Daily Papers

Diffusion Language Models (DLMs) offer a promising alternative for language modeling by enabling parallel decoding through iterative refinement. However, most DLMs rely on hard binary masking and discrete token assignments, which hinder the revision of early decisions and underutilize intermediate probabilistic representations. In this paper, we propose EvoToken-DLM, a novel diffusion-based language modeling approach that replaces hard binary masks with evolving soft token distributions. EvoToken-DLM enables a progressive transition from masked states to discrete outputs, supporting revisable decoding. To effectively support this evolution, we introduce continuous trajectory supervision, which aligns training objectives with iterative probabilistic updates. Extensive experiments across multiple benchmarks show that EvoToken-DLM consistently achieves superior performance, outperforming strong diffusion-based and masked DLM baselines. Project webpage: https://aim-uofa.github.io/EvoTokenDLM.

Group-advantage-based reinforcement learning methods, such as GRPO and DAPO, have demonstrated strong performance across diverse domains, including mathematical reasoning and text-to-image generation. However, their reliance on sample-level rewards introduces a key limitation as uniform credit assignment across all tokens fails to capture fine-grained, token-level contributions. To address this issue, we propose Guidance Contrastive Policy Optimization (GCPO), a novel algorithm that enables per-token credit assignment by contrasting model predictions under positive and negative prompts. Rather than uniformly broadcasting sample-level advantages, GCPO assigns token-level advantages proportional to the difference between these contrastive predictions, allowing more precise and informative learning signals. Empirically, we find that GCPO emphasizes semantically relevant regions such as visual areas aligned with textual prompts in text-to-image generation, and critical keywords within reasoning traces for chain-of-thought tasks. Through extensive experiments, GCPO consistently outperforms GRPO and DAPO baselines on both text-to-image generation and chain-of-thought reasoning benchmarks, demonstrating its effectiveness as a general and scalable optimization strategy for discrete policy learning.

The scaling of Large Language Models (LLMs) has driven significant performance gains but created substantial challenges in inference efficiency. While Mixture of Experts (MoEs) architectures address this by decoupling model size from inference cost, training MoEs from scratch is often unstable and compute intensive. Conversion of pre-trained dense models into sparse MoEs has emerged as an alternative solution; however, existing methods typically rely on heuristic neuron clustering or random splitting to partition the Feed-Forward Network (FFN) into experts. In this work, we propose DOT-MoE, a novel framework that formulates the decomposition of dense layers as a Differentiable Optimal Transport (DOT) problem. Instead of static heuristics, we model neuron assignment as a balanced transport problem, utilizing differentiable Sinkhorn-Knopp iterations to enforce strict expert capacity constraints. Furthermore, we utilize Straight-Through Estimators (STE) to jointly learn the discrete neuron-to-expert assignment and the token-to-expert routing policy end-to-end. Extensive experiments across multiple architectures and benchmarks demonstrate that DOT-MoE significantly outperforms structured pruning, heuristic clustering, and random-split baselines, retaining 90% of the original dense model's performance while reducing active parameters by 50%.

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/.

Self-supervised learning (SSL) proficiency in speech-related tasks has driven research into utilizing discrete tokens for speech tasks like recognition and translation, which offer lower storage requirements and great potential to employ natural language processing techniques. However, these studies, mainly single-task focused, faced challenges like overfitting and performance degradation in speech recognition tasks, often at the cost of sacrificing performance in multi-task scenarios. This study presents a comprehensive comparison and optimization of discrete tokens generated by various leading SSL models in speech recognition and synthesis tasks. We aim to explore the universality of speech discrete tokens across multiple speech tasks. Experimental results demonstrate that discrete tokens achieve comparable results against systems trained on FBank features in speech recognition tasks and outperform mel-spectrogram features in speech synthesis in subjective and objective metrics. These findings suggest that universal discrete tokens have enormous potential in various speech-related tasks. Our work is open-source and publicly available at https://github.com/k2-fsa/icefall.

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.

Human cognition typically involves thinking through abstract, fluid concepts rather than strictly using discrete linguistic tokens. Current reasoning models, however, are constrained to reasoning within the boundaries of human language, processing discrete token embeddings that represent fixed points in the semantic space. This discrete constraint restricts the expressive power and upper potential of such reasoning models, often causing incomplete exploration of reasoning paths, as standard Chain-of-Thought (CoT) methods rely on sampling one token per step. In this work, we introduce Soft Thinking, a training-free method that emulates human-like "soft" reasoning by generating soft, abstract concept tokens in a continuous concept space. These concept tokens are created by the probability-weighted mixture of token embeddings, which form the continuous concept space, enabling smooth transitions and richer representations that transcend traditional discrete boundaries. In essence, each generated concept token encapsulates multiple meanings from related discrete tokens, implicitly exploring various reasoning paths to converge effectively toward the correct answer. Empirical evaluations on diverse mathematical and coding benchmarks consistently demonstrate the effectiveness and efficiency of Soft Thinking, improving pass@1 accuracy by up to 2.48 points while simultaneously reducing token usage by up to 22.4% compared to standard CoT. Qualitative analysis further reveals that Soft Thinking outputs remain highly interpretable and readable, highlighting the potential of Soft Thinking to break the inherent bottleneck of discrete language-based reasoning. Code is available at https://github.com/eric-ai-lab/Soft-Thinking.

Visual generation with discrete tokens has gained significant attention as it enables a unified token prediction paradigm shared with language models, promising seamless multimodal architectures. However, current discrete generation methods remain limited to low-dimensional latent tokens (typically 8-32 dims), sacrificing the semantic richness essential for understanding. While high-dimensional pretrained representations (768-1024 dims) could bridge this gap, their discrete generation poses fundamental challenges. In this paper, we present Cubic Discrete Diffusion (CubiD), the first discrete generation model for high-dimensional representations. CubiD performs fine-grained masking throughout the high-dimensional discrete representation -- any dimension at any position can be masked and predicted from partial observations. This enables the model to learn rich correlations both within and across spatial positions, with the number of generation steps fixed at T regardless of feature dimensionality, where T ll hwd. On ImageNet-256, CubiD achieves state-of-the-art discrete generation with strong scaling behavior from 900M to 3.7B parameters. Crucially, we validate that these discretized tokens preserve original representation capabilities, demonstrating that the same discrete tokens can effectively serve both understanding and generation tasks. We hope this work will inspire future research toward unified multimodal architectures. Code is available at: https://github.com/YuqingWang1029/CubiD.

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.

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 use of continuous instead of discrete tokens during the Chain-of-Thought (CoT) phase of reasoning LLMs has garnered attention recently, based on the intuition that a continuous mixture of discrete tokens could simulate a superposition of several reasoning paths simultaneously. Theoretical results have formally proven that continuous tokens have much greater expressivity and can solve specific problems more efficiently. However, practical use of continuous tokens has been limited by strong training difficulties: previous works either just use continuous tokens at inference time on a pre-trained discrete-token model, or must distill the continuous CoT from ground-truth discrete CoTs and face computational costs that limit the CoT to very few tokens. This is the first work introducing a scalable method to learn continuous CoTs via reinforcement learning (RL), without distilling from reference discrete CoTs. We use "soft" tokens: mixtures of tokens together with noise on the input embedding to provide RL exploration. Computational overhead is minimal, enabling us to learn continuous CoTs with hundreds of tokens. On math reasoning benchmarks with Llama and Qwen models up to 8B, training with continuous CoTs match discrete-token CoTs for pass@1 and surpass them for pass@32, showing greater CoT diversity. In systematic comparisons, the best-performing scenario is to train with continuous CoT tokens then use discrete tokens for inference, meaning the "soft" models can be deployed in a standard way. Finally, we show continuous CoT RL training better preserves the predictions of the base model on out-of-domain tasks, thus providing a softer touch to the base model.

Discrete audio tokens have recently gained considerable attention for their potential to connect audio and language processing, enabling the creation of modern multimodal large language models. Ideal audio tokens must effectively preserve phonetic and semantic content along with paralinguistic information, speaker identity, and other details. While several types of audio tokens have been recently proposed, identifying the optimal tokenizer for various tasks is challenging due to the inconsistent evaluation settings in existing studies. To address this gap, we release the Discrete Audio and Speech Benchmark (DASB), a comprehensive leaderboard for benchmarking discrete audio tokens across a wide range of discriminative tasks, including speech recognition, speaker identification and verification, emotion recognition, keyword spotting, and intent classification, as well as generative tasks such as speech enhancement, separation, and text-to-speech. Our results show that, on average, semantic tokens outperform compression tokens across most discriminative and generative tasks. However, the performance gap between semantic tokens and standard continuous representations remains substantial, highlighting the need for further research in this field.

Token-level credit assignment remains a key obstacle for reinforcement learning (RL) in large language models (LLMs), where RL recipes typically treat all tokens equally, failing to distinguish decisive reasoning steps from routine formatting or fluent filler. Recent attempts leverage model-internal signals to assign finer-grained credit, but these are often point-wise heuristics that ignore the global structure of information propagation. We propose FlowTracer, an RL framework that traces answer-targeted reasoning flow on an attention-induced directed acyclic graph in which nodes correspond to tokens and edge capacities come from aggregated attention weights and derives token credit from this global structure. The edge capacities are reweighted to retain only the influence that can reach the answer region, while enforcing local flow conservation so intermediate tokens neither lose nor gain effective mass due to path length or irrelevant branches. On this graph, FlowTracer extracts an information-flow backbone connecting the question to the answer and scores tokens by flow throughput, revealing high-impact hubs and aggregation checkpoints that mediate long-range dependencies. These derived importances are used to shape token-level rewards, enabling learning signals to focus precisely on the tokens that route information toward (or away from) correct answers and delivering consistent performance gains across a range of reasoning tasks.

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.

Trainable input embedding tables are a standard component of modern language models. We ask whether they are actually necessary at the input interface. For a vocabulary of size V, exact token identity requires only K=lceil log_2 Vrceil bits. We replace the usual trainable Vtimes d_{model} input embedding matrix with fixed minimal binary token codes and a zero-parameter lift to model width. In our main setting, V=65{,}536, so K=16, and tokens are represented by fixed 16-dimensional binary codes tiled to d_{model}=1024. We also evaluate a fully table-free variant in which codes are generated from token IDs on the fly and randomly recoded by an invertible affine transform over F_2^K. Across matched 32-layer decoder-only models trained on approximately 17B tokens and evaluated over three independent training seeds, fixed minimal codes achieve comparable held-out validation perplexity to a standard learned-input baseline while removing 67.1M trainable input parameters. The fixed-code runs have a lower mean validation perplexity in our experiments, 2.36 versus 2.44, but the observed gap is within the measured seed-to-seed variation of 4.8\%; we therefore interpret the result as evidence that the trainable input table is not necessary, rather than as a statistically resolved superiority claim. The table-free affine-recoded variant remains close at 2.39 despite a slightly shorter training run. These results show that, in this regime, a trainable input embedding table is not necessary for useful language modeling. The output projection remains standard and trainable.

Contrastive learning-based vision-language pre-training approaches, such as CLIP, have demonstrated great success in many vision-language tasks. These methods achieve cross-modal alignment by encoding a matched image-text pair with similar feature embeddings, which are generated by aggregating information from visual patches and language tokens. However, direct aligning cross-modal information using such representations is challenging, as visual patches and text tokens differ in semantic levels and granularities. To alleviate this issue, we propose a Finite Discrete Tokens (FDT) based multimodal representation. FDT is a set of learnable tokens representing certain visual-semantic concepts. Both images and texts are embedded using shared FDT by first grounding multimodal inputs to FDT space and then aggregating the activated FDT representations. The matched visual and semantic concepts are enforced to be represented by the same set of discrete tokens by a sparse activation constraint. As a result, the granularity gap between the two modalities is reduced. Through both quantitative and qualitative analyses, we demonstrate that using FDT representations in CLIP-style models improves cross-modal alignment and performance in visual recognition and vision-language downstream tasks. Furthermore, we show that our method can learn more comprehensive representations, and the learned FDT capture meaningful cross-modal correspondence, ranging from objects to actions and attributes.

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.

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.

Large Language Models (LLMs) have exhibited remarkable performance on reasoning tasks. They utilize autoregressive token generation to construct reasoning trajectories, enabling the development of a coherent chain of thought. In this work, we explore the impact of individual tokens on the final outcomes of reasoning tasks. We identify the existence of ``critical tokens'' that lead to incorrect reasoning trajectories in LLMs. Specifically, we find that LLMs tend to produce positive outcomes when forced to decode other tokens instead of critical tokens. Motivated by this observation, we propose a novel approach - cDPO - designed to automatically recognize and conduct token-level rewards for the critical tokens during the alignment process. Specifically, we develop a contrastive estimation approach to automatically identify critical tokens. It is achieved by comparing the generation likelihood of positive and negative models. To achieve this, we separately fine-tune the positive and negative models on various reasoning trajectories, consequently, they are capable of identifying identify critical tokens within incorrect trajectories that contribute to erroneous outcomes. Moreover, to further align the model with the critical token information during the alignment process, we extend the conventional DPO algorithms to token-level DPO and utilize the differential likelihood from the aforementioned positive and negative model as important weight for token-level DPO learning.Experimental results on GSM8K and MATH500 benchmarks with two-widely used models Llama-3 (8B and 70B) and deepseek-math (7B) demonstrate the effectiveness of the propsoed approach cDPO.

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.

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.

Recent direct preference alignment algorithms (DPA), such as DPO, have shown great promise in aligning large language models to human preferences. While this has motivated the development of many new variants of the original DPO loss, understanding the differences between these recent proposals, as well as developing new DPA loss functions, remains difficult given the lack of a technical and conceptual framework for reasoning about the underlying semantics of these algorithms. In this paper, we attempt to remedy this by formalizing DPA losses in terms of discrete reasoning problems. Specifically, we ask: Given an existing DPA loss, can we systematically derive a symbolic expression that characterizes its semantics? How do the semantics of two losses relate to each other? We propose a novel formalism for characterizing preference losses for single model and reference model based approaches, and identify symbolic forms for a number of commonly used DPA variants. Further, we show how this formal view of preference learning sheds new light on both the size and structure of the DPA loss landscape, making it possible to not only rigorously characterize the relationships between recent loss proposals but also to systematically explore the landscape and derive new loss functions from first principles. We hope our framework and findings will help provide useful guidance to those working on human AI alignment.

Large language models (LLMs) reason over discrete token ID sequences, yet modern subword tokenizers routinely produce non-unique encodings: multiple token ID sequences can detokenize to identical surface strings. This representational mismatch creates an unmeasured fragility wherein reasoning processes can fail. LLMs may treat two internal representations as distinct "words" even when they are semantically identical at the text level. In this work, we show that tokenization can betray LLM reasoning through one-to-many token ID mappings. We introduce a tokenization-consistency probe that requires models to replace designated target words in context while leaving all other content unchanged. The task is intentionally simple at the surface level, enabling us to attribute failures to tokenizer-detokenizer artifacts rather than to knowledge gaps or parameter limitations. Through analysis of over 11000 replacement trials across state-of-the-art open-source LLMs, we find a non-trivial rate of outputs exhibit phantom edits: cases where models operate under the illusion of correct reasoning, a phenomenon arising from tokenizer-induced representational defects. We further analyze these cases and provide a taxonomy of eight systematic tokenizer artifacts, including whitespace-boundary shifts and intra-word resegmentation. These findings indicate that part of apparent reasoning deficiency originates in the tokenizer layer, motivating tokenizer-level remedies before incurring the cost of training ever-larger models on ever-larger corpora.

Discrete image tokenizers have emerged as a key component of modern vision and multimodal systems, providing a sequential interface for transformer-based architectures. However, most existing approaches remain primarily optimized for reconstruction and compression, often yielding tokens that capture local texture rather than object-level semantic structure. Inspired by the incremental and compositional nature of human communication, we introduce COMmunication inspired Tokenization (COMiT), a framework for learning structured discrete visual token sequences. COMiT constructs a latent message within a fixed token budget by iteratively observing localized image crops and recurrently updating its discrete representation. At each step, the model integrates new visual information while refining and reorganizing the existing token sequence. After several encoding iterations, the final message conditions a flow-matching decoder that reconstructs the full image. Both encoding and decoding are implemented within a single transformer model and trained end-to-end using a combination of flow-matching reconstruction and semantic representation alignment losses. Our experiments demonstrate that while semantic alignment provides grounding, attentive sequential tokenization is critical for inducing interpretable, object-centric token structure and substantially improving compositional generalization and relational reasoning over prior methods.

Current language models generate chain-of-thought traces by autoregressively sampling tokens from a finite vocabulary. While this discrete sampling has achieved remarkable success, conducting chain-of-thought with continuously-valued tokens (CoT2) offers a richer and more expressive alternative. Our work examines the benefits of CoT2 through logical reasoning tasks that inherently require search capabilities and provide optimization and exploration methods for CoT2. Theoretically, we show that CoT2 allows the model to track multiple traces in parallel and quantify its benefits for inference efficiency. Notably, one layer transformer equipped with CoT2 can provably solve the combinatorial "subset sum problem" given sufficient embedding dimension. These insights lead to a novel and effective supervision strategy where we match the softmax outputs to the empirical token distributions of a set of target traces. Complementing this, we introduce sampling strategies that unlock policy optimization and self-improvement for CoT2. Our first strategy samples and composes K discrete tokens at each decoding step to control the level of parallelism, and reduces to standard CoT when K=1. Our second strategy relies on continuous exploration over the probability simplex. Experiments confirm that policy optimization with CoT2 indeed improves the performance of the model beyond its initial discrete or continuous supervision.

Providers of LLM-as-a-service have predominantly adopted a simple pricing model: users pay a fixed price per token. Consequently, one may think that the price two different users would pay for the same output string under the same input prompt is the same. In our work, we show that, surprisingly, this is not (always) true. We find empirical evidence that, particularly for non-english outputs, both proprietary and open-weights LLMs often generate the same (output) string with multiple different tokenizations, even under the same input prompt, and this in turn leads to arbitrary price variation. To address the problem of tokenization multiplicity, we introduce canonical generation, a type of constrained generation that restricts LLMs to only generate canonical tokenizations -- the unique tokenization in which each string is tokenized during the training process of an LLM. Further, we introduce an efficient sampling algorithm for canonical generation based on the Gumbel-Max trick. Experiments on a variety of natural language tasks demonstrate that our sampling algorithm for canonical generation is comparable to standard sampling in terms of performance and runtime, and it solves the problem of tokenization multiplicity.

Transformer-based language models spread FLOPs uniformly across input sequences. In this work we demonstrate that transformers can instead learn to dynamically allocate FLOPs (or compute) to specific positions in a sequence, optimising the allocation along the sequence for different layers across the model depth. Our method enforces a total compute budget by capping the number of tokens (k) that can participate in the self-attention and MLP computations at a given layer. The tokens to be processed are determined by the network using a top-k routing mechanism. Since k is defined a priori, this simple procedure uses a static computation graph with known tensor sizes, unlike other conditional computation techniques. Nevertheless, since the identities of the k tokens are fluid, this method can expend FLOPs non-uniformly across the time and model depth dimensions. Thus, compute expenditure is entirely predictable in sum total, but dynamic and context-sensitive at the token-level. Not only do models trained in this way learn to dynamically allocate compute, they do so efficiently. These models match baseline performance for equivalent FLOPS and wall-clock times to train, but require a fraction of the FLOPs per forward pass, and can be upwards of 50\% faster to step during post-training sampling.

We propose a novel approach for learning interchangeable tokens in language models to obtain an extendable vocabulary that can generalize to new tokens. Our method is designed to address alpha-equivalence, the principle that renaming bound variables in a syntactic expression preserves semantics. This property arises in many formal languages such as temporal logics, in which all proposition symbols represent the same concept but are distinguishable from each other. To handle such tokens, we develop a dual-part embedding approach. The first part is shared across all interchangeable tokens, thereby enforcing that they represent the same core concept. The second part is randomly generated for each token, which enables distinguishability. We evaluate our method in a Transformer encoder-decoder model on two tasks: solving linear temporal logic formulae and copying with extendable vocabulary. Our method demonstrates promising generalization capabilities in addition to introducing a favorable inductive bias for alpha-equivalence.

We introduce a new balanced assignment of experts (BASE) layer for large language models that greatly simplifies existing high capacity sparse layers. Sparse layers can dramatically improve the efficiency of training and inference by routing each token to specialized expert modules that contain only a small fraction of the model parameters. However, it can be difficult to learn balanced routing functions that make full use of the available experts; existing approaches typically use routing heuristics or auxiliary expert-balancing loss functions. In contrast, we formulate token-to-expert allocation as a linear assignment problem, allowing an optimal assignment in which each expert receives an equal number of tokens. This optimal assignment scheme improves efficiency by guaranteeing balanced compute loads, and also simplifies training by not requiring any new hyperparameters or auxiliary losses. Code is publicly released at https://github.com/pytorch/fairseq/

Reinforcement learning from verifiable rewards (RLVR) has emerged as a central technique for improving the reasoning capabilities of large language models. Despite its effectiveness, how response-level rewards translate into token-level probability changes remains poorly understood. We introduce a discriminator view of RLVR updates, showing that the policy-gradient update direction implicitly acts as a linear discriminator over token-gradient vectors and thereby determines which token probabilities are increased or decreased during learning. Under standard sequence-level RLVR, this discriminator is constructed from positive- and negative-side centroids formed by advantage-weighted averaging of token-gradient vectors. However, such centroid construction can be dominated by shared high-frequency patterns, such as formatting tokens, diluting sparse yet discriminative directions that better distinguish high-reward responses from low-reward ones. To address this limitation, we propose DelTA, a discriminative token credit assignment method that estimates token coefficients to amplify side-specific token-gradient directions and downweight shared or weakly discriminative ones. These coefficients reweight a self-normalized RLVR surrogate, making the effective side-wise centroids more contrastive and thereby reshaping the RLVR update direction. On seven mathematical benchmarks, DelTA outperforms the strongest same-scale baselines by 3.26 and 2.62 average points on Qwen3-8B-Base and Qwen3-14B-Base, respectively. Additional results on code generation, a different backbone, and out-of-domain evaluations further demonstrate the generalization ability of DelTA.

Frontier LLMs are increasingly utilised across academia, society and industry. A commonly used unit for comparing models, their inputs and outputs, and estimating inference pricing is the token. In general, tokens are used as a stable currency, assumed to be broadly consistent across tokenizers and contexts, enabling direct comparisons. However, tokenization varies significantly across models and domains of text, making naive interpretation of token counts problematic. We quantify this variation by providing a comprehensive empirical analysis of tokenization, exploring the compression of sequences to tokens across different distributions of textual data. Our analysis challenges commonly held heuristics about token lengths, finding them to be overly simplistic. We hope the insights of our study add clarity and intuition toward tokenization in contemporary LLMs.

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.

Reinforcement Learning From Human Feedback (RLHF) has been a critical to the success of the latest generation of generative AI models. In response to the complex nature of the classical RLHF pipeline, direct alignment algorithms such as Direct Preference Optimization (DPO) have emerged as an alternative approach. Although DPO solves the same objective as the standard RLHF setup, there is a mismatch between the two approaches. Standard RLHF deploys reinforcement learning in a specific token-level MDP, while DPO is derived as a bandit problem in which the whole response of the model is treated as a single arm. In this work we rectify this difference, first we theoretically show that we can derive DPO in the token-level MDP as a general inverse Q-learning algorithm, which satisfies the Bellman equation. Using our theoretical results, we provide three concrete empirical insights. First, we show that because of its token level interpretation, DPO is able to perform some type of credit assignment. Next, we prove that under the token level formulation, classical search-based algorithms, such as MCTS, which have recently been applied to the language generation space, are equivalent to likelihood-based search on a DPO policy. Empirically we show that a simple beam search yields meaningful improvement over the base DPO policy. Finally, we show how the choice of reference policy causes implicit rewards to decline during training. We conclude by discussing applications of our work, including information elicitation in multi-tun dialogue, reasoning, agentic applications and end-to-end training of multi-model systems.

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.

Large Language Models (LLMs) have demonstrated remarkable performance in many applications, including challenging reasoning problems via chain-of-thoughts (CoTs) techniques that generate ``thinking tokens'' before answering the questions. While existing theoretical works demonstrate that CoTs with discrete tokens boost the capability of LLMs, recent work on continuous CoTs lacks a theoretical understanding of why it outperforms discrete counterparts in various reasoning tasks such as directed graph reachability, a fundamental graph reasoning problem that includes many practical domain applications as special cases. In this paper, we prove that a two-layer transformer with D steps of continuous CoTs can solve the directed graph reachability problem, where D is the diameter of the graph, while the best known result of constant-depth transformers with discrete CoTs requires O(n^2) decoding steps where n is the number of vertices (D<n). In our construction, each continuous thought vector is a superposition state that encodes multiple search frontiers simultaneously (i.e., parallel breadth-first search (BFS)), while discrete CoTs must choose a single path sampled from the superposition state, which leads to sequential search that requires many more steps and may be trapped into local solutions. We also performed extensive experiments to verify that our theoretical construction aligns well with the empirical solution obtained via training dynamics. Notably, encoding of multiple search frontiers as a superposition state automatically emerges in training continuous CoTs, without explicit supervision to guide the model to explore multiple paths simultaneously.

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.

In this technical note, we study the problem of inverse permutation learning in decoder-only transformers. Given a permutation and a string to which that permutation has been applied, the model is tasked with producing the original (``canonical'') string. We argue that this task models a natural robustness property across a variety of reasoning tasks, including long-context retrieval, multiple choice QA and in-context learning. Our primary contribution is an impossibility result: we show that an arbitrary depth, decoder-only transformer cannot learn this task. This result concerns the expressive capacity of decoder-only transformer models and is agnostic to training dynamics or sample complexity. We give a pair of alternative constructions under which inverse permutation learning is feasible. The first of these highlights the fundamental role of the causal attention mask, and reveals a gap between the expressivity of encoder-decoder transformers and the more popular decoder-only architecture. The latter result is more surprising: we show that simply padding the input with ``scratch tokens" yields a construction under which inverse permutation learning is possible. We conjecture that this may suggest an alternative mechanism by which chain-of-thought prompting or, more generally, intermediate ``thinking'' tokens can enable reasoning in large language models, even when these tokens encode no meaningful semantic information (e.g., the results of intermediate computations).

We design a suite of minimal algorithmic tasks that are a loose abstraction of open-ended real-world tasks. This allows us to cleanly and controllably quantify the creative limits of the present-day language model. Much like real-world tasks that require a creative, far-sighted leap of thought, our tasks require an implicit, open-ended stochastic planning step that either (a) discovers new connections in an abstract knowledge graph (like in wordplay, drawing analogies, or research) or (b) constructs new patterns (like in designing math problems or new proteins). In these tasks, we empirically and conceptually argue how next-token learning is myopic and memorizes excessively; comparatively, multi-token approaches, namely teacherless training and diffusion models, excel in producing diverse and original output. Secondly, in our tasks, we find that to elicit randomness from the Transformer without hurting coherence, it is better to inject noise right at the input layer (via a method we dub hash-conditioning) rather than defer to temperature sampling from the output layer. Thus, our work offers a principled, minimal test-bed for analyzing open-ended creative skills, and offers new arguments for going beyond next-token learning and softmax-based sampling. We make part of the code available under https://github.com/chenwu98/algorithmic-creativity

In arbitrary-order language models, it is an open question how to sample tokens in parallel from the correct joint distribution. With discrete diffusion models, the more tokens they generate in parallel, the less their predicted distributions adhere to the originally learned data distribution, as they rely on a conditional independence assumption that only works with infinitesimally small timesteps. We find that a different class of models, any-subset autoregressive models (AS-ARMs), holds the solution. As implied by the name, AS-ARMs can generate tokens in any order, and in parallel. Moreover, AS-ARMs support parallelized joint probability density estimation, allowing them to correct their own parallel-generated token distributions, via our Any-Subset Speculative Decoding (ASSD) algorithm. ASSD provably enables generation of tokens from the correct joint distribution, with the number of neural network calls upper bounded by the number of tokens predicted. We empirically verify that ASSD speeds up language generation, without sacrificing quality. Furthermore, we provide a mathematically justified scheme for training AS-ARMs for generation, and show that AS-ARMs achieve state-of-the-art performance among sub-200M parameter models on infilling benchmark tasks, and nearly match the performance of models 50X larger on code generation. Our theoretical and empirical results indicate that the once-forgotten AS-ARMs are a promising direction of language modeling.

Unified Multimodal Large Language Models (MLLMs) require a visual representation that simultaneously supports high-fidelity reconstruction, complex semantic extraction, and generative suitability. However, existing visual tokenizers typically struggle to satisfy these conflicting objectives within a single framework. In this paper, we introduce UniWeTok, a unified discrete tokenizer designed to bridge this gap using a massive binary codebook (2^{128}). For training framework, we introduce Pre-Post Distillation and a Generative-Aware Prior to enhance the semantic extraction and generative prior of the discrete tokens. In terms of model architecture, we propose a convolution-attention hybrid architecture with the SigLu activation function. SigLu activation not only bounds the encoder output and stabilizes the semantic distillation process but also effectively addresses the optimization conflict between token entropy loss and commitment loss. We further propose a three-stage training framework designed to enhance UniWeTok's adaptability cross various image resolutions and perception-sensitive scenarios, such as those involving human faces and textual content. On ImageNet, UniWeTok achieves state-of-the-art image generation performance (FID: UniWeTok 1.38 vs. REPA 1.42) while requiring a remarkably low training compute (Training Tokens: UniWeTok 33B vs. REPA 262B). On general-domain, UniWeTok demonstrates highly competitive capabilities across a broad range of tasks, including multimodal understanding, image generation (DPG Score: UniWeTok 86.63 vs. FLUX.1 [Dev] 83.84), and editing (GEdit Overall Score: UniWeTok 5.09 vs. OmniGen 5.06). We release code and models to facilitate community exploration of unified tokenizer and MLLM.

Diffusion large language models promise faster generation by refining many token positions in parallel, but this parallelism introduces a hidden control problem: which proposed tokens should be transferred into the partially decoded sequence at each step? We refer to this decision as token commitment. Existing frozen-generator decoders largely rely on hand-designed confidence rules or block-specific acceptance filters. We argue that token commitment can instead be learned as a reusable trace-state policy. We introduce TraceLock, a lightweight plug-in controller that instantiates this policy for a frozen diffusion language model. Since oracle commitment times are unavailable, TraceLock derives self-supervision from future stability: at decoding step t, a proposed token for position i is labeled stable if it matches the final token at position i after the full decoding trace completes. The controller scores variable-length trace states and decides which active token proposals should be committed to the partially decoded sequence. Once trained for a given frozen backbone, the controller can be deployed across local-window widths, generation lengths, and step budgets without retraining or per-setting calibration. Experiments on question answering, mathematical reasoning, and code generation show that TraceLock improves the quality-step tradeoff over heuristic and learned baselines, with particularly stable behavior under cross-setting deployment. Diagnostic analyses show that its decisions are not reducible to scalar confidence, suggesting that frozen diffusion language models expose a learnable space of commitment trajectories beyond confidence-based decoding. Code is available at https://github.com/BobSun98/TraceLock.

With the advancement of Self-supervised Learning (SSL) in speech-related tasks, there has been growing interest in utilizing discrete tokens generated by SSL for automatic speech recognition (ASR), as they offer faster processing techniques. However, previous studies primarily focused on multilingual ASR with Fbank features or English ASR with discrete tokens, leaving a gap in adapting discrete tokens for multilingual ASR scenarios. This study presents a comprehensive comparison of discrete tokens generated by various leading SSL models across multiple language domains. We aim to explore the performance and efficiency of speech discrete tokens across multiple language domains for both monolingual and multilingual ASR scenarios. Experimental results demonstrate that discrete tokens achieve comparable results against systems trained on Fbank features in ASR tasks across seven language domains with an average word error rate (WER) reduction of 0.31% and 1.76% absolute (2.80% and 15.70% relative) on dev and test sets respectively, with particularly WER reduction of 6.82% absolute (41.48% relative) on the Polish test set.

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.

Leveraging Large Language Models (LLMs) for generative recommendation has attracted significant research interest, where item tokenization is a critical step. It involves assigning item identifiers for LLMs to encode user history and generate the next item. Existing approaches leverage either token-sequence identifiers, representing items as discrete token sequences, or single-token identifiers, using ID or semantic embeddings. Token-sequence identifiers face issues such as the local optima problem in beam search and low generation efficiency due to step-by-step generation. In contrast, single-token identifiers fail to capture rich semantics or encode Collaborative Filtering (CF) information, resulting in suboptimal performance. To address these issues, we propose two fundamental principles for item identifier design: 1) integrating both CF and semantic information to fully capture multi-dimensional item information, and 2) designing order-agnostic identifiers without token dependency, mitigating the local optima issue and achieving simultaneous generation for generation efficiency. Accordingly, we introduce a novel set identifier paradigm for LLM-based generative recommendation, representing each item as a set of order-agnostic tokens. To implement this paradigm, we propose SETRec, which leverages CF and semantic tokenizers to obtain order-agnostic multi-dimensional tokens. To eliminate token dependency, SETRec uses a sparse attention mask for user history encoding and a query-guided generation mechanism for simultaneous token generation. We instantiate SETRec on T5 and Qwen (from 1.5B to 7B). Extensive experiments demonstrate its effectiveness under various scenarios (e.g., full ranking, warm- and cold-start ranking, and various item popularity groups). Moreover, results validate SETRec's superior efficiency and show promising scalability on cold-start items as model sizes increase.

Token embeddings, a mapping from discrete lexical symbols to continuous vectors, are at the heart of any language model (LM). However, lexical symbol meanings can also be determined and even redefined by their structural role in a long context. In this paper, we ask: is it possible for a language model to be performant without any fixed token embeddings? Such a language model would have to rely entirely on the co-occurence and repetition of tokens in the context rather than the a priori identity of any token. To answer this, we study lexinvariantlanguage models that are invariant to lexical symbols and therefore do not need fixed token embeddings in practice. First, we prove that we can construct a lexinvariant LM to converge to the true language model at a uniform rate that is polynomial in terms of the context length, with a constant factor that is sublinear in the vocabulary size. Second, to build a lexinvariant LM, we simply encode tokens using random Gaussian vectors, such that each token maps to the same representation within each sequence but different representations across sequences. Empirically, we demonstrate that it can indeed attain perplexity comparable to that of a standard language model, given a sufficiently long context. We further explore two properties of the lexinvariant language models: First, given text generated from a substitution cipher of English, it implicitly implements Bayesian in-context deciphering and infers the mapping to the underlying real tokens with high accuracy. Second, it has on average 4X better accuracy over synthetic in-context reasoning tasks. Finally, we discuss regularizing standard language models towards lexinvariance and potential practical applications.

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.

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.

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.

Recent advances in multimodal models highlight the pivotal role of image tokenization in high-resolution image generation. By compressing images into compact latent representations, tokenizers enable generative models to operate in lower-dimensional spaces, thereby improving computational efficiency and reducing complexity. Discrete tokenizers naturally align with the autoregressive paradigm but still lag behind continuous ones, limiting their adoption in multimodal systems. To address this, we propose SFTok, a discrete tokenizer that incorporates a multi-step iterative mechanism for precise reconstruction. By integrating self-forcing guided visual reconstruction and debias-and-fitting training strategy, SFTok resolves the training-inference inconsistency in multi-step process, significantly enhancing image reconstruction quality. At a high compression rate of only 64 tokens per image, SFTok achieves state-of-the-art reconstruction quality on ImageNet (rFID = 1.21) and demonstrates exceptional performance in class-to-image generation tasks (gFID = 2.29).

Current reinforcement learning from human feedback (RLHF) pipelines for large language model (LLM) alignment typically assign scalar rewards to sequences, using the final token as a surrogate indicator for the quality of the entire sequence. However, this leads to sparse feedback and suboptimal token-level credit assignment. In this work, we frame reward shaping as an optimization problem focused on token-level credit assignment. We propose a reward-shaping function leveraging explainability methods such as SHAP and LIME to estimate per-token rewards from the reward model. To learn parameters of this shaping function, we employ a bilevel optimization framework that integrates Bayesian Optimization and policy training to handle noise from the token reward estimates. Our experiments show that achieving a better balance of token-level reward attribution leads to performance improvements over baselines on downstream tasks and finds an optimal policy faster during training. Furthermore, we show theoretically that explainability methods that are feature additive attribution functions maintain the optimal policy as the original reward.

Autoregressive (AR) modeling, known for its next-token prediction paradigm, underpins state-of-the-art language and visual generative models. Traditionally, a ``token'' is treated as the smallest prediction unit, often a discrete symbol in language or a quantized patch in vision. However, the optimal token definition for 2D image structures remains an open question. Moreover, AR models suffer from exposure bias, where teacher forcing during training leads to error accumulation at inference. In this paper, we propose xAR, a generalized AR framework that extends the notion of a token to an entity X, which can represent an individual patch token, a cell (a ktimes k grouping of neighboring patches), a subsample (a non-local grouping of distant patches), a scale (coarse-to-fine resolution), or even a whole image. Additionally, we reformulate discrete token classification as continuous entity regression, leveraging flow-matching methods at each AR step. This approach conditions training on noisy entities instead of ground truth tokens, leading to Noisy Context Learning, which effectively alleviates exposure bias. As a result, xAR offers two key advantages: (1) it enables flexible prediction units that capture different contextual granularity and spatial structures, and (2) it mitigates exposure bias by avoiding reliance on teacher forcing. On ImageNet-256 generation benchmark, our base model, xAR-B (172M), outperforms DiT-XL/SiT-XL (675M) while achieving 20times faster inference. Meanwhile, xAR-H sets a new state-of-the-art with an FID of 1.24, running 2.2times faster than the previous best-performing model without relying on vision foundation modules (\eg, DINOv2) or advanced guidance interval sampling.

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.

Reinforcement learning (RL) is a pivotal task for enhancing Large Language Model (LLM) reasoning. Conventional algorithms, however, typically adhere to a coarse-grained credit assignment paradigm, applying a uniform reward to all tokens in a sequence, a critical flaw in long-chain reasoning tasks. In this paper, we address this challenge and propose Dynamic Entropy Weighting, a novel mechanism that facilitates fine-grained rewards through two new algorithms: Group Token Policy Optimization (GTPO), which assigns an entropy-weighted reward to each token, and the analogous algorithm Sequence-Level GRPO (GRPO-S). Our approach is founded on the hypothesis that high policy entropy within a reasoning path is a powerful heuristic for cognitive effort at pivotal junctures, which can be repurposed into a learning signal. By repurposing policy entropy for reward shaping, we achieve true per-token credit assignment. Experimental results across challenging reasoning benchmarks validate the superiority of our approach, showing our methods significantly outperform a strong DAPO baseline and confirming our entropy-weighting mechanism as the key driver of this performance boost.

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.

Large language models such as GPT and Llama are trained with a next-token prediction loss. In this work, we suggest that training language models to predict multiple future tokens at once results in higher sample efficiency. More specifically, at each position in the training corpus, we ask the model to predict the following n tokens using n independent output heads, operating on top of a shared model trunk. Considering multi-token prediction as an auxiliary training task, we measure improved downstream capabilities with no overhead in training time for both code and natural language models. The method is increasingly useful for larger model sizes, and keeps its appeal when training for multiple epochs. Gains are especially pronounced on generative benchmarks like coding, where our models consistently outperform strong baselines by several percentage points. Our 13B parameter models solves 12 % more problems on HumanEval and 17 % more on MBPP than comparable next-token models. Experiments on small algorithmic tasks demonstrate that multi-token prediction is favorable for the development of induction heads and algorithmic reasoning capabilities. As an additional benefit, models trained with 4-token prediction are up to 3 times faster at inference, even with large batch sizes.

Despite their ubiquity in language generation, it remains unknown why truncation sampling heuristics like nucleus sampling are so effective. We provide a theoretical explanation for the effectiveness of the truncation sampling by proving that truncation methods that discard tokens below some probability threshold (the most common type of truncation) can guarantee that all sampled tokens have nonzero true probability. However, thresholds are a coarse heuristic, and necessarily discard some tokens with nonzero true probability as well. In pursuit of a more precise sampling strategy, we show that we can leverage a known source of model errors, the softmax bottleneck, to prove that certain tokens have nonzero true probability, without relying on a threshold. Based on our findings, we develop an experimental truncation strategy and the present pilot studies demonstrating the promise of this type of algorithm. Our evaluations show that our method outperforms its threshold-based counterparts under automatic and human evaluation metrics for low-entropy (i.e., close to greedy) open-ended text generation. Our theoretical findings and pilot experiments provide both insight into why truncation sampling works, and make progress toward more expressive sampling algorithms that better surface the generative capabilities of large language models.

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

This paper challenges the dominance of continuous pipelines in visual generation. We systematically investigate the performance gap between discrete and continuous methods. Contrary to the belief that discrete tokenizers are intrinsically inferior, we demonstrate that the disparity arises primarily from the total number of bits allocated in the latent space (i.e., the compression ratio). We show that scaling up the codebook size effectively bridges this gap, allowing discrete tokenizers to match or surpass their continuous counterparts. However, existing discrete generation methods struggle to capitalize on this insight, suffering from performance degradation or prohibitive training costs with scaled codebook. To address this, we propose masked Bit AutoRegressive modeling (BAR), a scalable framework that supports arbitrary codebook sizes. By equipping an autoregressive transformer with a masked bit modeling head, BAR predicts discrete tokens through progressively generating their constituent bits. BAR achieves a new state-of-the-art gFID of 0.99 on ImageNet-256, outperforming leading methods across both continuous and discrete paradigms, while significantly reducing sampling costs and converging faster than prior continuous approaches. Project page is available at https://bar-gen.github.io/

We analyze a family of large language models in such a lightweight manner that can be done on a single GPU. Specifically, we focus on the OPT family of models ranging from 125m to 66b parameters and rely only on whether an FFN neuron is activated or not. First, we find that the early part of the network is sparse and represents many discrete features. Here, many neurons (more than 70% in some layers of the 66b model) are "dead", i.e. they never activate on a large collection of diverse data. At the same time, many of the alive neurons are reserved for discrete features and act as token and n-gram detectors. Interestingly, their corresponding FFN updates not only promote next token candidates as could be expected, but also explicitly focus on removing the information about triggering them tokens, i.e., current input. To the best of our knowledge, this is the first example of mechanisms specialized at removing (rather than adding) information from the residual stream. With scale, models become more sparse in a sense that they have more dead neurons and token detectors. Finally, some neurons are positional: them being activated or not depends largely (or solely) on position and less so (or not at all) on textual data. We find that smaller models have sets of neurons acting as position range indicators while larger models operate in a less explicit manner.

Chain-of-thoughts (CoT) requires large language models (LLMs) to generate intermediate steps before reaching the final answer, and has been proven effective to help LLMs solve complex reasoning tasks. However, the inner mechanism of CoT still remains largely unclear. In this paper, we empirically study the role of CoT tokens in LLMs on two compositional tasks: multi-digit multiplication and dynamic programming. While CoT is essential for solving these problems, we find that preserving only tokens that store intermediate results would achieve comparable performance. Furthermore, we observe that storing intermediate results in an alternative latent form will not affect model performance. We also randomly intervene some values in CoT, and notice that subsequent CoT tokens and the final answer would change correspondingly. These findings suggest that CoT tokens may function like variables in computer programs but with potential drawbacks like unintended shortcuts and computational complexity limits between tokens. The code and data are available at https://github.com/solitaryzero/CoTs_are_Variables.

Cross-tokenizer knowledge distillation allows a student model to learn from teachers with incompatible vocabularies. Prior work operates on hidden states or logits; the latter is preferred as a drop-in replacement requiring no auxiliary components. Logit-based methods either use only the correct-token probability, missing the full 'dark knowledge' in the teacher's distribution, or operate on the full output distribution, relying on strict token partitioning and/or unprincipled heuristic ranking. We identify two key shortcomings of full-distribution, logit-based methods: (i) an uncommon-token failure, where critical tokens fall into the unmatched subset (e.g., Llama's 1100 multi-digit numerals under digit-splitting Qwen supervision) and are suppressed during training, reducing GSM8k from 12.89 to 2.56 compared to same-tokenizer KD from a weaker teacher; and (ii) over-conservative matching, where strict 1-to-1 matching excludes near-equivalent tokens across surface forms. These failures require distinct remedies: eliminating the partition when critical tokens are misaligned, and refining it when alignment is reliable. We propose X-Token, an approach with two complementary loss formulations targeting these issues. P-KL removes partitioning and aligns the student's distribution with the teacher's via a sparse projection matrix W (initialized from tokenizer-level string rules) to address the uncommon-token failure. H-KL retains the hybrid form while relaxing matching to align each student token with its top-ranked teacher mapping under W. Both objectives share W and extend naturally to multiple teachers. Empirically, on Llama-3.2-1B, X-Token outperforms the current state of the art GOLD by +3.82 average points with a Qwen3-4B teacher and by +0.5 with a Phi-4-Mini teacher. Further, a two-teacher setup (Phi-4-mini + Llama-3B) improves over single-teacher distillation by +1.3 points.

Discrete flow matching generates text by iteratively transforming noise tokens into coherent language, but may require hundreds of forward passes. Distillation uses the multi-step trajectory to train a student to reproduce the process in a few steps. When the student underperforms, the usual explanation is insufficient capacity. We argue the opposite: the trajectory is the bottleneck, not the student. Each training trajectory is built through a chain of blind stochastic jumps with no evaluation of sequence quality; a single bad decision at an early midpoint propagates through subsequent steps, yet the student must imitate the result. Trajectory-Shaped Discrete Flow Matching (TS-DFM) replaces these blind jumps with guided navigation: a lightweight energy compass evaluates candidate continuations at each midpoint, selecting the most coherent. All shaping is training-only; inference cost is unchanged. On 170M-parameter language modeling, the shaped student at 8 steps achieves 32% lower perplexity than the 1,024-step teacher while being 128x faster, with gains consistent across source distributions and three evaluators of increasing scale. TS-DFM achieves the best perplexity of any discrete-generation baseline we compare against, including methods trained on 6x more data or using 5x larger models.

Autoregressive language models (ARMs) deliver strong likelihoods, but are inherently serial: they generate one token per forward pass, which limits throughput and inflates latency for long sequences. Diffusion Language Models (DLMs) parallelize across positions and thus appear promising for language generation, yet standard discrete diffusion typically needs hundreds to thousands of model evaluations to reach high quality, trading serial depth for iterative breadth. We introduce FS-DFM, Few-Step Discrete Flow-Matching. A discrete flow-matching model designed for speed without sacrificing quality. The core idea is simple: make the number of sampling steps an explicit parameter and train the model to be consistent across step budgets, so one big move lands where many small moves would. We pair this with a reliable update rule that moves probability in the right direction without overshooting, and with strong teacher guidance distilled from long-run trajectories. Together, these choices make few-step sampling stable, accurate, and easy to control. On language modeling benchmarks, FS-DFM with 8 sampling steps achieves perplexity parity with a 1,024-step discrete-flow baseline for generating 1,024 tokens using a similar-size model, delivering up to 128 times faster sampling and corresponding latency/throughput gains.

In recent years, there has been growing interest in representing speech with discrete tokens, which serve as pseudo-text for speech language models (speechLMs) and as efficient intermediate representations for downstream tasks. These tokens are typically categorized as acoustic and phonetic tokens: the former holds detailed acoustic information for reconstruction while the latter mainly captures linguistic content. In human speech communication, however, unnecessary acoustic details such as speaker information are abstracted, while both linguistic and prosodic information are utilized for speech comprehension and production. Given this, neither type of token seems an ideal representation for tasks sensitive to prosody, such as speechLMs. In this study, we propose the Phonological Tokenizer, a method that fine-tunes phonetic tokens via differentiable k-means with a multi-task objective of ASR and speech resynthesis. Experimental validation on diverse tasks confirms that our tokens retain phonological (both linguistic and prosodic) information while appropriately discarding speaker identity.

Recent advances in GPT-4o like multi-modality models have demonstrated remarkable progress for direct speech-to-speech conversation, with real-time speech interaction experience and strong speech understanding ability. However, current research focuses on discrete speech tokens to align with discrete text tokens for language modelling, which depends on an audio codec with residual connections or independent group tokens, such a codec usually leverages large scale and diverse datasets training to ensure that the discrete speech codes have good representation for varied domain, noise, style data reconstruction as well as a well-designed codec quantizer and encoder-decoder architecture for discrete token language modelling. This paper introduces Flow-Omni, a continuous speech token based GPT-4o like model, capable of real-time speech interaction and low streaming latency. Specifically, first, instead of cross-entropy loss only, we combine flow matching loss with a pretrained autoregressive LLM and a small MLP network to predict the probability distribution of the continuous-valued speech tokens from speech prompt. second, we incorporated the continuous speech tokens to Flow-Omni multi-modality training, thereby achieving robust speech-to-speech performance with discrete text tokens and continuous speech tokens together. Experiments demonstrate that, compared to discrete text and speech multi-modality training and its variants, the continuous speech tokens mitigate robustness issues by avoiding the inherent flaws of discrete speech code's representation loss for LLM.

Standard next-token prediction (NTP) supervises language models solely through discrete labels in the output logit space. We argue that this sparse one-hot supervision leaves the latent representation space under-constrained, allowing hidden states to drift into degenerate and anisotropic configurations that can limit generalization. To address this issue, we propose Next Implicit Token Prediction (NITP), which augments discrete prediction with dense continuous supervision directly in the representation space. NITP trains the model to predict the implicit semantic content of the next token, using shallow-layer representations from the same model as stable self-supervised targets. We provide theoretical analysis showing that NITP regularizes the optimization landscape by mitigating under-constrained degrees of freedom and encouraging a compact, structured representation geometry. Empirically, across dense and MoE models ranging from 0.5B to 9B parameters, NITP consistently improves downstream performance with negligible computational overhead. On a 9B MoE model, NITP achieves a 5.7% absolute improvement on MMLU-Pro, along with gains of 6.4% on C3 and 4.3% on CommonsenseQA, with approximately 2% additional training FLOPs and no additional inference cost. Our implementation is available at https://github.com/aHapBean/NITP.

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.

With adversarial or otherwise normal prompts, existing large language models (LLM) can be pushed to generate toxic discourses. One way to reduce the risk of LLMs generating undesired discourses is to alter the training of the LLM. This can be very restrictive due to demanding computation requirements. Other methods rely on rule-based or prompt-based token elimination, which are limited as they dismiss future tokens and the overall meaning of the complete discourse. Here, we center detoxification on the probability that the finished discourse is ultimately considered toxic. That is, at each point, we advise against token selections proportional to how likely a finished text from this point will be toxic. To this end, we formally extend the dead-end theory from the recent reinforcement learning (RL) literature to also cover uncertain outcomes. Our approach, called rectification, utilizes a separate but significantly smaller model for detoxification, which can be applied to diverse LLMs as long as they share the same vocabulary. Importantly, our method does not require access to the internal representations of the LLM, but only the token probability distribution at each decoding step. This is crucial as many LLMs today are hosted in servers and only accessible through APIs. When applied to various LLMs, including GPT-3, our approach significantly improves the generated discourse compared to the base LLMs and other techniques in terms of both the overall language and detoxification performance.

Latent tokens are gaining attention for enhancing reasoning in large language models (LLMs), yet their internal mechanisms remain unclear. This paper examines the problem from a reliability perspective, uncovering fundamental weaknesses: latent tokens function as uninterpretable placeholders rather than encoding faithful reasoning. While resistant to perturbation, they promote shortcut usage over genuine reasoning. We focus on Chain-of-Continuous-Thought (COCONUT), which claims better efficiency and stability than explicit Chain-of-Thought (CoT) while maintaining performance. We investigate this through two complementary approaches. First, steering experiments perturb specific token subsets, namely COCONUT and explicit CoT. Unlike CoT tokens, COCONUT tokens show minimal sensitivity to steering and lack reasoning-critical information. Second, shortcut experiments evaluate models under biased and out-of-distribution settings. Results on MMLU and HotpotQA demonstrate that COCONUT consistently exploits dataset artifacts, inflating benchmark performance without true reasoning. These findings reposition COCONUT as a pseudo-reasoning mechanism: it generates plausible traces that conceal shortcut dependence rather than faithfully representing reasoning processes.

Language models have graduated from being research prototypes to commercialized products offered as web APIs, and recent works have highlighted the multilingual capabilities of these products. The API vendors charge their users based on usage, more specifically on the number of ``tokens'' processed or generated by the underlying language models. What constitutes a token, however, is training data and model dependent with a large variance in the number of tokens required to convey the same information in different languages. In this work, we analyze the effect of this non-uniformity on the fairness of an API's pricing policy across languages. We conduct a systematic analysis of the cost and utility of OpenAI's language model API on multilingual benchmarks in 22 typologically diverse languages. We show evidence that speakers of a large number of the supported languages are overcharged while obtaining poorer results. These speakers tend to also come from regions where the APIs are less affordable to begin with. Through these analyses, we aim to increase transparency around language model APIs' pricing policies and encourage the vendors to make them more equitable.

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.

Large Language Models (LLMs) achieve impressive reasoning capabilities at the cost of substantial inference overhead, posing substantial deployment challenges. Although distilled Small Language Models (SLMs) significantly enhance efficiency, their performance suffers as they fail to follow LLMs' reasoning paths. Luckily, we reveal that only a small fraction of tokens genuinely diverge reasoning paths between LLMs and SLMs. Most generated tokens are either identical or exhibit neutral differences, such as minor variations in abbreviations or expressions. Leveraging this insight, we introduce **Roads to Rome (R2R)**, a neural token routing method that selectively utilizes LLMs only for these critical, path-divergent tokens, while leaving the majority of token generation to the SLM. We also develop an automatic data generation pipeline that identifies divergent tokens and generates token-level routing labels to train the lightweight router. We apply R2R to combine R1-1.5B and R1-32B models from the DeepSeek family, and evaluate on challenging math, coding, and QA benchmarks. With an average activated parameter size of 5.6B, R2R surpasses the average accuracy of R1-7B by 1.6x, outperforming even the R1-14B model. Compared to R1-32B, it delivers a 2.8x wall-clock speedup with comparable performance, advancing the Pareto frontier of test-time scaling efficiency. Our code is available at https://github.com/thu-nics/R2R.

The dominant approach to generating from language models subject to some constraint is locally constrained decoding (LCD), incrementally sampling tokens at each time step such that the constraint is never violated. Typically, this is achieved through token masking: looping over the vocabulary and excluding non-conforming tokens. There are two important problems with this approach. (i) Evaluating the constraint on every token can be prohibitively expensive -- LM vocabularies often exceed 100,000 tokens. (ii) LCD can distort the global distribution over strings, sampling tokens based only on local information, even if they lead down dead-end paths. This work introduces a new algorithm that addresses both these problems. First, to avoid evaluating a constraint on the full vocabulary at each step of generation, we propose an adaptive rejection sampling algorithm that typically requires orders of magnitude fewer constraint evaluations. Second, we show how this algorithm can be extended to produce low-variance, unbiased estimates of importance weights at a very small additional cost -- estimates that can be soundly used within previously proposed sequential Monte Carlo algorithms to correct for the myopic behavior of local constraint enforcement. Through extensive empirical evaluation in text-to-SQL, molecular synthesis, goal inference, pattern matching, and JSON domains, we show that our approach is superior to state-of-the-art baselines, supporting a broader class of constraints and improving both runtime and performance. Additional theoretical and empirical analyses show that our method's runtime efficiency is driven by its dynamic use of computation, scaling with the divergence between the unconstrained and constrained LM, and as a consequence, runtime improvements are greater for better models.

Diffusion language models (DLMs) have recently emerged as a strong alternative to autoregressive models by enabling parallel text generation. To improve inference efficiency and KV-cache compatibility, prior work commonly adopts block-based diffusion, decoding tokens block by block. However, this paradigm suffers from a structural limitation that we term Boundary-Induced Context Truncation (BICT): undecoded tokens near block boundaries are forced to commit without access to nearby future context, even when such context could substantially reduce uncertainty. This limitation degrades decoding certainty and generation quality, especially for tasks requiring precise reasoning, such as mathematical problem solving and code generation. We propose Deferred Commitment Decoding (DCD), a novel, training-free decoding strategy that mitigates this issue. DCD maintains a certainty-aware sliding window over masked tokens, resolving low-uncertainty tokens early while deferring high-uncertainty tokens until sufficient contextual evidence becomes available. Extensive experiments across multiple diffusion language models, benchmarks, and caching configurations show that DCD improves generation accuracy by 1.73% with comparable time on average compared to fixed block-based diffusion methods, with the most significant improvement reaching 16.5%. These results demonstrate that deferring token commitment based on uncertainty is a simple yet effective principle for improving both the quality and efficiency of diffusion language model decoding.

Autoregressive next token prediction language models offer powerful capabilities but face significant challenges in practical deployment due to the high computational and memory costs of inference, particularly during the decoding stage. We introduce Set Block Decoding (SBD), a simple and flexible paradigm that accelerates generation by integrating standard next token prediction (NTP) and masked token prediction (MATP) within a single architecture. SBD allows the model to sample multiple, not necessarily consecutive, future tokens in parallel, a key distinction from previous acceleration methods. This flexibility allows the use of advanced solvers from the discrete diffusion literature, offering significant speedups without sacrificing accuracy. SBD requires no architectural changes or extra training hyperparameters, maintains compatibility with exact KV-caching, and can be implemented by fine-tuning existing next token prediction models. By fine-tuning Llama-3.1 8B and Qwen-3 8B, we demonstrate that SBD enables a 3-5x reduction in the number of forward passes required for generation while achieving same performance as equivalent NTP training.

Despite Flow Matching and diffusion models having emerged as powerful generative paradigms for continuous variables such as images and videos, their application to high-dimensional discrete data, such as language, is still limited. In this work, we present Discrete Flow Matching, a novel discrete flow paradigm designed specifically for generating discrete data. Discrete Flow Matching offers several key contributions: (i) it works with a general family of probability paths interpolating between source and target distributions; (ii) it allows for a generic formula for sampling from these probability paths using learned posteriors such as the probability denoiser (x-prediction) and noise-prediction (epsilon-prediction); (iii) practically, focusing on specific probability paths defined with different schedulers considerably improves generative perplexity compared to previous discrete diffusion and flow models; and (iv) by scaling Discrete Flow Matching models up to 1.7B parameters, we reach 6.7% Pass@1 and 13.4% Pass@10 on HumanEval and 6.7% Pass@1 and 20.6% Pass@10 on 1-shot MBPP coding benchmarks. Our approach is capable of generating high-quality discrete data in a non-autoregressive fashion, significantly closing the gap between autoregressive models and discrete flow models.

Recent advancements in large language models (LLMs) have significantly enhanced their reasoning capabilities. However, they continue to struggle with basic character-level tasks, such as counting letters in words, a problem rooted in their tokenization process. While existing benchmarks have highlighted this weakness through basic character operations, such failures are often dismissed due to lacking practical relevance. Yet, many real-world applications, such as navigating text-based maps or interpreting structured tables, rely heavily on precise sub-token understanding. In this regard, we introduce SubTokenTest, a comprehensive benchmark that assesses sub-token understanding through practical, utility-driven tasks. Our benchmark includes ten tasks across four domains and isolates tokenization-related failures by decoupling performance from complex reasoning. We provide a comprehensive evaluation of nine advanced LLMs. Additionally, we investigate the impact of test-time scaling on sub-token reasoning and explore how character-level information is encoded within the hidden states.

Text-to-image diffusion models have demonstrated an unparalleled ability to generate high-quality, diverse images from a textual concept (e.g., "a doctor", "love"). However, the internal process of mapping text to a rich visual representation remains an enigma. In this work, we tackle the challenge of understanding concept representations in text-to-image models by decomposing an input text prompt into a small set of interpretable elements. This is achieved by learning a pseudo-token that is a sparse weighted combination of tokens from the model's vocabulary, with the objective of reconstructing the images generated for the given concept. Applied over the state-of-the-art Stable Diffusion model, this decomposition reveals non-trivial and surprising structures in the representations of concepts. For example, we find that some concepts such as "a president" or "a composer" are dominated by specific instances (e.g., "Obama", "Biden") and their interpolations. Other concepts, such as "happiness" combine associated terms that can be concrete ("family", "laughter") or abstract ("friendship", "emotion"). In addition to peering into the inner workings of Stable Diffusion, our method also enables applications such as single-image decomposition to tokens, bias detection and mitigation, and semantic image manipulation. Our code will be available at: https://hila-chefer.github.io/Conceptor/

Diffusion Language Models (DLMs) offer order-agnostic generation that can explore many possible decoding trajectories. However, current decoding methods commit to a single trajectory, limiting exploration in trajectory space. We introduce Order-Token Search to explore this space through jointly searching over generation order and token values. Its core is a likelihood estimator that scores denoising actions, enabling stable pruning and efficient exploration of diverse trajectories. Across mathematical reasoning and coding benchmarks, Order-Token Search consistently outperforms baselines on GSM8K, MATH500, Countdown, and HumanEval (3.1%, 3.8%, 7.9%, and 6.8% absolute over backbone), matching or surpassing diffu-GRPO post-trained d1-LLaDA. Our work establishes joint search as a key component for advancing decoding in DLMs.

We consider multi-draft speculative sampling, where the proposal sequences are sampled independently from different draft models. At each step, a token-level draft selection scheme takes a list of valid tokens as input and produces an output token whose distribution matches that of the target model. Previous works have demonstrated that the optimal scheme (which maximizes the probability of accepting one of the input tokens) can be cast as a solution to a linear program. In this work we show that the optimal scheme can be decomposed into a two-step solution: in the first step an importance sampling (IS) type scheme is used to select one intermediate token; in the second step (single-draft) speculative sampling is applied to generate the output token. For the case of two identical draft models we further 1) establish a necessary and sufficient condition on the distributions of the target and draft models for the acceptance probability to equal one and 2) provide an explicit expression for the optimal acceptance probability. Our theoretical analysis also motives a new class of token-level selection scheme based on weighted importance sampling. Our experimental results demonstrate consistent improvements in the achievable block efficiency and token rates over baseline schemes in a number of scenarios.

Despite its simplicity and efficacy, the high token expenditure of self-consistency can limit its practical utility. Here we investigate if self-consistency can be made more token-efficient for long chain-of-thought reasoning tasks, while preserving its parallelism, through early hypothesis pruning. Concretely, we generate all solutions in parallel, but periodically prune intermediate hypotheses that are deemed unnecessary based on two lightweight indicators: (a) the model's own confidence in individual hypotheses, and (b) lexical coverage of all current hypotheses by candidate subsets that are under consideration for continued retention. We design a fast weighted set cover algorithm that utilizes the two indicators; our evaluation of five LLMs on three math benchmarks shows that this method can improve token efficiency for all models, by 10-35% in many cases.

Large Language Models (LLMs) rely on the Key-Value (KV) Cache to store token history, enabling efficient decoding of tokens. As the KV-Cache grows, it becomes a major memory and computation bottleneck, however, there is an opportunity to alleviate this bottleneck, especially because prior research has shown that only a small subset of tokens contribute meaningfully to each decoding step. A key challenge in finding these critical tokens is that they are dynamic, and heavily input query-dependent. Existing methods either risk quality by evicting tokens permanently, or retain the full KV-Cache but rely on retrieving chunks (pages) of tokens at generation, failing at dense, context-rich tasks. Additionally, many existing KV-Cache sparsity methods rely on inaccurate proxies for token importance. To address these limitations, we introduce TokenButler, a high-granularity, query-aware predictor that learns to identify these critical tokens. By training a light-weight predictor with less than 1.2% parameter overhead, TokenButler prioritizes tokens based on their contextual, predicted importance. This improves perplexity & downstream accuracy by over 8% relative to SoTA methods for estimating token importance. We evaluate TokenButler on a novel synthetic small-context co-referential retrieval task, demonstrating near-oracle accuracy. Code, models and benchmarks: https://github.com/abdelfattah-lab/TokenButler

Recent breakthroughs in large language models (LLMs) have led to notable successes in complex reasoning tasks, such as mathematical problem solving. A common strategy for improving performance is parallel thinking, in which multiple reasoning traces are generated and the final prediction is made using aggregation schemes like majority voting or best-of-N decoding. However, two key challenges persist. First, multi-sample decoding incurs substantial inference latency, especially for long-form outputs. Second, effective mechanisms for reliably assessing the correctness of individual reasoning traces are still limited. To address these challenges, we introduce One-Token Verification (OTV), a computational method that estimates reasoning correctness in a single forward pass during generation. OTV is activated by a learnable token and integrated into the LLM via low-rank adaptation to probe internal reasoning signals through the key-value cache, supporting token-level correctness estimation at any stage of generation without disrupting primary reasoning. Experiments on mathematical reasoning benchmarks demonstrate that OTV consistently surpasses existing verifiers. Additionally, OTV reduces token usage by up to 90% through correctness-guided early termination, prioritizing shorter, more reliable solutions.

Large language models (LLMs) have achieved impressive success in text-formatted learning problems, and most popular LLMs have been deployed in a black-box fashion. Meanwhile, fine-tuning is usually necessary for a specific downstream task to obtain better performance, and this functionality is provided by the owners of the black-box LLMs. To fine-tune a black-box LLM, labeled data are always required to adjust the model parameters. However, in many real-world applications, LLMs can label textual datasets with even better quality than skilled human annotators, motivating us to explore the possibility of fine-tuning black-box LLMs with unlabeled data. In this paper, we propose unsupervised prompt learning for classification with black-box LLMs, where the learning parameters are the prompt itself and the pseudo labels of unlabeled data. Specifically, the prompt is modeled as a sequence of discrete tokens, and every token has its own to-be-learned categorical distribution. On the other hand, for learning the pseudo labels, we are the first to consider the in-context learning (ICL) capabilities of LLMs: we first identify reliable pseudo-labeled data using the LLM, and then assign pseudo labels to other unlabeled data based on the prompt, allowing the pseudo-labeled data to serve as in-context demonstrations alongside the prompt. Those in-context demonstrations matter: previously, they are involved when the prompt is used for prediction while they are not involved when the prompt is trained; thus, taking them into account during training makes the prompt-learning and prompt-using stages more consistent. Experiments on benchmark datasets show the effectiveness of our proposed algorithm. After unsupervised prompt learning, we can use the pseudo-labeled dataset for further fine-tuning by the owners of the black-box LLMs.

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.

With the introduction of transformer-based models for vision and language tasks, such as LLaVA and Chameleon, there has been renewed interest in the discrete tokenized representation of images. These models often treat image patches as discrete tokens, analogous to words in natural language, learning joint alignments between visual and human languages. However, little is known about the statistical behavior of these visual languages - whether they follow similar frequency distributions, grammatical structures, or topologies as natural languages. In this paper, we take a natural-language-centric approach to analyzing discrete visual languages and uncover striking similarities and fundamental differences. We demonstrate that, although visual languages adhere to Zipfian distributions, higher token innovation drives greater entropy and lower compression, with tokens predominantly representing object parts, indicating intermediate granularity. We also show that visual languages lack cohesive grammatical structures, leading to higher perplexity and weaker hierarchical organization compared to natural languages. Finally, we demonstrate that, while vision models align more closely with natural languages than other models, this alignment remains significantly weaker than the cohesion found within natural languages. Through these experiments, we demonstrate how understanding the statistical properties of discrete visual languages can inform the design of more effective computer vision models.

The representation disparity between visual generation and understanding imposes a critical gap in integrating these capabilities into a single framework. To bridge this gap, we introduce UniTok, a discrete visual tokenizer that encodes fine-grained details for generation while also capturing high-level semantics for understanding. Despite recent studies have shown that these objectives could induce loss conflicts in training, we reveal that the underlying bottleneck stems from limited representational capacity of discrete tokens. We address this by introducing multi-codebook quantization, which divides vector quantization with several independent sub-codebooks to expand the latent feature space, while avoiding training instability caused by overlarge codebooks. Our method significantly raises the upper limit of unified discrete tokenizers to match or even surpass domain-specific continuous tokenizers. For instance, UniTok achieves a remarkable rFID of 0.38 (versus 0.87 for SD-VAE) and a zero-shot accuracy of 78.6% (versus 76.2% for CLIP) on ImageNet. Our code is available at https://github.com/FoundationVision/UniTok.

Large Language Models (LLMs) have demonstrated impressive problem-solving capabilities in mathematics through step-by-step reasoning chains. However, they are susceptible to reasoning errors that impact the quality of subsequent reasoning chains and the final answer due to language models' autoregressive token-by-token generating nature. Recent works have proposed adopting external verifiers to guide the generation of reasoning paths, but existing works utilize models that have been trained with step-by-step labels to assess the correctness of token-by-token reasoning chains. Consequently, they struggle to recognize discriminative details of tokens within a reasoning path and lack the ability to evaluate whether an intermediate reasoning path is on a promising track toward the correct final answer. To amend the lack of sound and token-grained math-verification signals, we devise a novel training scheme for verifiers that apply token-level supervision with the expected cumulative reward (i.e., value). Furthermore, we propose a practical formulation of the cumulative reward by reducing it to finding the probability of future correctness of the final answer and thereby enabling the empirical estimation of the value. Experimental results on mathematical reasoning benchmarks show that Token-Supervised Value Model (TVM) can outperform step-by-step verifiers on GSM8K and MATH with Mistral and Llama.

Text and faces are among the most perceptually salient and practically important patterns in visual generation, yet they remain challenging for autoregressive generators built on discrete tokenization. A central bottleneck is the tokenizer: aggressive downsampling and quantization often discard the fine-grained structures needed to preserve readable glyphs and distinctive facial features. We attribute this gap to standard discrete-tokenizer objectives being weakly aligned with text legibility and facial fidelity, as these objectives typically optimize generic reconstruction while compressing diverse content uniformly. To address this, we propose InsightTok, a simple yet effective discrete visual tokenization framework that enhances text and face fidelity through localized, content-aware perceptual losses. With a compact 16k codebook and a 16x downsampling rate, InsightTok significantly outperforms prior tokenizers in text and face reconstruction without compromising general reconstruction quality. These gains consistently transfer to autoregressive image generation in InsightAR, producing images with clearer text and more faithful facial details. Overall, our results highlight the potential of specialized supervision in tokenizer training for advancing discrete image generation.

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.

Unsupervised text representation learning (TRL) is a fundamental task in natural language processing, which is beneficial for improving search and recommendations with the web's unlabeled texts. A recent empirical study finds that the high-quality representation aligns with the key token of the input text, uncovering the potential connection between representation space and vocabulary space. Inspired by the findings, we revisit the generative tasks and develop an unsupervised generative framework for TRL, Text2Token. The framework is based on the token target prediction task, utilizing carefully constructed target token distribution as supervisory signals. To construct the high-quality target token distribution, we analyze the token-alignment properties with advanced embedders and identify two essential categories of key tokens: (1) the meaningful tokens in the text and (2) semantically derived tokens beyond the text. Based on these insights, we propose two methods -- data-driven and model-derived -- to construct synthetic token targets from data or the LLM backbone. Experiments on the MTEB v2 benchmark demonstrate that Text2Token achieves performance competitive with the state-of-the-art embedder with unsupervised contrastive learning, LLM2Vec. Our analysis further shows that vocabulary and representation spaces optimize together and toward the optimum solution during training, providing new ideas and insights for future work.

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.

Recent advancements in reinforcement learning from human feedback have shown that utilizing fine-grained token-level reward models can substantially enhance the performance of Proximal Policy Optimization (PPO) in aligning large language models. However, it is challenging to leverage such token-level reward as guidance for Direct Preference Optimization (DPO), since DPO is formulated as a sequence-level bandit problem. To address this challenge, this work decomposes the sequence-level PPO into a sequence of token-level proximal policy optimization problems and then frames the problem of token-level PPO with token-level reward guidance, from which closed-form optimal token-level policy and the corresponding token-level reward can be derived. Using the obtained reward and Bradley-Terry model, this work establishes a framework of computable loss functions with token-level reward guidance for DPO, and proposes a practical reward guidance based on the induced DPO reward. This formulation enables different tokens to exhibit varying degrees of deviation from reference policy based on their respective rewards. Experiment results demonstrate that our method achieves substantial performance improvements over DPO, with win rate gains of up to 7.5 points on MT-Bench, 6.2 points on AlpacaEval 2, and 4.3 points on Arena-Hard. Code is available at https://github.com/dvlab-research/TGDPO.

When using agent-task datasets to enhance agent capabilities for Large Language Models (LLMs), current methodologies often treat all tokens within a sample equally. However, we argue that tokens serving different roles - specifically, reasoning tokens versus boilerplate tokens (e.g., those governing output format) - differ significantly in importance and learning complexity, necessitating their disentanglement and distinct treatment. To address this, we propose a novel Shuffle-Aware Discriminator (SHAD) for adaptive token discrimination. SHAD classifies tokens by exploiting predictability differences observed after shuffling input-output combinations across samples: boilerplate tokens, due to their repetitive nature among samples, maintain predictability, whereas reasoning tokens do not. Using SHAD, we propose the Reasoning-highlighted Fine-Tuning (RFT) method, which adaptively emphasizes reasoning tokens during fine-tuning, yielding notable performance gains over common Supervised Fine-Tuning (SFT).

Discrete speech representations have garnered recent attention for their efficacy in training transformer-based models for various speech-related tasks such as automatic speech recognition (ASR), translation, speaker verification, and joint speech-text foundational models. In this work, we present a comprehensive analysis on building ASR systems with discrete codes. We investigate different methods for codec training such as quantization schemes and time-domain vs spectral feature encodings. We further explore ASR training techniques aimed at enhancing performance, training efficiency, and noise robustness. Drawing upon our findings, we introduce a codec ASR pipeline that outperforms Encodec at similar bit-rate. Remarkably, it also surpasses the state-of-the-art results achieved by strong self-supervised models on the 143 languages ML-SUPERB benchmark despite being smaller in size and pretrained on significantly less data.

Current neural architectures lack a principled way to handle interchangeable tokens, i.e., symbols that are semantically equivalent yet distinguishable, such as bound variables. As a result, models trained on fixed vocabularies often struggle to generalize to unseen symbols, even when the underlying semantics remain unchanged. We propose a novel Transformer-based mechanism that is provably invariant to the renaming of interchangeable tokens. Our approach employs parallel embedding streams to isolate the contribution of each interchangeable token in the input, combined with an aggregated attention mechanism that enables structured information sharing across streams. Experimental results confirm the theoretical guarantees of our method and demonstrate substantial performance gains on open-vocabulary tasks that require generalization to novel symbols. Project page: https://bu-depend-lab.github.io/Symbol-Invariant-Transformer/

In this article we describe an efficient approach to guiding language model text generation with regular expressions and context-free grammars. Our approach adds little to no overhead to the token sequence generation process, and makes guided generation feasible in practice. An implementation is provided in the open source Python library Outlines.

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.

We present Future-KL Influenced Policy Optimization (FIPO), a reinforcement learning algorithm designed to overcome reasoning bottlenecks in large language models. While GRPO style training scales effectively, it typically relies on outcome-based rewards (ORM) that distribute a global advantage uniformly across every token in a trajectory. We argue that this coarse-grained credit assignment imposes a performance ceiling by failing to distinguish critical logical pivots from trivial tokens. FIPO addresses this by incorporating discounted future-KL divergence into the policy update, creating a dense advantage formulation that re-weights tokens based on their influence on subsequent trajectory behavior. Empirically, FIPO enables models to break through the length stagnation seen in standard baselines. Evaluated on Qwen2.5-32B, FIPO extends the average chain-of-thought length from roughly 4,000 to over 10,000 tokens and increases AIME 2024 Pass@1 accuracy from 50.0% to a peak of 58.0% (converging at approximately 56.0\%). This outperforms both DeepSeek-R1-Zero-Math-32B (around 47.0%) and o1-mini (approximately 56.0%). Our results suggest that establishing dense advantage formulations is a vital path for evolving ORM-based algorithms to unlock the full reasoning potential of base models. We open-source our training system, built on the verl framework.

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.

Metric-induced discrete flow matching (MI-DFM) exploits token-latent geometry for discrete generation, but its practical use is limited by two issues: heuristic schedulers requiring hyperparameter search, and finite-step path-tracking error from its first-order continuous-time Markov chain (CTMC) solver. We address both issues. First, we derive a kinetic-optimal scheduler for prescribed scalar-parameterized probability paths, and instantiate it for MI-DFM as a training-free numerical schedule that traverses the path at constant Fisher-Rao speed. Second, we introduce a finite-step moment correction that adjusts the jump probability while preserving the CTMC jump destination distribution. We validate the resulting method, GibbsTTS, on codec-based zero-shot text-to-speech (TTS). Under controlled comparisons with a unified architecture and large-scale dataset, GibbsTTS achieves the best objective naturalness and is preferred in subjective evaluations over masked discrete generative baselines. Additionally, in comparison with the evaluated state-of-the-art TTS systems, GibbsTTS shows strong speaker similarity, achieving the highest similarity on three of four test sets and ranking second on the fourth. Project page: https://ydqmkkx.github.io/GibbsTTSProject

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.

Autoregressive large language models (LLMs) scale well by expressing diverse tasks as sequences of discrete natural-language tokens and training with next-token prediction, which unifies comprehension and generation under self-supervision. Extending this paradigm to multimodal data requires a shared, discrete representation across modalities. However, most vision-language models (VLMs) still rely on a hybrid interface: discrete text tokens paired with continuous Vision Transformer (ViT) features. Because supervision is largely text-driven, these models are often biased toward understanding and cannot fully leverage large-scale self-supervised learning on non-text data. Recent work has explored discrete visual tokenization to enable fully autoregressive multimodal modeling, showing promising progress toward unified understanding and generation. Yet existing discrete vision tokens frequently lose information due to limited code capacity, resulting in noticeably weaker understanding than continuous-feature VLMs. We present Kelix, a fully discrete autoregressive unified model that closes the understanding gap between discrete and continuous visual representations.

The remarkable achievements of large language models (LLMs) have led many to conclude that they exhibit a form of intelligence. This is as opposed to explanations of their capabilities based on their ability to perform relatively simple manipulations of vast volumes of data. To illuminate the distinction between these explanations, we introduce a novel generative model that generates tokens on the basis of human-interpretable concepts represented as latent discrete variables. Under mild conditions, even when the mapping from the latent space to the observed space is non-invertible, we establish an identifiability result, i.e., the representations learned by LLMs through next-token prediction can be approximately modeled as the logarithm of the posterior probabilities of these latent discrete concepts given input context, up to an invertible linear transformation. This theoretical finding not only provides evidence that LLMs capture underlying generative factors, but also provide a unified prospective for understanding of the linear representation hypothesis. Taking this a step further, our finding motivates a reliable evaluation of sparse autoencoders by treating the performance of supervised concept extractors as an upper bound. Pushing this idea even further, it inspires a structural variant that enforces dependence among latent concepts in addition to promoting sparsity. Empirically, we validate our theoretical results through evaluations on both simulation data and the Pythia, Llama, and DeepSeek model families, and demonstrate the effectiveness of our structured sparse autoencoder.

Prompt engineering is crucial for deploying LLMs but is poorly understood mathematically. We formalize LLM systems as a class of discrete stochastic dynamical systems to explore prompt engineering through the lens of control theory. We investigate the reachable set of output token sequences R_y(mathbf x_0) for which there exists a control input sequence mathbf u for each mathbf y in R_y(mathbf x_0) that steers the LLM to output mathbf y from initial state sequence mathbf x_0. We offer analytic analysis on the limitations on the controllability of self-attention in terms of reachable set, where we prove an upper bound on the reachable set of outputs R_y(mathbf x_0) as a function of the singular values of the parameter matrices. We present complementary empirical analysis on the controllability of a panel of LLMs, including Falcon-7b, Llama-7b, and Falcon-40b. Our results demonstrate a lower bound on the reachable set of outputs R_y(mathbf x_0) w.r.t. initial state sequences mathbf x_0 sampled from the Wikitext dataset. We find that the correct next Wikitext token following sequence mathbf x_0 is reachable over 97% of the time with prompts of kleq 10 tokens. We also establish that the top 75 most likely next tokens, as estimated by the LLM itself, are reachable at least 85% of the time with prompts of kleq 10 tokens. Intriguingly, short prompt sequences can dramatically alter the likelihood of specific outputs, even making the least likely tokens become the most likely ones. This control-centric analysis of LLMs demonstrates the significant and poorly understood role of input sequences in steering output probabilities, offering a foundational perspective for enhancing language model system capabilities.

A widely used strategy to discover and understand language model mechanisms is circuit analysis. A circuit is a minimal subgraph of a model's computation graph that executes a specific task. We identify a gap in existing circuit discovery methods: they assume circuits are position-invariant, treating model components as equally relevant across input positions. This limits their ability to capture cross-positional interactions or mechanisms that vary across positions. To address this gap, we propose two improvements to incorporate positionality into circuits, even on tasks containing variable-length examples. First, we extend edge attribution patching, a gradient-based method for circuit discovery, to differentiate between token positions. Second, we introduce the concept of a dataset schema, which defines token spans with similar semantics across examples, enabling position-aware circuit discovery in datasets with variable length examples. We additionally develop an automated pipeline for schema generation and application using large language models. Our approach enables fully automated discovery of position-sensitive circuits, yielding better trade-offs between circuit size and faithfulness compared to prior work.

We present a novel approach to feature labeling using gradient descent in token-space. While existing methods typically use language models to generate hypotheses about feature meanings, our method directly optimizes label representations by using a language model as a discriminator to predict feature activations. We formulate this as a multi-objective optimization problem in token-space, balancing prediction accuracy, entropy minimization, and linguistic naturalness. Our proof-of-concept experiments demonstrate successful convergence to interpretable single-token labels across diverse domains, including features for detecting animals, mammals, Chinese text, and numbers. Although our current implementation is constrained to single-token labels and relatively simple features, the results suggest that token-space gradient descent could become a valuable addition to the interpretability researcher's toolkit.

Text-to-image (T2I) diffusion models rely on encoded prompts to guide the image generation process. Typically, these prompts are extended to a fixed length by adding padding tokens before text encoding. Despite being a default practice, the influence of padding tokens on the image generation process has not been investigated. In this work, we conduct the first in-depth analysis of the role padding tokens play in T2I models. We develop two causal techniques to analyze how information is encoded in the representation of tokens across different components of the T2I pipeline. Using these techniques, we investigate when and how padding tokens impact the image generation process. Our findings reveal three distinct scenarios: padding tokens may affect the model's output during text encoding, during the diffusion process, or be effectively ignored. Moreover, we identify key relationships between these scenarios and the model's architecture (cross or self-attention) and its training process (frozen or trained text encoder). These insights contribute to a deeper understanding of the mechanisms of padding tokens, potentially informing future model design and training practices in T2I systems.

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.

Despite their recent successes, Transformer-based large language models show surprising failure modes. A well-known example of such failure modes is their inability to length-generalize: solving problem instances at inference time that are longer than those seen during training. In this work, we further explore the root cause of this failure by performing a detailed analysis of model behaviors on the simple parity task. Our analysis suggests that length generalization failures are intricately related to a model's inability to perform random memory accesses within its context window. We present supporting evidence for this hypothesis by demonstrating the effectiveness of methodologies that circumvent the need for indexing or that enable random token access indirectly, through content-based addressing. We further show where and how the failure to perform random memory access manifests through attention map visualizations.

The rapid growth in the parameters of large language models (LLMs) has made inference latency a fundamental bottleneck, limiting broader application of LLMs. Speculative decoding represents a lossless approach to accelerate inference through a guess-and-verify paradigm, leveraging the parallel capabilities of modern hardware. Some speculative decoding methods rely on additional structures to guess draft tokens, such as small models or parameter-efficient architectures, which need extra training before use. Alternatively, retrieval-based train-free techniques build libraries from pre-existing corpora or by n-gram generation. However, they face challenges like large storage requirements, time-consuming retrieval, and limited adaptability. Observing that candidate tokens generated during the decoding process are likely to reoccur in future sequences, we propose Token Recycling. This approach stores candidate tokens in an adjacency matrix and employs a breadth-first search (BFS)-like algorithm on the matrix to construct a draft tree. The tree is then validated through tree attention. New candidate tokens from the decoding process are then used to update the matrix. Token Recycling requires \textless2MB of additional storage and achieves approximately 2x speedup across all sizes of LLMs. It significantly outperforms existing train-free methods by 30\% and even a training method by 25\%. It can be directly applied to any existing LLMs and tasks without the need for adaptation.

The development of state-of-the-art large language models is commonly understood as a two-stage process involving pre-training and post-training. We point out the need for an additional intermediate stage called reinforcement mid-training with potential for strong performance gains. In this paper, we formally define the problem and identify three key challenges: (1) inefficient training due to excessive reasoning steps, (2) disregard of the imbalanced token entropy distribution, and (3) underutilization of token information. To address these challenges, we propose RMT, a framework for efficient, adaptive, and unified reinforcement mid-training with various innovative components. In particular, we first introduce a dynamic token budget mechanism that constrains unnecessary reasoning steps and mitigates model overthinking. Next, we design a curriculum-based adaptive sampling method that fosters a progressive learning trajectory from easy to hard tokens. Finally, we present a dual training strategy that combines reinforcement learning with next-token prediction, ensuring targeted learning on key tokens and full exploitation of all token information. Extensive experiments demonstrate the superiority of RMT over state-of-the-art methods, achieving up to +64.91% performance improvement with only 21% of the reasoning length in language modeling. We also show that checkpoints obtained after reinforcement mid-training can benefit the subsequent post-training, yielding up to +18.76% improvement in the mathematical domain.

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.

Scaling the size of language models to tens of billions of parameters has led to impressive performance on a wide range of tasks. At generation, these models are used auto-regressively, requiring a forward pass for each generated token, and thus reading the full set of parameters from memory. This memory access forms the primary bottleneck for generation and it worsens as the model size increases. Moreover, executing a forward pass for multiple tokens in parallel often takes nearly the same time as it does for just one token. These two observations lead to the development of speculative sampling, where a second smaller model is used to draft a few tokens, that are then validated or rejected using a single forward pass of the large model. Unfortunately, this method requires two models that share the same tokenizer and thus limits its adoption. As an alternative, we propose to use parallel decoding as a way to draft multiple tokens from a single model with no computational cost, nor the need for a second model. Our approach only requires an additional input token that marks the words that will be generated simultaneously. We show promising performance (up to 30% speed-up) while requiring only as few as O(d_{emb}) additional parameters.

Text-to-Image (T2I) models often suffer from issues such as semantic leakage, incorrect feature binding, and omissions of key concepts in the generated image. This work studies these phenomena by looking into the role of information flow between textual token representations. To this end, we generate images by applying the diffusion component on a subset of contextual token representations in a given prompt and observe several interesting phenomena. First, in many cases, a word or multiword expression is fully represented by one or two tokens, while other tokens are redundant. For example, in "San Francisco's Golden Gate Bridge", the token "gate" alone captures the full expression. We demonstrate the redundancy of these tokens by removing them after textual encoding and generating an image from the resulting representation. Surprisingly, we find that this process not only maintains image generation performance but also reduces errors by 21\% compared to standard generation. We then show that information can also flow between different expressions in a sentence, which often leads to semantic leakage. Based on this observation, we propose a simple, training-free method to mitigate semantic leakage: replacing the leaked item's representation after the textual encoding with its uncontextualized representation. Remarkably, this simple approach reduces semantic leakage by 85\%. Overall, our work provides a comprehensive analysis of information flow across textual tokens in T2I models, offering both novel insights and practical benefits.

This paper reports the first brain-inspired large language model (BriLLM). This is a non-Transformer, non-GPT, non-traditional machine learning input-output controlled generative language model. The model is based on the Signal Fully-connected flowing (SiFu) definition on the directed graph in terms of the neural network, and has the interpretability of all nodes on the graph of the whole model, instead of the traditional machine learning model that only has limited interpretability at the input and output ends. In the language model scenario, the token is defined as a node in the graph. A randomly shaped or user-defined signal flow flows between nodes on the principle of "least resistance" along paths. The next token or node to be predicted or generated is the target of the signal flow. As a language model, BriLLM theoretically supports infinitely long n-gram models when the model size is independent of the input and predicted length of the model. The model's working signal flow provides the possibility of recall activation and innate multi-modal support similar to the cognitive patterns of the human brain. At present, we released the first BriLLM version in Chinese, with 4000 tokens, 32-dimensional node width, 16-token long sequence prediction ability, and language model prediction performance comparable to GPT-1. More computing power will help us explore the infinite possibilities depicted above.

Diffusion language models, especially masked discrete diffusion models, have achieved great success recently. While there are some theoretical and primary empirical results showing the advantages of latent reasoning with looped transformers or continuous chain-of-thoughts, continuous diffusion models typically underperform their discrete counterparts. In this paper, we argue that diffusion language models do not necessarily need to be in the discrete space. In particular, we prove that continuous diffusion models have stronger expressivity than discrete diffusions and looped transformers. We attribute the contradiction between the theoretical expressiveness and empirical performance to their practical trainability: while continuous diffusion provides intermediate supervision that looped transformers lack, they introduce additional difficulty decoding tokens into the discrete token space from the continuous representation space. We therefore propose Coevolutionary Continuous Discrete Diffusion (CCDD), which defines a joint multimodal diffusion process on the union of a continuous representation space and a discrete token space, leveraging a single model to simultaneously denoise in the joint space. By combining two modalities, CCDD is expressive with rich semantics in the latent space, as well as good trainability and sample quality with the help of explicit discrete tokens. We also propose effective architectures and advanced training/sampling techniques for CCDD, which reveals strong empirical performance in extensive language modeling experiments on real-world tasks.

On-policy distillation (OPD) is appealing for large language model (LLM) post-training because it evaluates teacher feedback on student-generated rollouts rather than fixed teacher traces. In long-horizon settings, however, the common sampled-token variant is fragile: it reduces distribution matching to a one-token signal and becomes increasingly unreliable as rollouts drift away from prefixes the teacher commonly visits. We revisit OPD from the estimator and implementation sides. Theoretically, token-level OPD is biased relative to sequence-level reverse-KL, but it has a much tighter worst-case variance bound; our toy study shows the same tradeoff empirically, with stronger future-reward coupling producing higher gradient variance and less stable learning. Empirically, we identify three failure modes of sampled-token OPD: an imbalanced one-token signal, unreliable teacher guidance on student-generated prefixes, and distortions caused by tokenizer or special-token mismatch. We address these issues with teacher top-K local support matching, implemented as truncated reverse-KL with top-p rollout sampling and special-token masking. Across single-task math reasoning and multi-task agentic-plus-math training, this objective yields more stable optimization and better downstream performance than sampled-token OPD.

Token-based masked generative models are gaining popularity for their fast inference time with parallel decoding. While recent token-based approaches achieve competitive performance to diffusion-based models, their generation performance is still suboptimal as they sample multiple tokens simultaneously without considering the dependence among them. We empirically investigate this problem and propose a learnable sampling model, Text-Conditioned Token Selection (TCTS), to select optimal tokens via localized supervision with text information. TCTS improves not only the image quality but also the semantic alignment of the generated images with the given texts. To further improve the image quality, we introduce a cohesive sampling strategy, Frequency Adaptive Sampling (FAS), to each group of tokens divided according to the self-attention maps. We validate the efficacy of TCTS combined with FAS with various generative tasks, demonstrating that it significantly outperforms the baselines in image-text alignment and image quality. Our text-conditioned sampling framework further reduces the original inference time by more than 50% without modifying the original generative model.

Large-scale language models often learn behaviors that are misaligned with user expectations. Generated text may contain offensive or toxic language, contain significant repetition, or be of a different sentiment than desired by the user. We consider the task of unlearning these misalignments by fine-tuning the language model on signals of what not to do. We introduce Quantized Reward Konditioning (Quark), an algorithm for optimizing a reward function that quantifies an (un)wanted property, while not straying too far from the original model. Quark alternates between (i) collecting samples with the current language model, (ii) sorting them into quantiles based on reward, with each quantile identified by a reward token prepended to the language model's input, and (iii) using a standard language modeling loss on samples from each quantile conditioned on its reward token, while remaining nearby the original language model via a KL-divergence penalty. By conditioning on a high-reward token at generation time, the model generates text that exhibits less of the unwanted property. For unlearning toxicity, negative sentiment, and repetition, our experiments show that Quark outperforms both strong baselines and state-of-the-art reinforcement learning methods like PPO (Schulman et al. 2017), while relying only on standard language modeling primitives.