Daily Papers

Recent training-free pruning approaches for Multimodal Large Language Models (MLLMs) effectively cut computational overhead by exploiting visual redundancy or text-vision attention. However, they frequently suffer from semantic degradation due to their task-agnostic design or unreliable attention estimates. Based on our empirical analysis, we have found that this issue arises because salient tokens in shallow layers persistently suppress emerging semantic ones through numerical inertia, leading to premature discarding of signals crucial for deep reasoning. To address the aforementioned issue, from the task-oriented aspects, we first reformulate training-free pruning as a minimization of the distortion in the final task loss and derive a tractable, token-wise upper bound to serve as a surrogate objective. Specifically, this formulation inherently reveals a previously neglected inter-layer term that accounts for gradients across layers. Accordingly, for the implementation, we propose DIPrune, a rank-based framework that employs a dual importance scoring mechanism to jointly optimize intra-layer static feature saliency and inter-layer dynamic semantic evolution. Extensive experiments on LLaVA and Qwen-VL demonstrate that DIPrune consistently achieves state-of-the-art results.

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

Sparse autoencoders (SAEs) are a promising approach to extracting features from neural networks, enabling model interpretability as well as causal interventions on model internals. SAEs generate sparse feature representations using a sparsifying activation function that implicitly defines a set of token-feature matches. We frame the token-feature matching as a resource allocation problem constrained by a total sparsity upper bound. For example, TopK SAEs solve this allocation problem with the additional constraint that each token matches with at most k features. In TopK SAEs, the k active features per token constraint is the same across tokens, despite some tokens being more difficult to reconstruct than others. To address this limitation, we propose two novel SAE variants, Feature Choice SAEs and Mutual Choice SAEs, which each allow for a variable number of active features per token. Feature Choice SAEs solve the sparsity allocation problem under the additional constraint that each feature matches with at most m tokens. Mutual Choice SAEs solve the unrestricted allocation problem where the total sparsity budget can be allocated freely between tokens and features. Additionally, we introduce a new auxiliary loss function, aux_zipf_loss, which generalises the aux_k_loss to mitigate dead and underutilised features. Our methods result in SAEs with fewer dead features and improved reconstruction loss at equivalent sparsity levels as a result of the inherent adaptive computation. More accurate and scalable feature extraction methods provide a path towards better understanding and more precise control of foundation models.

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.

The deployment of Large Language Models (LLMs) faces a critical bottleneck when handling lengthy inputs: the prohibitive memory footprint of the Key Value (KV) cache. To address this bottleneck, the token pruning paradigm leverages attention sparsity to selectively retain a small, critical subset of tokens. However, existing approaches fall short, with static methods risking irreversible information loss and dynamic strategies employing heuristics that insufficiently capture the query-dependent nature of token importance. We propose FASA, a novel framework that achieves query-aware token eviction by dynamically predicting token importance. FASA stems from a novel insight into RoPE: the discovery of functional sparsity at the frequency-chunk (FC) level. Our key finding is that a small, identifiable subset of "dominant" FCs consistently exhibits high contextual agreement with the full attention head. This provides a robust and computationally free proxy for identifying salient tokens. %making them a powerful and efficient proxy for token importance. Building on this insight, FASA first identifies a critical set of tokens using dominant FCs, and then performs focused attention computation solely on this pruned subset. % Since accessing only a small fraction of the KV cache, FASA drastically lowers memory bandwidth requirements and computational cost. Across a spectrum of long-context tasks, from sequence modeling to complex CoT reasoning, FASA consistently outperforms all token-eviction baselines and achieves near-oracle accuracy, demonstrating remarkable robustness even under constraint budgets. Notably, on LongBench-V1, FASA reaches nearly 100\% of full-KV performance when only keeping 256 tokens, and achieves 2.56times speedup using just 18.9\% of the cache on AIME24.

Prompt sensitivity, which refers to how strongly the output of a large language model (LLM) depends on the exact wording of its input prompt, raises concerns among users about the LLM's stability and reliability. In this work, we consider LLMs as multivariate functions and perform a first-order Taylor expansion, thereby analyzing the relationship between meaning-preserving prompts, their gradients, and the log probabilities of the model's next token. We derive an upper bound on the difference between log probabilities using the Cauchy-Schwarz inequality. We show that LLMs do not internally cluster similar inputs like smaller neural networks do, but instead disperse them. This dispersing behavior leads to an excessively high upper bound on the difference of log probabilities between two meaning-preserving prompts, making it difficult to effectively reduce to 0. In our analysis, we also show which types of meaning-preserving prompt variants are more likely to introduce prompt sensitivity risks in LLMs. In addition, we demonstrate that the upper bound is strongly correlated with an existing prompt sensitivity metric, PromptSensiScore. Moreover, by analyzing the logit variance, we find that prompt templates typically exert a greater influence on logits than the questions themselves. Overall, our results provide a general interpretation for why current LLMs can be highly sensitive to prompts with the same meaning, offering crucial evidence for understanding the prompt sensitivity of LLMs. Code for experiments is available at https://github.com/ku-nlp/Understanding_the_Prompt_Sensitivity.

Inference-time scaling via chain-of-thought (CoT) reasoning is a major driver of state-of-the-art LLM performance, but it comes with substantial latency and compute costs. We address a fundamental theoretical question: how many reasoning tokens are required to solve a problem as input size grows? By extending the bounded attention prefix oracle (BAPO) model--an abstraction of LLMs that quantifies the information flow required to solve a task--we prove lower bounds on the CoT tokens required for three canonical BAPO-hard tasks: binary majority, triplet matching, and graph reachability. We show that each requires Ω(n) reasoning tokens when the input size is n. We complement these results with matching or near-matching upper bounds via explicit constructions. Finally, our experiments with frontier reasoning models show approximately linear reasoning token scaling on these tasks and failures when constrained to smaller reasoning budgets, consistent with our theoretical lower bounds. Together, our results identify fundamental bottlenecks in inference-time compute through CoT and offer a principled tool for analyzing optimal reasoning length.

We provide new estimates of an asymptotic upper bound on the entropy of English using the large language model LLaMA-7B as a predictor for the next token given a window of past tokens. This estimate is significantly smaller than currently available estimates in cover1978convergent, lutati2023focus. A natural byproduct is an algorithm for lossless compression of English text which combines the prediction from the large language model with a lossless compression scheme. Preliminary results from limited experiments suggest that our scheme outperforms state-of-the-art text compression schemes such as BSC, ZPAQ, and paq8h.

We classify and re-examine some of the current approaches to improve the performance-computes trade-off of language models, including (1) non-causal models (such as masked language models), (2) extension of batch length with efficient attention, (3) recurrence, (4) conditional computation and (5) retrieval. We identify some limitations (1) - (4) suffer from. For example, (1) currently struggles with open-ended text generation with the output loosely constrained by the input as well as performing general textual tasks like GPT-2/3 due to its need for a specific fine-tuning dataset. (2) and (3) do not improve the prediction of the first sim 10^3 tokens. Scaling up a model size (e.g. efficiently with (4)) still results in poor performance scaling for some tasks. We argue (5) would resolve many of these limitations, and it can (a) reduce the amount of supervision and (b) efficiently extend the context over the entire training dataset and the entire past of the current sample. We speculate how to modify MARGE to perform unsupervised causal modeling that achieves (b) with the retriever jointly trained.

Mid-prefill pruning can reduce the sequence processed by deeper transformer layers, but attention concentration alone does not certify that discarded context is dispensable. We formulate EntroPrefill as a Renyi-guided proposal mechanism coupled to explicit constraints on discarded attention mass. Sink-isolated, regularized head pooling respects grouped-query attention while exposing a quantitative trade-off between specialization and worst-head coverage. We derive a mixture-to-head deletion envelope, a computable upper bound on feasible token removal, and a finite-sample observer guarantee that remains valid when the pruning layer is selected adaptively. We then establish a conditional transformer perturbation bound with explicit sufficient Lipschitz constants and a first-token decision-margin corollary. A counterexample shows why shallow observations alone cannot imply an unconditional future-output guarantee. The systems analysis distinguishes query-head unions, physical page allocation, and KV-transfer payload, and gives an arithmetic break-even condition for pruning. This manuscript is theoretical in scope: it defines the procedure, its assumptions, and its formal limits, but does not report measured acceleration or task-accuracy preservation. Experiments are reserved for subsequent validation of the assumptions, approximation tightness, and end-to-end resource trade-offs.

Fine tuning has been regarded as a de facto approach for adapting large language models (LLMs) to downstream tasks, but the high training memory consumption inherited from LLMs makes this process inefficient. Among existing memory efficient approaches, activation-related optimization has proven particularly effective, as activations consistently dominate overall memory consumption. Although prior arts offer various activation optimization strategies, their data-agnostic nature ultimately results in ineffective and unstable fine tuning. In this paper, we propose TokenSeek, a universal plugin solution for various transformer-based models through instance-aware token seeking and ditching, achieving significant fine-tuning memory savings (e.g., requiring only 14.8% of the memory on Llama3.2 1B) with on-par or even better performance. Furthermore, our interpretable token seeking process reveals the underlying reasons for its effectiveness, offering valuable insights for future research on token efficiency. Homepage: https://runjia.tech/iclr_tokenseek/

Large Language Models (LLMs) have benefited enormously from scaling, yet these gains are bounded by five fundamental limitations: (1) hallucination, (2) context compression, (3) reasoning degradation, (4) retrieval fragility, and (5) multimodal misalignment. While existing surveys describe these phenomena empirically, they lack a rigorous theoretical synthesis connecting them to the foundational limits of computation, information, and learning. This work closes that gap by presenting a unified, proof-informed framework that formalizes the innate theoretical ceilings of LLM scaling. First, computability and uncomputability imply an irreducible residue of error: for any computably enumerable model family, diagonalization guarantees inputs on which some model must fail, and undecidable queries (e.g., halting-style tasks) induce infinite failure sets for all computable predictors. Second, information-theoretic and statistical constraints bound attainable accuracy even on decidable tasks, finite description length enforces compression error, and long-tail factual knowledge requires prohibitive sample complexity. Third, geometric and computational effects compress long contexts far below their nominal size due to positional under-training, encoding attenuation, and softmax crowding. We further show how likelihood-based training favors pattern completion over inference, how retrieval under token limits suffers from semantic drift and coupling noise, and how multimodal scaling inherits shallow cross-modal alignment. Across sections, we pair theorems and empirical evidence to outline where scaling helps, where it saturates, and where it cannot progress, providing both theoretical foundations and practical mitigation paths like bounded-oracle retrieval, positional curricula, and sparse or hierarchical attention.

A unique aspect of ColBERT is its use of [MASK] tokens in queries to score documents (query augmentation). Prior work shows [MASK] tokens weighting non-[MASK] query terms, emphasizing certain tokens over others , rather than introducing whole new terms as initially proposed. We begin by demonstrating that a term weighting behavior previously reported for [MASK] tokens in ColBERTv1 holds for ColBERTv2. We then examine the effect of changing the number of [MASK] tokens from zero to up to four times past the query input length used in training, both for first stage retrieval, and for scoring candidates, observing an initial decrease in performance with few [MASK]s, a large increase when enough [MASK]s are added to pad queries to an average length of 32, then a plateau in performance afterwards. Additionally, we compare baseline performance to performance when the query length is extended to 128 tokens, and find that differences are small (e.g., within 1% on various metrics) and generally statistically insignificant, indicating performance does not collapse if ColBERT is presented with more [MASK] tokens than expected.

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

Speculative decoding accelerates large language model inference by drafting multiple candidate tokens and verifying them in a single forward pass. Candidates are organized as a tree: deeper trees accept more tokens per step, but adding depth requires sacrificing breadth (fallback options) under a fixed verification budget. Existing training-free methods draft from a single token source and shape their trees without distinguishing candidate quality across origins. We observe that two common training-free token sources - n-gram matches copied from the input context, and statistical predictions from prior forward passes - differ dramatically in acceptance rate (~6x median gap, range 2-18x across five models and five benchmarks). We prove that when such a quality gap exists, the optimal tree is anisotropic (asymmetric): reliable tokens should form a deep chain while unreliable tokens spread as wide branches, breaking through the depth limit of balanced trees. We realize this structure in GOOSE, a training-free framework that builds an adaptive spine tree - a deep chain of high-acceptance context-matched tokens with wide branches of low-acceptance alternatives at each node. We prove that the number of tokens accepted per step is at least as large as that of either source used alone. On five LLMs (7B-33B) and five benchmarks, GOOSE achieves 1.9-4.3x lossless speedup, outperforming balanced-tree baselines by 12-33% under the same budget.

Modern language models can contain billions of parameters, raising the question of whether they can generalize beyond the training data or simply regurgitate their training corpora. We provide the first non-vacuous generalization bounds for pretrained large language models (LLMs), indicating that language models are capable of discovering regularities that generalize to unseen data. In particular, we derive a compression bound that is valid for the unbounded log-likelihood loss using prediction smoothing, and we extend the bound to handle subsampling, accelerating bound computation on massive datasets. To achieve the extreme level of compression required for non-vacuous generalization bounds, we devise SubLoRA, a low-dimensional non-linear parameterization. Using this approach, we find that larger models have better generalization bounds and are more compressible than smaller models.

Token-level adaptive computation seeks to reduce inference cost by allocating more computation to harder tokens and less to easier ones. However, prior work is primarily evaluated on natural-language benchmarks using task-level metrics, where token-level difficulty is unobservable and confounded with architectural factors, making it unclear whether compute allocation truly aligns with underlying complexity. We address this gap through three contributions. First, we introduce a complexity-controlled evaluation paradigm using algorithmic and synthetic language tasks with parameterized difficulty, enabling direct testing of token-level compute allocation. Second, we propose ANIRA, a unified recurrent Transformer framework that supports per-token variable-depth computation while isolating compute allocation decisions from other model factors. Third, we use this framework to conduct a systematic analysis of token-level adaptive computation across alignment with complexity, generalization, and decision timing. Our results show that compute allocation aligned with task complexity can emerge without explicit difficulty supervision, but such alignment does not imply algorithmic generalization: models fail to extrapolate to unseen input sizes despite allocating additional computation. We further find that early compute decisions rely on static structural cues, whereas online halting more closely tracks algorithmic execution state.

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.

Deploying transformer models in practice is challenging due to their inference cost, which scales quadratically with input sequence length. To address this, we present a novel Learned Token Pruning (LTP) method which adaptively removes unimportant tokens as an input sequence passes through transformer layers. In particular, LTP prunes tokens with an attention score below a threshold value which is learned for each layer during training. Our threshold-based method allows the length of the pruned sequence to vary adaptively based on the input sequence, and avoids algorithmically expensive operations such as top-k token selection. We extensively test the performance of LTP on GLUE tasks and show that our method outperforms the prior state-of-the-art token pruning methods by up to ~2.5% higher accuracy with the same amount of FLOPs. In particular, LTP achieves up to 2.1x FLOPs reduction with less than 1% accuracy drop, which results in up to 1.9x and 2.0x throughput improvement on Intel Haswell CPUs and NVIDIA V100 GPUs, respectively. Furthermore, we demonstrate that LTP is more robust than prior methods to variations on input sentence lengths. Our code has been developed in PyTorch and has been open-sourced.

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.

Recent studies show that in supervised fine-tuning (SFT) of large language models (LLMs), data quality matters more than quantity. While most data cleaning methods concentrate on filtering entire samples, the quality of individual tokens within a sample can vary significantly. After pre-training, even in high-quality samples, patterns or phrases that are not task-related can be redundant, uninformative, or even harmful. Continuing to fine-tune on these patterns may offer limited benefit and even degrade downstream task performance. In this paper, we investigate token quality from a noisy-label perspective and propose a generic token cleaning pipeline for SFT tasks. Our method filters out uninformative tokens while preserving those carrying key task-specific information. Specifically, we first evaluate token quality by examining the influence of model updates on each token, then apply a threshold-based separation. The token influence can be measured in a single pass with a fixed reference model or iteratively with self-evolving reference models. The benefits and limitations of both methods are analyzed theoretically by error upper bounds. Extensive experiments show that our framework consistently improves downstream performance. Code is available at https://github.com/UCSC-REAL/TokenCleaning.

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.

Large language models display remarkable capabilities in logical and mathematical reasoning, allowing them to solve complex tasks. Interestingly, these abilities emerge in networks trained on the simple task of next-token prediction. In this work, we present a theoretical framework for studying auto-regressive next-token predictors. We demonstrate that even simple models such as linear next-token predictors, trained on Chain-of-Thought (CoT) data, can approximate any function efficiently computed by a Turing machine. We introduce a new complexity measure -- length complexity -- which measures the number of intermediate tokens in a CoT sequence required to approximate some target function, and analyze the interplay between length complexity and other notions of complexity. Finally, we show experimentally that simple next-token predictors, such as linear networks and shallow Multi-Layer Perceptrons (MLPs), display non-trivial performance on text generation and arithmetic tasks. Our results demonstrate that the power of language models can be attributed, to a great extent, to the auto-regressive next-token training scheme, and not necessarily to a particular choice of architecture.

A range of recent works addresses the problem of compression of sequence of tokens into a shorter sequence of real-valued vectors to be used as inputs instead of token embeddings or key-value cache. These approaches allow to reduce the amount of compute in existing language models. Despite relying on powerful models as encoders, the maximum attainable lossless compression ratio is typically not higher than x10. This fact is highly intriguing because, in theory, the maximum information capacity of large real-valued vectors is far beyond the presented rates even for 16-bit precision and a modest vector size. In this work, we explore the limits of compression by replacing the encoder with a per-sample optimization procedure. We show that vectors with compression ratios up to x1500 exist, which highlights two orders of magnitude gap between existing and practically attainable solutions. Furthermore, we empirically show that the compression limits are determined not by the length of the input but by the amount of uncertainty to be reduced, namely, the cross-entropy loss on this sequence without any conditioning. The obtained limits highlight the substantial gap between the theoretical capacity of input embeddings and their practical utilization, suggesting significant room for optimization in model design.

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.

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.

User representation learning in real-world industrial scenarios is commonly scaled by increasing user amount, behavioral sequence length and model size. However, existing methods face two challenges: (i) Bottleneck for raw data scaling at billion-scale capacity, as performance exhibit diminishing performance gains with larger-scale raw text user behavioral input, which can be mitigated by tokenization. (ii) Lack of quantitative analysis of how tokenization configurations should scale with data size. In this report, we propose User Behavioral Densing Law for characterizing the quantitative relationship between data scale and the minimum sufficient tokenization capacity. Firstly, we conduct a pilot study on raw & tokenized scaling comparison on billion-scale Alipay dataset, revealing the raw data scaling bottleneck and the sustained gains enabled by tokenization. To derive the scaling pattern governing the minimum sufficient tokenization configuration at different data scales, theoretical analysis and systematic experiments are employed to summarize the quantitative scaling pattern. We find an approximately linear relationship between the logarithms of minimum sufficient tokenization capacity and input data size measured by tokens, and the scaling slope varies systematically with the tokenization method and data source, reflecting differences in representation-space redundancy and intra-source uniqueness. Guided by the proposed law, we further develop ALGN, an adaptive variable-length tokenization method that improves capacity allocation. Extensive experiments across diverse data sources, tokenization methods, and downstream tasks demonstrate the generalizability and reliability of the User Behavioral Densing Law, providing practical guidance for tokenization configuration selection in large-scale user representation learning. Moreover, ALGN outperforms existing baselines.

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.

Deploying pre-trained transformer models like BERT on downstream tasks in resource-constrained scenarios is challenging due to their high inference cost, which grows rapidly with input sequence length. In this work, we propose a constraint-aware and ranking-distilled token pruning method ToP, which selectively removes unnecessary tokens as input sequence passes through layers, allowing the model to improve online inference speed while preserving accuracy. ToP overcomes the limitation of inaccurate token importance ranking in the conventional self-attention mechanism through a ranking-distilled token distillation technique, which distills effective token rankings from the final layer of unpruned models to early layers of pruned models. Then, ToP introduces a coarse-to-fine pruning approach that automatically selects the optimal subset of transformer layers and optimizes token pruning decisions within these layers through improved L_0 regularization. Extensive experiments on GLUE benchmark and SQuAD tasks demonstrate that ToP outperforms state-of-the-art token pruning and model compression methods with improved accuracy and speedups. ToP reduces the average FLOPs of BERT by 8.1x while achieving competitive accuracy on GLUE, and provides a real latency speedup of up to 7.4x on an Intel CPU.

Long-context inference in large language models is bottlenecked by the quadratic cost of full attention. Existing efficient alternatives often rely either on native sparse training or on heuristic token eviction, creating an undesirable trade-off among efficiency, training cost, and accuracy. In this work, we show that full-attention LLMs are already intrinsically sparse and can be transformed into highly sparse models with only minimal adaptation. Our approach is built on three observations: (1) only a small subset of attention heads truly requires full long-context processing; (2) long-range retrieval is governed primarily by a low-dimensional subspace, allowing relevant tokens to be retrieved efficiently with a 16-dimensional indexer; and (3) the useful token budget is strongly query-dependent, making dynamic top-p selection more suitable than fixed top-k sparsification. Based on these insights, we propose RTPurbo, which retains the full KV cache only for retrieval heads and introduces a lightweight token indexer for sparse attention. By exploiting the model's intrinsic sparsity, RTPurbo achieves sparsification with only a few hundred training steps. Experiments on long-context benchmarks and reasoning tasks show that RTPurbo preserves near-lossless accuracy while delivering substantial efficiency gains, including up to a 9.36times prefill speedup at 1M context and about a 2.01times decode speedup. These results suggest that strong sparse inference can be obtained from standard full-attention training without expensive native sparse pretraining.

Large Language Models (LLMs) typically generate outputs token by token using a fixed compute budget, leading to inefficient resource utilization. To address this shortcoming, recent advancements in mixture of expert (MoE) models, speculative decoding, and early exit strategies leverage the insight that computational demands can vary significantly based on the complexity and nature of the input. However, identifying optimal routing patterns for dynamic execution remains an open challenge, limiting the full potential of these adaptive methods. To address this need, we study adaptive computation in LLMs more systematically. We propose a novel framework that integrates smaller auxiliary modules within each Feed-Forward Network layer of the LLM. This design enables dynamic routing of tokens based on task complexity: tokens can be processed by either the small or big modules at each layer, or even bypass certain layers entirely. This allows us to introduce a novel notion of a token's difficulty, defined by its potential to benefit from additional computational resources. Importantly, by employing oracles to identify optimal patterns of adaptive computations, we gain valuable insights into the internal workings of LLMs and the routing processes in a simplified heterogeneous MoE setup. We show that trained routers operate differently from oracles and often yield suboptimal solutions. Notably, activating a large module in just one layer outperforms models that use large modules across all layers, underscoring the gap between practical implementations of routing in MoE models and theoretical optima for adaptive computation.

Large language model (LLM) tokenizers act as structured compressors: by mapping text to discrete token sequences, they determine token count (and thus compute and context usage) and the statistical structure seen by downstream models. Despite their central role in LLM pipelines, the link between tokenization, compression efficiency and induced structure is not well understood. We empirically demonstrate that tokenizer training scale redistributes entropy: as training data grows, the token stream becomes more diverse in aggregate (higher unigram entropy) yet markedly more predictable in-context (lower higher-order conditional entropies), indicating that tokenization absorbs substantial short-range regularity although these gains degrade under train-test domain mismatch. To ground these observations, we first benchmark i) pretrained GPT-family tokenizers as black-box compressors across various domains, and ii) learned tokenizers across configurations spanning vocabulary size, training scale, and domain. Next, we study tokenization as a transform for universal compression and introduce a compression-aware BPE variant. Finally, we adopt a channel lens and introduce capacity-utilization metrics to analyze tokenizer behaviour and outline implications for downstream modeling. Put together, our results expose various trade-offs between compression, induced structure, and robustness under domain shift, and motivate principled, compression-aware tokenizer design.

The deployment of large language models (LLMs) in real-world applications is increasingly limited by their high inference cost. While recent advances in dynamic token-level computation allocation attempt to improve efficiency by selectively activating model components per token, existing methods rely on greedy routing--a myopic execute-or-skip mechanism that often leads to irreversible information loss and suboptimal token selection. This paper introduces informed routing, a new paradigm that proactively addresses these issues. The key insight is to assess not only a token's immediate importance but also its recoverability, i.e., how well its transformation can be approximated. To this end, we propose the Lightweight Feature Forecaster (LFF), a small predictive module that estimates a unit's output before routing decisions are made. This enables a flexible execute-or-approximate policy that preserves model fidelity while drastically reducing computation. Extensive experiments on both language modeling and reasoning tasks show that informed routing achieves state-of-the-art efficiency-performance trade-offs across multiple sparsity levels. Notably, even without final LoRA fine-tuning, our method matches or surpasses strong baselines that require full fine-tuning, all while reducing training time by over 50%. The code is available at: https://github.com/EIT-NLP/informed-routing

Generative recommender systems have recently attracted attention by formulating next-item prediction as an autoregressive sequence generation task. However, most existing methods optimize standard next-token likelihood and implicitly treat all tokens as equally informative, which is misaligned with semantic-ID-based generation. Accordingly, we propose two complementary information-gain-based token-weighting strategies tailored to generative recommendation with semantic IDs. Front-Greater Weighting captures conditional semantic information gain by prioritizing early tokens that most effectively reduce candidate-item uncertainty given their prefixes and encode coarse semantics. Frequency Weighting models marginal information gain under long-tailed item and token distributions, upweighting rare tokens to counteract popularity bias. Beyond individual strategies, we introduce a multi-target learning framework with curriculum learning that jointly optimizes the two token-weighted objectives alongside standard likelihood, enabling stable optimization and adaptive emphasis across training stages. Extensive experiments on benchmark datasets show that our method consistently outperforms strong baselines and existing token-weighting approaches, with improved robustness, strong generalization across different semantic-ID constructions, and substantial gains on both head and tail items. Code is available at https://github.com/CHIUWEINING/Token-Weighted-Multi-Target-Learning-for-Generative-Recommenders-with-Curriculum-Learning.

We introduce BigO(Bench), a novel coding benchmark designed to evaluate the capabilities of generative language models in understanding and generating code with specified time and space complexities. This benchmark addresses the gap in current evaluations that often overlook the ability of models to comprehend and produce code constrained by computational complexity. BigO(Bench) includes tooling to infer the algorithmic complexity of any Python function from profiling measurements, including human- or LLM-generated solutions. BigO(Bench) also includes of set of 3,105 coding problems and 1,190,250 solutions from Code Contests annotated with inferred (synthetic) time and space complexity labels from the complexity framework, as well as corresponding runtime and memory footprint values for a large set of input sizes. We present results from evaluating multiple state-of-the-art language models on this benchmark, highlighting their strengths and weaknesses in handling complexity requirements. In particular, token-space reasoning models are unrivaled in code generation but not in complexity understanding, hinting that they may not generalize well to tasks for which no reward was given at training time.

Multi-Token Prediction (MTP) has been proposed as an auxiliary objective to improve next-token prediction (NTP) in language model training but shows inconsistent improvements, underperforming in standard NLP benchmarks. We argue that MTP's exact future token prediction is too difficult as an auxiliary loss. Instead, we propose Token Order Prediction (TOP), which trains models to order upcoming tokens by their proximity using a learning-to-rank loss. TOP requires only a single additional unembedding layer compared to MTP's multiple transformer layers. We pretrain models of 340M, 1.8B, and 7B parameters using NTP, MTP, and TOP objectives. Results on eight standard NLP benchmarks show that TOP overall outperforms both NTP and MTP even at scale. Our code is available at https://github.com/zaydzuhri/token-order-prediction

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

We introduce the finite-horizon first-order rank profile of a language L subseteq Σ^*: the least quantifier rank needed by an FO[<] sentence to classify membership in L correctly on all words of length at most n. The invariant measures quantifier depth only; formula size is deliberately not bounded. First, we prove a rank calculus that is independent of regularity. Every language satisfies ρ_L(n) le lceil log_2 n rceil + 4, via balanced first-order distance formulas and exact-word definitions. Moreover, sup_n ρ_L(n) < infty holds exactly when L is globally FO[<]-definable, and the supremum equals the minimum quantifier rank of such a definition. Second, for regular languages we prove a sharp aperiodicity gap: if the syntactic monoid of L is aperiodic, then ρ_L(n) = O(1); otherwise ρ_L(n) = log_2 n + O_L(1). The lower bound extracts a nontrivial cyclic component from the syntactic monoid and combines it with an Ehrenfeucht-Fraisse power lemma for long repetitions of a fixed word. Thus, for full FO[<] quantifier rank, regular languages admit no intermediate finite-horizon growth between bounded and logarithmic rank.

Sparse attention visits few keys, yet finding them can still require scoring every key with every indexer head. We introduce DoSA (Dots Sparse Attention), a lossless method for making this computation conditional while preserving exact token selection. Its central observation is that Top-K selection requires sufficient evidence to reject a candidate, not necessarily its full score. A seed set supplies a lower bound on the winning threshold. Nonnegative head projections and joint residual bounds upper-bound positive contributions, while activation-informed aggregation bounds the magnitude subtracted by negative heads. The certificate directs full scoring toward candidates that remain eligible; exact-score filtering further reduces writeback and selection work. We establish the certificate and its exact-selection conditions, and analyze how geometry and selection margins govern its effectiveness. Our GPU implementation accelerates the complete Indexer by up to 2.74 times over SGLang and 1.69 times over LiteTopK across English, Chinese, and code workloads. End-to-end evaluation on GLM-5.2 and DeepSeek-V3.2 achieves up to 1.94 times and 1.50 times time-to-first-token speedups over the two baselines, respectively.

Large Language Models (LLMs) are increasingly used in production systems, powering applications such as chatbots, summarization, and question answering. Despite their success, controlling the length of their response remains a significant challenge, particularly for tasks requiring structured outputs or specific levels of detail. In this work, we propose a method to adapt pre-trained decoder-only LLMs for precise control of response length. Our approach incorporates a secondary length-difference positional encoding (LDPE) into the input embeddings, which counts down to a user-set response termination length. Fine-tuning with LDPE allows the model to learn to terminate responses coherently at the desired length, achieving mean token errors of less than 3 tokens. We also introduce Max New Tokens++, an extension that enables flexible upper-bound length control, rather than an exact target. Experimental results on tasks such as question answering and document summarization demonstrate that our method enables precise length control without compromising response quality.

As the context limits of Large Language Models (LLMs) increase, the range of possible applications and downstream functions broadens. In many real-world tasks, decisions depend on details scattered across collections of often disparate documents containing mostly irrelevant information. Long-context LLMs appear well-suited to this form of complex information retrieval and reasoning, which has traditionally proven costly and time-consuming. However, although the development of longer context models has seen rapid gains in recent years, our understanding of how effectively LLMs use their context has not kept pace. To address this, we conduct a set of retrieval experiments designed to evaluate the capabilities of 17 leading LLMs, such as their ability to follow threads of information through the context window. Strikingly, we find that many models are remarkably threadsafe: capable of simultaneously following multiple threads without significant loss in performance. Still, for many models, we find the effective context limit is significantly shorter than the supported context length, with accuracy decreasing as the context window grows. Our study also highlights the important point that token counts from different tokenizers should not be directly compared -- they often correspond to substantially different numbers of written characters. We release our code and long-context experimental data.

With the development of large language models (LLMs), the ability to handle longer contexts has become a key capability for Web applications such as cross-document understanding and LLM-powered search systems. However, this progress faces two major challenges: performance degradation due to sequence lengths out-of-distribution, and excessively long inference times caused by the quadratic computational complexity of attention. These issues hinder the application of LLMs in long-context scenarios. In this paper, we propose Dynamic Token-Level KV Cache Selection (TokenSelect), a model-agnostic, training-free method for efficient and accurate long-context inference. TokenSelect builds upon the observation of non-contiguous attention sparsity, using Query-Key dot products to measure per-head KV Cache criticality at token-level. By per-head soft voting mechanism, TokenSelect selectively involves a small number of critical KV cache tokens in the attention calculation without sacrificing accuracy. To further accelerate TokenSelect, we designed the Selection Cache based on observations of consecutive Query similarity and implemented efficient dot product kernel, significantly reducing the overhead of token selection. A comprehensive evaluation of TokenSelect demonstrates up to 23.84x speedup in attention computation and up to 2.28x acceleration in end-to-end latency, while providing superior performance compared to state-of-the-art long-context inference methods.

Large language models (LLMs) reach high accuracy in mathematical reasoning, but individual traces on the same problem diverge; some arrive at the correct answer while others fail. Prior work analyzes failure at the step, chunk, or sentence level, or at tokens where failure has already occurred. Neither identifies the precise token that triggers the shift toward failure. We introduce the cliff token, a token where the token-wise potential drops significantly under an adaptive threshold that scales with the local token-wise potential, based on a one-sided two-proportion z-test. Across seven models and three mathematical reasoning benchmarks (GSM1K, MATH500, AIME 2025), cliff tokens act as failure triggers; deleting the first cliff token and resampling recovers pass@64 to 1.0, while keeping it limits recovery to between 0.71 and 1.00. We further introduce a cliff taxonomy of deterministic, uncertain, and sampled-off cliffs, defined by greedy choice and token entropy. Each type has distinct probabilistic characteristics, and the taxonomy generalizes across model scales. Finally, we validate the taxonomy via single-token preference optimization at cliff positions (Cliff-DPO). Trained on GSM8K, Cliff-DPO improves accuracy across benchmarks by up to +6.6. Optimizing at uncertain and sampled-off cliffs improves reasoning, while deterministic cliffs do not.

We study three complementary techniques for training compute-efficient language models. (1) Selective supervision and per-token efficiency. Selective Ground Truth Token Training (SGT) concentrates supervision on the ~15% of output tokens that carry semantic payload. Through positive gradient coupling in position-shared transformer weights -- a token-level instance of auxiliary-task transfer -- the remaining 85% of unsupervised tokens still improve substantially, giving a 4.5x per-supervised-token efficiency (at the step-100 eval optimum, ~67% of the full-sequence loss reduction is recovered from 15% of the supervision). We prove that this improvement on unsupervised tokens is guaranteed whenever the gradient coupling coefficient gamma-bar = 0.72 is positive (Theorem 1), and show the effect is a property of natural-language structure: it collapses on shuffled text. (2) Depth compression with recurrent recovery. A 48-layer, 1B-parameter transformer is compressed to 6 layers (227M) by averaging adjacent layers and restored through learned recurrent unrolling. With 34 effective recurrent layers it reaches a held-out loss of 2.934, within measurement noise of a 566M dense model at 2.926 -- a 2.5x reduction in parameters. (3) Fusion of compressed experts. Assembling several compressed models as a Mixture of Efficient Experts (MoEE) with multi-token prediction improves over each single expert at comparable active parameters: a 2-expert MoEE reaches loss 2.789 versus 2.926 for the best single compressed model. We validate these techniques on CHERRY-1.8B, a Korean foundation model whose every trainable parameter derives from our own training runs. We are explicit throughout about the scope of the evidence (one model family, Korean data, loss-based metrics) and about which claims are established versus prospective.

Large language models (LLMs) typically employ greedy decoding or low-temperature sampling for reasoning tasks, reflecting a perceived trade-off between diversity and accuracy. We challenge this convention by introducing top-nsigma, a novel sampling method that operates directly on pre-softmax logits by leveraging a statistical threshold. Our key insight is that logits naturally separate into a Gaussian-distributed noisy region and a distinct informative region, enabling efficient token filtering without complex probability manipulations. Unlike existing methods (e.g., top-p, min-p) that inadvertently include more noise tokens at higher temperatures, top-nsigma maintains a stable sampling space regardless of temperature scaling. We also provide a theoretical analysis of top-nsigma to better understand its behavior. The extensive experimental results across four reasoning-focused datasets demonstrate that our method not only outperforms existing sampling approaches but also surpasses greedy decoding, while maintaining consistent performance even at high temperatures.

Large language models (LLMs) have shown remarkable performance in various natural language processing tasks. However, a primary constraint they face is the context limit, i.e., the maximum number of tokens they can process. Previous works have explored architectural changes and modifications in positional encoding to relax the constraint, but they often require expensive training or do not address the computational demands of self-attention. In this paper, we present Hierarchical cOntext MERging (HOMER), a new training-free scheme designed to overcome the limitations. HOMER uses a divide-and-conquer algorithm, dividing long inputs into manageable chunks. Each chunk is then processed collectively, employing a hierarchical strategy that merges adjacent chunks at progressive transformer layers. A token reduction technique precedes each merging, ensuring memory usage efficiency. We also propose an optimized computational order reducing the memory requirement to logarithmically scale with respect to input length, making it especially favorable for environments with tight memory restrictions. Our experiments demonstrate the proposed method's superior performance and memory efficiency, enabling the broader use of LLMs in contexts requiring extended context. Code is available at https://github.com/alinlab/HOMER.

The opacity of massive pretraining corpora in Large Language Models (LLMs) raises significant privacy and copyright concerns, making pretraining data detection a critical challenge. Existing state-of-the-art methods typically rely on token likelihoods, yet they often overlook the gap between the target token and the model's top-1 prediction, as well as local correlations between adjacent tokens. In this work, we propose Gap-K%, a novel pretraining data detection method grounded in the optimization dynamics of LLM pretraining. By analyzing the next-token prediction objective, we observe that discrepancies between the model's top-1 prediction and the target token induce strong gradient signals, which are explicitly penalized during training. Motivated by this, Gap-K% leverages the log probability gap between the top-1 predicted token and the target token, incorporating a sliding window strategy to capture local correlations and mitigate token-level fluctuations. Extensive experiments on the WikiMIA and MIMIR benchmarks demonstrate that Gap-K% achieves state-of-the-art performance, consistently outperforming prior baselines across various model sizes and input lengths.

Byte-Pair Encoding (BPE) is a popular algorithm used for tokenizing data in NLP, despite being devised initially as a compression method. BPE appears to be a greedy algorithm at face value, but the underlying optimization problem that BPE seeks to solve has not yet been laid down. We formalize BPE as a combinatorial optimization problem. Via submodular functions, we prove that the iterative greedy version is a 1{{sigma(mu^star)}}(1-e^{-{sigma(mu^star)}})-approximation of an optimal merge sequence, where {sigma(mu^star)} is the total backward curvature with respect to the optimal merge sequence mu^star. Empirically the lower bound of the approximation is approx 0.37. We provide a faster implementation of BPE which improves the runtime complexity from Oleft(N Mright) to Oleft(N log Mright), where N is the sequence length and M is the merge count. Finally, we optimize the brute-force algorithm for optimal BPE using memoization.

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

Tokenization is 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.

In the classical transformer attention scheme, we are given three n times d size matrices Q, K, V (the query, key, and value tokens), and the goal is to compute a new n times d size matrix D^{-1} exp(QK^top) V where D = diag( exp(QK^top) {bf 1}_n ). In this work, we study a generalization of attention which captures triple-wise correlations. This generalization is able to solve problems about detecting triple-wise connections that were shown to be impossible for transformers. The potential downside of this generalization is that it appears as though computations are even more difficult, since the straightforward algorithm requires cubic time in n. However, we show that in the bounded-entry setting (which arises in practice, and which is well-studied in both theory and practice), there is actually a near-linear time algorithm. More precisely, we show that bounded entries are both necessary and sufficient for quickly performing generalized computations: bullet On the positive side, if all entries of the input matrices are bounded above by o(sqrt[3]{log n}) then we show how to approximate the ``tensor-type'' attention matrix in n^{1+o(1)} time. bullet On the negative side, we show that if the entries of the input matrices may be as large as Omega(sqrt[3]{log n}), then there is no algorithm that runs faster than n^{3-o(1)} (assuming the Strong Exponential Time Hypothesis from fine-grained complexity theory). We also show that our construction, algorithms, and lower bounds naturally generalize to higher-order tensors and correlations. Interestingly, the higher the order of the tensors, the lower the bound on the entries needs to be for an efficient algorithm. Our results thus yield a natural tradeoff between the boundedness of the entries, and order of the tensor one may use for more expressive, efficient attention computation.

We introduce a new tokenizer for language models that minimizes the average tokens per character, thereby reducing the number of tokens needed to represent text during training and to generate text during inference. Our method, which we refer to as the Length-MAX tokenizer, obtains its vocabulary by casting a length-weighted objective maximization as a graph partitioning problem and developing a greedy approximation algorithm. On FineWeb and diverse domains, it yields 14--18\% fewer tokens than Byte Pair Encoding (BPE) across vocabulary sizes from 10K to 50K, and the reduction is 13.0\% when the size is 64K. Training GPT-2 models at 124M, 355M, and 1.3B parameters from scratch with five runs each shows 18.5\%, 17.2\%, and 18.5\% fewer steps, respectively, to reach a fixed validation loss, and 13.7\%, 12.7\%, and 13.7\% lower inference latency, together with a 16\% throughput gain at 124M, while consistently improving on downstream tasks including reducing LAMBADA perplexity by 11.7\% and enhancing HellaSwag accuracy by 4.3\%. Moreover, the Length-MAX tokenizer achieves 99.62\% vocabulary coverage and the out-of-vocabulary rate remains low at 0.12\% on test sets. These results demonstrate that optimizing for average token length, rather than frequency alone, offers an effective approach to more efficient language modeling without sacrificing -- and often improving -- downstream performance. The tokenizer is compatible with production systems and reduces embedding and KV-cache memory by 18\% at inference.

Top-k decoding is a widely used method for sampling from LLMs: at each token, only the largest k next-token-probabilities are kept, and the next token is sampled after re-normalizing them to sum to unity. Top-k and other sampling methods are motivated by the intuition that true next-token distributions are sparse, and the noisy LLM probabilities need to be truncated. However, to our knowledge, a precise theoretical motivation for the use of top-k decoding is missing. In this work, we develop a theoretical framework that both explains and generalizes top-k decoding. We view decoding at a fixed token as the recovery of a sparse probability distribution. We consider Bregman decoders obtained by minimizing a separable Bregman divergence (for both the primal and dual cases) with a sparsity-inducing ell_0 regularization. Despite the combinatorial nature of the objective, we show how to optimize it efficiently for a large class of divergences. We show that the optimal decoding strategies are greedy, and further that the loss function is discretely convex in k, so that binary search provably and efficiently finds the optimal k. We show that top-k decoding arises as a special case for the KL divergence, and identify new decoding strategies that have distinct behaviors (e.g., non-linearly up-weighting larger probabilities after re-normalization).

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

Million-level token inputs in long-context tasks pose significant computational and memory challenges for Large Language Models (LLMs). Recently, DeepSeek-OCR conducted research into the feasibility of Contexts Optical Compression and achieved preliminary results. Inspired by this, we introduce Context Cascade Compression C3 to explore the upper limits of text compression. Our method cascades two LLMs of different sizes to handle the compression and decoding tasks. Specifically, a small LLM, acting as the first stage, performs text compression by condensing a long context into a set of latent tokens (e.g., 32 or 64 in length), achieving a high ratio of text tokens to latent tokens. A large LLM, as the second stage, then executes the decoding task on this compressed context. Experiments show that at a 20x compression ratio (where the number of text tokens is 20 times the number of latent tokens), our model achieves 98% decoding accuracy, compared to approximately 60% for DeepSeek-OCR. When we further increase the compression ratio to 40x, the accuracy is maintained at around 93%. This indicates that in the domain of context compression, C3 Compression demonstrates superior performance and feasibility over optical character compression. C3 uses a simpler, pure-text pipeline that ignores factors like layout, color, and information loss from a visual encoder. This also suggests a potential upper bound for compression ratios in future work on optical character compression, OCR, and related fields. Codes and model weights are publicly accessible at https://github.com/liufanfanlff/C3-Context-Cascade-Compression

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

Cross Attention is a popular method for retrieving information from a set of context tokens for making predictions. At inference time, for each prediction, Cross Attention scans the full set of O(N) tokens. In practice, however, often only a small subset of tokens are required for good performance. Methods such as Perceiver IO are cheap at inference as they distill the information to a smaller-sized set of latent tokens L < N on which cross attention is then applied, resulting in only O(L) complexity. However, in practice, as the number of input tokens and the amount of information to distill increases, the number of latent tokens needed also increases significantly. In this work, we propose Tree Cross Attention (TCA) - a module based on Cross Attention that only retrieves information from a logarithmic O(log(N)) number of tokens for performing inference. TCA organizes the data in a tree structure and performs a tree search at inference time to retrieve the relevant tokens for prediction. Leveraging TCA, we introduce ReTreever, a flexible architecture for token-efficient inference. We show empirically that Tree Cross Attention (TCA) performs comparable to Cross Attention across various classification and uncertainty regression tasks while being significantly more token-efficient. Furthermore, we compare ReTreever against Perceiver IO, showing significant gains while using the same number of tokens for inference.

Chain-of-thought prompting has emerged as a powerful technique for enabling large language models (LLMs) to solve complex reasoning tasks. However, these reasoning chains can be verbose, raising concerns about efficiency. In response, recent works have sought to decrease response lengths through simple prompting strategies (e.g. 'be concise'). In this work, we conduct the first systematic study of the relationship between reasoning length and model performance across a diverse range of compression instructions (e.g. 'use 10 words or less' or 'remove all punctuation'). In doing so, we discover a universal tradeoff between reasoning length and accuracy that persists across even very distinct reasoning chains. We demonstrate that this tradeoff emerges from a sharp threshold behavior at the question level: each task has an intrinsic 'token complexity' - a minimal number of tokens required for successful problem-solving. We show how token complexity enables us to compute information-theoretic limits on the accuracy-compression tradeoff, and find that prompt-based compression strategies operate far from these theoretical limits. This suggests there may be significant room for improvement and our framework provides a benchmark to help researchers evaluate progress in reasoning efficiency. Our work also highlights the importance of adaptive compression -- giving shorter responses for easier questions -- and we show that token complexity is a useful tool for measuring this capability.

Scaling laws enable the optimal selection of data amount and language model size, yet the impact of the data unit, the token, on this relationship remains underexplored. In this work, we systematically investigate how the information granularity of tokens, controlled by the compression rate (i.e., average bytes of text per token), affects scaling trends. We train 988 latent tokenized models (BLT) ranging from 50M to 7B parameters that enable setting the desired compression rate. This flexibility allows us to study the role of compression rate well beyond 4.57 bytes per token obtained with a popular BPE tokenizer. Our experiments reveal that in compute-optimal configurations, model parameter counts scale proportionally to data size measured in bytes, not in tokens as commonly perceived (Kaplan et al., 2020; Hoffmann et al., 2022). Furthermore, we discover that the optimal compression rate differs from the one obtained with BPE and decreases with compute. These findings generalize to both latent and subword tokenization, as well as to languages other than English, guiding language model developers on tokenization scheme selection for maximal compute efficiency.

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

Recent work has shown that training loss scales as a power law with both model size and the number of tokens, and that achieving compute-optimal models requires scaling model size and token count together. However, these scaling laws assume an infinite supply of data and apply primarily in compute-bound settings. As modern large language models increasingly rely on massive internet-scale datasets, the assumption that they are compute-bound is becoming less valid. This shift highlights the need for architectures that prioritize token efficiency. In this work, we investigate the use of the 2-simplicial Transformer, an architecture that generalizes standard dot-product attention to trilinear functions through an efficient Triton kernel implementation. We demonstrate that the 2-simplicial Transformer achieves better token efficiency than standard Transformers: for a fixed token budget, similarly sized models outperform their dot-product counterparts on tasks involving mathematics, coding, reasoning, and logic. We quantify these gains by demonstrating that 2-simplicial attention changes the exponent in the scaling laws for knowledge and reasoning tasks compared to dot product attention.

Limited by the context window size of Large Language Models(LLMs), handling various tasks with input tokens exceeding the upper limit has been challenging, whether it is a simple direct retrieval task or a complex multi-hop reasoning task. Although various methods have been proposed to enhance the long-context processing capabilities of LLMs, they either incur substantial post-training costs, or require additional tool modules(e.g.,RAG), or have not shown significant improvement in realistic tasks. Our work observes the correlation between the attention distribution and generated answers across each layer, and establishes the attention allocation aligns with retrieval-augmented capabilities through experiments. Drawing on the above insights, we propose a novel method InfiniRetri that leverages the LLMs's own attention information to enable accurate retrieval across inputs of infinitely length. Our evaluations indicate that InfiniRetri achieves 100% accuracy in the Needle-In-a-Haystack(NIH) test over 1M tokens using a 0.5B parameter model, surpassing other method or larger models and setting a new state-of-the-art(SOTA). Moreover, our method achieves significant performance improvements on real-world benchmarks, with a maximum 288% improvement. In addition, InfiniRetri can be applied to any Transformer-based LLMs without additional training and substantially reduces inference latency and compute overhead in long texts. In summary, our comprehensive studies show InfiniRetri's potential for practical applications and creates a paradigm for retrievaling information using LLMs own capabilities under infinite-length tokens. Code will be released in link.

As large language models (LLMs) process increasing context windows, the memory usage of KV cache has become a critical bottleneck during inference. The mainstream KV compression methods, including KV pruning and KV quantization, primarily focus on either token or precision dimension and seldom explore the efficiency of their combination. In this paper, we comprehensively investigate the token-precision trade-off in KV cache compression. Experiments demonstrate that storing more tokens in the KV cache with lower precision, i.e., quantized pruning, can significantly enhance the long-context performance of LLMs. Furthermore, in-depth analysis regarding token-precision trade-off from a series of key aspects exhibit that, quantized pruning achieves substantial improvements in retrieval-related tasks and consistently performs well across varying input lengths. Moreover, quantized pruning demonstrates notable stability across different KV pruning methods, quantization strategies, and model scales. These findings provide valuable insights into the token-precision trade-off in KV cache compression. We plan to release our code in the near future.

Resource constraints increasingly determine what can be trained, fine-tuned, and deployed in large language models (LLMs), yet efficiency is often studied through isolated techniques rather than as an interacting system of limits. This survey adopts a constraint-centric perspective and organizes recent progress around three coupled bottlenecks: data efficiency (what to train on), memory efficiency (how to fit training), and compute budget awareness (when and where to spend FLOPs). On the data axis, we review selection and pruning methods that maximize learning per token, ranging from scalable proxy signals based on learning dynamics to gradient- and influence-based scoring, as well as difficulty-aware and curriculum-style strategies. We highlight emerging evidence that different notions of good data dominate in different regimes, implying that optimal subsets depend on the task objective and resource budget rather than being universal. On the systems side, we show that GPU memory, not raw compute, is often the dominant bottleneck in fine-tuning, and that effective scaling requires jointly reducing weight storage, optimizer states, and activation memory rather than optimizing any single component in isolation. Beyond memory, we frame training and inference as compute-governed processes in which optimization, data selection, and decoding must explicitly account for finite FLOP budgets. We review evidence for compute-optimal allocation and stopping rules, where computation should be halted or reallocated once marginal performance gains fall below a budget-dependent threshold. Together, these results unify compute-aware data selection, scaling laws, and adaptive inference under a common principle of resource-conditioned decision-making.

The prefill stage in long-context LLM inference remains a computational bottleneck. Recent token-ranking heuristics accelerate inference by selectively processing a subset of semantically relevant tokens. However, existing methods suffer from unstable token importance estimation, often varying between layers. Evaluating token-ranking quality independently from heuristic-specific architectures is challenging. To address this, we introduce an Answer-Informed Oracle, which defines ground-truth token importance by measuring attention from generated answers back to the prompt. This oracle reveals that existing heuristics exhibit high variance across layers: rankings can degrade sharply at specific layers, a failure mode invisible to end-to-end benchmarks. The diagnosis suggests a simple fix: aggregate scores across layers rather than relying on any single one. We implement this as Cross-Layer Attention Aggregation (CLAA), which closes the gap to the oracle upper bound and reduces Time-to-First-Token (TTFT) by up to 39\% compared to the Full KV Cache baseline.

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.

Recent reasoning Large Language Models (LLMs) demonstrate remarkable problem-solving abilities but often generate long thinking traces whose utility is unclear. Our work aims to improve their efficiency, enabling them to reach high performance without overthinking. First, we analyze the entropy of token probabilities in reasoning traces. Across three models, we observe a consistent U-shaped entropy pattern: high entropy on easy problems despite high accuracy, low entropy on problems with medium difficulty, and high entropy on hard problems reflecting uncertainty. Specifically, we notice 22--25\% entropy reduction from easy to medium difficulty regions, suggesting an {overthinking} phenomenon on easy instances. Building on these insights, we introduce DiffAdapt, a lightweight framework that selects Easy/Normal/Hard inference strategies per question based on their difficulty and reasoning trace entropy. Each inference strategy consists of a fixed prompt, temperature and maximum token length. In contrast to existing efficiency optimization methods, our approach does not fine-tune base LLM but a small probe that classifies LLM's final hidden state, allowing inexpensive adaptation. We comprehensively evaluate our method on five models and eight benchmarks. Our method achieves comparable or improved accuracy while reducing token usage by up to 22.4\%, establishing a practical path toward compute-efficient reasoning.

Large language models increasingly rely on long chains of thought to improve accuracy, yet such gains come with substantial inference-time costs. We revisit token-efficient post-training and argue that existing sequence-level reward-shaping methods offer limited control over how reasoning effort is allocated across tokens. To bridge the gap, we propose IAPO, an information-theoretic post-training framework that assigns token-wise advantages based on each token's conditional mutual information (MI) with the final answer. This yields an explicit, principled mechanism for identifying informative reasoning steps and suppressing low-utility exploration. We provide a theoretical analysis showing that our IAPO can induce monotonic reductions in reasoning verbosity without harming correctness. Empirically, IAPO consistently improves reasoning accuracy while reducing reasoning length by up to 36%, outperforming existing token-efficient RL methods across various reasoning datasets. Extensive empirical evaluations demonstrate that information-aware advantage shaping is a powerful and general direction for token-efficient post-training. The code is available at https://github.com/YinhanHe123/IAPO.

Machine unlearning has emerged as a critical capability for addressing privacy, safety, and regulatory concerns in large language models (LLMs). Existing methods operate at the sequence level, applying uniform updates across all tokens despite only a subset encoding the knowledge targeted for removal. This introduces gradient noise, degrades utility, and leads to suboptimal forgetting. We propose TokenUnlearn, a token-level attribution framework that identifies and selectively targets critical tokens. Our approach combines knowledge-aware signals via masking, and entropy-aware signals to yield importance scores for precise token selection. We develop two complementary strategies: hard selection, applying unlearning only to high-importance tokens, and soft weighting, modulating gradient contributions based on importance scores. Both extend existing methods to token-level variants. Theoretical analysis shows token-level selection improves gradient signal-to-noise ratio. Experiments on TOFU and WMDP benchmarks across three model architectures demonstrate consistent improvements over sequence-level baselines in both forgetting effectiveness and utility preservation.

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.

We present Neural Attention Search (NAtS), a framework that automatically evaluates the importance of each token within a sequence and determines if the corresponding token can be dropped after several steps. This approach can efficiently reduce the KV cache sizes required by transformer-based models during inference and thus reduce inference costs. In this paper, we design a search space that contains three token types: (i) Global Tokens will be preserved and queried by all the following tokens. (ii) Local Tokens survive until the next global token appears. (iii) Sliding Window Tokens have an impact on the inference of a fixed size of the next following tokens. Similar to the One-Shot Neural Architecture Search approach, this token-type information can be learned jointly with the architecture weights via a learnable attention mask. Experiments on both training a new transformer from scratch and fine-tuning existing large language models show that NAtS can efficiently reduce the KV cache size required for the models while maintaining the models' performance.

Large language models encode impressively broad world knowledge in their parameters. However, the knowledge in static language models falls out of date, limiting the model's effective "shelf life." While online fine-tuning can reduce this degradation, we find that naively fine-tuning on a stream of documents leads to a low level of information uptake. We hypothesize that online fine-tuning does not sufficiently attend to important information. That is, the gradient signal from important tokens representing factual information is drowned out by the gradient from inherently noisy tokens, suggesting that a dynamic, context-aware learning rate may be beneficial. We therefore propose learning which tokens to upweight. We meta-train a small, autoregressive model to reweight the language modeling loss for each token during online fine-tuning, with the objective of maximizing the out-of-date base question-answering model's ability to answer questions about a document after a single weighted gradient step. We call this approach Context-aware Meta-learned Loss Scaling (CaMeLS). Across three different distributions of documents, our experiments find that CaMeLS provides substantially improved information uptake on streams of thousands of documents compared with standard fine-tuning and baseline heuristics for reweighting token losses.

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.

Increasing demand for Large Language Models (LLMs) services imposes substantial deployment and computation costs on providers. LLM routing offers a cost-efficient solution by directing queries to the optimal LLM based on model and query features. However, existing works primarily focus on offline scenarios and struggle to adapt to online settings with high query volume and constrained token budgets. In this work, we introduce the first training-free algorithm for online routing scenarios. Our algorithm leverages approximate nearest neighbor search to efficiently estimate query features and performs a one-time optimization over a small set of initial queries to learn a routing strategy that guides future routing. We provide theoretical guarantees demonstrating that our algorithm achieves a competitive ratio of 1 - o(1) under natural assumptions, which is further validated by extensive experiments across 3 benchmark datasets and 8 baselines, showing an average improvement of 3.55times in overall performance, 1.85times in cost efficiency, and nearly 4.25times in throughput. Our code is available at https://github.com/fzwark/PORT.

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 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.

Vision tokens in multimodal large language models often dominate huge computational overhead due to their excessive length compared to linguistic modality. Abundant recent methods aim to solve this problem with token pruning, which first defines an importance criterion for tokens and then prunes the unimportant vision tokens during inference. However, in this paper, we show that the importance is not an ideal indicator to decide whether a token should be pruned. Surprisingly, it usually results in inferior performance than random token pruning and leading to incompatibility to efficient attention computation operators.Instead, we propose DART (Duplication-Aware Reduction of Tokens), which prunes tokens based on its duplication with other tokens, leading to significant and training-free acceleration. Concretely, DART selects a small subset of pivot tokens and then retains the tokens with low duplication to the pivots, ensuring minimal information loss during token pruning. Experiments demonstrate that DART can prune 88.9% vision tokens while maintaining comparable performance, leading to a 1.99times and 2.99times speed-up in total time and prefilling stage, respectively, with good compatibility to efficient attention operators. Our codes are available at https://github.com/ZichenWen1/DART.

Code large language models acquire programming capabilities from large code corpora, but can also memorize implementations that later require removal. Code unlearning is needed to control their continued reproduction when copyright or security concerns arise. However, targeted and retained code share computational patterns, creating a tension between forgetting specific implementations and preserving general programming ability. We propose UNBIND, a code unlearning framework that separately considers which hidden states correspond to the target code and how to suppress its reproduction. By constructing separate directions for these objectives, UNBIND achieves selective unlearning at inference time while keeping model weights fixed. Our evaluation covers fourteen baselines across two code models and two corpora. UNBIND achieves the highest joint forgetting and utility score in every setting. It reduces target code reproduction by 97.3\% to 99.1\% as measured by F-BLEU, with at most two fewer HumanEval+ and six fewer MBPP+ problems solved than the original models. In repeated extraction tests under a fixed budget, the number of targets yielding exact spans of at least 50 tokens falls from 188--262 to 0--2 out of 300 per setting. No extracted span reaches 100 tokens, and the mean best recovery ratio ranges from 0.43\% to 6.45\%. Multilingual and related-code evaluations further show effective forgetting with limited impact on useful programming capabilities, supporting UNBIND as a practical approach to selective code unlearning.

The recent explosion in the capabilities of large language models has led to a wave of interest in how best to prompt a model to perform a given task. While it may be tempting to simply choose a prompt based on average performance on a validation set, this can lead to a deployment where unexpectedly poor responses are generated, especially for the worst-off users. To mitigate this prospect, we propose Prompt Risk Control, a lightweight framework for selecting a prompt based on rigorous upper bounds on families of informative risk measures. We offer methods for producing bounds on a diverse set of metrics, including quantities that measure worst-case responses and disparities in generation quality across the population of users. In addition, we extend the underlying statistical bounding techniques to accommodate the possibility of distribution shifts in deployment. Experiments on applications such as open-ended chat, medical question summarization, and code generation highlight how such a framework can foster responsible deployment by reducing the risk of the worst outcomes.

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.

Understanding how and what pre-trained language models (PLMs) learn about language is an open challenge in natural language processing. Previous work has focused on identifying whether they capture semantic and syntactic information, and how the data or the pre-training objective affects their performance. However, to the best of our knowledge, no previous work has specifically examined how information loss in input token characters affects the performance of PLMs. In this study, we address this gap by pre-training language models using small subsets of characters from individual tokens. Surprisingly, we find that pre-training even under extreme settings, i.e. using only one character of each token, the performance retention in standard NLU benchmarks and probing tasks compared to full-token models is high. For instance, a model pre-trained only on single first characters from tokens achieves performance retention of approximately 90\% and 77\% of the full-token model in SuperGLUE and GLUE tasks, respectively.

Unlearning in large language models (LLMs) has emerged as a promising safeguard against adversarial behaviors. When the forgetting loss is applied uniformly without considering token-level semantic importance, model utility can be unnecessarily degraded. Recent studies have explored token-wise loss regularizers that prioritize informative tokens, but largely rely on ground-truth confidence or external linguistic parsers, which limits their ability to capture contextual information or the model's overall predictive state. Intuitively, function words like "the" primarily serve syntactic roles and are highly predictable with little ambiguity, but informative words admit multiple plausible alternatives with greater uncertainty. Based on this intuition, we propose Entropy-guided Token Weighting (ETW), a token-level unlearning regularizer that uses entropy of the predictive distribution as a proxy for token informativeness. We demonstrate that informative tokens tend to have higher entropy, whereas structural tokens tend to have lower entropy. This behavior enables ETW to achieve more effective unlearning while better preserving model utility than existing token-level approaches.

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

Many pre-trained language models (PLMs) exhibit suboptimal performance on mid- and low-resource languages, largely due to limited exposure to these languages during pre-training. A common strategy to address this is to introduce new tokens specific to the target languages, initialize their embeddings, and apply continual pre-training on target-language data. Among such methods, OFA (Liu et al., 2024a) proposes a similarity-based subword embedding initialization heuristic that is both effective and efficient. However, OFA restricts target-language token embeddings to be convex combinations of a fixed number of source-language embeddings, which may limit expressiveness. To overcome this limitation, we propose HYPEROFA, a hypernetwork-based approach for more adaptive token embedding initialization. The hypernetwork is trained to map from an external multilingual word vector space to the PLMs token embedding space using source-language tokens. Once trained, it can generate flexible embeddings for target-language tokens, serving as a good starting point for continual pretraining. Experiments demonstrate that HYPEROFA consistently outperforms random initialization baseline and matches or exceeds the performance of OFA in both continual pre-training convergence and downstream task performance. We make the code publicly available.

We systematically investigate multi-token prediction (MTP) capabilities within LLMs pre-trained for next-token prediction (NTP). We first show that such models inherently possess MTP capabilities via numerical marginalization over intermediate token probabilities, though performance is data-dependent and improves with model scale. Furthermore, we explore the challenges of integrating MTP heads into frozen LLMs and find that their hidden layers are strongly specialized for NTP, making adaptation non-trivial. Finally, we show that while joint training of MTP heads with the backbone improves performance, it cannot fully overcome this barrier, prompting further research in this direction. Our findings provide a deeper understanding of MTP applied to pretrained LLMs, informing strategies for accelerating inference through parallel token prediction.

Speculative decoding (SD) has become a popular technique to accelerate Large Language Model (LLM) inference, yet its real-world effectiveness remains unclear as prior evaluations rely on research prototypes and unrealistically small batch sizes. We present, to our knowledge, the first systematic study of SD on a production-grade and widely deployed inference engine (vLLM), covering multiple SD variants (n-gram, EAGLE/EAGLE-3, Draft-Model, Multi-Token Prediction) across diverse workloads, model scales, and batch sizes. We analyze key factors governing SD performance, and quantify a theoretical upper bound on SD speedup. Our results show that verification by the target model dominates the execution, while acceptance length varies markedly across output token positions, requests, and datasets. Comparing measured performance with theoretical bounds reveals substantial gaps between observed and theoretical upper bounds, and we leverage this observation to highlight new research opportunities that our study opens up in improving SD.

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

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

Many important optimization problems, such as the minimum spanning tree and minimum-cost flow, can be solved optimally by a greedy method. In this work, we study a learning variant of these problems, where the model of the problem is unknown and has to be learned by interacting repeatedly with the environment in the bandit setting. We formalize our learning problem quite generally, as learning how to maximize an unknown modular function on a known polymatroid. We propose a computationally efficient algorithm for solving our problem and bound its expected cumulative regret. Our gap-dependent upper bound is tight up to a constant and our gap-free upper bound is tight up to polylogarithmic factors. Finally, we evaluate our method on three problems and demonstrate that it is practical.

We explore a class of adversarial attacks targeting the activations of language models. By manipulating a relatively small subset of model activations, a, we demonstrate the ability to control the exact prediction of a significant number (in some cases up to 1000) of subsequent tokens t. We empirically verify a scaling law where the maximum number of target tokens t_max predicted depends linearly on the number of tokens a whose activations the attacker controls as t_max = kappa a. We find that the number of bits of control in the input space needed to control a single bit in the output space (what we call attack resistance chi) is remarkably constant between approx 16 and approx 25 over 2 orders of magnitude of model sizes for different language models. Compared to attacks on tokens, attacks on activations are predictably much stronger, however, we identify a surprising regularity where one bit of input steered either via activations or via tokens is able to exert control over a similar amount of output bits. This gives support for the hypothesis that adversarial attacks are a consequence of dimensionality mismatch between the input and output spaces. A practical implication of the ease of attacking language model activations instead of tokens is for multi-modal and selected retrieval models, where additional data sources are added as activations directly, sidestepping the tokenized input. This opens up a new, broad attack surface. By using language models as a controllable test-bed to study adversarial attacks, we were able to experiment with input-output dimensions that are inaccessible in computer vision, especially where the output dimension dominates.

LLM alignment remains a critical challenge. Inference-time methods provide a flexible alternative to fine-tuning, but their uniform computational effort often yields suboptimal alignment. We hypothesize that for many alignment tasks, the initial tokens of a response are disproportionately more critical. To leverage this principle, we introduce AdaSearch, a novel blockwise search strategy. It adaptively allocates a fixed computational budget using a sampling schedule, focusing search effort on these critical tokens. We apply AdaSearch to sequential decoding and introduce its tree-search counterpart, AdaBeam. Our comprehensive evaluation across eight LLMs demonstrates that AdaSearch outperforms strong Best-of-N and fine-tuning baselines. Specifically, win-rates improve by over 10% for harmlessness generation, controlled sentiment generation, and for mathematical reasoning tasks relative to Best-of-N.

The quadratic complexity of attention remains the central bottleneck in long-context inference for large language models. Prior acceleration methods either sparsify the attention map with structured patterns or permanently evict tokens at specific layers, which can retain irrelevant tokens or rely on irreversible early decisions despite the layer-/head-wise dynamics of token importance. In this paper, we propose Token Sparse Attention, a lightweight and dynamic token-level sparsification mechanism that compresses per-head Q, K, V to a reduced token set during attention and then decompresses the output back to the original sequence, enabling token information to be reconsidered in subsequent layers. Furthermore, Token Sparse Attention exposes a new design point at the intersection of token selection and sparse attention. Our approach is fully compatible with dense attention implementations, including Flash Attention, and can be seamlessly composed with existing sparse attention kernels. Experimental results show that Token Sparse Attention consistently improves accuracy-latency trade-off, achieving up to times3.23 attention speedup at 128K context with less than 1% accuracy degradation. These results demonstrate that dynamic and interleaved token-level sparsification is a complementary and effective strategy for scalable long-context inference.

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.

Large language model pretraining is compute-intensive, yet many tokens contribute marginally to learning, resulting in inefficiency. We introduce Efficient Selective Language Modeling (ESLM), a risk-aware algorithm that improves training efficiency and distributional robustness by performing online token-level batch selection. ESLM leverages per-token statistics (e.g., entropy or loss) and applies value-at-risk thresholding to retain only the most informative tokens per batch. This data-centric mechanism reshapes the training loss, prioritizing high-risk tokens and eliminating redundant gradient computation. We frame ESLM as a bilevel game: the model competes with a masking adversary that selects worst-case token subsets under a constrained thresholding rule. In the loss-based setting, ESLM recovers conditional value-at-risk loss minimization, providing a principled connection to distributionally robust optimization. We extend our approach to Ada-ESLM, which adaptively tunes the selection confidence during training. Experiments on GPT-2 pretraining show that ESLM significantly reduces training FLOPs while maintaining or improving both perplexity and downstream performance compared to baselines. Our approach also scales across model sizes, pretraining corpora, and integrates naturally with knowledge distillation.

Token-level reweighting is a simple yet effective mechanism for controlling supervised fine-tuning, but common indicators are largely one-dimensional: the ground-truth probability reflects downstream alignment, while token entropy reflects intrinsic uncertainty induced by the pre-training prior. Ignoring entropy can misidentify noisy or easily replaceable tokens as learning-critical, while ignoring probability fails to reflect target-specific alignment. RankTuner introduces a probability--entropy calibration signal, the Relative Rank Indicator, which compares the rank of the ground-truth token with its expected rank under the prediction distribution. The inverse indicator is used as a token-wise Relative Scale to reweight the fine-tuning objective, focusing updates on truly under-learned tokens without over-penalizing intrinsically uncertain positions. Experiments on multiple backbones show consistent improvements on mathematical reasoning benchmarks, transfer gains on out-of-distribution reasoning, and pre code generation performance over probability-only or entropy-only reweighting baselines.

Supervised fine-tuning of code LLMs typically applies uniform cross-entropy loss to all response tokens, implicitly assuming that every token provides equally useful learning signal. Recent token-level selection methods challenge this assumption in natural-language SFT by supervising only high-value tokens. However, directly transferring token-level masking to code can break syntactically and semantically coherent program units, because code depends on structural completeness and definition-use relations. We therefore propose CodeBlock, a structure-aware sparse supervision framework that selects structure-complete code evidence rather than isolated tokens. CodeBlock first selects high-quality instruction-response pairs, then partitions code responses into syntactically coherent coding items, estimates their utility by aggregating generalized cross-entropy over core logic tokens, and reranks them with data-flow reach and bridge signals to prioritize blocks that propagate or connect important program dependencies. During training, the full response remains available as context, while loss is applied only to selected code items and informative natural-language tokens. Experiments on six code-generation benchmarks show that CodeBlock achieves stronger average pass@1 than full-token SFT and competitive selection baselines, while using only 1.9% of supervised response tokens.

Recent advancements in the reasoning capabilities of large language models (LLMs) show that employing group relative policy optimization (GRPO) algorithm for reinforcement learning (RL) training allows the models to use more thinking/reasoning tokens for generating better responses. However, LLMs can generate only a finite amount of tokens while maintaining attention to the previously generated tokens. This limit, also known as the context size of an LLM, is a bottleneck in LLM reasoning with arbitrarily large number of tokens. To think beyond the limit of context size, an LLM must employ a modular thinking strategy to reason over multiple rounds. In this work, we propose MOTIF: Modular Thinking via Reinforcement Finetuning -- an RL training method for generating thinking tokens in multiple rounds, effectively allowing the model to think with additional context size. We trained the open-source model Qwen2.5-3B-Instruct on GSM8K dataset via parameter efficient fine-tuning and tested its accuracy on MATH500 and AIME2024 benchmarks. Our experiments show 3.8\% and 3.3\% improvements over vanilla GRPO based training in the respective benchmarks. Furthermore, this improvement was achieved with only 15\% of samples, thus demonstrating sample efficiency of MOTIF. Our code and models are available at https://github.com/purbeshmitra/MOTIF and https://huggingface.co/purbeshmitra/MOTIF, respectively.

Reasoning capability has advanced rapidly in large language models (LLMs), leading to an increasing size of key-value (KV) cache in both prefilling and decoding stages. Existing KV cache compression methods mainly rely on attention weights to estimate token importance. While attention effectively captures contextual relevance, it overlooks complementary information-theoretic signals related to predictive uncertainty and token informativeness. In this paper, we revisit token importance from a forward-looking perspective and introduce Forward Influence, a metric that measures how compressed tokens affect future contexts. Our analysis reveals that tokens selected by attention scores mainly influence nearby contexts, whereas tokens associated with high predictive uncertainty exhibit substantially stronger influence on distant future contexts. Based on the observation, we propose InfoKV, an entropy-aware KV cache compression framework that incorporates information-theoretic signals. It combines token-level predictive uncertainty with layer-wise representation evolution and integrates the resulting entropy scores with attention scores during reasoning. Experiments on long-context reasoning benchmarks with Llama-3.1, Llama-3.2, and DeepSeek-R1 demonstrate that InfoKV consistently outperforms existing attention-based KV compression methods in both long prefilling and decoding scenarios.

Decoding-based regression, which reformulates regression as a sequence generation task, has emerged as a promising paradigm of applying large language models for numerical prediction. However, its progress is hindered by the misalignment between discrete token-level objectives (e.g., cross-entropy) and continuous numerical values. Existing approaches relying on token-level constraints often fail to capture the global magnitude of the target value, limiting their precision and generalization. In this paper, we propose to unlock the potential of decoding-based regression via Reinforcement Learning (RL). We formulate the generation process as a Markov Decision Process, utilizing sequence-level rewards to enforce global numerical coherence. Extensive experiments on tabular regression and code metric regression demonstrate that our method (specifically with ReMax and GRPO) consistently outperforms both state-of-the-art token-level baselines and traditional regression heads, showing the superiority of introducing sequence-level signals. Our analysis further reveals that RL significantly enhances sampling efficiency and predictive precision, establishing decoding-based regression as a robust and accurate paradigm for general-purpose numerical prediction.

Obtaining a single-vector representation from a Large Language Model's (LLM) token-level outputs is a critical step for nearly all sentence-level tasks. However, standard pooling methods like mean or max aggregation treat tokens as an independent set, discarding the rich relational structure captured by the model's self-attention layers and making them susceptible to signal dilution. To address this, we introduce GLOT, a lightweight, structure-aware pooling module that reframes pooling as relational learning followed by aggregation. Operating on the outputs of a frozen LLM, GLOT first constructs a latent token-similarity graph, then refines token representations with a graph neural network, and finally aggregates them using a readout layer. Experimentally, our approach is remarkably robust and efficient: on a diagnostic stress test where 90% of tokens are random distractors, GLOT maintains over 97% accuracy while baseline methods collapse. Furthermore, it is competitive with state-of-the-art techniques on benchmarks like GLUE and MTEB with 20x fewer trainable parameters and speeds up the training time by over 100x compared with parameter-efficient fine-tuning methods. Supported by a theoretical analysis of its expressive power, our work shows that learning over token graphs is a powerful paradigm for the efficient adaptation of frozen LLMs. Our code is published at https://github.com/ipsitmantri/GLOT.

Transformers-based models, such as BERT, have been one of the most successful deep learning models for NLP. Unfortunately, one of their core limitations is the quadratic dependency (mainly in terms of memory) on the sequence length due to their full attention mechanism. To remedy this, we propose, BigBird, a sparse attention mechanism that reduces this quadratic dependency to linear. We show that BigBird is a universal approximator of sequence functions and is Turing complete, thereby preserving these properties of the quadratic, full attention model. Along the way, our theoretical analysis reveals some of the benefits of having O(1) global tokens (such as CLS), that attend to the entire sequence as part of the sparse attention mechanism. The proposed sparse attention can handle sequences of length up to 8x of what was previously possible using similar hardware. As a consequence of the capability to handle longer context, BigBird drastically improves performance on various NLP tasks such as question answering and summarization. We also propose novel applications to genomics data.

Diffusion language models (DLMs) enable fast generation by predicting multiple tokens in parallel, but their practical adoption remains limited by a persistent quality gap relative to comparably sized autoregressive (AR) models. We attribute this gap to a computation-difficulty mismatch: within a partially observed sequence, some unknown tokens are easy to predict, while others require substantially more computation. Existing DLMs nevertheless apply uniform computational depth to all unknown positions at each denoising step. We introduce ALoDLM, which replaces uniform computation with token-adaptive latent recurrence. At each denoising step, ALoDLM iteratively refines latent representations and allocates computation according to token difficulty. Tokens ready to commit are fed back as discrete context, while unresolved tokens retain and further refine their latent states through additional recurrent passes. To learn token prediction and computation allocation jointly, we formulate token-wise computation schedules as latent variables and derive a conditional negative evidence lower bound (NELBO). We train ALoDLM at 1.7B and 8B parameter scales. Across eleven benchmarks, ALoDLM outperforms all evaluated DLMs and the corresponding AR baselines in average benchmark score at both scales. ALoDLM also retains fast parallel decoding, yielding a strong quality-efficiency trade-off among evaluated autoregressive and diffusion models under optimized inference engines.

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

How many tokens from its context does a language model actually use, and what determines that number? We study this question through self-attention. Without retraining, we retain only the tokens with the highest attention weights at each head, layer, and query, keeping their original weights unchanged. By varying the selected set size and measuring the increase in negative log-likelihood (NLL), we estimate the effective attention set size needed to stay within a chosen loss tolerance. Relatively small selected sets can keep NLL close to the full-attention baseline, although the required size varies across models. Attention-based selection substantially outperforms random selection. Selected sets exhibit geometric structure, although geometric separation alone does not establish that model loss is preserved. Extending context while evaluating the same prediction targets increases the required set size, while its fraction of context decreases over the tested range. Experiments with a fixed supporting fact show that additional background pushes its tokens down the attention ranking and reduces their attention mass. Renormalizing the retained weights can substantially reduce the required set size, showing that it also depends on how selected representations are combined. Conditional theoretical models explain how competition and attention-mass retention can produce growing set sizes without more distinct information to retrieve. These results provide a way to measure effective attention set size in language models and investigate its dependence on context, competition, and aggregation.

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

Efficient long-context processing remains a crucial challenge for contemporary large language models (LLMs), especially in resource-constrained environments. Soft compression architectures promise to extend effective context length by replacing long token sequences with smaller sets of learned compressed tokens. Yet, the limits of compressibility -- and when compression begins to erase task-relevant content -- remain underexplored. In this paper, we define token overflow as a regime in which compressed representations no longer contain sufficient information to answer a given query, and propose a methodology to characterize and detect it. In the xRAG soft-compression setting, we find that query-agnostic saturation statistics reliably separate compressed from uncompressed token representations, providing a practical tool for identifying compressed tokens but showing limited overflow detection capability. Lightweight probing classifiers over both query and context xRAG representations detect overflow with 0.72 AUC-ROC on average on HotpotQA, SQuADv2, and TriviaQA datasets, demonstrating that incorporating query information improves detection performance. These results advance from query-independent diagnostics to query-aware detectors, enabling low-cost pre-LLM gating to mitigate compression-induced errors.

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

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

While frontier large language models demonstrate strong reasoning and mathematical capabilities, the practical process of training domain-specialized scientific language models from raw sources remains under-documented. In this work, we present a detailed case study of training a 1.36B-parameter scientific language model directly from raw arXiv LaTeX sources spanning mathematics, computer science, and theoretical physics. We describe an end-to-end pipeline covering metadata filtering, archive validation, LaTeX extraction, text normalization, domain-aware tokenization, and dense transformer training under constrained compute (2xA100 GPUs). Through 24 experimental runs, we analyze training stability, scaling behavior, data yield losses, and infrastructure bottlenecks. Our findings highlight how preprocessing decisions significantly affect usable token volume, how tokenization impacts symbolic stability, and how storage and I/O constraints can rival compute as limiting factors. We further analyze convergence dynamics and show stable training behavior in a data-rich regime (52B pretraining tokens). Rather than proposing a novel architecture, this work provides an engineering-grounded, transparent account of training a small scientific language model from scratch. We hope these insights support researchers operating under moderate compute budgets who seek to build domain-specialized models.

Large pre-trained language models for textual data have an unconstrained output space; at each decoding step, they can produce any of 10,000s of sub-word tokens. When fine-tuned to target constrained formal languages like SQL, these models often generate invalid code, rendering it unusable. We propose PICARD (code and trained models available at https://github.com/ElementAI/picard), a method for constraining auto-regressive decoders of language models through incremental parsing. PICARD helps to find valid output sequences by rejecting inadmissible tokens at each decoding step. On the challenging Spider and CoSQL text-to-SQL translation tasks, we show that PICARD transforms fine-tuned T5 models with passable performance into state-of-the-art solutions.

Transformer models are foundational to natural language processing (NLP) and computer vision. Despite various recent works devoted to reducing the quadratic cost of such models (as a function of the sequence length n), dealing with ultra long sequences efficiently (e.g., with more than 16K tokens) remains challenging. Applications such as answering questions based on an entire book or summarizing a scientific article are inefficient or infeasible. In this paper, we propose to significantly reduce the dependency of a Transformer model's complexity on n, by compressing the input into a representation whose size r is independent of n at each layer. Specifically, by exploiting the fact that in many tasks, only a small subset of special tokens (we call VIP-tokens) are most relevant to the final prediction, we propose a VIP-token centric compression (Vcc) scheme which selectively compresses the input sequence based on their impact on approximating the representation of these VIP-tokens. Compared with competitive baselines, the proposed algorithm not only is efficient (achieving more than 3times efficiency improvement compared to baselines on 4K and 16K lengths), but also achieves competitive or better performance on a large number of tasks. Further, we show that our algorithm can be scaled to 128K tokens (or more) while consistently offering accuracy improvement.

Deepseek's Engram, a conditional memory module, was introduced to trade-off storage versus reasoning in large language models. However, the module relies on token-level N-gram hashing for Engram embedding lookup, introducing a tight coupling to the tokenizer used: a model with a different tokenizer would have to train its own Engram embeddings from scratch. To improve the reusability of Engram embeddings, we propose a change to the hashing routine, enabling compatibility between Engram models using different tokenizers. Instead of modelling disjoint N-gram spaces, we treat N-gram as a method to sample potentially useful byte sequences, from all possible byte sequences across tokens. We replace the XOR-based hashing with the general polynomial hashing with a joint embedding space across N. This work investigates the possible trade-offs and shows that this simple substitution produces comparable performance and achieves tokenizer-agnosticism: hash equivalence for byte-equivalent token sequences.

Recently, large language models (LLMs) have demonstrated superior performance across various tasks by adhering to scaling laws, which significantly increase model size. However, the huge computation overhead during inference hinders the deployment in industrial applications. Many works leverage traditional compression approaches to boost model inference, but these always introduce additional training costs to restore the performance and the pruning results typically show noticeable performance drops compared to the original model when aiming for a specific level of acceleration. To address these issues, we propose a fine-grained token-wise pruning approach for the LLMs, which presents a learnable router to adaptively identify the less important tokens and skip them across model blocks to reduce computational cost during inference. To construct the router efficiently, we present a search-based sparsity scheduler for pruning sparsity allocation, a trainable router combined with our proposed four low-dimensional factors as input and three proposed losses. We conduct extensive experiments across different benchmarks on different LLMs to demonstrate the superiority of our method. Our approach achieves state-of-the-art (SOTA) pruning results, surpassing other existing pruning methods. For instance, our method outperforms BlockPruner and ShortGPT by approximately 10 points on both LLaMA2-7B and Qwen1.5-7B in accuracy retention at comparable token sparsity levels.

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.

Large language models are typically trained under uniform token weighting, which allows frequent and low-information tokens to dominate learning and can increase the tendency to memorize surface-level text spans. To address this, we present an information-weighted cross-entropy loss that rescales token-level contributions using TF-IDF statistics, emphasizing semantically informative tokens while down-weighting ubiquitous ones. Experiments on five decoder-only LLMs ranging from 1.1B to 13B parameters show consistent reductions in memorized substring length while preserving perplexity and downstream task performance. Under LoRA fine-tuning, TF-IDF reduces average substring memorization length by 14% across all five models. Under full-weight fine-tuning on TinyLLaMA 1.1B, the reduction reaches 58%. Our approach is architecture-agnostic and can be incorporated into existing training pipelines with less than 3% computational overhead, offering a lightweight and principled way to mitigate memorization without disrupting standard training dynamics.

Scaling the context size of large language models (LLMs) enables them to perform various new tasks, e.g., book summarization. However, the memory cost of the Key and Value (KV) cache in attention significantly limits the practical applications of LLMs. Recent works have explored token pruning for KV cache reduction in LLMs, relying solely on attention scores as a token importance indicator. However, our investigation into value vector norms revealed a notably non-uniform pattern questioning their reliance only on attention scores. Inspired by this, we propose a new method: Value-Aware Token Pruning (VATP) which uses both attention scores and the ell_{1} norm of value vectors to evaluate token importance. Extensive experiments on LLaMA2-7B-chat and Vicuna-v1.5-7B across 16 LongBench tasks demonstrate VATP's superior performance.

The increasing context window size in Large Language Models (LLMs), such as the GPT and LLaMA series, has improved their ability to tackle complex, long-text tasks, but at the cost of inference efficiency, particularly regarding memory and computational complexity. Existing methods, including selective token retention and window-based attention, improve efficiency but risk discarding important tokens needed for future text generation. In this paper, we propose an approach that enhances LLM efficiency without token loss by reducing the memory and computational load of less important tokens, rather than discarding them.We address two challenges: 1) investigating the distribution of important tokens in the context, discovering recent tokens are more important than distant tokens in context, and 2) optimizing resources for distant tokens by sharing attention scores across layers. The experiments show that our method saves 35% KV cache without compromising the performance.

Although transformers are remarkably effective for many tasks, there are some surprisingly easy-looking regular languages that they struggle with. Hahn shows that for languages where acceptance depends on a single input symbol, a transformer's classification decisions become less and less confident (that is, with cross-entropy approaching 1 bit per string) as input strings get longer and longer. We examine this limitation using two languages: PARITY, the language of bit strings with an odd number of 1s, and FIRST, the language of bit strings starting with a 1. We demonstrate three ways of overcoming the limitation suggested by Hahn's lemma. First, we settle an open question by constructing a transformer that recognizes PARITY with perfect accuracy, and similarly for FIRST. Second, we use layer normalization to bring the cross-entropy of both models arbitrarily close to zero. Third, when transformers need to focus on a single position, as for FIRST, we find that they can fail to generalize to longer strings; we offer a simple remedy to this problem that also improves length generalization in machine translation.

Retrieval-Augmented Generation (RAG) systems face significant performance gaps when applied to technical domains requiring precise information extraction from complex documents. Current evaluation methodologies relying on document-level metrics inadequately capture token-resolution retrieval accuracy that is critical for domain-related documents. We propose a framework combining granular evaluation metrics with synthetic data generation to optimize domain-specific RAG performance. First, we introduce token-aware metrics Precision Omega and Intersection-over-Union (IoU) that quantify context preservation versus information density trade-offs inherent in technical texts. Second, we develop a reasoning model-driven pipeline using instruction-tuned LLMs (DeepSeek-R1, DeepSeek-R1 distilled variants, and Phi-4) to generate context-anchored QA pairs with discontinuous reference spans across three specialized corpora: SEC 10-K filings (finance), biomedical abstracts (PubMed), and APT threat reports (cybersecurity). Our empirical analysis reveals critical insights: smaller chunks (less than 10 tokens) improve precision by 31-42% (IoU = 0.071 vs. baseline 0.053) at recall costs (-18%), while domain-specific embedding strategies yield 22% variance in optimal chunk sizing (5-20 tokens). The DeepSeek-R1-Distill-Qwen-32B model demonstrates superior concept alignment (+14% mean IoU over alternatives), though no configuration universally dominates. Financial texts favor larger chunks for risk factor coverage (Recall = 0.81 at size = 20), whereas cybersecurity content benefits from atomic segmentation, Precision Omega = 0.28 at size = 5. Our code is available on https://github.com/aryan-jadon/Synthetic-Data-Generation-and-Evaluation-using-Reasoning-Model

Language model (LM) decoding is based on the next-token prediction (NTP) probability distribution. For neural LMs (e.g., Transformer-based), NTP distribution is essentially a softmax-regularized dot product between an encoded input context (query) and fixed vocabulary representations (keys). In this paper, we study the effect of the key distribution on the NTP distribution, with a focus on whether the similarity between keys will trigger spurious correlations in NTP. Through knowledge-probing tasks, we show that in the NTP distribution, the few top-ranked tokens are typically accurate. However, the middle-ranked prediction is highly biased towards the tokens that are distributionally (not necessarily semantically) similar to these top ones. For instance, if "P" is predicted as the top-1 token, "A"-"Z" will all be ranked high in NTP, no matter whether they can lead to correct decoding results. This hurts the sampling diversity and makes the sampling of correct, long-tail results hopeless and noisy. We attempt to alleviate this issue via a novel in-context method that iteratively pushes the query representation away from explored regions. Specifically, we include the explored decoding results in the context and prompt the LM to generate something else, which encourages the LM to produce a query representation that has small dot products with explored keys. Experiments on knowledge-probing tasks show that our method leads to efficient navigation away from explored keys to correct new keys. We further extend our method to open-ended and chain-of-thought (for reasoning) generation. Experiment results show that ICN contributes to better generation diversity and improved self-consistency voting performance. Finally, we discuss potential training issues caused by the fixed key space together with the challenges and possible ways to address them in future research.