop character-level BPE tokenizers (4K, 8K, and 16K vocabulary sizes) for text correction tasks like OCR post-processing. These tokenizers keep consistent token boundaries between error-containing and correct text, making it easier for models to learn correction patterns. These tokenizers help professional applications by fitting more text in context windows, reducing computational needs, and preserving the meaning of domain-specific terms. Our analysis shows these efficiency gains directly benefit the processing of long legal and financial documents. We release all tokenizers and code through GitHub and Hugging Face to support further research in specialized tokenization.

Tokenization is a fundamental preprocessing step in NLP, directly impacting large language models' (LLMs) ability to capture syntactic, morphosyntactic, and semantic structures. This paper introduces a novel framework for systematically evaluating tokenization strategies, addressing challenges in morphologically rich and low-resource languages. Using a Turkish dataset of 6,200 multiple-choice questions from the Massive Multitask Language Understanding (MMLU) benchmark, the framework assesses tokenizers across five key metrics: vocabulary size, token count, processing time, language-specific token percentages (\%TR), and token purity. These metrics provide a structured approach to evaluating how well tokenizers preserve linguistic structures. While \%TR measures the proportion of valid words in the target language, \%Pure assesses the alignment of tokens with meaningful linguistic units, such as roots and valid morphemes, minimizing semantic fragmentation. The findings reveal that \%TR, introduced as a critical metric, exhibits a stronger correlation with downstream performance (e.g., MMLU scores) than token purity, emphasizing its role in improving model accuracy. Additionally, larger model parameters do not necessarily yield better tokenization quality or enhanced results, highlighting the importance of tailored tokenization strategies that prioritize linguistic alignment. This framework sets a new standard for developing robust tokenization methods optimized for morphologically complex and low-resource languages. Future work will refine morphological analysis, explore domain-specific customizations, and conduct cross-linguistic evaluations to further enhance tokenization practices.

Large Language Models (LLMs) typically represent numbers using multiple tokens, which requires the model to aggregate these tokens to interpret numerical values. This fragmentation makes both training and inference less efficient and adversely affects the model's performance on number-related tasks. Inspired by the observation that pre-trained LLMs internally learn Fourier-like features for number tokens, we propose Fourier Number Embedding (FoNE), a novel method that directly maps numbers into the embedding space with their Fourier features. FoNE encodes each number as a single token with only two embedding dimensions per digit, effectively capturing numerical values without fragmentation. This compact representation accelerates both training and inference. Compared to traditional subword and digit-wise embeddings, FoNE not only reduces computational overhead but also achieves higher accuracy across various numerical tasks including addition, subtraction and multiplication. On 6-digit decimal addition, FoNE requires 64times less data to achieve 99% accuracy than subword and digit-wise embeddings while using 3times and 6times fewer tokens per number, respectively. Furthermore, FoNE is the only method that yields 100% accuracy on over 100,000 test examples for addition, subtraction, and multiplication. The codes and visualization are available at https://fouriernumber.github.io/.

Subword tokenization is the de facto standard for tokenization in neural language models and machine translation systems. Three advantages are frequently cited in favor of subwords: shorter encoding of frequent tokens, compositionality of subwords, and ability to deal with unknown words. As their relative importance is not entirely clear yet, we propose a tokenization approach that enables us to separate frequency (the first advantage) from compositionality. The approach uses Huffman coding to tokenize words, by order of frequency, using a fixed amount of symbols. Experiments with CS-DE, EN-FR and EN-DE NMT show that frequency alone accounts for 90%-95% of the scores reached by BPE, hence compositionality has less importance than previously thought.

Tokenization is a foundational step in Natural Language Processing (NLP) tasks, bridging raw text and language models. Existing tokenization approaches like Byte-Pair Encoding (BPE) originate from the field of data compression, and it has been suggested that the effectiveness of BPE stems from its ability to condense text into a relatively small number of tokens. We test the hypothesis that fewer tokens lead to better downstream performance by introducing PathPiece, a new tokenizer that segments a document's text into the minimum number of tokens for a given vocabulary. Through extensive experimentation we find this hypothesis not to be the case, casting doubt on the understanding of the reasons for effective tokenization. To examine which other factors play a role, we evaluate design decisions across all three phases of tokenization: pre-tokenization, vocabulary construction, and segmentation, offering new insights into the design of effective tokenizers. Specifically, we illustrate the importance of pre-tokenization and the benefits of using BPE to initialize vocabulary construction. We train 64 language models with varying tokenization, ranging in size from 350M to 2.4B parameters, all of which are made publicly available.

State-of-the-art language models are autoregressive and operate on subword units known as tokens. Specifically, one must encode the conditioning string into a list of tokens before passing to the language models for next-token prediction. We show that popular encoding schemes, such as maximum prefix encoding (MPE) and byte-pair-encoding (BPE), induce a sampling bias that cannot be mitigated with more training or data. To counter this universal problem, for each encoding scheme above, we propose a novel algorithm to obtain unbiased estimates from any language model trained on tokenized data. Our methods do not require finetuning the model, and the complexity, defined as the number of model runs, scales linearly with the sequence length in the case of MPE. As a result, we show that one can simulate token-free behavior from a tokenized language model. We empirically verify the correctness of our method through a Markov-chain setup, where it accurately recovers the transition probabilities, as opposed to the conventional method of directly prompting tokens into the language model.

Tokenization is an important text preprocessing step to prepare input tokens for deep language models. WordPiece and BPE are de facto methods employed by important models, such as BERT and GPT. However, the impact of tokenization can be different for morphologically rich languages, such as Turkic languages, where many words can be generated by adding prefixes and suffixes. We compare five tokenizers at different granularity levels, i.e. their outputs vary from smallest pieces of characters to the surface form of words, including a Morphological-level tokenizer. We train these tokenizers and pretrain medium-sized language models using RoBERTa pretraining procedure on the Turkish split of the OSCAR corpus. We then fine-tune our models on six downstream tasks. Our experiments, supported by statistical tests, reveal that Morphological-level tokenizer has challenging performance with de facto tokenizers. Furthermore, we find that increasing the vocabulary size improves the performance of Morphological and Word-level tokenizers more than that of de facto tokenizers. The ratio of the number of vocabulary parameters to the total number of model parameters can be empirically chosen as 20% for de facto tokenizers and 40% for other tokenizers to obtain a reasonable trade-off between model size and performance.

Tokenization is associated with many poorly understood shortcomings in language models (LMs), yet remains an important component for long sequence scaling purposes. This work studies how tokenization impacts model performance by analyzing and comparing the stochastic behavior of tokenized models with their byte-level, or token-free, counterparts. We discover that, even when the two models are statistically equivalent, their predictive distributions over the next byte can be substantially different, a phenomenon we term as "tokenization bias''. To fully characterize this phenomenon, we introduce the Byte-Token Representation Lemma, a framework that establishes a mapping between the learned token distribution and its equivalent byte-level distribution. From this result, we develop a next-byte sampling algorithm that eliminates tokenization bias without requiring further training or optimization. In other words, this enables zero-shot conversion of tokenized LMs into statistically equivalent token-free ones. We demonstrate its broad applicability with two use cases: fill-in-the-middle (FIM) tasks and model ensembles. In FIM tasks where input prompts may terminate mid-token, leading to out-of-distribution tokenization, our method mitigates performance degradation and achieves an approximately 18% improvement in FIM coding benchmarks, consistently outperforming the standard token healing fix. For model ensembles where each model employs a distinct vocabulary, our approach enables seamless integration, resulting in improved performance (up to 3.7%) over individual models across various standard baselines in reasoning, knowledge, and coding.

Building effective neural machine translation (NMT) models for very low-resourced and morphologically rich African indigenous languages is an open challenge. Besides the issue of finding available resources for them, a lot of work is put into preprocessing and tokenization. Recent studies have shown that standard tokenization methods do not always adequately deal with the grammatical, diacritical, and tonal properties of some African languages. That, coupled with the extremely low availability of training samples, hinders the production of reliable NMT models. In this paper, using Fon language as a case study, we revisit standard tokenization methods and introduce Word-Expressions-Based (WEB) tokenization, a human-involved super-words tokenization strategy to create a better representative vocabulary for training. Furthermore, we compare our tokenization strategy to others on the Fon-French and French-Fon translation tasks.

The rapid advancement of large language models (LLMs) has led to significant improvements in natural language processing but also poses challenges due to their high computational and energy demands. This paper introduces a series of research efforts focused on Super Tiny Language Models (STLMs), which aim to deliver high performance with significantly reduced parameter counts. We explore innovative techniques such as byte-level tokenization with a pooling mechanism, weight tying, and efficient training strategies. These methods collectively reduce the parameter count by 90% to 95% compared to traditional models while maintaining competitive performance. This series of papers will explore into various subproblems, including tokenizer-free models, self-play based training, and alternative training objectives, targeting models with 10M, 50M, and 100M parameters. Our ultimate goal is to make high-performance language models more accessible and practical for a wide range of applications.

Recent image generative models typically capture the image distribution in a pre-constructed latent space, relying on a frozen image tokenizer. However, there exists a significant discrepancy between the reconstruction and generation distribution, where current tokenizers only prioritize the reconstruction task that happens before generative training without considering the generation errors during sampling. In this paper, we comprehensively analyze the reason for this discrepancy in a discrete latent space, and, from which, we propose a novel tokenizer training scheme including both main-training and post-training, focusing on improving latent space construction and decoding respectively. During the main training, a latent perturbation strategy is proposed to simulate sampling noises, \ie, the unexpected tokens generated in generative inference. Specifically, we propose a plug-and-play tokenizer training scheme, which significantly enhances the robustness of tokenizer, thus boosting the generation quality and convergence speed, and a novel tokenizer evaluation metric, \ie, pFID, which successfully correlates the tokenizer performance to generation quality. During post-training, we further optimize the tokenizer decoder regarding a well-trained generative model to mitigate the distribution difference between generated and reconstructed tokens. With a sim400M generator, a discrete tokenizer trained with our proposed main training achieves a notable 1.60 gFID and further obtains 1.36 gFID with the additional post-training. Further experiments are conducted to broadly validate the effectiveness of our post-training strategy on off-the-shelf discrete and continuous tokenizers, coupled with autoregressive and diffusion-based generators.

The transferability of deep neural networks (DNNs) has made significant progress in image and language processing. However, due to the heterogeneity among tables, such DNN bonus is still far from being well exploited on tabular data prediction (e.g., regression or classification tasks). Condensing knowledge from diverse domains, language models (LMs) possess the capability to comprehend feature names from various tables, potentially serving as versatile learners in transferring knowledge across distinct tables and diverse prediction tasks, but their discrete text representation space is inherently incompatible with numerical feature values in tables. In this paper, we present TP-BERTa, a specifically pre-trained LM for tabular data prediction. Concretely, a novel relative magnitude tokenization converts scalar numerical feature values to finely discrete, high-dimensional tokens, and an intra-feature attention approach integrates feature values with the corresponding feature names. Comprehensive experiments demonstrate that our pre-trained TP-BERTa leads the performance among tabular DNNs and is competitive with Gradient Boosted Decision Tree models in typical tabular data regime.

Byte Pair Encoding (BPE) tokenizers, widely used in Large Language Models, face challenges in multilingual settings, including penalization of non-Western scripts and the creation of tokens with partial UTF-8 sequences. Pretokenization, often reliant on complex regular expressions, can also introduce fragility and unexpected edge cases. We propose SCRIPT (Script Category Representation in PreTokenization), a novel encoding scheme that bypasses UTF-8 byte conversion by using initial tokens based on Unicode script and category properties. This approach enables a simple, rule-based pretokenization strategy that respects script boundaries, offering a robust alternative to pretokenization strategies based on regular expressions. We also introduce and validate a constrained BPE merging strategy that enforces character integrity, applicable to both SCRIPT-BPE and byte-based BPE. Our experiments demonstrate that SCRIPT-BPE achieves competitive compression while eliminating encoding-based penalties for non-Latin-script languages.

Tokenization is the first -- and often least scrutinized -- step of most NLP pipelines. Standard algorithms for learning tokenizers rely on frequency-based objectives, which favor languages dominant in the training data and consequently leave lower-resource languages with tokenizations that are disproportionately longer, morphologically implausible, or even riddled with <UNK> placeholders. This phenomenon ultimately amplifies computational and financial inequalities between users from different language backgrounds. To remedy this, we introduce Parity-aware Byte Pair Encoding (BPE), a variant of the widely-used BPE algorithm. At every merge step, Parity-aware BPE maximizes the compression gain of the currently worst-compressed language, trading a small amount of global compression for cross-lingual parity. We find empirically that Parity-aware BPE leads to more equitable token counts across languages, with negligible impact on global compression rate and no substantial effect on language-model performance in downstream tasks.

Image tokenization plays a critical role in reducing the computational demands of modeling high-resolution images, significantly improving the efficiency of image and multimodal understanding and generation. Recent advances in 1D latent spaces have reduced the number of tokens required by eliminating the need for a 2D grid structure. In this paper, we further advance compact discrete image representation by introducing 1D binary image latents. By representing each image as a sequence of binary vectors, rather than using traditional one-hot codebook tokens, our approach preserves high-resolution details while maintaining the compactness of 1D latents. To the best of our knowledge, our text-to-image models are the first to achieve competitive performance in both diffusion and auto-regressive generation using just 128 discrete tokens for images up to 1024x1024, demonstrating up to a 32-fold reduction in token numbers compared to standard VQ-VAEs. The proposed 1D binary latent space, coupled with simple model architectures, achieves marked improvements in speed training and inference speed. Our text-to-image models allow for a global batch size of 4096 on a single GPU node with 8 AMD MI300X GPUs, and the training can be completed within 200 GPU days. Our models achieve competitive performance compared to modern image generation models without any in-house private training data or post-training refinements, offering a scalable and efficient alternative to conventional tokenization methods.

Image tokenization has enabled major advances in autoregressive image generation by providing compressed, discrete representations that are more efficient to process than raw pixels. While traditional approaches use 2D grid tokenization, recent methods like TiTok have shown that 1D tokenization can achieve high generation quality by eliminating grid redundancies. However, these methods typically use a fixed number of tokens and thus cannot adapt to an image's inherent complexity. We introduce FlexTok, a tokenizer that projects 2D images into variable-length, ordered 1D token sequences. For example, a 256x256 image can be resampled into anywhere from 1 to 256 discrete tokens, hierarchically and semantically compressing its information. By training a rectified flow model as the decoder and using nested dropout, FlexTok produces plausible reconstructions regardless of the chosen token sequence length. We evaluate our approach in an autoregressive generation setting using a simple GPT-style Transformer. On ImageNet, this approach achieves an FID<2 across 8 to 128 tokens, outperforming TiTok and matching state-of-the-art methods with far fewer tokens. We further extend the model to support to text-conditioned image generation and examine how FlexTok relates to traditional 2D tokenization. A key finding is that FlexTok enables next-token prediction to describe images in a coarse-to-fine "visual vocabulary", and that the number of tokens to generate depends on the complexity of the generation task.

Tokenization plays a critical role in language modeling, yet existing approaches such as Byte-Pair Encoding (BPE) or WordPiece operate purely on frequency statistics, ignoring the underlying semantic structure of text. This leads to over-tokenization of semantically redundant spans and underutilization of contextual coherence, particularly in long-context scenarios. In this work, we propose SemToken, a semantic-aware tokenization framework that jointly reduces token redundancy and improves computation efficiency. SemToken first extracts contextual semantic embeddings via lightweight encoders and performs local semantic clustering to merge semantically equivalent tokens. Then, it allocates heterogeneous token granularity based on semantic density, allowing finer-grained tokenization in content-rich regions and coarser compression in repetitive or low-entropy spans. SemToken can be seamlessly integrated with modern language models and attention acceleration methods. Experiments on long-context language modeling benchmarks such as WikiText-103 and LongBench show that SemToken achieves up to 2.4times reduction in token count and 1.9times speedup, with negligible or no degradation in perplexity and downstream accuracy. Our findings suggest that semantic structure offers a promising new axis for optimizing tokenization and computation in large language models.

While language models are increasingly utilized in materials science, typical models rely on frequency-centric tokenization methods originally developed for natural language processing. However, these methods frequently produce excessive fragmentation and semantic loss, failing to maintain the structural and semantic integrity of material concepts. To address this issue, we propose MATTER, a novel tokenization approach that integrates material knowledge into tokenization. Based on MatDetector trained on our materials knowledge base and a re-ranking method prioritizing material concepts in token merging, MATTER maintains the structural integrity of identified material concepts and prevents fragmentation during tokenization, ensuring their semantic meaning remains intact. The experimental results demonstrate that MATTER outperforms existing tokenization methods, achieving an average performance gain of 4% and 2% in the generation and classification tasks, respectively. These results underscore the importance of domain knowledge for tokenization strategies in scientific text processing. Our code is available at https://github.com/yerimoh/MATTER

Numerical reasoning over natural language has been a long-standing goal for the research community. However, cutting-edge language models have proven difficult to reliably generalize to a broad range of numbers, although they have shown proficiency in reasoning over common and simple numbers. In this paper, we propose a novel method to elicit and exploit the numerical reasoning knowledge hidden in pre-trained language models using simple anchor numbers. Concretely, we first leverage simple numbers as anchors to probe the implicitly inferred arithmetic expressions from language models, and then explicitly apply the expressions on complex numbers to get corresponding answers. To inversely elicit arithmetic expressions, we transform and formulate the task as an analytically solvable linear system. Experimental results on several numerical reasoning benchmarks demonstrate that our approach significantly improves numerical reasoning capabilities of existing LMs. More importantly, our approach is training-free and simply works in the inference phase, making it highly portable and achieving consistent performance benefits across a variety of language models (GPT-3, T5, BART, etc) in all zero-shot, few-shot, and fine-tuning scenarios.

Text Normalization is an integral part of any text-to-speech synthesis system. In a natural language text, there are elements such as numbers, dates, abbreviations, etc. that belong to other semiotic classes. They are called non-standard words (NSW) and need to be expanded into ordinary words. For this purpose, it is necessary to identify the semiotic class of each NSW. The taxonomy of semiotic classes adapted to the Lithuanian language is presented in the work. Sets of rules are created for detecting and expanding NSWs based on regular expressions. Experiments with three completely different data sets were performed and the accuracy was assessed. Causes of errors are explained and recommendations are given for the development of text normalization rules.

When used with deep learning, the symbolic music modality is often coupled with language model architectures. To do so, the music needs to be tokenized, i.e. converted into a sequence of discrete tokens. This can be achieved by different approaches, as music can be composed of simultaneous tracks, of simultaneous notes with several attributes. Until now, the proposed tokenizations rely on small vocabularies of tokens describing the note attributes and time events, resulting in fairly long token sequences, and a sub-optimal use of the embedding space of language models. Recent research has put efforts on reducing the overall sequence length by merging embeddings or combining tokens. In this paper, we show that Byte Pair Encoding, a compression technique widely used for natural language, significantly decreases the sequence length while increasing the vocabulary size. By doing so, we leverage the embedding capabilities of such models with more expressive tokens, resulting in both better results and faster inference in generation and classification tasks. The source code is shared on Github, along with a companion website. Finally, BPE is directly implemented in MidiTok, allowing the reader to easily benefit from this method.

Large Language Models (LLMs) based on transformer architectures have revolutionized a variety of domains, with tokenization playing a pivotal role in their pre-processing and fine-tuning stages. In multilingual models, particularly those tailored for Indic languages, effective tokenization is crucial for optimizing performance. This paper presents a comprehensive evaluation of tokenizers used by 12 LLMs across all 22 official languages of India, with a focus on comparing the efficiency of their tokenization processes. We employed the Normalized Sequence Length (NSL) as a key metric in our analysis. Our findings reveal that the SUTRA tokenizer outperforms all other models, including several Indic-specific models, excelling in 14 languages. Notable insights include the SUTRA tokenizer's superior handling of Indic languages, GPT-4o's advancement over its predecessor GPT-4 in processing Indian languages, and the limited performance of Project Indus in certain languages. This study underscores the critical importance of developing targeted tokenization strategies for multilingual and Indic-centric models, laying the groundwork for future improvements in tokenizer design to enhance linguistic coverage and model efficiency.

The rapid advancement of large language models (LLMs) has intensified the need for effective mechanisms to transform continuous multimodal data into discrete representations suitable for language-based processing. Discrete tokenization, with vector quantization (VQ) as a central approach, offers both computational efficiency and compatibility with LLM architectures. Despite its growing importance, there is a lack of a comprehensive survey that systematically examines VQ techniques in the context of LLM-based systems. This work fills this gap by presenting the first structured taxonomy and analysis of discrete tokenization methods designed for LLMs. We categorize 8 representative VQ variants that span classical and modern paradigms and analyze their algorithmic principles, training dynamics, and integration challenges with LLM pipelines. Beyond algorithm-level investigation, we discuss existing research in terms of classical applications without LLMs, LLM-based single-modality systems, and LLM-based multimodal systems, highlighting how quantization strategies influence alignment, reasoning, and generation performance. In addition, we identify key challenges including codebook collapse, unstable gradient estimation, and modality-specific encoding constraints. Finally, we discuss emerging research directions such as dynamic and task-adaptive quantization, unified tokenization frameworks, and biologically inspired codebook learning. This survey bridges the gap between traditional vector quantization and modern LLM applications, serving as a foundational reference for the development of efficient and generalizable multimodal systems. A continuously updated version is available at: https://github.com/jindongli-Ai/LLM-Discrete-Tokenization-Survey.

While making investment decisions by reading financial documents, investors need to differentiate between in-claim and outof-claim numerals. In this paper, we present a tool which does it automatically. It extracts context embeddings of the numerals using one of the transformer based pre-trained language model called BERT. After this, it uses a Logistic Regression based model to detect whether the numerals is in-claim or out-of-claim. We use FinNum-3 (English) dataset to train our model. After conducting rigorous experiments we achieve a Macro F1 score of 0.8223 on the validation set. We have open-sourced this tool and it can be accessed from https://github.com/sohomghosh/FiNCAT_Financial_Numeral_Claim_Analysis_Tool

Tokenization significantly influences language models(LMs)' performance. This paper traces the evolution of tokenizers from word-level to subword-level, analyzing how they balance tokens and types to enhance model adaptability while controlling complexity. Despite subword tokenizers like Byte Pair Encoding (BPE) overcoming many word tokenizer limitations, they encounter difficulties in handling non-Latin languages and depend heavily on extensive training data and computational resources to grasp the nuances of multiword expressions (MWEs). This article argues that tokenizers, more than mere technical tools, should drawing inspiration from the cognitive science about human language processing. This study then introduces the "Principle of Least Effort" from cognitive science, that humans naturally seek to reduce cognitive effort, and discusses the benefits of this principle for tokenizer development. Based on this principle, the paper proposes that the Less-is-Better (LiB) model could be a new approach for LLM tokenizer. The LiB model can autonomously learn an integrated vocabulary consisting of subwords, words, and MWEs, which effectively reduces both the numbers of tokens and types. Comparative evaluations show that the LiB tokenizer outperforms existing word and BPE tokenizers, presenting an innovative method for tokenizer development, and hinting at the possibility of future cognitive science-based tokenizers being more efficient.

Recent dynamic tokenisation methods operate directly on bytes and pool their latent representations into patches. This bears similarities to computational models of word segmentation that determine lexical boundaries using spikes in an autoregressive model's prediction error. Inspired by this connection, we explore whether grouping predictable bytes - rather than pooling their representations - can yield a useful fixed subword vocabulary. We propose a new information-driven subword tokeniser, ByteSpan, that uses an external byte-level LM during training to identify contiguous predictable byte sequences and group them into subwords. Experiments show that ByteSpan yields efficient vocabularies with higher morphological alignment scores than BPE for English. Multilingual experiments show similar compression and R\'enyi efficiency for 25 languages.

Recent advancements in large language models(LLMs), such as GPT-4 and GPT-4o, have shown exceptional performance, especially in languages with abundant resources like English, thanks to extensive datasets that ensure robust training. Conversely, these models exhibit limitations when processing under-resourced languages such as Chinese and Korean, where issues including hallucinatory responses remain prevalent. This paper traces the roots of these disparities to the tokenization process inherent to these models. Specifically, it explores how the tokenizers vocabulary, often used to speed up the tokenization process and reduce tokens but constructed independently of the actual model training data, inadequately represents non-English languages. This misrepresentation results in the propagation of under-trained or untrained tokens, which perpetuate biases and pose serious concerns related to data security and ethical standards. We aim to dissect the tokenization mechanics of GPT-4o, illustrating how its simplified token-handling methods amplify these risks and offer strategic solutions to mitigate associated security and ethical issues. Through this study, we emphasize the critical need to rethink tokenization frameworks to foster more equitable and secure AI technologies. The code and data are available at https://github.com/yeyimilk/LLMGPT4o

Tokenization is a fundamental step in natural language processing, breaking text into units that computational models can process. While learned subword tokenizers have become the de-facto standard, they present challenges such as large vocabularies, limited adaptability to new domains or languages, and sensitivity to spelling errors and variations. To overcome these limitations, we investigate a hierarchical architecture for autoregressive language modelling that combines character-level and word-level processing. It employs a lightweight character-level encoder to convert character sequences into word embeddings, which are then processed by a word-level backbone model and decoded back into characters via a compact character-level decoder. This method retains the sequence compression benefits of word-level tokenization without relying on a rigid, predefined vocabulary. We demonstrate, at scales up to 7 billion parameters, that hierarchical transformers match the downstream task performance of subword-tokenizer-based models while exhibiting significantly greater robustness to input perturbations. Additionally, during continued pretraining on an out-of-domain language, our model trains almost twice as fast, achieves superior performance on the target language, and retains more of its previously learned knowledge. Hierarchical transformers pave the way for NLP systems that are more robust, flexible, and generalizable across languages and domains.

Static subword tokenization algorithms have been an essential component of recent works on language modeling. However, their static nature results in important flaws that degrade the models' downstream performance and robustness. In this work, we propose MANTa, a Module for Adaptive Neural TokenizAtion. MANTa is a differentiable tokenizer trained end-to-end with the language model. The resulting system offers a trade-off between the expressiveness of byte-level models and the speed of models trained using subword tokenization. In addition, our tokenizer is highly explainable since it produces an explicit segmentation of sequences into blocks. We evaluate our pre-trained model on several English datasets from different domains as well as on synthetic noise. We find that MANTa improves robustness to character perturbations and out-of-domain data. We then show that MANTa performs comparably to other models on the general-domain GLUE benchmark. Finally, we show that it is considerably faster than strictly byte-level models.

Common subword tokenization algorithms like BPE and UnigramLM assume that text can be split into meaningful units by concatenative measures alone. This is not true for languages such as Hebrew and Arabic, where morphology is encoded in root-template patterns, or Malay and Georgian, where split affixes are common. We present SPLINTER, a pre-processing step which rearranges text into a linear form that better represents such nonconcatenative morphologies, enabling meaningful contiguous segments to be found by the tokenizer. We demonstrate SPLINTER's merit using both intrinsic measures evaluating token vocabularies in Hebrew, Arabic, and Malay; as well as on downstream tasks using BERT-architecture models trained for Hebrew.

Recent language models have shown impressive multilingual performance, even when not explicitly trained for it. Despite this, there are concerns about the quality of their outputs across different languages. In this paper, we show how disparity in the treatment of different languages arises at the tokenization stage, well before a model is even invoked. The same text translated into different languages can have drastically different tokenization lengths, with differences up to 15 times in some cases. These disparities persist even for tokenizers that are intentionally trained for multilingual support. Character-level and byte-level models also exhibit over 4 times the difference in the encoding length for some language pairs. This induces unfair treatment for some language communities in regard to the cost of accessing commercial language services, the processing time and latency, as well as the amount of content that can be provided as context to the models. Therefore, we make the case that we should train future language models using multilingually fair subword tokenizers.

Discrete visual tokenizers transform images into a sequence of tokens, enabling token-based visual generation akin to language models. However, this process is inherently challenging, as it requires both compressing visual signals into a compact representation and discretizing them into a fixed set of codes. Traditional discrete tokenizers typically learn the two tasks jointly, often leading to unstable training, low codebook utilization, and limited reconstruction quality. In this paper, we introduce CODA(COntinuous-to-Discrete Adaptation), a framework that decouples compression and discretization. Instead of training discrete tokenizers from scratch, CODA adapts off-the-shelf continuous VAEs -- already optimized for perceptual compression -- into discrete tokenizers via a carefully designed discretization process. By primarily focusing on discretization, CODA ensures stable and efficient training while retaining the strong visual fidelity of continuous VAEs. Empirically, with 6 times less training budget than standard VQGAN, our approach achieves a remarkable codebook utilization of 100% and notable reconstruction FID (rFID) of 0.43 and 1.34 for 8 times and 16 times compression on ImageNet 256times 256 benchmark.

The pretraining data of today's strongest language models is opaque. In particular, little is known about the proportions of various domains or languages represented. In this work, we tackle a task which we call data mixture inference, which aims to uncover the distributional make-up of training data. We introduce a novel attack based on a previously overlooked source of information -- byte-pair encoding (BPE) tokenizers, used by the vast majority of modern language models. Our key insight is that the ordered list of merge rules learned by a BPE tokenizer naturally reveals information about the token frequencies in its training data: the first merge is the most common byte pair, the second is the most common pair after merging the first token, and so on. Given a tokenizer's merge list along with data samples for each category of interest, we formulate a linear program that solves for the proportion of each category in the tokenizer's training set. Importantly, to the extent to which tokenizer training data is representative of the pretraining data, we indirectly learn about the pretraining data. In controlled experiments, we show that our attack recovers mixture ratios with high precision for tokenizers trained on known mixtures of natural languages, programming languages, and data sources. We then apply our approach to off-the-shelf tokenizers released with recent LMs. We confirm much publicly disclosed information about these models, and also make several new inferences: GPT-4o's tokenizer is much more multilingual than its predecessors, training on 39% non-English data; Llama3 extends GPT-3.5's tokenizer primarily for multilingual (48%) use; GPT-3.5's and Claude's tokenizers are trained on predominantly code (~60%). We hope our work sheds light on current design practices for pretraining data, and inspires continued research into data mixture inference for LMs.

Subword tokenization has become the de-facto standard for tokenization, although comparative evaluations of subword vocabulary quality across languages are scarce. Existing evaluation studies focus on the effect of a tokenization algorithm on the performance in downstream tasks, or on engineering criteria such as the compression rate. We present a new evaluation paradigm that focuses on the cognitive plausibility of subword tokenization. We analyze the correlation of the tokenizer output with the response time and accuracy of human performance on a lexical decision task. We compare three tokenization algorithms across several languages and vocabulary sizes. Our results indicate that the UnigramLM algorithm yields less cognitively plausible tokenization behavior and a worse coverage of derivational morphemes, in contrast with prior work.

Tokenization efficiency plays a critical role in the performance and cost of large language models (LLMs), yet most models rely on static tokenizers optimized for general-purpose corpora. These tokenizers' fixed vocabularies often fail to adapt to domain- or language-specific inputs, leading to longer token sequences and higher computational costs. We introduce zip2zip, a framework that enables LLMs to dynamically adjust token vocabulary at inference time, allowing for fewer generated tokens and thus faster inference. zip2zip consists of three key components: (1) a tokenizer based on Lempel-Ziv-Welch (LZW) compression that incrementally compresses tokens into reusable "hypertokens" on the fly; (2) an embedding layer that computes embeddings for newly formed hypertokens at runtime; and (3) a causal language modeling variant that trains the model to operate on hypertokenized, compressed sequences. We show that an existing LLM can be zip2zip-fied in 10 GPU-hours via parameter-efficient finetuning. The resulting zip2zip LLMs effectively learn to use hypertokens at inference time, reducing input and output sequence length by 20-60\%, with significant improvements in inference latency.

While subword tokenizers such as BPE and WordPiece are typically used to build vocabularies for NLP models, the method of decoding text into a sequence of tokens from these vocabularies is often left unspecified, or ill-suited to the method in which they were constructed. We provide a controlled analysis of seven tokenizer inference methods across four different algorithms and three vocabulary sizes, performed on a novel intrinsic evaluation suite we curated for English, combining measures rooted in morphology, cognition, and information theory. We show that for the most commonly used tokenizers, greedy inference performs surprisingly well; and that SaGe, a recently-introduced contextually-informed tokenizer, outperforms all others on morphological alignment.

In this paper, we explore the idea of training large language models (LLMs) over highly compressed text. While standard subword tokenizers compress text by a small factor, neural text compressors can achieve much higher rates of compression. If it were possible to train LLMs directly over neurally compressed text, this would confer advantages in training and serving efficiency, as well as easier handling of long text spans. The main obstacle to this goal is that strong compression tends to produce opaque outputs that are not well-suited for learning. In particular, we find that text na\"ively compressed via Arithmetic Coding is not readily learnable by LLMs. To overcome this, we propose Equal-Info Windows, a novel compression technique whereby text is segmented into blocks that each compress to the same bit length. Using this method, we demonstrate effective learning over neurally compressed text that improves with scale, and outperforms byte-level baselines by a wide margin on perplexity and inference speed benchmarks. While our method delivers worse perplexity than subword tokenizers for models trained with the same parameter count, it has the benefit of shorter sequence lengths. Shorter sequence lengths require fewer autoregressive generation steps, and reduce latency. Finally, we provide extensive analysis of the properties that contribute to learnability, and offer concrete suggestions for how to further improve the performance of high-compression tokenizers.

Effective training of today's large language models (LLMs) depends on large batches and long sequences for throughput and accuracy. To handle variable-length sequences on hardware accelerators, it is common practice to introduce padding tokens, so that all sequences in a batch have the same length. We show in this paper that the variation in sequence lengths in common NLP datasets is such that up to 50% of all tokens can be padding. In less common, but not extreme, cases (e.g. GLUE-cola with sequence length 128), the ratio is up to 89%. Existing methods to address the resulting inefficiency are complicated by the need to avoid cross-contamination in self-attention, by a reduction in accuracy when sequence ordering information is lost, or by customized kernel implementations only valid for specific accelerators. This paper introduces a new formalization of sequence packing in the context of the well-studied bin packing problem, and presents new algorithms based on this formulation which, for example, confer a 2x speedup for phase 2 pre-training in BERT. We show how existing models can be adapted to ensure mathematical equivalence between the original and packed models, meaning that packed models can be trained with existing pre-training and fine-tuning practices.

Representing speech as discrete tokens provides a framework for transforming speech into a format that closely resembles text, thus enabling the use of speech as an input to the widely successful large language models (LLMs). Currently, while several speech tokenizers have been proposed, there is ambiguity regarding the properties that are desired from a tokenizer for specific downstream tasks and its overall generalizability. Evaluating the performance of tokenizers across different downstream tasks is a computationally intensive effort that poses challenges for scalability. To circumvent this requirement, we present STAB (Speech Tokenizer Assessment Benchmark), a systematic evaluation framework designed to assess speech tokenizers comprehensively and shed light on their inherent characteristics. This framework provides a deeper understanding of the underlying mechanisms of speech tokenization, thereby offering a valuable resource for expediting the advancement of future tokenizer models and enabling comparative analysis using a standardized benchmark. We evaluate the STAB metrics and correlate this with downstream task performance across a range of speech tasks and tokenizer choices.

Neural networks have a reputation for being better at solving statistical or approximate problems than at performing calculations or working with symbolic data. In this paper, we show that they can be surprisingly good at more elaborated tasks in mathematics, such as symbolic integration and solving differential equations. We propose a syntax for representing mathematical problems, and methods for generating large datasets that can be used to train sequence-to-sequence models. We achieve results that outperform commercial Computer Algebra Systems such as Matlab or Mathematica.

In infilling tasks, sub-tokens, representing instances where a complete token is segmented into two parts, often emerge at the boundaries of prefixes, middles, and suffixes. Traditional methods focused on training models at the token level, leading to sub-optimal performance in character-level infilling tasks during the inference stage. Alternately, some approaches considered character-level infilling, but they relied on predicting sub-tokens in inference, yet this strategy diminished ability in character-level infilling tasks due to the large perplexity of the model on sub-tokens. In this paper, we introduce FIM-SE, which stands for Fill-In-the-Middle with both Starting and Ending character constraints. The proposed method addresses character-level infilling tasks by utilizing a line-level format to avoid predicting any sub-token in inference. In addition, we incorporate two special tokens to signify the rest of the incomplete lines, thereby enhancing generation guidance. Extensive experiments demonstrate that our proposed approach surpasses previous methods, offering a significant advantage. Code is available at https://github.com/SenseLLM/FIM-SE.

Language models have demonstrated impressive ability in context understanding and generative performance. Inspired by the recent success of language foundation models, in this paper, we propose LMTraj (Language-based Multimodal Trajectory predictor), which recasts the trajectory prediction task into a sort of question-answering problem. Departing from traditional numerical regression models, which treat the trajectory coordinate sequence as continuous signals, we consider them as discrete signals like text prompts. Specially, we first transform an input space for the trajectory coordinate into the natural language space. Here, the entire time-series trajectories of pedestrians are converted into a text prompt, and scene images are described as text information through image captioning. The transformed numerical and image data are then wrapped into the question-answering template for use in a language model. Next, to guide the language model in understanding and reasoning high-level knowledge, such as scene context and social relationships between pedestrians, we introduce an auxiliary multi-task question and answering. We then train a numerical tokenizer with the prompt data. We encourage the tokenizer to separate the integer and decimal parts well, and leverage it to capture correlations between the consecutive numbers in the language model. Lastly, we train the language model using the numerical tokenizer and all of the question-answer prompts. Here, we propose a beam-search-based most-likely prediction and a temperature-based multimodal prediction to implement both deterministic and stochastic inferences. Applying our LMTraj, we show that the language-based model can be a powerful pedestrian trajectory predictor, and outperforms existing numerical-based predictor methods. Code is publicly available at https://github.com/inhwanbae/LMTrajectory .

Current image tokenization methods require a large number of tokens to capture the information contained within images. Although the amount of information varies across images, most image tokenizers only support fixed-length tokenization, leading to inefficiency in token allocation. In this study, we introduce One-D-Piece, a discrete image tokenizer designed for variable-length tokenization, achieving quality-controllable mechanism. To enable variable compression rate, we introduce a simple but effective regularization mechanism named "Tail Token Drop" into discrete one-dimensional image tokenizers. This method encourages critical information to concentrate at the head of the token sequence, enabling support of variadic tokenization, while preserving state-of-the-art reconstruction quality. We evaluate our tokenizer across multiple reconstruction quality metrics and find that it delivers significantly better perceptual quality than existing quality-controllable compression methods, including JPEG and WebP, at smaller byte sizes. Furthermore, we assess our tokenizer on various downstream computer vision tasks, including image classification, object detection, semantic segmentation, and depth estimation, confirming its adaptability to numerous applications compared to other variable-rate methods. Our approach demonstrates the versatility of variable-length discrete image tokenization, establishing a new paradigm in both compression efficiency and reconstruction performance. Finally, we validate the effectiveness of tail token drop via detailed analysis of tokenizers.

We present UTF8Tokenizer, a minimalist byte-level tokenizer that maps text exactly to IDs corresponding to the bytes underlying the text's UTF-8 encoding (e.g., byte x09 is token ID 9). Unlike prior byte-level approaches (Xue et al., 2021; Pagnoni et al., 2025), our implementation never introduces out-of-range IDs (i.e. there is no token ID 256) or auxiliary tokens: all special behavior (e.g., padding, boundaries, conversation structure, attention segments, tool calling, "thinking" spans, etc.) is encoded using C0 control bytes - just as ASCII was originally designed to embed control information alongside printable text. These design principles yield practical benefits: (1) faster tokenization (14x) and significantly lower host-device transfer (8x less than int64); (2) simple, shareable 256*d embedding tables that can be aligned across models; and (3) a training-time enhancement via bit-biased embeddings, which exposes per-byte bit structure and can be added to the embedding table post-training, removing inference costs. Our HuggingFace-compatible implementation improves language modeling convergence.

Transformer based models, like BERT and RoBERTa, have achieved state-of-the-art results in many Natural Language Processing tasks. However, their memory footprint, inference latency, and power consumption are prohibitive efficient inference at the edge, and even at the data center. While quantization can be a viable solution for this, previous work on quantizing Transformer based models use floating-point arithmetic during inference, which cannot efficiently utilize integer-only logical units such as the recent Turing Tensor Cores, or traditional integer-only ARM processors. In this work, we propose I-BERT, a novel quantization scheme for Transformer based models that quantizes the entire inference with integer-only arithmetic. Based on lightweight integer-only approximation methods for nonlinear operations, e.g., GELU, Softmax, and Layer Normalization, I-BERT performs an end-to-end integer-only BERT inference without any floating point calculation. We evaluate our approach on GLUE downstream tasks using RoBERTa-Base/Large. We show that for both cases, I-BERT achieves similar (and slightly higher) accuracy as compared to the full-precision baseline. Furthermore, our preliminary implementation of I-BERT shows a speedup of 2.4-4.0x for INT8 inference on a T4 GPU system as compared to FP32 inference. The framework has been developed in PyTorch and has been open-sourced.

Language models (LMs) are bound to their tokenizer, which maps raw text to a sequence of vocabulary items (tokens). This restricts their flexibility: for example, LMs trained primarily on English may still perform well in other natural and programming languages, but have vastly decreased efficiency due to their English-centric tokenizer. To mitigate this, we should be able to swap the original LM tokenizer with an arbitrary one, on the fly, without degrading performance. Hence, in this work we define a new problem: Zero-Shot Tokenizer Transfer (ZeTT). The challenge at the core of ZeTT is finding embeddings for the tokens in the vocabulary of the new tokenizer. Since prior heuristics for initializing embeddings often perform at chance level in a ZeTT setting, we propose a new solution: we train a hypernetwork taking a tokenizer as input and predicting the corresponding embeddings. We empirically demonstrate that the hypernetwork generalizes to new tokenizers both with encoder (e.g., XLM-R) and decoder LLMs (e.g., Mistral-7B). Our method comes close to the original models' performance in cross-lingual and coding tasks while markedly reducing the length of the tokenized sequence. We also find that the remaining gap can be quickly closed by continued training on less than 1B tokens. Finally, we show that a ZeTT hypernetwork trained for a base (L)LM can also be applied to fine-tuned variants without extra training. Overall, our results make substantial strides toward detaching LMs from their tokenizer.

Tokenization plays a pivotal role in natural language processing (NLP), shaping how text is segmented and interpreted by language models. While subword methods such as Byte Pair Encoding (BPE) and WordPiece have been effective, they often struggle with morphologically rich and agglutinative languages because they rely on frequency rather than linguistic structure. We introduce a hybrid tokenization framework that combines rule-based morphological analysis with statistical subword segmentation. The method uses phonological normalization, root-affix dictionaries, and a novel algorithm that balances morpheme preservation with vocabulary efficiency. It assigns shared identifiers to phonologically variant affixes (e.g., -ler and -lar) and altered root forms (e.g., kitap vs. kitab{\i}), reducing redundancy while maintaining semantic integrity. Special tokens are added for whitespace and case, including an UPPERCASE marker to avoid vocabulary inflation from capitalization. BPE is integrated for out-of-vocabulary coverage without harming morphological coherence. On the TR-MMLU benchmark, the tokenizer achieves the highest Turkish Token Percentage (90.29\%) and Pure Token Percentage (85.8\%). Comparisons with tokenizers from LLaMA, Gemma, and GPT show more linguistically meaningful and coherent tokens. Although demonstrated on Turkish, the approach is language-independent and adaptable to other languages, offering a practical path toward more interpretable and effective multilingual NLP systems.

Image tokenization, the process of transforming raw image pixels into a compact low-dimensional latent representation, has proven crucial for scalable and efficient image generation. However, mainstream image tokenization methods generally have limited compression rates, making high-resolution image generation computationally expensive. To address this challenge, we propose to leverage language for efficient image tokenization, and we call our method Text-Conditioned Image Tokenization (TexTok). TexTok is a simple yet effective tokenization framework that leverages language to provide high-level semantics. By conditioning the tokenization process on descriptive text captions, TexTok allows the tokenization process to focus on encoding fine-grained visual details into latent tokens, leading to enhanced reconstruction quality and higher compression rates. Compared to the conventional tokenizer without text conditioning, TexTok achieves average reconstruction FID improvements of 29.2% and 48.1% on ImageNet-256 and -512 benchmarks respectively, across varying numbers of tokens. These tokenization improvements consistently translate to 16.3% and 34.3% average improvements in generation FID. By simply replacing the tokenizer in Diffusion Transformer (DiT) with TexTok, our system can achieve a 93.5x inference speedup while still outperforming the original DiT using only 32 tokens on ImageNet-512. TexTok with a vanilla DiT generator achieves state-of-the-art FID scores of 1.46 and 1.62 on ImageNet-256 and -512 respectively. Furthermore, we demonstrate TexTok's superiority on the text-to-image generation task, effectively utilizing the off-the-shelf text captions in tokenization.

Generative models, widely utilized in various applications, can often struggle with prompts corresponding to partial tokens. This struggle stems from tokenization, where partial tokens fall out of distribution during inference, leading to incorrect or nonsensical outputs. This paper examines a technique to alleviate the tokenization artifact on text completion in generative models, maintaining performance even in regular non-subword cases. The method, termed token alignment, involves backtracking to the last complete tokens and ensuring the model's generation aligns with the prompt. This approach showcases marked improvement across many partial token scenarios, including nuanced cases like space-prefix and partial indentation, with only a minor time increase. The technique and analysis detailed in this paper contribute to the continuous advancement of generative models in handling partial inputs, bearing relevance for applications like code completion and text autocompletion.

Commonly used image tokenizers produce a 2D grid of spatially arranged tokens. In contrast, so-called 1D image tokenizers represent images as highly compressed one-dimensional sequences of as few as 32 discrete tokens. We find that the high degree of compression achieved by a 1D tokenizer with vector quantization enables image editing and generative capabilities through heuristic manipulation of tokens, demonstrating that even very crude manipulations -- such as copying and replacing tokens between latent representations of images -- enable fine-grained image editing by transferring appearance and semantic attributes. Motivated by the expressivity of the 1D tokenizer's latent space, we construct an image generation pipeline leveraging gradient-based test-time optimization of tokens with plug-and-play loss functions such as reconstruction or CLIP similarity. Our approach is demonstrated for inpainting and text-guided image editing use cases, and can generate diverse and realistic samples without requiring training of any generative model.

Pre-tokenization, the initial step in many modern tokenization pipelines, segments text into smaller units called pretokens, typically splitting on whitespace and punctuation. While this process encourages having full, individual words as tokens, it introduces a fundamental limitation in most tokenization algorithms such as Byte Pair Encoding (BPE). Specifically, pre-tokenization causes the distribution of tokens in a corpus to heavily skew towards common, full-length words. This skewed distribution limits the benefits of expanding to larger vocabularies, since the additional tokens appear with progressively lower counts. To overcome this barrier, we propose BoundlessBPE, a modified BPE algorithm that relaxes the pretoken boundary constraint. Our approach selectively merges two complete pretokens into a larger unit we term a superword. Superwords are not necessarily semantically cohesive. For example, the pretokens " of" and " the" might be combined to form the superword " of the". This merging strategy results in a substantially more uniform distribution of tokens across a corpus than standard BPE, and compresses text more effectively, with an approximate 20% increase in bytes per token.

While humans effortlessly draw visual objects and shapes by adaptively allocating attention based on their complexity, existing multimodal large language models (MLLMs) remain constrained by rigid token representations. Bridging this gap, we propose ALTo, an adaptive length tokenizer for autoregressive mask generation. To achieve this, a novel token length predictor is designed, along with a length regularization term and a differentiable token chunking strategy. We further build ALToLLM that seamlessly integrates ALTo into MLLM. Preferences on the trade-offs between mask quality and efficiency is implemented by group relative policy optimization (GRPO). Experiments demonstrate that ALToLLM achieves state-of-the-art performance with adaptive token cost on popular segmentation benchmarks. Code and models are released at https://github.com/yayafengzi/ALToLLM.

Effective image tokenization is crucial for both multi-modal understanding and generation tasks due to the necessity of the alignment with discrete text data. To this end, existing approaches utilize vector quantization (VQ) to project pixels onto a discrete codebook and reconstruct images from the discrete representation. However, compared with the continuous latent space, the limited discrete codebook space significantly restrict the representational ability of these image tokenizers. In this paper, we propose GaussianToken: An Effective Image Tokenizer with 2D Gaussian Splatting as a solution. We first represent the encoded samples as multiple flexible featured 2D Gaussians characterized by positions, rotation angles, scaling factors, and feature coefficients. We adopt the standard quantization for the Gaussian features and then concatenate the quantization results with the other intrinsic Gaussian parameters before the corresponding splatting operation and the subsequent decoding module. In general, GaussianToken integrates the local influence of 2D Gaussian distribution into the discrete space and thus enhances the representation capability of the image tokenizer. Competitive reconstruction performances on CIFAR, Mini-ImageNet, and ImageNet-1K demonstrate the effectiveness of our framework. Our code is available at: https://github.com/ChrisDong-THU/GaussianToken.

Augmenting large language models (LLMs) with auxiliary tokens has emerged as a promising strategy for enhancing model performance. In this work, we introduce a lightweight method termed latent tokens; these are dummy tokens that may be non-interpretable in natural language but steer the autoregressive decoding process of a Transformer-based LLM via the attention mechanism. The proposed latent tokens can be seamlessly integrated with a pre-trained Transformer, trained in a parameter-efficient manner, and applied flexibly at inference time, while adding minimal complexity overhead to the existing infrastructure of standard Transformers. We propose several hypotheses about the underlying mechanisms of latent tokens and design synthetic tasks accordingly to verify them. Numerical results confirm that the proposed method noticeably outperforms the baselines, particularly in the out-of-distribution generalization scenarios, highlighting its potential in improving the adaptability of LLMs.

Pretrained language models (LLMs) are often constrained by their fixed tokenization schemes, leading to inefficiencies and performance limitations, particularly for multilingual or specialized applications. This tokenizer lock-in presents significant challenges. standard methods to overcome this often require prohibitive computational resources. Although tokenizer replacement with heuristic initialization aims to reduce this burden, existing methods often require exhaustive residual fine-tuning and still may not fully preserve semantic nuances or adequately address the underlying compression inefficiencies. Our framework introduces two innovations: first, Tokenadapt, a model-agnostic tokenizer transplantation method, and second, novel pre-tokenization learning for multi-word Supertokens to enhance compression and reduce fragmentation. Tokenadapt initializes new unique token embeddings via a hybrid heuristic that combines two methods: a local estimate based on subword decomposition using the old tokenizer, and a global estimate utilizing the top-k semantically similar tokens from the original vocabulary. This methodology aims to preserve semantics while significantly minimizing retraining requirements. Empirical investigations validate both contributions: the transplantation heuristic successfully initializes unique tokens, markedly outperforming conventional baselines and sophisticated methods including Transtokenizer and ReTok, while our Supertokens achieve notable compression gains. Our zero-shot perplexity results demonstrate that the TokenAdapt hybrid initialization consistently yields lower perplexity ratios compared to both ReTok and TransTokenizer baselines across different base models and newly trained target tokenizers. TokenAdapt typically reduced the overall perplexity ratio significantly compared to ReTok, yielding at least a 2-fold improvement in these aggregate scores.

The number of tokens it takes to encode parallel text in different languages is known to vary. These disparities are called token premiums. Having high token premiums leads to less throughput during training and increases costs at inference. In this paper, we show that even after controlling for dataset size, vocabulary size, and data content, monolingual tokenizers exhibit a wide range of token premiums across languages. To understand the cross-linguistic differences that cause these token premiums, we train a suite of approximately 7,000 comparable monolingual tokenizers for 97 languages, manipulating tokenization algorithm, vocabulary size, and dataset size. We measure token premiums and test for a relationship between factors such as data similarity (between tokenizer training and evaluation), vocabulary size, and pre-tokenization. We also investigate the role of language-specific features such as writing system and word length. We find that similarity between training and test data does not impact token premiums, but vocabulary size and pre-tokenization do. While simply increasing vocabulary size does not lead to reduced token premium effects, we can determine an ``optimal'' vocabulary size for each language to achieve significantly reduced token premium effects. We also train superword tokenizers which allow merges over whitespaces, and we find that they both reduce token premium effects and improve compression overall. Thus, intervening on the vocabulary size or the pre-tokenizer significantly reduces crosslingual token premium effects.

Many NLP models operate over sequences of subword tokens produced by hand-crafted tokenization rules and heuristic subword induction algorithms. A simple universal alternative is to represent every computerized text as a sequence of bytes via UTF-8, obviating the need for an embedding layer since there are fewer token types (256) than dimensions. Surprisingly, replacing the ubiquitous embedding layer with one-hot representations of each byte does not hurt performance; experiments on byte-to-byte machine translation from English to 10 different languages show a consistent improvement in BLEU, rivaling character-level and even standard subword-level models. A deeper investigation reveals that the combination of embeddingless models with decoder-input dropout amounts to token dropout, which benefits byte-to-byte models in particular.

Tokenization algorithms that merge the units of a base vocabulary into larger, variable-rate units have become standard in natural language processing tasks. This idea, however, has been mostly overlooked when the vocabulary consists of phonemes or Discrete Acoustic Units (DAUs), an audio-based representation that is playing an increasingly important role due to the success of discrete language-modeling techniques. In this paper, we showcase the advantages of tokenization of phonetic units and of DAUs on three prediction tasks: grapheme-to-phoneme, grapheme-to-DAUs, and unsupervised speech generation using DAU language modeling. We demonstrate that tokenization yields significant improvements in terms of performance, as well as training and inference speed, across all three tasks. We also offer theoretical insights to provide some explanation for the superior performance observed.

Speculative decoding emerges as a pivotal technique for enhancing the inference speed of Large Language Models (LLMs). Despite recent research aiming to improve prediction efficiency, multi-sample speculative decoding has been overlooked due to varying numbers of accepted tokens within a batch in the verification phase. Vanilla method adds padding tokens in order to ensure that the number of new tokens remains consistent across samples. However, this increases the computational and memory access overhead, thereby reducing the speedup ratio. We propose a novel method that can resolve the issue of inconsistent tokens accepted by different samples without necessitating an increase in memory or computing overhead. Furthermore, our proposed method can handle the situation where the prediction tokens of different samples are inconsistent without the need to add padding tokens. Sufficient experiments demonstrate the efficacy of our method. Our code is available at https://github.com/niyunsheng/EMS-SD.

By encoding time series as a string of numerical digits, we can frame time series forecasting as next-token prediction in text. Developing this approach, we find that large language models (LLMs) such as GPT-3 and LLaMA-2 can surprisingly zero-shot extrapolate time series at a level comparable to or exceeding the performance of purpose-built time series models trained on the downstream tasks. To facilitate this performance, we propose procedures for effectively tokenizing time series data and converting discrete distributions over tokens into highly flexible densities over continuous values. We argue the success of LLMs for time series stems from their ability to naturally represent multimodal distributions, in conjunction with biases for simplicity, and repetition, which align with the salient features in many time series, such as repeated seasonal trends. We also show how LLMs can naturally handle missing data without imputation through non-numerical text, accommodate textual side information, and answer questions to help explain predictions. While we find that increasing model size generally improves performance on time series, we show GPT-4 can perform worse than GPT-3 because of how it tokenizes numbers, and poor uncertainty calibration, which is likely the result of alignment interventions such as RLHF.

Tokenization imposes a fixed granularity on the input text, freezing how a language model operates on data and how far in the future it predicts. Byte Pair Encoding (BPE) and similar schemes split text once, build a static vocabulary, and leave the model stuck with that choice. We relax this rigidity by introducing an autoregressive U-Net that learns to embed its own tokens as it trains. The network reads raw bytes, pools them into words, then pairs of words, then up to 4 words, giving it a multi-scale view of the sequence. At deeper stages, the model must predict further into the future -- anticipating the next few words rather than the next byte -- so deeper stages focus on broader semantic patterns while earlier stages handle fine details. When carefully tuning and controlling pretraining compute, shallow hierarchies tie strong BPE baselines, and deeper hierarchies have a promising trend. Because tokenization now lives inside the model, the same system can handle character-level tasks and carry knowledge across low-resource languages.

A fundamental issue in machine learning is the robustness of the model with respect to changes in the input. In natural language processing, models typically contain a first embedding layer, transforming a sequence of tokens into vector representations. While the robustness with respect to changes of continuous inputs is well-understood, the situation is less clear when considering discrete changes, for instance replacing a word by another in an input sentence. Our work formally proves that popular embedding schemes, such as concatenation, TF-IDF, and Paragraph Vector (a.k.a. doc2vec), exhibit robustness in the H\"older or Lipschitz sense with respect to the Hamming distance. We provide quantitative bounds for these schemes and demonstrate how the constants involved are affected by the length of the document. These findings are exemplified through a series of numerical examples.

Pipelined NLP systems have largely been superseded by end-to-end neural modeling, yet nearly all commonly-used models still require an explicit tokenization step. While recent tokenization approaches based on data-derived subword lexicons are less brittle than manually engineered tokenizers, these techniques are not equally suited to all languages, and the use of any fixed vocabulary may limit a model's ability to adapt. In this paper, we present CANINE, a neural encoder that operates directly on character sequences, without explicit tokenization or vocabulary, and a pre-training strategy that operates either directly on characters or optionally uses subwords as a soft inductive bias. To use its finer-grained input effectively and efficiently, CANINE combines downsampling, which reduces the input sequence length, with a deep transformer stack, which encodes context. CANINE outperforms a comparable mBERT model by 2.8 F1 on TyDi QA, a challenging multilingual benchmark, despite having 28% fewer model parameters.

In this paper we address the scarcity of annotated data for NArabizi, a Romanized form of North African Arabic used mostly on social media, which poses challenges for Natural Language Processing (NLP). We introduce an enriched version of NArabizi Treebank (Seddah et al., 2020) with three main contributions: the addition of two novel annotation layers (named entity recognition and offensive language detection) and a re-annotation of the tokenization, morpho-syntactic and syntactic layers that ensure annotation consistency. Our experimental results, using different tokenization schemes, showcase the value of our contributions and highlight the impact of working with non-gold tokenization for NER and dependency parsing. To facilitate future research, we make these annotations publicly available. Our enhanced NArabizi Treebank paves the way for creating sophisticated language models and NLP tools for this under-represented language.

Tokenization is an important preprocessing step in the training and inference of large language models (LLMs). While there has been extensive research on the expressive power of the neural achitectures used in LLMs, the impact of tokenization has not been well understood. In this work, we demonstrate that tokenization, irrespective of the algorithm used, acts as an inverse homomorphism between strings and tokens. This suggests that the character space of the source language and the token space of the tokenized language are homomorphic, preserving the structural properties of the source language. Additionally, we explore the concept of proper tokenization, which refers to an unambiguous tokenization returned from the tokenizer. Our analysis reveals that the expressiveness of neural architectures in recognizing context-free languages is not affected by tokenization.

High-quality, large-scale corpora are the cornerstone of building foundation models. In this work, we introduce MathPile, a diverse and high-quality math-centric corpus comprising about 9.5 billion tokens. Throughout its creation, we adhered to the principle of ``less is more'', firmly believing in the supremacy of data quality over quantity, even in the pre-training phase. Our meticulous data collection and processing efforts included a complex suite of preprocessing, prefiltering, language identification, cleaning, filtering, and deduplication, ensuring the high quality of our corpus. Furthermore, we performed data contamination detection on downstream benchmark test sets to eliminate duplicates. We hope our MathPile can help to enhance the mathematical reasoning abilities of language models. We plan to open-source different versions of \mathpile with the scripts used for processing, to facilitate future developments in this field.

Tokenization is widely used in large language models because it significantly improves performance. However, tokenization imposes several disadvantages, such as performance biases, increased adversarial vulnerability, decreased character-level modeling performance, and increased modeling complexity. To address these disadvantages without sacrificing performance, we propose SpaceByte, a novel byte-level decoder architecture that closes the performance gap between byte-level and subword autoregressive language modeling. SpaceByte consists of a byte-level Transformer model, but with extra larger transformer blocks inserted in the middle of the layers. We find that performance is significantly improved by applying these larger blocks only after certain bytes, such as space characters, which typically denote word boundaries. Our experiments show that for a fixed training and inference compute budget, SpaceByte outperforms other byte-level architectures and roughly matches the performance of tokenized Transformer architectures.

The tokenization of speech with neural audio codec models is a vital part of modern AI pipelines for the generation or understanding of speech, alone or in a multimodal context. Traditionally such tokenization models have concentrated on low parameter-count architectures using only components with strong inductive biases. In this work we show that by scaling a transformer architecture with large parameter count to this problem, and applying a flexible Finite Scalar Quantization (FSQ) based bottleneck, it is possible to reach state-of-the-art speech quality at extremely low bit-rates of 400 or 700 bits-per-second. The trained models strongly out-perform existing baselines in both objective and subjective tests.

Large Language Models have proven highly successful at modelling a variety of tasks. However, this comes at a steep computational cost that hinders wider industrial uptake. In this pa005 per, we present MWT: a Multi-Word Tokenizer that goes beyond word boundaries by representing frequent multi-word expressions as single tokens. MWTs produce a more compact and efficient tokenization that yields two benefits: (1) Increase in performance due to a greater coverage of input data given a fixed sequence length and budget; (2) Faster and lighter inference due to the ability to reduce the sequence length with negligible drops in performance. Our results show that MWT is more robust across shorter sequence lengths, thus allowing for major speedups via early sequence truncation.

This study investigates the impact of morphological typology on tokenization and language modeling performance. We focus on languages with synthetic and analytical morphological structures and examine their productivity when tokenized using the byte-pair encoding (BPE) algorithm. We compare the performance of models trained with similar amounts of data in different languages. Our experiments reveal that languages with synthetic features exhibit greater subword regularity and productivity with BPE tokenization and achieve better results in language modeling tasks. We also observe that the typological continuum from linguistic theory is reflected in several experiments. These findings suggest a correlation between morphological typology and BPE tokenization efficiency.

According to Algorithmic Information Theory (AIT) -- Intelligent representations compress data into the shortest possible program that can reconstruct its content, exhibiting low Kolmogorov Complexity (KC). In contrast, most visual representation learning systems use fixed-length representations for all inputs, ignoring variations in complexity or familiarity. Recent adaptive tokenization methods address this by allocating variable-length representations but typically require test-time search over multiple encodings to find the most predictive one. Inspired by Kolmogorov Complexity principles, we propose a single-pass adaptive tokenizer, KARL, which predicts the appropriate number of tokens for an image in a single forward pass, halting once its approximate KC is reached. The token count serves as a proxy for the minimum description length. KARL's training procedure closely resembles the Upside-Down Reinforcement Learning paradigm, as it learns to conditionally predict token halting based on a desired reconstruction quality. KARL matches the performance of recent adaptive tokenizers while operating in a single pass. We present scaling laws for KARL, analyzing the role of encoder/decoder size, continuous vs. discrete tokenization and more. Additionally, we offer a conceptual study drawing an analogy between Adaptive Image Tokenization and Algorithmic Information Theory, examining the predicted image complexity (KC) across axes such as structure vs. noise and in- vs. out-of-distribution familiarity -- revealing alignment with human intuition.

To improve language models' proficiency in mathematical reasoning via continual pretraining, we introduce a novel strategy that leverages base language models for autonomous data selection. Departing from conventional supervised fine-tuning or trained classifiers with human-annotated data, our approach utilizes meta-prompted language models as zero-shot verifiers to autonomously evaluate and select high-quality mathematical content, and we release the curated open-source AutoMathText dataset encompassing over 200GB of data. To demonstrate the efficacy of our method, we continuously pretrained a 7B-parameter Mistral language model on the AutoMathText dataset, achieving substantial improvements in downstream performance on the MATH dataset with a token amount reduced by orders of magnitude compared to previous continuous pretraining works. Our method showcases a 2 times increase in pretraining token efficiency compared to baselines, underscoring the potential of our approach in enhancing models' mathematical reasoning capabilities. The AutoMathText dataset is available at https://huggingface.co/datasets/math-ai/AutoMathText. The code is available at https://github.com/yifanzhang-pro/AutoMathText.

Byte Pair Encoding (BPE) serves as a foundation method for text tokenization in the Natural Language Processing (NLP) field. Despite its wide adoption, the original BPE algorithm harbors an inherent flaw: it inadvertently introduces a frequency imbalance for tokens in the text corpus. Since BPE iteratively merges the most frequent token pair in the text corpus while keeping all tokens that have been merged in the vocabulary, it unavoidably holds tokens that primarily represent subwords of complete words and appear infrequently on their own in the text corpus. We term such tokens as Scaffold Tokens. Due to their infrequent appearance in the text corpus, Scaffold Tokens pose a learning imbalance issue for language models. To address that issue, we propose Scaffold-BPE, which incorporates a dynamic scaffold token removal mechanism by parameter-free, computation-light, and easy-to-implement modifications to the original BPE. This novel approach ensures the exclusion of low-frequency Scaffold Tokens from the token representations for the given texts, thereby mitigating the issue of frequency imbalance and facilitating model training. On extensive experiments across language modeling tasks and machine translation tasks, Scaffold-BPE consistently outperforms the original BPE, well demonstrating its effectiveness and superiority.

Masked Language Modeling (MLM) has been one of the most prominent approaches for pretraining bidirectional text encoders due to its simplicity and effectiveness. One notable concern about MLM is that the special [MASK] symbol causes a discrepancy between pretraining data and downstream data as it is present only in pretraining but not in fine-tuning. In this work, we offer a new perspective on the consequence of such a discrepancy: We demonstrate empirically and theoretically that MLM pretraining allocates some model dimensions exclusively for representing [MASK] tokens, resulting in a representation deficiency for real tokens and limiting the pretrained model's expressiveness when it is adapted to downstream data without [MASK] tokens. Motivated by the identified issue, we propose MAE-LM, which pretrains the Masked Autoencoder architecture with MLM where [MASK] tokens are excluded from the encoder. Empirically, we show that MAE-LM improves the utilization of model dimensions for real token representations, and MAE-LM consistently outperforms MLM-pretrained models across different pretraining settings and model sizes when fine-tuned on the GLUE and SQuAD benchmarks.

In multilingual settings, non-Latin scripts and low-resource languages are usually disadvantaged in terms of language models' utility, efficiency, and cost. Specifically, previous studies have reported multiple modeling biases that the current tokenization algorithms introduce to non-Latin script languages, the main one being over-segmentation. In this work, we propose MAGNET; multilingual adaptive gradient-based tokenization to reduce over-segmentation via adaptive gradient-based subword tokenization. MAGNET learns to predict segment boundaries between byte tokens in a sequence via sub-modules within the model, which act as internal boundary predictors (tokenizers). Previous gradient-based tokenization methods aimed for uniform compression across sequences by integrating a single boundary predictor during training and optimizing it end-to-end through stochastic reparameterization alongside the next token prediction objective. However, this approach still results in over-segmentation for non-Latin script languages in multilingual settings. In contrast, MAGNET offers a customizable architecture where byte-level sequences are routed through language-script-specific predictors, each optimized for its respective language script. This modularity enforces equitable segmentation granularity across different language scripts compared to previous methods. Through extensive experiments, we demonstrate that in addition to reducing segmentation disparities, MAGNET also enables faster language modelling and improves downstream utility.

Current language models (LMs) use a fixed, static subword tokenizer. This choice, often taken for granted, typically results in degraded efficiency and capabilities in languages other than English, and makes it challenging to apply LMs to new domains or languages. To address these issues, we propose retrofitting LMs with dynamic tokenization: a way to dynamically decide on token boundaries based on the input text. For encoder-style models, we introduce a subword-merging algorithm inspired by byte-pair encoding (BPE), but at a batch level. We merge frequent subword sequences in a batch, then apply a pretrained embedding-prediction hypernetwork to compute the token embeddings on-the-fly. When applied with word-level boundaries, this on average reduces token sequence lengths by >20% across 14 languages on XNLI with XLM-R while degrading its task performance by less than 2%. For decoder-style models, we apply dynamic tokenization in two ways: 1) for prefilling, maintaining performance of Mistral-7B almost completely with up to 40% sequence reduction - relative to the word-level; and 2) via an approximate nearest neighbor index, achieving fast generation with a one million token vocabulary, demonstrating scalability to even larger, dynamic vocabularies. Overall, our findings show that dynamic tokenization substantially improves inference speed and promotes fairness across languages, making a leap towards overcoming the limitations of static tokenization and enabling more equitable and adaptable LMs.

In generative modeling, tokenization simplifies complex data into compact, structured representations, creating a more efficient, learnable space. For high-dimensional visual data, it reduces redundancy and emphasizes key features for high-quality generation. Current visual tokenization methods rely on a traditional autoencoder framework, where the encoder compresses data into latent representations, and the decoder reconstructs the original input. In this work, we offer a new perspective by proposing denoising as decoding, shifting from single-step reconstruction to iterative refinement. Specifically, we replace the decoder with a diffusion process that iteratively refines noise to recover the original image, guided by the latents provided by the encoder. We evaluate our approach by assessing both reconstruction (rFID) and generation quality (FID), comparing it to state-of-the-art autoencoding approach. We hope this work offers new insights into integrating iterative generation and autoencoding for improved compression and generation.

Large Language Models (LLMs) have proven their exceptional capabilities in performing language-related tasks. However, their deployment poses significant challenges due to their considerable memory and storage requirements. In response to this issue, weight-only quantization, particularly 3 and 4-bit weight-only quantization, has emerged as one of the most viable solutions. As the number of bits decreases, the quantization grid broadens, thus emphasizing the importance of up and down rounding. While previous studies have demonstrated that fine-tuning up and down rounding with the addition of perturbations can enhance accuracy in some scenarios, our study is driven by the precise and limited boundary of these perturbations, where only the threshold for altering the rounding value is of significance. Consequently, we propose a concise and highly effective approach for optimizing the weight rounding task. Our method, named SignRound, involves lightweight block-wise tuning using signed gradient descent, enabling us to achieve outstanding results within 400 steps. SignRound outperforms the established baseline of rounding-to-nearest (RTN) and competes impressively against recent methods, without introducing additional inference overhead. The source code will be publicly available at https://github.com/intel/neural-compressor soon.

This paper proposes a fundamentally new paradigm for image generation through set-based tokenization and distribution modeling. Unlike conventional methods that serialize images into fixed-position latent codes with a uniform compression ratio, we introduce an unordered token set representation to dynamically allocate coding capacity based on regional semantic complexity. This TokenSet enhances global context aggregation and improves robustness against local perturbations. To address the critical challenge of modeling discrete sets, we devise a dual transformation mechanism that bijectively converts sets into fixed-length integer sequences with summation constraints. Further, we propose Fixed-Sum Discrete Diffusion--the first framework to simultaneously handle discrete values, fixed sequence length, and summation invariance--enabling effective set distribution modeling. Experiments demonstrate our method's superiority in semantic-aware representation and generation quality. Our innovations, spanning novel representation and modeling strategies, advance visual generation beyond traditional sequential token paradigms. Our code and models are publicly available at https://github.com/Gengzigang/TokenSet.

The large number of parameters of some prominent language models, such as BERT, makes their fine-tuning on downstream tasks computationally intensive and energy hungry. Previously researchers were focused on lower bit-width integer data types for the forward propagation of language models to save memory and computation. As for the backward propagation, however, only 16-bit floating-point data type has been used for the fine-tuning of BERT. In this work, we use integer arithmetic for both forward and back propagation in the fine-tuning of BERT. We study the effects of varying the integer bit-width on the model's metric performance. Our integer fine-tuning uses integer arithmetic to perform forward propagation and gradient computation of linear, layer-norm, and embedding layers of BERT. We fine-tune BERT using our integer training method on SQuAD v1.1 and SQuAD v2., and GLUE benchmark. We demonstrate that metric performance of fine-tuning 16-bit integer BERT matches both 16-bit and 32-bit floating-point baselines. Furthermore, using the faster and more memory efficient 8-bit integer data type, integer fine-tuning of BERT loses an average of 3.1 points compared to the FP32 baseline.

Recent image generation schemes typically capture image distribution in a pre-constructed latent space relying on a frozen image tokenizer. Though the performance of tokenizer plays an essential role to the successful generation, its current evaluation metrics (e.g. rFID) fail to precisely assess the tokenizer and correlate its performance to the generation quality (e.g. gFID). In this paper, we comprehensively analyze the reason for the discrepancy of reconstruction and generation qualities in a discrete latent space, and, from which, we propose a novel plug-and-play tokenizer training scheme to facilitate latent space construction. Specifically, a latent perturbation approach is proposed to simulate sampling noises, i.e., the unexpected tokens sampled, from the generative process. With the latent perturbation, we further propose (1) a novel tokenizer evaluation metric, i.e., pFID, which successfully correlates the tokenizer performance to generation quality and (2) a plug-and-play tokenizer training scheme, which significantly enhances the robustness of tokenizer thus boosting the generation quality and convergence speed. Extensive benchmarking are conducted with 11 advanced discrete image tokenizers with 2 autoregressive generation models to validate our approach. The tokenizer trained with our proposed latent perturbation achieve a notable 1.60 gFID with classifier-free guidance (CFG) and 3.45 gFID without CFG with a sim400M generator. Code: https://github.com/lxa9867/ImageFolder.

Binarization, which converts weight parameters to binary values, has emerged as an effective strategy to reduce the size of large language models (LLMs). However, typical binarization techniques significantly diminish linguistic effectiveness of LLMs. To address this issue, we introduce a novel binarization technique called Mixture of Scales (BinaryMoS). Unlike conventional methods, BinaryMoS employs multiple scaling experts for binary weights, dynamically merging these experts for each token to adaptively generate scaling factors. This token-adaptive approach boosts the representational power of binarized LLMs by enabling contextual adjustments to the values of binary weights. Moreover, because this adaptive process only involves the scaling factors rather than the entire weight matrix, BinaryMoS maintains compression efficiency similar to traditional static binarization methods. Our experimental results reveal that BinaryMoS surpasses conventional binarization techniques in various natural language processing tasks and even outperforms 2-bit quantization methods, all while maintaining similar model size to static binarization techniques.

Recently, multimodal large language models (MM-LLMs) have achieved significant success in various tasks, but their high computational costs limit widespread application. The main computational burden arises from processing concatenated text and visual tokens in the LLM layer, where input token length directly affects efficiency. Our analysis of visual tokens reveals that their similarity to the CLS token follows a long-tail distribution, with only a few showing high similarity. To address this, we propose a dynamic pruning algorithm that identifies the inflection point in the visual CLS token similarity curve, enabling effective trimming of visual markers to accelerate model performance. Additionally, we perform a second round of pruning in the LLM layer, filtering out low-correlation tokens through the interaction between visual and textual features. Experimental results demonstrate that our method achieves performance comparable to the original while utilizing only 22% of the original token quantity. Our source code will be made publicly available upon acceptance.

Visual tokenization remains a core challenge in unifying visual understanding and generation within the autoregressive paradigm. Existing methods typically employ tokenizers in discrete latent spaces to align with the tokens from large language models, where the quantization errors can limit semantic expressiveness and degrade the capability of vision-language understanding. To address this, we introduce MingTok, a new family of visual tokenizers with a continuous latent space, for unified autoregressive generation and understanding. While understanding tasks favor discriminative high-dimensional features, generation tasks prefer compact low-level codes. Thus, to reconcile these competing demands, MingTok adopts a three-stage sequential architecture involving low-level encoding, semantic expansion, and visual reconstruction. Built on top of it, Ming-UniVision eliminates the need for task-specific visual representations, and unifies diverse vision-language tasks under a single autoregrsssive prediction paradigm. By formulating both understanding and generation as next-token prediction in a shared continuous space, it seamlessly supports multi-round, in-context tasks such as iterative understanding, generation and editing. Empirically, we find that using a unified continuous visual representation reconciles the competing requirements on the tokenizers by the understanding and generation tasks, thereby leading to state-of-the-art level performance across both domains. We hope our findings will facilitate unified visual tokenization in the continuous domain. Inference code and model weights are released to benefit community.

This study introduces a novel knowledge enhanced tokenisation mechanism, K-Tokeniser, for clinical text processing. Technically, at initialisation stage, K-Tokeniser populates global representations of tokens based on semantic types of domain concepts (such as drugs or diseases) from either a domain ontology like Unified Medical Language System or the training data of the task related corpus. At training or inference stage, sentence level localised context will be utilised for choosing the optimal global token representation to realise the semantic-based tokenisation. To avoid pretraining using the new tokeniser, an embedding initialisation approach is proposed to generate representations for new tokens. Using three transformer-based language models, a comprehensive set of experiments are conducted on four real-world datasets for evaluating K-Tokeniser in a wide range of clinical text analytics tasks including clinical concept and relation extraction, automated clinical coding, clinical phenotype identification, and clinical research article classification. Overall, our models demonstrate consistent improvements over their counterparts in all tasks. In particular, substantial improvements are observed in the automated clinical coding task with 13\% increase on Micro F_1 score. Furthermore, K-Tokeniser also shows significant capacities in facilitating quicker converge of language models. Specifically, using K-Tokeniser, the language models would only require 50\% of the training data to achieve the best performance of the baseline tokeniser using all training data in the concept extraction task and less than 20\% of the data for the automated coding task. It is worth mentioning that all these improvements require no pre-training process, making the approach generalisable.

Diffusion models have emerged as a promising approach for text generation, with recent works falling into two main categories: discrete and continuous diffusion models. Discrete diffusion models apply token corruption independently using categorical distributions, allowing for different diffusion progress across tokens but lacking fine-grained control. Continuous diffusion models map tokens to continuous spaces and apply fine-grained noise, but the diffusion progress is uniform across tokens, limiting their ability to capture semantic nuances. To address these limitations, we propose \underline{N}on-simultan\underline{e}ous C\underline{o}ntinuous \underline{Diff}usion Models (NeoDiff), a novel diffusion model that integrates the strengths of both discrete and continuous approaches. NeoDiff introduces a Poisson diffusion process for the forward process, enabling a flexible and fine-grained noising paradigm, and employs a time predictor for the reverse process to adaptively modulate the denoising progress based on token semantics. Furthermore, NeoDiff utilizes an optimized schedule for inference to ensure more precise noise control and improved performance. Our approach unifies the theories of discrete and continuous diffusion models, offering a more principled and effective framework for text generation. Experimental results on several text generation tasks demonstrate NeoDiff's superior performance compared to baselines of non-autoregressive continuous and discrete diffusion models, iterative-based methods and autoregressive diffusion-based methods. These results highlight NeoDiff's potential as a powerful tool for generating high-quality text and advancing the field of diffusion-based text generation.

Recent works have widely adopted large language model pretraining for source code, suggested source code-specific pretraining objectives and investigated the applicability of various Transformer-based language model architectures for source code. This work investigates another important aspect of such models, namely the effect of different subtokenization options, and aims at identifying most effective and length-efficient subtokenizations, taking into account code specifics. We propose subtokenziation that reduces average length by 17% without downstream performance drop, and show that a carefully chosen subtokenization may improve quality by 0.5-2%, possibly with some length increase.

Subword tokenization is a common method for vocabulary building in Neural Machine Translation (NMT) models. However, increasingly complex tasks have revealed its disadvantages. First, a vocabulary cannot be modified once it is learned, making it hard to adapt to new words. Second, in multilingual translation, the imbalance in data volumes across different languages spreads to the vocabulary, exacerbating translations involving low-resource languages. While byte-based tokenization addresses these issues, byte-based models struggle with the low information density inherent in UTF-8 byte sequences. Previous works enhance token semantics through local contextualization but fail to select an appropriate contextualizing scope based on the input. Consequently, we propose the Multi-Scale Contextualization (MSC) method, which learns contextualized information of varying scales across different hidden state dimensions. It then leverages the attention module to dynamically integrate the multi-scale contextualized information. Experiments show that MSC significantly outperforms subword-based and other byte-based methods in both multilingual and out-of-domain scenarios. Code can be found in https://github.com/ictnlp/Multiscale-Contextualization.

As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.

Quantization techniques can reduce the size of Deep Neural Networks and improve inference latency and throughput by taking advantage of high throughput integer instructions. In this paper we review the mathematical aspects of quantization parameters and evaluate their choices on a wide range of neural network models for different application domains, including vision, speech, and language. We focus on quantization techniques that are amenable to acceleration by processors with high-throughput integer math pipelines. We also present a workflow for 8-bit quantization that is able to maintain accuracy within 1% of the floating-point baseline on all networks studied, including models that are more difficult to quantize, such as MobileNets and BERT-large.

Tokenization is fundamental to pretrained language models (PLMs). Existing tokenization methods for Chinese PLMs typically treat each character as an indivisible token. However, they ignore the unique feature of the Chinese writing system where additional linguistic information exists below the character level, i.e., at the sub-character level. To utilize such information, we propose sub-character (SubChar for short) tokenization. Specifically, we first encode the input text by converting each Chinese character into a short sequence based on its glyph or pronunciation, and then construct the vocabulary based on the encoded text with sub-word segmentation. Experimental results show that SubChar tokenizers have two main advantages over existing tokenizers: 1) They can tokenize inputs into much shorter sequences, thus improving the computational efficiency. 2) Pronunciation-based SubChar tokenizers can encode Chinese homophones into the same transliteration sequences and produce the same tokenization output, hence being robust to homophone typos. At the same time, models trained with SubChar tokenizers perform competitively on downstream tasks. We release our code and models at https://github.com/thunlp/SubCharTokenization to facilitate future work.

Autoregressive large language models (LLMs) have made remarkable progress in various natural language generation tasks. However, they incur high computation cost and latency resulting from the autoregressive token-by-token generation. To address this issue, several approaches have been proposed to reduce computational cost using early-exit strategies. These strategies enable faster text generation using reduced computation without applying the full computation graph to each token. While existing token-level early exit methods show promising results for online inference, they cannot be readily applied for batch inferencing and Key-Value caching. This is because they have to wait until the last token in a batch exits before they can stop computing. This severely limits the practical application of such techniques. In this paper, we propose a simple and effective token-level early exit method, SkipDecode, designed to work seamlessly with batch inferencing and KV caching. It overcomes prior constraints by setting up a singular exit point for every token in a batch at each sequence position. It also guarantees a monotonic decrease in exit points, thereby eliminating the need to recompute KV Caches for preceding tokens. Rather than terminating computation prematurely as in prior works, our approach bypasses lower to middle layers, devoting most of the computational resources to upper layers, allowing later tokens to benefit from the compute expenditure by earlier tokens. Our experimental results show that SkipDecode can obtain 2x to 5x inference speedups with negligible regression across a variety of tasks. This is achieved using OPT models of 1.3 billion and 6.7 billion parameters, all the while being directly compatible with batching and KV caching optimization techniques.

Large language models have revolutionized natural language processing by leveraging self-supervised pretraining on vast textual data. Inspired by this success, researchers have investigated complicated speech tokenization methods to discretize continuous speech signals so that language modeling techniques can be applied to speech data. However, existing approaches either model semantic tokens, potentially losing acoustic information, or model acoustic tokens, risking the loss of semantic information. Having multiple token types also complicates the architecture and requires additional pretraining. Here we show that discretizing mel-filterbank channels into discrete intensity bins produces a simple representation (dMel), that performs better than other existing speech tokenization methods. Using a transformer decoder-only architecture for speech-text modeling, we comprehensively evaluate different speech tokenization methods on speech recognition (ASR), speech synthesis (TTS). Our results demonstrate the effectiveness of dMel in achieving high performance on both tasks within a unified framework, paving the way for efficient and effective joint modeling of speech and text.

Masked diffusion models (MDMs) have emerged as a popular research topic for generative modeling of discrete data, thanks to their superior performance over other discrete diffusion models, and are rivaling the auto-regressive models (ARMs) for language modeling tasks. The recent effort in simplifying the masked diffusion framework further leads to alignment with continuous-space diffusion models and more principled training and sampling recipes. In this paper, however, we reveal that both training and sampling of MDMs are theoretically free from the time variable, arguably the key signature of diffusion models, and are instead equivalent to masked models. The connection on the sampling aspect is drawn by our proposed first-hitting sampler (FHS). Specifically, we show that the FHS is theoretically equivalent to MDMs' original generation process while significantly alleviating the time-consuming categorical sampling and achieving a 20times speedup. In addition, our investigation raises doubts about whether MDMs can truly beat ARMs. We identify, for the first time, an underlying numerical issue, even with the commonly used 32-bit floating-point precision, which results in inaccurate categorical sampling. We show that the numerical issue lowers the effective temperature both theoretically and empirically, and the resulting decrease in token diversity makes previous evaluations, which assess the generation quality solely through the incomplete generative perplexity metric, somewhat unfair.

Subword tokenization has been widely successful in text-based natural language processing (NLP) tasks with Transformer-based models. As Transformer models become increasingly popular in symbolic music-related studies, it is imperative to investigate the efficacy of subword tokenization in the symbolic music domain. In this paper, we explore subword tokenization techniques, such as byte-pair encoding (BPE), in symbolic music generation and its impact on the overall structure of generated songs. Our experiments are based on three types of MIDI datasets: single track-melody only, multi-track with a single instrument, and multi-track and multi-instrument. We apply subword tokenization on post-musical tokenization schemes and find that it enables the generation of longer songs at the same time and improves the overall structure of the generated music in terms of objective metrics like structure indicator (SI), Pitch Class Entropy, etc. We also compare two subword tokenization methods, BPE and Unigram, and observe that both methods lead to consistent improvements. Our study suggests that subword tokenization is a promising technique for symbolic music generation and may have broader implications for music composition, particularly in cases involving complex data such as multi-track songs.

Image tokenizers are crucial for visual generative models, e.g., diffusion models (DMs) and autoregressive (AR) models, as they construct the latent representation for modeling. Increasing token length is a common approach to improve the image reconstruction quality. However, tokenizers with longer token lengths are not guaranteed to achieve better generation quality. There exists a trade-off between reconstruction and generation quality regarding token length. In this paper, we investigate the impact of token length on both image reconstruction and generation and provide a flexible solution to the tradeoff. We propose ImageFolder, a semantic tokenizer that provides spatially aligned image tokens that can be folded during autoregressive modeling to improve both generation efficiency and quality. To enhance the representative capability without increasing token length, we leverage dual-branch product quantization to capture different contexts of images. Specifically, semantic regularization is introduced in one branch to encourage compacted semantic information while another branch is designed to capture the remaining pixel-level details. Extensive experiments demonstrate the superior quality of image generation and shorter token length with ImageFolder tokenizer.

Transformer-based language models, more specifically BERT-based architectures have achieved state-of-the-art performance in many downstream tasks. However, for a relatively low-resource language such as Thai, the choices of models are limited to training a BERT-based model based on a much smaller dataset or finetuning multi-lingual models, both of which yield suboptimal downstream performance. Moreover, large-scale multi-lingual pretraining does not take into account language-specific features for Thai. To overcome these limitations, we pretrain a language model based on RoBERTa-base architecture on a large, deduplicated, cleaned training set (78GB in total size), curated from diverse domains of social media posts, news articles and other publicly available datasets. We apply text processing rules that are specific to Thai most importantly preserving spaces, which are important chunk and sentence boundaries in Thai before subword tokenization. We also experiment with word-level, syllable-level and SentencePiece tokenization with a smaller dataset to explore the effects on tokenization on downstream performance. Our model wangchanberta-base-att-spm-uncased trained on the 78.5GB dataset outperforms strong baselines (NBSVM, CRF and ULMFit) and multi-lingual models (XLMR and mBERT) on both sequence classification and token classification tasks in human-annotated, mono-lingual contexts.

We present any4, a learned 4-bit weight quantization solution for large language models (LLMs) providing arbitrary numeric representations without requiring pre-processing of weights or activations. any4 yields higher accuracy compared to other related 4-bit numeric representation types: int4, fp4 and nf4, as evaluated on a range of model sizes, generations and families (Llama 2, Llama 3, Mistral and Mixtral). While any4 does not require preprocessing of weights or activations, it is also competitive with orthogonal techniques that require such preprocessing (e.g., AWQ and GPTQ). We also experiment with any3 and any2 and show competitiveness at lower bits. Additionally, we show that we can calibrate using a single curated diverse sample rather than hundreds of samples from a dataset as done in most quantization approaches. We also open source tinygemm, a latency optimized GPU matrix multiplication library for LLMs, that implements any4 using a GPU-efficient lookup table strategy along with other common quantization methods. We open source our code at https://github.com/facebookresearch/any4 .

Language models typically tokenize raw text into sequences of subword identifiers from a predefined vocabulary, a process inherently sensitive to typographical errors, length variations, and largely oblivious to the internal structure of tokens-issues we term the curse of tokenization. In this study, we delve into these drawbacks and demonstrate that large language models (LLMs) remain susceptible to these problems. This study systematically investigates these challenges and their impact on LLMs through three critical research questions: (1) complex problem solving, (2) token structure probing, and (3) resilience to typographical variation. Our findings reveal that scaling model parameters can mitigate the issue of tokenization; however, LLMs still suffer from biases induced by typos and other text format variations. Our experiments show that subword regularization such as BPE-dropout can mitigate this issue. We will release our code and data to facilitate further research.

Autoregressive visual generation models typically rely on tokenizers to compress images into tokens that can be predicted sequentially. A fundamental dilemma exists in token representation: discrete tokens enable straightforward modeling with standard cross-entropy loss, but suffer from information loss and tokenizer training instability; continuous tokens better preserve visual details, but require complex distribution modeling, complicating the generation pipeline. In this paper, we propose TokenBridge, which bridges this gap by maintaining the strong representation capacity of continuous tokens while preserving the modeling simplicity of discrete tokens. To achieve this, we decouple discretization from the tokenizer training process through post-training quantization that directly obtains discrete tokens from continuous representations. Specifically, we introduce a dimension-wise quantization strategy that independently discretizes each feature dimension, paired with a lightweight autoregressive prediction mechanism that efficiently model the resulting large token space. Extensive experiments show that our approach achieves reconstruction and generation quality on par with continuous methods while using standard categorical prediction. This work demonstrates that bridging discrete and continuous paradigms can effectively harness the strengths of both approaches, providing a promising direction for high-quality visual generation with simple autoregressive modeling. Project page: https://yuqingwang1029.github.io/TokenBridge.

Image tokenizers form the foundation of modern text-to-image generative models but are notoriously difficult to train. Furthermore, most existing text-to-image models rely on large-scale, high-quality private datasets, making them challenging to replicate. In this work, we introduce Text-Aware Transformer-based 1-Dimensional Tokenizer (TA-TiTok), an efficient and powerful image tokenizer that can utilize either discrete or continuous 1-dimensional tokens. TA-TiTok uniquely integrates textual information during the tokenizer decoding stage (i.e., de-tokenization), accelerating convergence and enhancing performance. TA-TiTok also benefits from a simplified, yet effective, one-stage training process, eliminating the need for the complex two-stage distillation used in previous 1-dimensional tokenizers. This design allows for seamless scalability to large datasets. Building on this, we introduce a family of text-to-image Masked Generative Models (MaskGen), trained exclusively on open data while achieving comparable performance to models trained on private data. We aim to release both the efficient, strong TA-TiTok tokenizers and the open-data, open-weight MaskGen models to promote broader access and democratize the field of text-to-image masked generative models.

The assumption across nearly all language model (LM) tokenization schemes is that tokens should be subwords, i.e., contained within word boundaries. While providing a seemingly reasonable inductive bias, is this common practice limiting the potential of modern LMs? Whitespace is not a reliable delimiter of meaning, as evidenced by multi-word expressions (e.g., "by the way"), crosslingual variation in the number of words needed to express a concept (e.g., "spacesuit helmet" in German is "raumanzughelm"), and languages that do not use whitespace at all (e.g., Chinese). To explore the potential of tokenization beyond subwords, we introduce a "superword" tokenizer, SuperBPE, which incorporates a simple pretokenization curriculum into the byte-pair encoding (BPE) algorithm to first learn subwords, then superwords that bridge whitespace. This brings dramatic improvements in encoding efficiency: when fixing the vocabulary size to 200k, SuperBPE encodes a fixed piece of text with up to 33% fewer tokens than BPE on average. In experiments, we pretrain 8B transformer LMs from scratch while fixing the model size, vocabulary size, and train compute, varying *only* the algorithm for learning the vocabulary. Our model trained with SuperBPE achieves an average +4.0% absolute improvement over the BPE baseline across 30 downstream tasks (including +8.2% on MMLU), while simultaneously requiring 27% less compute at inference time. In analysis, we find that SuperBPE results in segmentations of text that are more uniform in per-token difficulty. Qualitatively, this may be because SuperBPE tokens often capture common multi-word expressions that function semantically as a single unit. SuperBPE is a straightforward, local modification to tokenization that improves both encoding efficiency and downstream performance, yielding better language models overall.

Recent advances in image tokenizers, such as VQ-VAE, have enabled text-to-image generation using auto-regressive methods, similar to language modeling. However, these methods have yet to leverage pre-trained language models, despite their adaptability to various downstream tasks. In this work, we explore this gap by adapting a pre-trained language model for auto-regressive text-to-image generation, and find that pre-trained language models offer limited help. We provide a two-fold explanation by analyzing tokens from each modality. First, we demonstrate that image tokens possess significantly different semantics compared to text tokens, rendering pre-trained language models no more effective in modeling them than randomly initialized ones. Second, the text tokens in the image-text datasets are too simple compared to normal language model pre-training data, which causes the catastrophic degradation of language models' capability.

Diffusion models have revolutionized generative tasks, especially in the domain of text-to-image synthesis; however, their iterative denoising process demands substantial computational resources. In this paper, we present a novel acceleration strategy that integrates token-level pruning with caching techniques to tackle this computational challenge. By employing noise relative magnitude, we identify significant token changes across denoising iterations. Additionally, we enhance token selection by incorporating spatial clustering and ensuring distributional balance. Our experiments demonstrate reveal a 50%-60% reduction in computational costs while preserving the performance of the model, thereby markedly increasing the efficiency of diffusion models. The code is available at https://github.com/ada-cheng/CAT-Pruning

Large Language Models (LLMs) are proficient in natural language processing tasks, but their deployment is often restricted by extensive parameter sizes and computational demands. This paper focuses on post-training quantization (PTQ) in LLMs, specifically 4-bit weight and 8-bit activation (W4A8) quantization, to enhance computational efficiency -- a topic less explored compared to weight-only quantization. We present two innovative techniques: activation-quantization-aware scaling (AQAS) and sequence-length-aware calibration (SLAC) to enhance PTQ by considering the combined effects on weights and activations and aligning calibration sequence lengths to target tasks. Moreover, we introduce dINT, a hybrid data format combining integer and denormal representations, to address the underflow issue in W4A8 quantization, where small values are rounded to zero. Through rigorous evaluations of LLMs, including OPT and LLaMA, we demonstrate that our techniques significantly boost task accuracies to levels comparable with full-precision models. By developing arithmetic units compatible with dINT, we further confirm that our methods yield a 2times hardware efficiency improvement compared to 8-bit integer MAC unit.

Recent advancements in large language models have facilitated the execution of complex language tasks, not only in English but also in non-English languages. However, the tokenizers of most language models, such as Llama, trained on English-centric corpora, tend to excessively fragment tokens in non-English languages. This issue is especially pronounced in non-roman alphabetic languages, which are often divided at a character or even Unicode level, leading to slower text generation. To address this, our study introduces a novel framework designed to expedite text generation in these languages. This framework predicts larger linguistic units than those of conventional multilingual tokenizers and is specifically tailored to the target language, thereby reducing the number of decoding steps required. Our empirical results demonstrate that the proposed framework increases the generation speed by a factor of 1.9 compared to standard decoding while maintaining the performance of a pre-trained multilingual model on monolingual tasks.

A multilingual tokenizer is a fundamental component of multilingual neural machine translation. It is trained from a multilingual corpus. Since a skewed data distribution is considered to be harmful, a sampling strategy is usually used to balance languages in the corpus. However, few works have systematically answered how language imbalance in tokenizer training affects downstream performance. In this work, we analyze how translation performance changes as the data ratios among languages vary in the tokenizer training corpus. We find that while relatively better performance is often observed when languages are more equally sampled, the downstream performance is more robust to language imbalance than we usually expected. Two features, UNK rate and closeness to the character level, can warn of poor downstream performance before performing the task. We also distinguish language sampling for tokenizer training from sampling for model training and show that the model is more sensitive to the latter.

While tokenization is a key step in language modeling, with effects on model training and performance, it remains unclear how to effectively evaluate tokenizer quality. One proposed dimension of tokenizer quality is the extent to which tokenizers preserve linguistically meaningful subwords, aligning token boundaries with morphological boundaries within a word. We expand MorphScore (Arnett & Bergen, 2025), which previously covered 22 languages, to support a total of 70 languages. The updated MorphScore offers more flexibility in evaluation and addresses some of the limitations of the original version. We then correlate our alignment scores with downstream task performance for five pre-trained languages models on seven tasks, with at least one task in each of the languages in our sample. We find that morphological alignment does not explain very much variance in model performance, suggesting that morphological alignment alone does not measure dimensions of tokenization quality relevant to model performance.

Building on the foundations of language modeling in natural language processing, Next Token Prediction (NTP) has evolved into a versatile training objective for machine learning tasks across various modalities, achieving considerable success. As Large Language Models (LLMs) have advanced to unify understanding and generation tasks within the textual modality, recent research has shown that tasks from different modalities can also be effectively encapsulated within the NTP framework, transforming the multimodal information into tokens and predict the next one given the context. This survey introduces a comprehensive taxonomy that unifies both understanding and generation within multimodal learning through the lens of NTP. The proposed taxonomy covers five key aspects: Multimodal tokenization, MMNTP model architectures, unified task representation, datasets \& evaluation, and open challenges. This new taxonomy aims to aid researchers in their exploration of multimodal intelligence. An associated GitHub repository collecting the latest papers and repos is available at https://github.com/LMM101/Awesome-Multimodal-Next-Token-Prediction

We study the text generation task under the approach of pre-trained language models (PLMs). Typically, an auto-regressive (AR) method is adopted for generating texts in a token-by-token manner. Despite many advantages of AR generation, it usually suffers from inefficient inference. Therefore, non-autoregressive (NAR) models are proposed to generate all target tokens simultaneously. However, NAR models usually generate texts of lower quality due to the absence of token dependency in the output text. In this paper, we propose ELMER: an efficient and effective PLM for NAR text generation to explicitly model the token dependency during NAR generation. By leveraging the early exit technique, ELMER enables the token generations at different layers, according to their prediction confidence (a more confident token will exit at a lower layer). Besides, we propose a novel pre-training objective, Layer Permutation Language Modeling, to pre-train ELMER by permuting the exit layer for each token in sequences. Experiments on three text generation tasks show that ELMER significantly outperforms NAR models and further narrows the performance gap with AR PLMs (\eg ELMER (29.92) vs BART (30.61) ROUGE-L in XSUM) while achieving over 10 times inference speedup.

Tasks that require character-level reasoning, such as counting or locating characters within words, remain challenging for contemporary language models. A common conjecture is that language models' reliance on subword units, rather than characters, contributes to their struggles with character-level tasks, yet recent studies offer conflicting conclusions about the role of tokenization, leaving its impact unclear. To address this gap, we introduce CharBench, a comprehensive benchmark of character-level tasks that is two orders of magnitude larger than existing alternatives. We evaluate a diverse range of leading open-weight and proprietary models on CharBench and find that it presents a significant challenge to modern LLMs, with an average accuracy of 43.6% and 32.3% on some tasks. We present an in-depth analysis of how intrinsic properties of words and their segmentations into tokens correspond to model performance. For counting tasks, we find that tokenization properties are weakly correlated with correctness, while the length of the queried word and the actual character count play a more significant part. In contrast, for tasks requiring intra-word positional understanding, performance is negatively correlated with the length of the token containing the queried character, suggesting that longer tokens obscure character position information for LLMs. We encourage future work to build on the benchmark and evaluation methodology introduced here as tools for improving model performance on such tasks.

Understanding the locus of semantic representation in large language models (LLMs) is crucial for interpretability and architectural innovation. The dominant paradigm posits that trainable input embeddings serve as foundational "meaning vectors." This paper challenges that view. We construct Transformer models where the embedding layer is entirely frozen, with vectors derived not from data, but from the visual structure of Unicode glyphs. These non-semantic, precomputed visual embeddings are fixed throughout training. Our method is compatible with any tokenizer, including a novel Unicode-centric tokenizer we introduce to ensure universal text coverage. Despite the absence of trainable, semantically initialized embeddings, our models converge, generate coherent text, and, critically, outperform architecturally identical models with trainable embeddings on the MMLU reasoning benchmark. We attribute this to "representational interference" in conventional models, where the embedding layer is burdened with learning both structural and semantic features. Our results indicate that high-level semantics are not inherent to input embeddings but are an emergent property of the Transformer's compositional architecture and data scale. This reframes the role of embeddings from meaning containers to structural primitives. We release all code and models to foster further research.

Most widely-used pre-trained language models operate on sequences of tokens corresponding to word or subword units. By comparison, token-free models that operate directly on raw text (bytes or characters) have many benefits: they can process text in any language out of the box, they are more robust to noise, and they minimize technical debt by removing complex and error-prone text preprocessing pipelines. Since byte or character sequences are longer than token sequences, past work on token-free models has often introduced new model architectures designed to amortize the cost of operating directly on raw text. In this paper, we show that a standard Transformer architecture can be used with minimal modifications to process byte sequences. We characterize the trade-offs in terms of parameter count, training FLOPs, and inference speed, and show that byte-level models are competitive with their token-level counterparts. We also demonstrate that byte-level models are significantly more robust to noise and perform better on tasks that are sensitive to spelling and pronunciation. As part of our contribution, we release a new set of pre-trained byte-level Transformer models based on the T5 architecture, as well as all code and data used in our experiments.