Daily Papers

RLVR trains language models to reason by rewarding correct final answers. A widely used algorithm, group-relative policy optimization (GRPO), gives every token of a solution the same credit, so dense process rewards have been proposed to credit intermediate steps, for example with a Monte-Carlo reward that scores each step by sampling continuations from it. Comparing such a reward with GRPO per training update, or vetting it with a gradient test on a single batch, leaves out what it costs: in our setting, the continuations alone take 91% of all generated tokens. We introduce a matched-compute protocol that gives every training intervention the same budget, measured in generated tokens and training GPU-hours, and tests it in preregistered studies with controls for side effects. Across 1,668 runs on six models, matching compute reverses the ranking. On Qwen2.5-1.5B, the Monte-Carlo reward leads standard GRPO per update, yet ends 14.3 percentage points lower at equal tokens and 7.8 points lower at equal training time, and none of four dense-reward variants outperforms GRPO even with as much training time. A per-token gradient test orders these rewards as training does but overestimates each by one to two points, as much as the gains it is meant to detect. In contrast, training on the prompts whose predicted success is nearest 1/2 improves accuracy at matched compute, by 1.7 points on Qwen3-0.6B and 0.8 on Qwen2.5-1.5B. These gains replicate on fresh seeds and unseen problems, and a simple rule, that the candidate prompts are predicted to fail more often than not, predicted where they appear in five of six preregistered tests. Both gains come early in training, and standard GRPO with twice the initial learning rate comes within half a point of them. We argue that training interventions should be validated at matched compute, which overturns some apparent gains and confirms others.

Letting a language model take gradient steps on the text it is reading, known as dynamic evaluation, lowers its loss on the rest of the document. Its behaviour on hybrid linear-attention architectures, on diffusion language models, and on standard long-context benchmarks has not been measured. We measure it. With one SGD step per 128-token chunk on the MLP output projections of the last quarter of blocks, no training, and a 2k-token window, softmax-attention models (Qwen3-1.7B, Qwen3-4B, Gemma-4-E4B) lose 5-8% of their next-token loss over a document and outperform the same frozen model given the full 32k-token context. Hybrid Gated-DeltaNet models (Qwen3.5-4B, Qwen3.8-27B) gain under 1% at every learning rate: the linear-attention blocks already perform the adaptation. The mechanism transfers to masked-diffusion models with a larger effect, 8% on Nemotron-Diffusion-8B and 17-20% on DiffusionGemma-26B, once the rate is lowered and updates are clipped. Across RULER, BABILong, LongBench-v2, SCOTUS, HotpotQA, MuSiQue, ContractNLI and citation completion, at 100 or more items on two model sizes, weights updated on the full document recover none of the accuracy lost to context truncation: the adaptation is style and vocabulary, not retrieval. Writing facts with the next-token loss stores the prompt format rather than the fact (30% recall under chat prompting against 80% in context) and costs 36-38 GSM8K points at every dose. Writing a conclusion as behaviour instead, by distilling the model's own conclusion-conditioned judgments into a low-rank adapter, reaches the in-context ceiling (0.83 and 0.88 against 0.84 and 0.88 on 100 games) with GSM8K unchanged, and the conclusion can come from an inquiry loop that found it by asking information-gain questions.

Test-Time Training (TTT) enables long-context processing via continuous weight updates during inference, but current methods struggle to balance the expressivity of per-token update dynamics with the hardware efficiency of chunk-wise approximations. We propose E^2-TTT (Expressive and Efficient TTT) to bridge this gap. Under the standard approximation of taking gradients at the chunk-start weights, we derive a closed-form state transition that exactly reproduces the chunk-end fast-weight and momentum states of the per-token recurrence. This enables fully parallelized chunk-level training while preserving the temporal structure of the update rule that prior chunk-wise methods discard. We validate E^2-TTT by training models up to 1.3B parameters from scratch. It performs on par with previous TTT and hybrid attention baselines in language modeling while outperforming them on in-context retrieval. Its advantage is most pronounced in length extrapolation: on the standard ``Needle in a Haystack'' passkey test, it retains over 90% accuracy at 8times the training context length. Meanwhile, E^2-TTT can match the training throughput of efficient chunk-wise methods, demonstrating that it effectively reconciles expressivity with efficiency. The code is available at https://github.com/zeyun-zhong/E2-TTT.

Large language model (LLM) agents allocate test-time compute adaptively as they revise solutions, use tools, explore alternatives, and decide when to stop. This test-time strategy makes it difficult to measure how agent performance scales. We study open-ended tasks that provide continuous scores for intermediate submissions, making progress observable throughout long trajectories. We propose Elo-per-token analysis, which tracks the best solution found at each token budget and uses a Bradley-Terry model to aggregate within-task orderings into Elo ratings across tasks with different score scales. We apply it to four general-purpose agents on four open-ended benchmarks, with sessions of up to 100M tokens, and to three feedback-driven LLM optimization harnesses in controlled single-task interventions. Independent sampling provides a theoretically characterized reference, for which Elo grows linearly with log compute. Against this reference, agents can initially convert tokens into Elo faster than independent sampling, but their marginal gains diminish and eventually fall below the reference. In contrast, the strongest historical human contestants improve superlinearly over contest time on shared AtCoder Heuristic Contest tasks, providing evidence of continual learning and substantial headroom after agents slow down. We define the scaling inflection point as the per-session budget where marginal Elo gains match the independent-sampling reference. Using this point as the per-session budget, we split 100M tokens across parallel sessions on FrontierCS Polyomino Packing, gaining +264 Elo over one long session and +355 over ten short sessions.

On-policy distillation offers dense, per-token supervision for training reasoning models; however, it remains unclear under which conditions this signal is beneficial and under which it is detrimental. Which teacher model should be used, and in the case of self-distillation, which specific context should serve as the supervisory signal? Does the optimal choice vary from one token to the next? At present, addressing these questions typically requires costly training runs whose aggregate performance metrics obscure the dynamics at the level of individual tokens. We introduce a training-free diagnostic framework that operates at the highest resolution: per token, per question, and per teacher. We derive an ideal per-node gradient defined as the parameter update that maximally increases the student's probability of success. We then develop a scalable targeted-rollout algorithm to estimate this gradient efficiently, even for long chains of intermediate thoughts. The gradient alignment score, defined as the cosine similarity between this ideal gradient and any given distillation gradient, quantifies the extent to which a particular configuration approximates the ideal signal. Across a range of self-distillation settings and external teacher models, we observe that distillation guidance exhibits substantially higher alignment with the ideal on incorrect rollouts than on correct ones, where the student already performs well and the teacher's signal tends to become noisy. Furthermore, we find that the optimal distillation context depends jointly on the student model's capacity and the target task, and that no single universally effective configuration emerges. These findings motivate the use of per-task, per-token diagnostic analyses for distillation.

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

Large language model unlearning is consistently fragile under relearn attacks. On TOFU, fine-tuning on twenty forget examples substantially recovers held-out forget-set ROUGE for every method we evaluate, and we trace this fragility to optimization geometry. The per-token answer margin of fourteen post-hoc methods spanning gradient, preference, and distillation families converges into a narrow band above the retain reference in 41 of 42 method--size cells, a regularity we call the margin cliff. We prove that this cliff follows whenever the retain coupling holds the diagnostic log-odds of forget content above a floor, a condition that token-saturating losses induce at stationarity and that we verify directly on 34 of 42 cells. Margin Calibration (MC) is a plug-in polish adding a non-saturating margin hinge anchored at the reference's per-token margin plus a KL probe on a disjoint instruction corpus, restoring forget-side pressure where the native loss saturates. Under a stated gradient-dominance condition, whose on-trajectory gradient signature we measure by instrumenting the polish, its stationary set lies on the cliff-crossing side, yielding an attack-budget upper bound on the relearn margin lift. Across TOFU (three Llama-3 sizes, three forget tiers), MUSE-News on Llama-2-7B-hf, and a Phi-3.5 panel, a single frozen configuration wins all 14 head-to-head forget aggregates and all populated relearn cells (panel-mean post-attack ROUGE-L 0.41 to 0.18) and lowers raw membership AUC on 13/14, with reduced retain-side utility as the main cost. A deployment variant matches these gains without a retain-trained reference.

Reinforcement-learning-based post-training has become a key approach for improving the reasoning ability of large language models, but its token-level learning signals remain poorly understood. This work studies their heterogeneity through attention entropy, which measures how concentrated or diffuse the contextual support is for each response token. We first show that token-level RL objectives are sparsely estimable: uniformly random 20 percent token subsets preserve much of the full-token held-out performance, suggesting substantial redundancy in token-level updates. However, entropy-structured subsets behave very differently. Low-attention-entropy tokens, which we call anchors, rely on concentrated support, produce stable gradients aligned with full-token updates, and provide a reliable optimization backbone, but tend to plateau on harder benchmarks. High-attention-entropy tokens, which we call explorers, aggregate more diffuse context and induce larger but more volatile gradients. Explorer-only training is unstable on average, though rare successful runs suggest that these tokens may contain useful hard-reasoning signals when optimization remains stable. We support this anchor-explorer spectrum with evidence-gathering analyses, entropy dynamics, gradient-geometry diagnostics, and controls showing that position, predictive entropy, and loss normalization do not explain the observed asymmetry. Finally, a dynamic entropy-aware soft-reweighting intervention improves Qwen3-8B-Base from 34.39 to 37.40 held-out average in the strongest setting. These findings suggest that attention entropy reveals optimization-relevant structure in token-level RL signals, and that uniform token averaging can obscure meaningful heterogeneity in reasoning post-training.

The Mixture-of-Experts (MoE) has gained increasing attention in studying Large Vision-Language Models (LVLMs). It uses a sparse model to replace the dense model, achieving comparable performance while activating fewer parameters during inference, thus significantly reducing the inference cost. Existing MoE methods in LVLMs encourage different experts to handle different tokens, and they usually employ a router to predict the routing of each token. However, the predictions are based solely on sample features and do not truly reveal the optimization directions of tokens. This may lead to severe optimization interference between different tokens assigned to an expert. To address this problem, this paper proposes a novel method based on token-level gradient analysis, i.e., Solving Token Gradient Conflict (STGC). Specifically, we first use token-level gradients to identify conflicting tokens in experts. After that, we add a specialized loss tailored to eliminate conflicts among tokens within each expert. Our method can serve as a plug-in for diverse Large Vision-Language Models, and extensive experimental results demonstrate its effectiveness. The code will be publicly available at https://github.com/longrongyang/STGC.

Data attribution methods for Language Models (LMs) are typically evaluated using downstream tasks like fact retrieval. However, existing evaluations vary multiple dataset properties simultaneously, making it impossible to isolate exactly why an attribution algorithm fails. To diagnose these failures, we explore the design space of LLM data attribution, with a primary focus on evaluation. We introduce the Controlled Attribution Benchmark (CATT) for fact tracing, in which we fine-tune LLMs on entirely fictitious knowledge, providing unambiguous ground truth for attribution. This synthetic setup allows us to systematically alter one dataset configuration at a time, such as document redundancy and lexical distractors. With this configurable evaluation, we demonstrate that redundancy and distractors consistently degrade attribution performance. Rather than proposing a new estimator, we examine two design choices that are underexplored: the loss used to compute gradients and how per-token attribution scores are aggregated into a document score. We find that the true causal evidence within a training document is highly localized, but standard methods dilute this evidence into noise by averaging attribution scores across the entire document. We find that replacing standard cross-entropy loss gradients with the negative log-odds gradients surfaces the critical tokens from other uninformative ones. We can then aggregate only the top token scores to improve ground truth recall by 35 to 72 percentage points across multiple baselines on our diagnostic benchmark. The negative log-odds correction also generalizes to FTRACE-TREX, improving counterfactual retraining performance for every method we test, by up to 4.9x.

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.

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.

Split language models keep input text on a client but send intermediate representations to a server. Attacks can reconstruct text from these messages. Comparing privacy evaluations is difficult when attackers see different messages, know different model weights or use different datasets and recovery measures. We present LLM-Attacker, a framework that records these choices and lets researchers check, compare and extend an evaluation. Compatible attacks reuse recorded messages, and their predictions are saved for independent scoring. The scoring rule requires a linked undefended reference before a defence can pass. Reports also identify attacks that remain untested. In a controlled GPT-2 experiment, adding gradients returned during training increased token recovery from 94.20% to 97.38% and exact-document recovery from 13.71% to 37.77%. The 95% interval for the token gain lay above the two-percentage-point threshold fixed before testing. This experiment is shared with a companion study; here, it tests how the evaluation responds to a change in attacker access. Further studies measure how corpus choice and compression defences affect recovery, compare an adapted published attack with its reference implementation, and test the measurement code. The framework reports implementation checks separately from measured attack effectiveness. Each privacy claim should state the attacker, dataset and scoring rule, report its controls and identify untested attacks.

Large Vision-Language Models (VLMs) enable strong multimodal reasoning but incur heavy inference costs from redundant visual tokens. Token pruning alleviates this issue, yet existing approaches face limitations. Attention-based methods rely on raw attention scores, which are often unstable across layers and heads and can lead to redundant selections. Diversity-based methods improve robustness by selecting tokens far apart in feature space but risk dropping regions needed for accurate prediction. We propose \ours, a training-free framework built on a simple intuition: tokens with higher sensitivity are more likely to influence the model's output, and they should also capture complementary visual cues rather than overlapping information. To achieve this, we estimate token sensitivity using zeroth-order perturbations at the projection layer, a shallow and computationally light component of the model. This approach measures how small random perturbations affect the projection outputs, allowing us to approximate each token's influence through lightweight forward passes without backpropagation. Extensive experiments across multiple VLMs and benchmarks show that \ours consistently outperforms prior methods, pruning up to 94.4\% of tokens while maintaining accuracy and significantly improving efficiency, achieving up to 2.30x faster end-to-end inference over the baseline.

The problem of pre-training data detection for large language models (LLMs) has received growing attention due to its implications in critical issues like copyright violation and test data contamination. The current state-of-the-art approach, Min-K%, measures the raw token probability which we argue may not be the most informative signal. Instead, we propose Min-K%++ to normalize the token probability with statistics of the categorical distribution over the whole vocabulary, which accurately reflects the relative likelihood of the target token compared with other candidate tokens in the vocabulary. Theoretically, we back up our method by showing that the statistic it estimates is explicitly optimized during LLM training, thus serving as a reliable indicator for detecting training data. Empirically, on the WikiMIA benchmark, Min-K%++ outperforms the SOTA Min-K% by 6.2% to 10.5% in detection AUROC averaged over five models. On the more challenging MIMIR benchmark, Min-K%++ consistently improves upon Min-K% and performs on par with reference-based method, despite not requiring an extra reference model.

Reinforcement Learning (RL) for Large Language Models (LLMs) often suffers from training collapse in long-horizon tasks due to exploding gradient variance. To mitigate this, a baseline is commonly introduced for advantage computation; however, traditional value models remain difficult to optimize, and standard group-based baselines overlook sequence heterogeneity. Although classic optimal baseline theory can achieve global variance reduction, it neglects token heterogeneity and requires prohibitive gradient-based computation. In this work, we derive the Optimal Token Baseline (OTB) from first principles, proving that gradient updates should be weighted inversely to their cumulative gradient norm. To ensure efficiency, we propose the Logit-Gradient Proxy that approximates the gradient norm using only forward-pass probabilities. Our method achieves training stability and matches the performance of large group sizes (N=32) with only N=4, reducing token consumption by over 65% across single-turn and tool-integrated reasoning tasks.

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 how the next-token prediction of an autoregressive Transformer language model changes under small perturbations of earlier input token embeddings. Motivated by operator learning and iterative solvers for differential equations, we investigate how the influence of one token on another decays with distance in a trained model. In multilevel methods for differential equations, such as domain decomposition, multigrid, and multilevel preconditioning, one often exploits a separation between strong local interactions and weaker but essential global interactions. The latter correspond to the long tail of the Green's function and are typically handled by a coarse-level operator. Inspired by this perspective, we compute an empirical, distance-resolved gradient profile of token dependencies using autograd. Experiments on trained Pythia models and Qwen2.5-0.5B show that, over the measured distance range, the median Jacobian sensitivity is much better described by a power-law-type decay than by an exponential alternative: the diagonal-normalized profile is well described by $overline G(r) approx γ+β(r+1)^{-p} with exponents p \approx 0.7--0.9 (typically 0.8--0.9$). This behavior appears on coherent text from Gutenberg and WikiText-103. Token-shuffling experiments show that the power-law profile persists even when syntax and prediction quality collapse, whereas randomly initialized models do not exhibit it. The slowly decaying long-range sensitivity thus appears to be a learned property of trained autoregressive Transformer operators. These findings suggest that hierarchical or coarse-level mechanisms in language models may be able to exploit the long-tailed sensitivity profiles.

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.

Customizing an LLM judge to a specific task or domain often involves optimizing its prompt across multiple evaluation criteria simultaneously. Textual gradient methods automate this for a single judge criterion, however they produce natural-language critiques, not numerical vectors. Thus, the conflict-resolution toolkit of multi-task learning (PCGrad, MGDA) doesn't apply to the multi-objective textual gradient setting. We test five decomposition modes of textual gradient optimizers by varying how much cross-task information the loss, gradient and optimizer LLMs share. In 6 of 10 configurations, we observe that optimization never improves over the initial prompt. Gradient specificity drops by 59% (from 9.0 to 3.7) when the gradient LLM processes multiple criteria jointly. Separately, we observe that naively combining per-task instructions into a single prompt degrades Spearman's rho by -5.3%. These results identify two separable failure modes: optimization-time gradient dilution and inference-time instruction interference, which together constrain the design space for multi-objective judge customization using textual feedback.

The rise of human-AI collaborative writing has created a growing need for fine-grained detection methods that support localizing likely LLM-generated content in mixed-authorship documents. Existing methods for detecting LLM-generated text mainly focus on document-level classification and cannot identify which parts of the text are generated by LLMs. This paper introduces a new method to address this urgent need. Our method operates at the token level, the natural unit of modern language models, and builds on existing token-level detection scores. The key idea is to smooth adjacent token scores to reduce their variability, while using an adaptive Lepski-type rule to select the bandwidth according to the local authorship structure. Our method is simple to implement and does not require token-level labeled data for training. Theoretically, we characterize this trade-off and show that the proposed method achieves favorable mean square error performance in estimating the underlying signal. Empirically, we demonstrate strong performance of our method against a wide range of baselines in both synthetic datasets and a realistic dataset. We deploy a publicly accessible website that implements the methods as well.

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.

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

In this paper we introduce token time continuous diffusion (TTCD), a new diffusion language model which (a) operates in continuous space, deterministically mapping Gaussian noise to a final token canvas with no further sampling, and crucially (b) incorporates a new notion of per-token times, with some tokens proceeding from noise to token at a faster rate than others. Continuous space modeling helps TTCD avoid the parallel sampling of multiple tokens, which is a key source of inaccuracy at high speedups for models that iterate purely in discrete space. The notion of per-token times helps TTCD to better model conditional generation, allows for more sure tokens to proceed at a faster rate, and allows for differentiated inter-token influences during refinement. TTCD outperforms discrete models at high speedups. We train a 160M parameter TTCD model on OpenWebText, and then self-distill it; we find that at high speedups we are comparable in unconditional generation quality, and outperform in conditional generation, several existing models of similar size trained, on the same data, and self-distilled. We achieve similar gains in Sudoku solving as well.

Modern ML systems ingest data aggregated from diverse sources, such as synthetic, human-annotated, and live customer traffic. Understanding which examples are important to the performance of a learning algorithm is crucial for efficient model training. Recently, a growing body of literature has given rise to various "influence scores," which use training artifacts such as model confidence or checkpointed gradients to identify important subsets of data. However, these methods have primarily been developed in computer vision settings, and it remains unclear how well they generalize to language-based tasks using pretrained models. In this paper, we explore the applicability of influence scores in language classification tasks. We evaluate a diverse subset of these scores on the SNLI dataset by quantifying accuracy changes in response to pruning training data through random and influence-score-based sampling. We then stress-test one of the scores -- "variance of gradients" (VoG) from Agarwal et al. (2022) -- in an NLU model stack that was exposed to dynamic user speech patterns in a voice assistant type of setting. Our experiments demonstrate that in many cases, encoder-based language models can be finetuned on roughly 50% of the original data without degradation in performance metrics. Along the way, we summarize lessons learned from applying out-of-the-box implementations of influence scores, quantify the effects of noisy and class-imbalanced data, and offer recommendations on score-based sampling for better accuracy and training efficiency.

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

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.

The choice of post-training data for large language models substantially affects downstream performance. Gradient-based data selection is a popular approach that ranks training data by how well their gradients align with those of a small validation set. However, ranking with full-parameter gradients requires an expensive backward pass on every sample, making computation intractable for large candidate pools. This raises a natural question: can we approximate full-gradient features at a fraction of the cost? Conveniently, we find that output-layer gradients suffice for effective data selection, yet require only the cheaper forward pass. We implement this as LESSER, a drop-in wrapper for selection methods that reduces the feature-extraction FLOP cost by 9.7times for SFT and 3.0times for RL benchmarks, while tracking full-gradient performance on downstream tasks. Empirically, we find that even when output-layer and full gradients rank individual samples differently, they select batches with aligned gradients.

The rapid advancement in large language models (LLMs) has significantly enhanced their ability to generate coherent and contextually relevant text, raising concerns about the misuse of AI-generated content and making it critical to detect it. However, the task remains challenging, particularly in unseen domains or with unfamiliar LLMs. Leveraging LLM next-token distribution outputs offers a theoretically appealing approach for detection, as they encapsulate insights from the models' extensive pre-training on diverse corpora. Despite its promise, zero-shot methods that attempt to operationalize these outputs have met with limited success. We hypothesize that one of the problems is that they use the mean to aggregate next-token distribution metrics across tokens, when some tokens are naturally easier or harder to predict and should be weighted differently. Based on this idea, we propose the Perplexity Attention Weighted Network (PAWN), which uses the last hidden states of the LLM and positions to weight the sum of a series of features based on metrics from the next-token distribution across the sequence length. Although not zero-shot, our method allows us to cache the last hidden states and next-token distribution metrics on disk, greatly reducing the training resource requirements. PAWN shows competitive and even better performance in-distribution than the strongest baselines (fine-tuned LMs) with a fraction of their trainable parameters. Our model also generalizes better to unseen domains and source models, with smaller variability in the decision boundary across distribution shifts. It is also more robust to adversarial attacks, and if the backbone has multilingual capabilities, it presents decent generalization to languages not seen during supervised training, with LLaMA3-1B reaching a mean macro-averaged F1 score of 81.46% in cross-validation with nine languages.

Adam has been shown to outperform gradient descent on large language models by a larger margin than on other tasks, but it is unclear why. We show that a key factor in this performance gap is the heavy-tailed class imbalance found in language tasks. When trained with gradient descent, the loss of infrequent words decreases more slowly than the loss of frequent ones. This leads to a slow decrease on the average loss as most samples come from infrequent words. On the other hand, Adam and sign-based methods are less sensitive to this problem. To establish that this behavior is caused by class imbalance, we show empirically that it can be reproduced across architectures and data types, on language transformers, vision CNNs, and linear models. On a linear model with cross-entropy loss, we show that class imbalance leads to imbalanced, correlated gradients and Hessians that have been hypothesized to benefit Adam. We also prove that, in continuous time, gradient descent converges slowly on low-frequency classes while sign descent does not.

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

Vision-Language Models demonstrate remarkable capabilities but often struggle with compositional reasoning, exhibiting vulnerabilities regarding word order and attribute binding. This limitation arises from a scarcity of informative samples needed to differentiate subtle semantic variations during contrastive pretraining. Although hard negative mining offers a promising remedy, existing methods lack explicit mechanisms to dictate which linguistic elements undergo modification. Instead of engineering generative architectures, this study establishes lexical concreteness as a fundamental determinant of negative sample efficacy. Modifying highly concrete terms generates more pronounced structural and visual discrepancies, providing a substantially stronger learning signal. Leveraging this principle, ConcretePlant is proposed to systematically isolate and manipulate perceptually grounded concepts. Analyses of the InfoNCE further reveals a severe gradient imbalance, where easily distinguishable pairs disproportionately overwhelm the optimization process and restrict the bandwidth available for nuanced learning. To resolve this degradation, the Cement loss is formulated utilizing a margin-based approach. By correlating psycholinguistic scores with sample difficulty, this objective dynamically calibrates the penalization applied to individual training pairs. Comprehensive evaluations substantiate these theoretical claims. The integrated framework, designated as Slipform, achieves state-of-the-art accuracy across diverse compositional evaluation benchmarks, general cross-modal retrieval, single and multi label linear probing.

Suppose Alice trains an open-weight language model and Bob uses a blackbox derivative of Alice's model to produce text. Can Alice prove that Bob is using her model, either by querying Bob's derivative model (query setting) or from the text alone (observational setting)? We formulate this question as an independence testing problem--in which the null hypothesis is that Bob's model or text is independent of Alice's randomized training run--and investigate it through the lens of palimpsestic memorization in language models: models are more likely to memorize data seen later in training, so we can test whether Bob is using Alice's model using test statistics that capture correlation between Bob's model or text and the ordering of training examples in Alice's training run. If Alice has randomly shuffled her training data, then any significant correlation amounts to exactly quantifiable statistical evidence against the null hypothesis, regardless of the composition of Alice's training data. In the query setting, we directly estimate (via prompting) the likelihood Bob's model gives to Alice's training examples and order; we correlate the likelihoods of over 40 fine-tunes of various Pythia and OLMo base models ranging from 1B to 12B parameters with the base model's training data order, achieving a p-value on the order of at most 1e-8 in all but six cases. In the observational setting, we try two approaches based on estimating 1) the likelihood of Bob's text overlapping with spans of Alice's training examples and 2) the likelihood of Bob's text with respect to different versions of Alice's model we obtain by repeating the last phase (e.g., 1%) of her training run on reshuffled data. The second approach can reliably distinguish Bob's text from as little as a few hundred tokens; the first does not involve any retraining but requires many more tokens (several hundred thousand) to achieve high power.

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

As the scale of training corpora for large language models (LLMs) grows, model developers become increasingly reluctant to disclose details on their data. This lack of transparency poses challenges to scientific evaluation and ethical deployment. Recently, pretraining data detection approaches, which infer whether a given text was part of an LLM's training data through black-box access, have been explored. The Min-K\% Prob method, which has achieved state-of-the-art results, assumes that a non-training example tends to contain a few outlier words with low token probabilities. However, the effectiveness may be limited as it tends to misclassify non-training texts that contain many common words with high probabilities predicted by LLMs. To address this issue, we introduce a divergence-based calibration method, inspired by the divergence-from-randomness concept, to calibrate token probabilities for pretraining data detection. We compute the cross-entropy (i.e., the divergence) between the token probability distribution and the token frequency distribution to derive a detection score. We have developed a Chinese-language benchmark, PatentMIA, to assess the performance of detection approaches for LLMs on Chinese text. Experimental results on English-language benchmarks and PatentMIA demonstrate that our proposed method significantly outperforms existing methods. Our code and PatentMIA benchmark are available at https://github.com/zhang-wei-chao/DC-PDD.

Recent endeavors to accelerate inference in Multimodal Large Language Models (MLLMs) have primarily focused on visual token compression. The effectiveness of these methods is typically assessed by measuring the accuracy drop on established benchmarks, comparing model performance before and after compression. However, these benchmarks are originally designed to assess the perception and reasoning capabilities of MLLMs, rather than to evaluate compression techniques. As a result, directly applying them to visual token compression introduces a task mismatch. Strikingly, our investigation reveals that simple image downsampling consistently outperforms many advanced compression methods across multiple widely used benchmarks. Through extensive experiments, we make the following observations: (i) Current benchmarks are noisy for the visual token compression task. (ii) Down-sampling is able to serve as a data filter to evaluate the difficulty of samples in the visual token compression task. Motivated by these findings, we introduce VTC-Bench, an evaluation framework that incorporates a data filtering mechanism to denoise existing benchmarks, thereby enabling fairer and more accurate assessment of visual token compression methods. All data and code are available at https://github.com/Chenfei-Liao/VTC-Bench.

Large Language Models (LLMs) are widely deployed in real-world applications, yet little is known about their training dynamics at the token level. Evaluation typically relies on aggregated training loss, measured at the batch level, which overlooks subtle per-token biases arising from (i) varying token-level dynamics and (ii) structural biases introduced by hyperparameters. While weight decay is commonly used to stabilize training, we reveal that it silently introduces performance biases detectable only at the token level. In fact, we empirically show across different dataset sizes, model architectures and sizes ranging from 270M to 3B parameters that as weight decay increases, low-frequency tokens are disproportionately depreciated. This is particularly concerning, as these neglected low-frequency tokens represent the vast majority of the token distribution in most languages, calling for novel regularization techniques that ensure fairness across all available tokens.

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.

Keyword-matching benchmarks can credit small models for tool use they never perform. We document such a false positive in a matched-architecture pair of Spanish security language models and propose a ladder of strict, cheap diagnostics. A 661.6M parameter model (approx. 65% code/technical text; no dedicated SFT) and a 1,109M model (web-heavy multi-phase curriculum; 6B-token tool-SFT) share decoder, tokenizer, and special tokens, scoring almost identically on lenient tool-use metrics (B4: 0.660 vs. 0.650). Verbatim-reproduction checks on training examples separate them completely: the 600M emits valid tool calls with generalized arguments on 6/6 examples; the 1B does so on 0/6 across checkpoints. A first-token probe localizes the 1B's failure to a missing prior (prob. 10^{-4}--10^{-5} on <|tool_call|>), which was erased by its web-heavy training phase. A targeted SFT recipe (diverse corpus, 5x higher learning rate, 2,202 steps, ~3.3 GPU-hours) repairs the 1B using three orders of magnitude fewer tokens than the failed phase. On all 269 corpus rows, valid emission rises from 0.100 to 0.959 (600M: 0.926). On 238 unseen prompts, the repaired 1B passes 0.536 vs. the 600M's 0.428 (p = 0.004). Embedding-drift checks show the repair did not move the trigger token's tied embedding (97.7% of the bf16 table remains bit-identical), meaning changes live in the surrounding network. Both models over-trigger, rarely answering negative prompts without a call (0.09 for 600M, 0.17 for repaired 1B). Factorial analyses confirm all repair configurations install the format, though suppression benefits from a diverse corpus remain a hypothesis due to seed sensitivity. This cheap diagnostic ladder costs minutes of CPU time and should gate tool-use claims on small models.

Tokenization is a key component of autoregressive (AR) generative models, converting raw data into more manageable units for modeling. Commonly, tokens describe local information, such as regions of pixels in images or word pieces in text, and AR generation predicts these tokens in a fixed order. A worthwhile question is whether token structures affect the ability to steer the generation through test-time search, where multiple candidate generations are explored and evaluated by a verifier. Using image generation as our testbed, we hypothesize that recent 1D ordered tokenizers with coarse-to-fine structure can be more amenable to search than classical 2D grid structures. This is rooted in the fact that the intermediate states in coarse-to-fine sequences carry semantic meaning that verifiers can reliably evaluate, enabling effective steering during generation. Through controlled experiments, we find that AR models trained on coarse-to-fine ordered tokens exhibit improved test-time scaling behavior compared to grid-based counterparts. Moreover, we demonstrate that, thanks to the ordered structure, pure test-time search over token sequences (i.e., without training an AR model) can perform training-free text-to-image generation when guided by an image-text verifier. Beyond this, we systematically study how classical search algorithms (best-of-N, beam search, lookahead search) interact with different token structures, as well as the role of different verifiers and AR priors. Our results highlight the impact of token structure on inference-time scalability and provide practical guidance for test-time scaling in AR models.

We set out to reproduce a recent hallucination-mitigation result on the POPE benchmark. The LLaVA-1.5-7B baseline we measured, 82.21 F1 on the adversarial split, sat 1.21 to 8.67 points above the adversarial baselines we planned to compare against (81.00, 79.30, and 73.54). We looked at the evaluation code and found a readout choice that moves F1 on its own. A two-token logit readout decides yes versus no by comparing two vocabulary IDs, 3582 ("yes") and 1217 ("no"). Across 9,000 greedy-decode questions spanning all three splits, neither ID is generated even once. The model emits " Yes" (token 3869) and " No" (token 1939), because SentencePiece prepends a space byte after the prompt suffix "ASSISTANT:". Read with an eight-token lookup that covers the space-prefixed surface forms, LLaVA-1.5-7B scores F1 0.8221, 0.8498, and 0.8713 on the adversarial, popular, and random splits. That 6.13-point adversarial shift exceeds the adversarial gain reported by five of the six papers we surveyed. None of them states its readout, and our reference ran under 4-bit NF4 quantization, so we cannot say how much of any reported gain a matched evaluation would keep. That comparison stays unresolved until readout and precision are matched. On the fixed baseline we run nine inference-time corrections of our own (none beat it) and dissect why the adversarial split resists logit-level intervention. In a 3,000-question probe, wrong predictions draw more image attention than correct ones (Cohen's d=-0.46, p=1.4times10^{-24}), the opposite of what grounding-based corrections assume. A four-readout audit across four further VLMs from three tokenizer families confirms the confound is protocol-level, not model-specific: porting the LLaVA-1.5 IDs verbatim drops F1 to 0.00 on the two disjoint-vocabulary models, whereas a tokenizer-derived readout holds between 0.80 and 0.92.

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.

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.

The disconnect between tokenizer creation and model training in language models has been known to allow for certain inputs, such as the infamous SolidGoldMagikarp token, to induce unwanted behaviour. Although such `glitch tokens' that are present in the tokenizer vocabulary, but are nearly or fully absent in training, have been observed across a variety of different models, a consistent way of identifying them has been missing. We present a comprehensive analysis of Large Language Model (LLM) tokenizers, specifically targeting this issue of detecting untrained and under-trained tokens. Through a combination of tokenizer analysis, model weight-based indicators, and prompting techniques, we develop effective methods for automatically detecting these problematic tokens. Our findings demonstrate the prevalence of such tokens across various models and provide insights into improving the efficiency and safety of language models.

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

Momentum based optimizers are central to a wide range of machine learning applications. These typically rely on an Exponential Moving Average (EMA) of gradients, which decays exponentially the present contribution of older gradients. This accounts for gradients being local linear approximations which lose their relevance as the iterate moves along the loss landscape. This work questions the use of a single EMA to accumulate past gradients and empirically demonstrates how this choice can be sub-optimal: a single EMA cannot simultaneously give a high weight to the immediate past, and a non-negligible weight to older gradients. Building on this observation, we propose AdEMAMix, a simple modification of the Adam optimizer with a mixture of two EMAs to better take advantage of past gradients. Our experiments on language modeling and image classification show -- quite surprisingly -- that gradients can stay relevant for tens of thousands of steps. They help to converge faster, and often to lower minima: e.g., a 1.3B parameter AdEMAMix LLM trained on 101B tokens performs comparably to an AdamW model trained on 197B tokens (+95%). Moreover, our method significantly slows-down model forgetting during training. Our work motivates further exploration of different types of functions to leverage past gradients, beyond EMAs.

We describe our submission to the MedReason 2026 challenge, covering multiple-choice (MCQ) and open-ended (OE) medical visual question answering (VQA) under fully offline, containerized inference. Our first finding is that MCQ retrieval must compare answer semantics rather than answer labels: labels are independently assigned per question, so copying a retrieved neighbor's label transfers no useful information, whereas scoring each current option's text against correct-answer text from similar training cases raises retrieval-only accuracy from 20.0\% to 57.5\% on a 200-case retrieval-excluded development holdout. Our second finding attributes the submitted system's accuracy: holding the task-specific MCQ Low-Rank Adaptation (LoRA) adapter fixed and varying the number \(k\) of in-prompt retrieved examples changes accuracy by at most one case --- 187/200 (93.5\%) at both \(k=0\) and the adapter's training-time \(k=1\), 188/200 (94.0\%) at the packaged runtime's default \(k=3\) --- and the submitted confidence-gated override adds no net accuracy on top of \(k=3\), selecting the VLM in 198/200 cases. With the final MCQ adapter fixed, retrieval changes accuracy by at most one case, and gating provides no net gain. On 20 OE cases, token-F1 and RaTEScore~zhao2024ratescore decrease as \(k\) grows, but paired sign tests on token-F1 differences are nonsignificant (\(p \ge 0.29\)); a single-annotator comparison found 6/20 wrong-anchor errors for the final configuration and 14/20 for an earlier configuration that jointly differed in routing, adapter, and prompting. The system reaches 94.0\% MCQ accuracy on the development holdout and 93.20\% on the organizer's official pre-evaluation, versus 29.43\% for the off-the-shelf reference baseline, while both of the organizer's open-ended scores are lower than that baseline's (ground-truth agreement 1.245 versus 1.588, visual accuracy 1.995 versus 2.696, each out of 4).

We introduce Adam, an algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments. The method is straightforward to implement, is computationally efficient, has little memory requirements, is invariant to diagonal rescaling of the gradients, and is well suited for problems that are large in terms of data and/or parameters. The method is also appropriate for non-stationary objectives and problems with very noisy and/or sparse gradients. The hyper-parameters have intuitive interpretations and typically require little tuning. Some connections to related algorithms, on which Adam was inspired, are discussed. We also analyze the theoretical convergence properties of the algorithm and provide a regret bound on the convergence rate that is comparable to the best known results under the online convex optimization framework. Empirical results demonstrate that Adam works well in practice and compares favorably to other stochastic optimization methods. Finally, we discuss AdaMax, a variant of Adam based on the infinity norm.

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.

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

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.

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.

Reinforcement learning has become a central component of large language model (LLM) post-training, yet token-level credit lacks a generally accepted mathematical definition, leaving its relationship to commonly used training signals unclear. We formulate three regularity conditions, namely Completeness, Prefix Consistency, and Neutrality, and prove that they uniquely determine token-level credit. This characterization provides a unified basis for explaining phenomena across existing algorithms and guides the development of an improved actor-critic training procedure. Through this lens, an ideal teacher in On-Policy Distillation (OPD) acts as an implicit critic, yielding an expected policy gradient proportional to that induced by token-level credit. Response-level REINFORCE Leave-One-Out (RLOO) signals match the expected policy-gradient contribution of token-level credit despite their coarser granularity. We further establish approximate credit sparsity under bounded outcome rewards and show how intermediate critic errors in Generalized Advantage Estimation (GAE) can become comparable to the underlying credit. These motivate Policy Aligned Critic Training (PACT), which adopts an Actor-then-Critic update order to apply importance sampling correction to critic training and better align the critic with the updated policy. In agentic mathematical reasoning, PACT achieves 72.87% average accuracy across four benchmarks, outperforming GRPO and PPO by 8.80 and 13.16 percentage points, respectively. On SWE-bench Verified, PACT achieves a pass rate of 67.4%, outperforming PPO, GRPO, and SAO by 2.4, 2.0, and 3.8 percentage points, respectively.

Standard transformer architectures apply the same number of layers to every token regardless of contextual difficulty. We present Token-Selective Attention (TSA), a learned per-token gate on residual updates between consecutive transformer blocks. Each gate is a lightweight two-layer multi-layer perceptron (MLP) that produces a continuous halting probability, making the mechanism end-to-end differentiable with 1.7% parameter overhead and no changes to the base architecture. Notably, TSA learns difficulty-proportional routing without any explicit depth pressure: even at λ=0 (no depth regularisation), the task-loss gradient alone drives the router to skip 20% of token-layer operations. On character-level language modeling, TSA saved 14-23% of token-layer operations (TLOps) across Tiny-Shakespeare and enwik8 at <0.5% quality loss. At matched efficiency, TSA achieved 0.7% lower validation loss than early exit, and the learned routing transfers directly to inference-time sparse execution for real wall-clock speedup.

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.

Brazilian Portuguese remains under-served by open language models, and the few that exist are difficult to reproduce and are often compared without measures of uncertainty. We release Manacá-1B, an open decoder-only model of 1.72 billion parameters trained from scratch for Brazilian Portuguese with a fully containerized, reproducible pipeline. The pretraining is stable, with zero skipped or NaN steps and self-recovering loss spikes, and we release its full log and dynamics. We evaluate the model against nine open baselines on four Portuguese benchmarks under a single harness. Every comparison reports a standard error and a paired significance test, and the harness is validated against previously published numbers. On last-word prediction Manacá-1B is the strongest model below the 7B scale, exceeding both Tucano-1b1 and Tucano-2b4 on LAMBADA-PT with large paired margins; it is competitive on commonsense completion and near chance on multiple-choice reasoning, as are all small base models. Along the way we document a concrete evaluation pitfall: converting a SentencePiece tokenizer with case-folding normalization to the HuggingFace fast format silently drops the normalizer, routing every capitalized token to byte-fallback and depressing scores in a way that is invisible in aggregate metrics. The uncorrected tokenizer lowered LAMBADA-PT accuracy from 45.3 to 25.0; we quantify the effect and provide a one-line fix that reproduces the training tokenizer exactly. Code, raw training and evaluation logs, per-example prediction vectors, the model weights, and the corrected tokenizer are released so that every number in this paper can be recomputed.

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.

Language models strongly rely on frequency information because they maximize the likelihood of tokens during pre-training. As a consequence, language models tend to not generalize well to tokens that are seldom seen during training. Moreover, maximum likelihood training has been discovered to give rise to anisotropy: representations of tokens in a model tend to cluster tightly in a high-dimensional cone, rather than spreading out over their representational capacity. Our work introduces a method for quantifying the frequency bias of a language model by assessing sentence-level perplexity with respect to token-level frequency. We then present a method for reducing the frequency bias of a language model by inducing a syntactic prior over token representations during pre-training. Our Syntactic Smoothing method adjusts the maximum likelihood objective function to distribute the learning signal to syntactically similar tokens. This approach results in better performance on infrequent English tokens and a decrease in anisotropy. We empirically show that the degree of anisotropy in a model correlates with its frequency bias.

Visual inputs in vision-language models (VLMs) are often encoded into substantially longer token sequences than text, making visual tokens a major bottleneck for efficient inference. Abundant recent methods address this bottleneck by scoring token importance and pruning low-scoring tokens in a single pass. However, one-shot scoring is insufficient because a token's prompt-relevant usefulness depends on the evidence already retained. Motivated by this insight, we introduce DIVE (Dynamic Iterative Visual Evidence Construction), a training-free framework that recasts visual-token pruning as dynamic evidence construction. DIVE repeatedly selects the remaining token with the highest residual-conditioned score, updates the visual and prompt residuals to discount the evidence already explained, and re-evaluates the remaining tokens. This select-update-re-evaluate process builds a retained set of complementary, prompt-relevant evidence. Experiments across eight image-understanding benchmarks show that DIVE consistently preserves performance across token budgets. With an 88.9% reduction in visual tokens, DIVE retains 98.2% of the uncompressed model's average performance. Code is available at https://github.com/Zhong-Chenchen/DIVE.git.

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.

Vision-language models improve perception by feeding increasingly long visual token sequences into language backbones, but the resulting inference cost raises a basic scaling question: as multimodal models grow, how many visual tokens are actually needed, and how should they be allocated under a fixed visual token budget? Existing training-free pruning methods typically answer this with one-shot proxies such as decoder attention, visual similarity, or conditional diversity. We argue that visual token pruning is better viewed as task-conditioned evidence search, especially under aggressive compression and across model scales. We propose F^3A, a training-free router for visual token pruning that operates before the language model consumes image tokens. F^3A builds lightweight question-conditioned cues, matches them to visual-grid tokens through frozen sparse sensing heads, and allocates a fixed vision token budget via coarse evidence localization, local refinement, coverage-preserving competition, and recovery of under-covered regions. It requires no model training, no extra LLM forward pass and preserves the original multimodal prompting and decoding pipeline.

Recent work found that LLMs are sensitive to a wide range of arbitrary prompt dimensions, including the type of delimiters, answer enumerators, instruction wording, and more. This throws into question popular single-prompt evaluation practices. We present DOVE (Dataset Of Variation Evaluation) a large-scale dataset containing prompt perturbations of various evaluation benchmarks. In contrast to previous work, we examine LLM sensitivity from an holistic perspective, and assess the joint effects of perturbations along various dimensions, resulting in thousands of perturbations per instance. We evaluate several model families against DOVE, leading to several findings, including efficient methods for choosing well-performing prompts, observing that few-shot examples reduce sensitivity, and identifying instances which are inherently hard across all perturbations. DOVE consists of more than 250M prompt perturbations and model outputs, which we make publicly available to spur a community-wide effort toward meaningful, robust, and efficient evaluation. Browse the data, contribute, and more: https://slab-nlp.github.io/DOVE/

Classifier-free guidance (CFG) has become an essential component of modern diffusion models to enhance both generation quality and alignment with input conditions. However, CFG requires specific training procedures and is limited to conditional generation. To address these limitations, we propose Token Perturbation Guidance (TPG), a novel method that applies perturbation matrices directly to intermediate token representations within the diffusion network. TPG employs a norm-preserving shuffling operation to provide effective and stable guidance signals that improve generation quality without architectural changes. As a result, TPG is training-free and agnostic to input conditions, making it readily applicable to both conditional and unconditional generation. We further analyze the guidance term provided by TPG and show that its effect on sampling more closely resembles CFG compared to existing training-free guidance techniques. Extensive experiments on SDXL and Stable Diffusion 2.1 show that TPG achieves nearly a 2times improvement in FID for unconditional generation over the SDXL baseline, while closely matching CFG in prompt alignment. These results establish TPG as a general, condition-agnostic guidance method that brings CFG-like benefits to a broader class of diffusion models. The code is available at https://github.com/TaatiTeam/Token-Perturbation-Guidance

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

Thinking Tokens (TT) have been proposed as an unsupervised method to facilitate reasoning in language models. However, despite their conceptual appeal, our findings show that TTs marginally improves performance and consistently underperforms compared to Chain-of-Thought (CoT) reasoning across multiple benchmarks. We hypothesize that this underperformance stems from the reliance on a single embedding for TTs, which results in inconsistent learning signals and introduces noisy gradients. This paper provides a comprehensive empirical analysis to validate this hypothesis and discusses the implications for future research on unsupervised reasoning in LLMs.

Feature attribution methods (FAs), such as gradients and attention, are widely employed approaches to derive the importance of all input features to the model predictions. Existing work in natural language processing has mostly focused on developing and testing FAs for encoder-only language models (LMs) in classification tasks. However, it is unknown if it is faithful to use these FAs for decoder-only models on text generation, due to the inherent differences between model architectures and task settings respectively. Moreover, previous work has demonstrated that there is no `one-wins-all' FA across models and tasks. This makes the selection of a FA computationally expensive for large LMs since input importance derivation often requires multiple forward and backward passes including gradient computations that might be prohibitive even with access to large compute. To address these issues, we present a model-agnostic FA for generative LMs called Recursive Attribution Generator (ReAGent). Our method updates the token importance distribution in a recursive manner. For each update, we compute the difference in the probability distribution over the vocabulary for predicting the next token between using the original input and using a modified version where a part of the input is replaced with RoBERTa predictions. Our intuition is that replacing an important token in the context should have resulted in a larger change in the model's confidence in predicting the token than replacing an unimportant token. Our method can be universally applied to any generative LM without accessing internal model weights or additional training and fine-tuning, as most other FAs require. We extensively compare the faithfulness of ReAGent with seven popular FAs across six decoder-only LMs of various sizes. The results show that our method consistently provides more faithful token importance distributions.

We present a method to formulate algorithm discovery as program search, and apply it to discover optimization algorithms for deep neural network training. We leverage efficient search techniques to explore an infinite and sparse program space. To bridge the large generalization gap between proxy and target tasks, we also introduce program selection and simplification strategies. Our method discovers a simple and effective optimization algorithm, Lion (Evo\textbf{Lved Sign Momentum}). It is more memory-efficient than Adam as it only keeps track of the momentum. Different from adaptive optimizers, its update has the same magnitude for each parameter calculated through the sign operation. We compare Lion with widely used optimizers, such as Adam and Adafactor, for training a variety of models on different tasks. On image classification, Lion boosts the accuracy of ViT by up to 2% on ImageNet and saves up to 5x the pre-training compute on JFT. On vision-language contrastive learning, we achieve 88.3% zero-shot and 91.1% fine-tuning accuracy on ImageNet, surpassing the previous best results by 2% and 0.1%, respectively. On diffusion models, Lion outperforms Adam by achieving a better FID score and reducing the training compute by up to 2.3x. For autoregressive, masked language modeling, and fine-tuning, Lion exhibits a similar or better performance compared to Adam. Our analysis of Lion reveals that its performance gain grows with the training batch size. It also requires a smaller learning rate than Adam due to the larger norm of the update produced by the sign function. Additionally, we examine the limitations of Lion and identify scenarios where its improvements are small or not statistically significant. The implementation of Lion is publicly available.

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.

In this paper we introduce Feature Gradients, a gradient-based search algorithm for feature selection. Our approach extends a recent result on the estimation of learnability in the sublinear data regime by showing that the calculation can be performed iteratively (i.e., in mini-batches) and in linear time and space with respect to both the number of features D and the sample size N . This, along with a discrete-to-continuous relaxation of the search domain, allows for an efficient, gradient-based search algorithm among feature subsets for very large datasets. Crucially, our algorithm is capable of finding higher-order correlations between features and targets for both the N > D and N < D regimes, as opposed to approaches that do not consider such interactions and/or only consider one regime. We provide experimental demonstration of the algorithm in small and large sample-and feature-size settings.

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.

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.

Modern language models often have open weights but closed training data. We formalize the problem of data approximation from model weights and propose several baselines and metrics. We develop a gradient-based approach that selects the highest-matching data from a large public text corpus and show its effectiveness at recovering useful data given only weights of the original and finetuned models. Even when none of the true training data is known, our method is able to locate a small subset of public Web documents can be used to train a model to close to the original model performance given models trained for both classification and supervised-finetuning. On the AG News classification task, our method improves performance from 65% (using randomly selected data) to 80%, approaching the expert benchmark of 88%. When applied to a model trained with SFT on MSMARCO web documents, our method reduces perplexity from 3.3 to 2.3, compared to an expert LLAMA model's perplexity of 2.0.

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

On-policy distillation (OPD) supervises a student on its own trajectories with token-level signals from a frozen teacher, yet how a sampled loss allocates updates across tokens remains poorly understood. We analyze the gradient of the per-token K2 estimator of reverse KL with respect to the student logits. The ell_1 norm of this gradient factorizes into the absolute teacher--student log-probability gap and a student-side softmax factor that grows as the sampled token becomes less likely under the student. In our math-distillation runs, these per-token norms are highly non-uniform: low-student-probability tokens account for a disproportionate share of their sum and are also enriched in large teacher--student gaps. As a lightweight intervention suggested by this analysis, we study Surprise-aware Reweighting (SuRe), a detached, bounded weighting rule that further amplifies this existing allocation. Across two Qwen3 student scales, SuRe improves several math metrics over vanilla OPD and shows no clear degradation on the selected out-of-domain benchmarks. Our primary contribution is therefore a gradient-level characterization of reverse-KL OPD trained with the K2 estimator, with SuRe as one empirical instantiation.

Recent progress in large language models (LLMs) highlights the power of scaling test-time compute to achieve strong performance on complex tasks, such as mathematical reasoning and code generation. This raises a critical question: how should model training be modified to optimize performance under a subsequent test-time compute strategy and budget? To explore this, we focus on pass@N, a simple test-time strategy that searches for a correct answer in N independent samples. We show, surprisingly, that training with cross-entropy (CE) loss can be {it misaligned} with pass@N in that pass@N accuracy {it decreases} with longer training. We explain the origins of this misalignment in terms of model overconfidence induced by CE, and experimentally verify our prediction of overconfidence as an impediment to scaling test-time compute via pass@N. Furthermore we suggest a principled, modified training loss that is better aligned to pass@N by limiting model confidence and rescuing pass@N test performance. Our algorithm demonstrates improved mathematical reasoning on MATH and MiniF2F benchmarks under several scenarios: (1) providing answers to math questions; and (2) proving theorems by searching over proof trees of varying shapes. Overall our work underscores the importance of co-designing two traditionally separate phases of LLM development: training-time protocols and test-time search and reasoning strategies.

An increasing number of autoregressive models, such as MAR, FlowAR, xAR, and Harmon adopt diffusion sampling to improve the quality of image generation. However, this strategy leads to low inference efficiency, because it usually takes 50 to 100 steps for diffusion to sample a token. This paper explores how to effectively address this issue. Our key motivation is that as more tokens are generated during the autoregressive process, subsequent tokens follow more constrained distributions and are easier to sample. To intuitively explain, if a model has generated part of a dog, the remaining tokens must complete the dog and thus are more constrained. Empirical evidence supports our motivation: at later generation stages, the next tokens can be well predicted by a multilayer perceptron, exhibit low variance, and follow closer-to-straight-line denoising paths from noise to tokens. Based on our finding, we introduce diffusion step annealing (DiSA), a training-free method which gradually uses fewer diffusion steps as more tokens are generated, e.g., using 50 steps at the beginning and gradually decreasing to 5 steps at later stages. Because DiSA is derived from our finding specific to diffusion in autoregressive models, it is complementary to existing acceleration methods designed for diffusion alone. DiSA can be implemented in only a few lines of code on existing models, and albeit simple, achieves 5-10times faster inference for MAR and Harmon and 1.4-2.5times for FlowAR and xAR, while maintaining the generation quality.

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.

Vision Large Language Models (VLLMs) incur high computational costs due to their reliance on hundreds of visual tokens to represent images. While token pruning offers a promising solution for accelerating inference, this paper, however, identifies a key observation: in deeper layers (e.g., beyond the 20th), existing training-free pruning methods perform no better than random pruning. We hypothesize that this degradation is caused by "vanishing token information", where visual tokens progressively lose their salience with increasing network depth. To validate this hypothesis, we quantify a token's information content by measuring the change in the model output probabilities upon its removal. Using this proposed metric, our analysis of the information of visual tokens across layers reveals three key findings: (1) As layers deepen, the information of visual tokens gradually becomes uniform and eventually vanishes at an intermediate layer, which we term as "information horizon", beyond which the visual tokens become redundant; (2) The position of this horizon is not static; it extends deeper for visually intensive tasks, such as Optical Character Recognition (OCR), compared to more general tasks like Visual Question Answering (VQA); (3) This horizon is also strongly correlated with model capacity, as stronger VLLMs (e.g., Qwen2.5-VL) employ deeper visual tokens than weaker models (e.g., LLaVA-1.5). Based on our findings, we show that simple random pruning in deep layers efficiently balances performance and efficiency. Moreover, integrating random pruning consistently enhances existing methods. Using DivPrune with random pruning achieves state-of-the-art results, maintaining 96.9% of Qwen-2.5-VL-7B performance while pruning 50% of visual tokens. The code will be publicly available at https://github.com/YahongWang1/Information-Horizon.

We introduce methods to quantify how Large Language Models (LLMs) encode and store contextual information, revealing that tokens often seen as minor (e.g., determiners, punctuation) carry surprisingly high context. Notably, removing these tokens -- especially stopwords, articles, and commas -- consistently degrades performance on MMLU and BABILong-4k, even if removing only irrelevant tokens. Our analysis also shows a strong correlation between contextualization and linearity, where linearity measures how closely the transformation from one layer's embeddings to the next can be approximated by a single linear mapping. These findings underscore the hidden importance of filler tokens in maintaining context. For further exploration, we present LLM-Microscope, an open-source toolkit that assesses token-level nonlinearity, evaluates contextual memory, visualizes intermediate layer contributions (via an adapted Logit Lens), and measures the intrinsic dimensionality of representations. This toolkit illuminates how seemingly trivial tokens can be critical for long-range understanding.

Parallel generation is widely regarded as an inherent advantage of diffusion large language models. Yet our fixed-quota evaluation of four representative models reveals severe degradation across mathematics and code, with all scores below 15% at 16 tokens per step. Token-level probes identify local predictive potential near the observed prefix, especially in mathematical text. We propose RePara, which reinforces short consecutive token blocks through group-relative policy optimization and reduces rollout and log-probability recomputation costs. On LLaDA and SDAR, \ours improves GSM8K and MATH-500 accuracy over JustGRPO under reduced denoising budgets, with a 1.96x training-step speedup in our LLaDA/MATH setup.

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

Multi-teacher on-policy distillation (MOPD) aims to combine the strengths of RL-trained teachers in a single student, but how teacher signals affect parameter changes remains underexplored. We study Qwen3-1.7B with four domain teachers trained with RL from the same initialization as the student, comparing gradients, optimizer updates, and task learning curves, with additional SmolLM3-3B diagnostics. We find that several factors influence teacher signals. First, loss averaging implicitly weights responses: token averaging favors longer responses, and equalizing domain contributions retains this weighting within domains. Second, Adam's first moment reduces differences in parameter updates: the cosine similarity is 0.83 between teachers and 0.96 between averaging rules, despite differences in raw gradients. Third, BF16 rounding hides small changes: about 97\% of FP32 master weights differ from initialization, but only 7--11\% of BF16 weights do. Finally, the top-64 intersection KL gradient closely matches Qwen's full-vocabulary gradient, but the effect on task performance depends on averaging: mathematics accuracy is 2.6 points higher than with sampled-token policy-gradient (PG) under response averaging and 2.1 points lower under global token averaging.

Recent prompt optimisation approaches use the generative nature of language models to produce prompts -- even rivaling the performance of human-curated prompts. In this paper, we demonstrate that randomly sampling tokens from the model vocabulary as ``separators'' can be as effective as language models for prompt-style text classification. Our experiments show that random separators are competitive baselines, having less than a 1% difference compared to previous self-optimisation methods and showing a 12% average relative improvement over strong human baselines across nine text classification tasks and eight language models. We further analyse this phenomenon in detail using three different random generation strategies, establishing that the language space is rich with potentially good separators, with a greater than 40% average chance that a randomly drawn separator performs better than human-curated separators. These observations challenge the common assumption that an effective prompt should be human readable or task relevant and establish a strong baseline for prompt optimisation research.

To fully understand the behavior of a large language model (LLM) requires our understanding of its input space. If this input space differs from our assumption, our understanding of and conclusions about the LLM is likely flawed, regardless of its architecture. Here, we elucidate the structure of the token embeddings, the input domain for LLMs, both empirically and theoretically. We present a generalized and statistically testable model where the neighborhood of each token splits into well-defined signal and noise dimensions. This model is based on a generalization of a manifold called a fiber bundle, so we denote our hypothesis test as the ``fiber bundle null.'' Failing to reject the null is uninformative, but rejecting it at a specific token indicates that token has a statistically significant local structure, and so is of interest to us. By running our test over several open-source LLMs, each with unique token embeddings, we find that the null is frequently rejected, and so the token subspace is provably not a fiber bundle and hence also not a manifold. As a consequence of our findings, when an LLM is presented with two semantically equivalent prompts, and if one prompt contains a token implicated by our test, that prompt will likely exhibit more output variability proportional to the local signal dimension of the token.

In large language models (LLMs), each block operates on the residual stream to map input token sequences to output token distributions. However, most of the interpretability literature focuses on internal latent representations, leaving token-space dynamics underexplored. The high dimensionality and categoricity of token distributions hinder their analysis, as standard statistical descriptors are not suitable. We show that the entropy of logit-lens predictions overcomes these issues. In doing so, it provides a per-layer scalar, permutation-invariant metric. We introduce Entropy-Lens to distill the token-space dynamics of the residual stream into a low-dimensional signal. We call this signal the entropy profile. We apply our method to a variety of model sizes and families, showing that (i) entropy profiles uncover token prediction dynamics driven by expansion and pruning strategies; (ii) these dynamics are family-specific and invariant under depth rescaling; (iii) they are characteristic of task type and output format; (iv) these strategies have unequal impact on downstream performance, with the expansion strategy usually being more critical. Ultimately, our findings further enhance our understanding of the residual stream, enabling a granular assessment of how information is processed across model depth.

Practicing conversations with large language models (LLMs) presents a promising alternative to traditional in-person language learning. However, most LLMs generate text at a near-native level of complexity, making them ill-suited for beginner learners (CEFR: A1-A2). In this paper, we investigate whether controllable generation techniques -- specifically modular methods that do not require model fine-tuning -- can adapt LLM outputs to better support absolute beginners. We evaluate these methods through both automatic metrics and a user study with university-level learners of Japanese. Our findings show that while prompting alone fails to control output difficulty, the use of future discriminators (Yang and Klein, 2021) significantly improves output comprehensibility (from 40.4\% to 84.3\%). We further introduce a novel token-level evaluation metric, Token Miss Rate (TMR), that quantifies the proportion of incomprehensible tokens per utterance and correlates strongly with human judgments. To support future research in AI-assisted language learning, we release our code, models, annotation tools, and dataset.

Next token prediction paradigm has been prevailing for autoregressive models in the era of LLMs. The current default sampling choice for popular LLMs is temperature scaling together with nucleus sampling to balance diversity and coherence. Nevertheless, such approach leads to inferior performance in various NLP tasks when the model is not certain about testing questions. To this end, we propose a brand new training-free decoding strategy, dubbed as Cautious Next Token Prediction (CNTP). In the decoding process, if the model has comparatively high prediction entropy at a certain step, we sample multiple trials starting from the step independently and stop when encountering any punctuation. Then we select the trial with the lowest perplexity score viewed as the most probable and reliable trial path given the model's capacity. The trial number is negatively correlated with the prediction confidence, i.e., the less confident the model is, the more trials it should sample. This is consistent with human beings' behaviour: when feeling uncertain or unconfident, one tends to think more creatively, exploring multiple thinking paths, to cautiously select the path one feels most confident about. Extensive experiments on both LLMs and MLLMs show that our proposed CNTP approach outperforms existing standard decoding strategies consistently by a clear margin. Moreover, the integration of CNTP with self consistency can further improve over vanilla self consistency. We believe our proposed CNTP has the potential to become one of the default choices for LLM decoding. Code is available at https://github.com/wyzjack/CNTP.

The computational cost of training multimodal large language models (MLLMs) grows rapidly with the number of processed tokens. Existing efficiency methods mainly target inference via token reduction or merging, offering limited benefits during training. We introduce ReGATE (Reference-Guided Adaptive Token Elision), an adaptive token pruning method for accelerating MLLM training. ReGATE adopts a teacher-student framework, in which a frozen teacher LLM provides per-token guidance losses that are fused with an exponential moving average of the student's difficulty estimates. This adaptive scoring mechanism dynamically selects informative tokens while skipping redundant ones in the forward pass, substantially reducing computation without altering the model architecture. Across three representative MLLMs, ReGATE matches the peak accuracy of standard training on MVBench up to 2times faster, using only 38% of the tokens. With extended training, it even surpasses the baseline across multiple multimodal benchmarks, cutting total token usage by over 41%.

Large Language Models (LLMs) have shown impressive performance as general purpose agents, but their abilities remain highly dependent on prompts which are hand written with onerous trial-and-error effort. We propose a simple and nonparametric solution to this problem, Automatic Prompt Optimization (APO), which is inspired by numerical gradient descent to automatically improve prompts, assuming access to training data and an LLM API. The algorithm uses minibatches of data to form natural language ``gradients'' that criticize the current prompt. The gradients are then ``propagated'' into the prompt by editing the prompt in the opposite semantic direction of the gradient. These gradient descent steps are guided by a beam search and bandit selection procedure which significantly improves algorithmic efficiency. Preliminary results across three benchmark NLP tasks and the novel problem of LLM jailbreak detection suggest that Automatic Prompt Optimization can outperform prior prompt editing techniques and improve an initial prompt's performance by up to 31\%, by using data to rewrite vague task descriptions into more precise annotation instructions.

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

This paper describes a system designed to distinguish between AI-generated and human-written scientific excerpts in the DAGPap24 competition hosted within the Fourth Workshop on Scientific Document Processing. In this competition the task is to find artificially generated token-level text fragments in documents of a scientific domain. Our work focuses on the use of a multi-task learning architecture with two heads. The application of this approach is justified by the specificity of the task, where class spans are continuous over several hundred characters. We considered different encoder variations to obtain a state vector for each token in the sequence, as well as a variation in splitting fragments into tokens to further feed into the input of a transform-based encoder. This approach allows us to achieve a 9% quality improvement relative to the baseline solution score on the development set (from 0.86 to 0.95) using the average macro F1-score, as well as a score of 0.96 on a closed test part of the dataset from the competition.

Deep neural networks (DNN) have been widely applied in modern life, including critical domains like autonomous driving, making it essential to ensure the reliability and robustness of DNN-powered systems. As an analogy to code coverage metrics for testing conventional software, researchers have proposed neuron coverage metrics and coverage-driven methods to generate DNN test cases. However, Yan et al. doubt the usefulness of existing coverage criteria in DNN testing. They show that a coverage-driven method is less effective than a gradient-based method in terms of both uncovering defects and improving model robustness. In this paper, we conduct a replication study of the work by Yan et al. and extend the experiments for deeper analysis. A larger model and a dataset of higher resolution images are included to examine the generalizability of the results. We also extend the experiments with more test case generation techniques and adjust the process of improving model robustness to be closer to the practical life cycle of DNN development. Our experiment results confirm the conclusion from Yan et al. that coverage-driven methods are less effective than gradient-based methods. Yan et al. find that using gradient-based methods to retrain cannot repair defects uncovered by coverage-driven methods. They attribute this to the fact that the two types of methods use different perturbation strategies: gradient-based methods perform differentiable transformations while coverage-driven methods can perform additional non-differentiable transformations. We test several hypotheses and further show that even coverage-driven methods are constrained only to perform differentiable transformations, the uncovered defects still cannot be repaired by adversarial training with gradient-based methods. Thus, defensive strategies for coverage-driven methods should be further studied.

Recent Multimodal Large Language Models (MLLMs) have demonstrated strong performance in visual grounding, establishing themselves as a general interface for various vision-language applications. This progress has driven the development of token pruning methods to mitigate the high computational costs associated with processing numerous visual tokens. However, we observe that pruning significantly weakens the model's grounding ability, leading to incorrect predictions and drastic performance degradation. In Referring Expression Comprehension (REC), for instance, pruning causes the accuracy of LLaVA on the RefCOCO validation set to drop from 56.14% to 15.34%. Our analysis identifies misaligned position IDs after pruning as the primary cause of this degradation, as both the order and value of these IDs are crucial for maintaining performance in grounding tasks. To address this issue, we propose Grounding-Aware Token Pruning (GAP), a simple yet effective adjustment to position IDs that recovers REC accuracy back to 51.42%, which is 90% of the original performance in the without pruning setting, all while requiring no additional training, memory, or computational overhead. Applied to models such as Shikra, MiniGPTv2, and the LLaVA series, our method consistently improves performance across various token pruning strategies.

Contrastive pretraining techniques for text classification has been largely studied in an unsupervised setting. However, oftentimes labeled data from related tasks which share label semantics with current task is available. We hypothesize that using this labeled data effectively can lead to better generalization on current task. In this paper, we propose a novel way to effectively utilize labeled data from related tasks with a graph based supervised contrastive learning approach. We formulate a token-graph by extrapolating the supervised information from examples to tokens. Our formulation results in an embedding space where tokens with high/low probability of belonging to same class are near/further-away from one another. We also develop detailed theoretical insights which serve as a motivation for our method. In our experiments with 13 datasets, we show our method outperforms pretraining schemes by 2.5% and also example-level contrastive learning based formulation by 1.8% on average. In addition, we show cross-domain effectiveness of our method in a zero-shot setting by 3.91% on average. Lastly, we also demonstrate our method can be used as a noisy teacher in a knowledge distillation setting to significantly improve performance of transformer based models in low labeled data regime by 4.57% on average.

Reinforcement mid-training lets language models learn internal thoughts from unlabeled text, but efficient token-level credit assignment remains challenging. Existing group-relative methods require costly repeated generation. Learned critics offer single-rollout feedback, but accurate return prediction alone does not ensure reliable policy updates. Our analysis shows how training--inference mismatch and PPO clipping prevent a common offset in advantage estimates from cancelling out, introducing additional update drift. We propose , a twin-critic method that calibrates token-level advantages from a single generated trajectory. After warmup and held-out qualification, the critics provide two advantage estimates, combined using action-dependent weights learned through a conditional-moment saddle-point objective. This objective brings the average advantage at each prefix toward zero, while a signal-retention constraint prevents the correction from erasing the learning signal. Sharing information across text positions avoids repeated sampling of each prefix. Theoretically, we characterize optimal mixing under the signal-retention constraint and establish an upper bound on residual mean-induced drift. Experiments show that, compared with the state-of-the-art critic-free method, improves mean benchmark performance by 7.8\% and reduces mean training-step time by up to 63.4\%.

Language model performance depends on identifying the optimal mixture of data groups to train on (e.g., law, code, math). Prior work has proposed a diverse set of methods to efficiently learn mixture proportions, ranging from fitting regression models over training runs to dynamically updating proportions throughout training. Surprisingly, we find that no existing method consistently outperforms a simple stratified sampling baseline in terms of average test perplexity. To understand this inconsistency, we unify existing methods into a standard framework, showing they are equivalent to solving a common optimization problem: minimize average loss subject to a method-specific mixing law -- an implicit assumption on the relationship between loss and mixture proportions. This framework suggests that measuring the fidelity of a method's mixing law can offer insights into its performance. Empirically, we find that existing methods set their mixing law parameters inaccurately, resulting in the inconsistent mixing performance we observe. Using this insight, we derive a new online method named Aioli, which directly estimates the mixing law parameters throughout training and uses them to dynamically adjust proportions. Aioli outperforms stratified sampling on 6 out of 6 datasets by an average of 0.27 test perplexity points, whereas existing methods fail to consistently beat stratified sampling, doing up to 6.9 points worse. Moreover, in a practical setting where proportions are learned on shorter runs due to computational constraints, Aioli can dynamically adjust these proportions over the full training run, consistently improving performance over existing methods by up to 12.012 test perplexity points.

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

On-Policy Distillation (OPD) trains a student on its own generations using teacher feedback. With different tokenizers, comparing teacher and student predictions requires alignment at both sequence and vocabulary levels. In this paper, we examine whether expanding this alignment coverage improves learning. Across three heterogeneous teacher--student pairs on mathematical reasoning and code generation, strict 1:1 groups already cover most student-generated tokens despite substantial vocabulary mismatch. On responses sampled from the students before distillation, the shared vocabulary retains nearly all teacher and student probability mass at strictly aligned positions on average. Restricting reverse KL to a student-selected top-16 subset of the shared vocabulary at each strict position achieves accuracy comparable to full shared-vocabulary OPD, outperforming the evaluated cross-tokenizer baselines. Adding mean squared error supervision on span log-probabilities in mismatch groups gives complete supervision coverage, yet reduces accuracy. At checkpoints from training with only the strict loss, the span gradients show weak or negative directional agreement with the strict gradients and grow in magnitude relative to them. These diagnostics may help explain the accuracy drop from adding span supervision. Our findings motivate a shift from maximizing alignment coverage to prioritizing supervision reliability: compact supervision at strict positions can be more effective than broader coverage that introduces weakly aligned or conflicting training signals.

While previous distribution shift detection approaches can identify if a shift has occurred, these approaches cannot localize which specific features have caused a distribution shift -- a critical step in diagnosing or fixing any underlying issue. For example, in military sensor networks, users will want to detect when one or more of the sensors has been compromised, and critically, they will want to know which specific sensors might be compromised. Thus, we first define a formalization of this problem as multiple conditional distribution hypothesis tests and propose both non-parametric and parametric statistical tests. For both efficiency and flexibility, we then propose to use a test statistic based on the density model score function (i.e. gradient with respect to the input) -- which can easily compute test statistics for all dimensions in a single forward and backward pass. Any density model could be used for computing the necessary statistics including deep density models such as normalizing flows or autoregressive models. We additionally develop methods for identifying when and where a shift occurs in multivariate time-series data and show results for multiple scenarios using realistic attack models on both simulated and real world data.

While increasing training compute has significantly improved the performance of large language models (LLMs), similar gains have not been observed when scaling inference compute. We hypothesize that the primary issue lies in the uniformity of LLM outputs, which leads to inefficient sampling as models repeatedly generate similar but inaccurate responses. Motivated by an intriguing relationship between solution accuracy and response diversity, we propose DivSampling -- a novel and versatile sampling technique designed to enhance the diversity of candidate solutions by introducing prompt perturbations.DivSampling incorporates two categories of perturbations: task-agnostic approaches, which are general and not tailored to any specific task, and task-specific approaches, which are customized based on task content. Our theoretical analysis demonstrates that, under mild assumptions, the error rates of responses generated from diverse prompts are significantly lower compared to those produced by stationary prompts. Comprehensive evaluations across various tasks -- including reasoning, mathematics, and code generation -- highlight the effectiveness of DivSampling in improving solution accuracy. This scalable and efficient approach offers a new perspective on optimizing test-time inference, addressing limitations in current sampling strategies.

In autoregressive language models, each token is sampled by conditioning on all the past tokens; the overall string has thus been sampled from the correct underlying joint distribution represented by the model. In contrast, masked diffusion language models generate text by unmasking tokens out of order and potentially in parallel. Generating an overall string sampled from the correct underlying joint distribution would (again) require exactly one token unmasking in every full-model forward pass. The more tokens unmasked in parallel, the further away the string is from the true joint; this can be seen in the resulting drop in accuracy (but, increase in speed). In this paper we devise a way to {\em approximately} sample multiple tokens from the joint distribution in a single full-model forward pass; we do so by developing a new lightweight single-layer ``sampler" on top of an existing large diffusion LM. One forward pass of the full model can now be followed by multiple forward passes of only this sampler layer, to yield multiple unmasked tokens. Our sampler is trained to mimic exact joint sampling from the (frozen) full model. We show the effectiveness of our approximate joint sampling for both pretrained-only (Dream-7B-Base) and instruction-tuned (Dream-7B-Instruct) models on language modeling and math \& coding tasks. When four tokens are unmasked for each full-model denoising step, our sampling algorithm achieves a MAUVE score of 0.87 (vs marginal baseline of 0.31) with respect to the true joint distribution.

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

Diffusion language models can write several tokens in one forward pass, and they decide during generation how many passes to spend. Two outputs of the same token length can therefore vary a lot in cost. To understand the underlying factors of this cost variation, we analyze two diffusion models across 10 tasks. We find that the number of forward passes per token depends heavily on the task. Text copied or lightly edited from the input is cheap, while open-ended writing is costly. In DiffusionGemma, generating a token for story writing requires more than three times as many forward passes as for grammar correction. Two output properties explain much of this gap: how much of it is new relative to the input, and how rare its words are within the task. The same holds within a single response when thinking is involved. The final answer is cheap when it repeats the model's reasoning trace and costly when it adds something new. In multilingual generation, we find that highly tokenized languages also require more passes per token, adding to the cost they already pay with more tokens. Finally, cost tracks correctness: on the same math problem, wrong answers take more passes per token than correct ones, and weighting candidate answers by decoding speed beats majority voting by up to 4.2 points at no extra cost. Taken together, our results show that diffusion's computational advantage depends on how much of the output is already determined, while its decoding effort offers a practical signal for making inference more efficient and reliable.

The recent development of Large Language Models (LLMs) has been accompanied by an effervescence of novel ideas and methods to better optimize the loss of deep learning models. Claims from those methods are myriad: from faster convergence to removing reliance on certain hyperparameters. However, the diverse experimental protocols used to validate these claims make direct comparisons between methods challenging. This study presents a comprehensive evaluation of recent optimization techniques across standardized LLM pretraining scenarios, systematically varying model size, batch size, and training duration. Through careful tuning of each method, we provide guidance to practitioners on which optimizer is best suited for each scenario. For researchers, our work highlights promising directions for future optimization research. Finally, by releasing our code and making all experiments fully reproducible, we hope our efforts can help the development and rigorous benchmarking of future methods.

The remarkable success of pretrained language models has motivated the study of what kinds of knowledge these models learn during pretraining. Reformulating tasks as fill-in-the-blanks problems (e.g., cloze tests) is a natural approach for gauging such knowledge, however, its usage is limited by the manual effort and guesswork required to write suitable prompts. To address this, we develop AutoPrompt, an automated method to create prompts for a diverse set of tasks, based on a gradient-guided search. Using AutoPrompt, we show that masked language models (MLMs) have an inherent capability to perform sentiment analysis and natural language inference without additional parameters or finetuning, sometimes achieving performance on par with recent state-of-the-art supervised models. We also show that our prompts elicit more accurate factual knowledge from MLMs than the manually created prompts on the LAMA benchmark, and that MLMs can be used as relation extractors more effectively than supervised relation extraction models. These results demonstrate that automatically generated prompts are a viable parameter-free alternative to existing probing methods, and as pretrained LMs become more sophisticated and capable, potentially a replacement for finetuning.

Reasoning-focused LLMs improve answer quality by generating longer reasoning traces, but the additional tokens dramatically increase serving cost, motivating inference optimization. We extend and apply Puzzle, a post-training neural architecture search (NAS) framework, to gpt-oss-120B to produce gpt-oss-puzzle-88B, a deployment-optimized derivative. Our approach combines heterogeneous MoE expert pruning, selective replacement of full-context attention with window attention, FP8 KV-cache quantization with calibrated scales, and post-training reinforcement learning to recover accuracy, while maintaining low generation length. In terms of per-token speeds, on an 8XH100 node we achieve 1.63X and 1.22X throughput speedups in long-context and short-context settings, respectively. gpt-oss-puzzle-88B also delivers throughput speedups of 2.82X on a single NVIDIA H100 GPU. However, because token counts can change with reasoning effort and model variants, per-token throughput (tok/s) and latency (ms/token) do not necessarily lead to end-to-end speedups: a 2X throughput gain is erased if traces grow 2X. Conversely, throughput gains can be spent on more reasoning tokens to improve accuracy; we therefore advocate request-level efficiency metrics that normalize throughput by tokens generated and trace an accuracy--speed frontier across reasoning efforts. We show that gpt-oss-puzzle-88B improves over gpt-oss-120B along the entire frontier, delivering up to 1.29X higher request-level efficiency. Across various benchmarks, gpt-oss-puzzle-88B matches or slightly exceeds the parent on suite-average accuracy across reasoning efforts, with retention ranging from 100.8% (high) to 108.2% (low), showing that post-training architecture search can substantially reduce inference costs without sacrificing quality.

AI-text detection generally asks whether a machine wrote a text. As AI becomes an increasingly integral and accepted part of writing, the more relevant question is no longer whether AI was used, but how much of the text reflects human contribution. A prominent line of work estimates this by measuring how predictive a person's prompt is of the final text. We show that this measure can be easily manipulated. We introduce SPECIFICITY PADDING that simply asks the model to copy a few random IDs from the prompt, and that alone makes a title-only request look more human than one that supplies the article's key ideas. A context-swap audit then holds each document fixed, and only shows or hides the IDs to the evaluator. The score of the unchanged text swings by a third to half of its scale, and it rises for every document we test, on news and scientific abstracts, across varied LLMs from 3.8B to 753B parameters. The same articles can average 85\% human or 15\% human depending only on which prompt is on record, and even with no prompt at all, the output-only variant rewards the random strings themselves. An exact identity, the credit ledger, explains why. The score is a surprisal-weighted average over the text, so rare strings that the context makes copyable collect the credit, whatever they mean. A two-point bound marks a deeper limit. If the prompt could have been machine-written, every transcript-only method must, in the worst case, miss by half the contribution at stake. Likelihood-based scores alone cannot reliably establish human contribution without evidence of what the person added and how the text was produced.

Single-prompt accuracy is the dominant way to benchmark language models, but it can miss reliability failures that matter. We evaluate a 15-model open-weight corpus, with the main reliability analyses focused on 10 instruct models across five classification and reasoning benchmarks under five prompt variants each, measuring accuracy, token-probability calibration, verbal-confidence calibration, verbal parse rate, and prompt-perturbation spread for every (model x dataset x variant) cell. We find three broad results. First, evaluation design can materially change the conclusion. Switching Expected Calibration Error (ECE) token from a raw to a label-set-normalised definition changes per-cell calibration by a mean absolute 0.149. More strikingly, pairing a chain-of-thought prompt with a first-character evaluator on ARC-Challenge reduces apparent accuracy by 72-88% across all five primary models; two independent repair procedures recover 93.8% and 102.7% of the lost performance, indicating an evaluator-side rather than model-side failure. Second, confidence signals are fragile. On MMLU-Pro, every primary model verbally reports confidence substantially above both its accuracy and its token-probability confidence on the same rows, and verbal parse rate can collapse for a single model on a single prompt variant. Third, prompt robustness does not track parameter count reliably. Across 10 instruct models, the correlation between model size and prompt-perturbation spread ranges from -0.244 to 0.474 across benchmarks. Taken together, these results show that reliability conclusions for small language models depend not only on the model being evaluated, but also on the evaluation pipeline used to measure it. We argue that calibration definitions, evaluator logic, verbal parseability, and prompt robustness should be reported explicitly when making reliability claims.

We introduce a general method for improving the convergence rate of gradient-based optimizers that is easy to implement and works well in practice. We demonstrate the effectiveness of the method in a range of optimization problems by applying it to stochastic gradient descent, stochastic gradient descent with Nesterov momentum, and Adam, showing that it significantly reduces the need for the manual tuning of the initial learning rate for these commonly used algorithms. Our method works by dynamically updating the learning rate during optimization using the gradient with respect to the learning rate of the update rule itself. Computing this "hypergradient" needs little additional computation, requires only one extra copy of the original gradient to be stored in memory, and relies upon nothing more than what is provided by reverse-mode automatic differentiation.

Multimodal large language models (MLLMs) incur substantial inference cost due to the processing of hundreds of visual tokens per image. Although token pruning has proven effective for accelerating inference, determining when and where to prune remains largely heuristic. Existing approaches typically rely on static, empirically selected layers, which limit interpretability and transferability across models. In this work, we introduce a matrix-entropy perspective and identify an "Entropy Collapse Layer" (ECL), where the information content of visual representations exhibits a sharp and consistent drop, which provides a principled criterion for selecting the pruning stage. Building on this observation, we propose EntropyPrune, a novel matrix-entropy-guided token pruning framework that quantifies the information value of individual visual tokens and prunes redundant ones without relying on attention maps. Moreover, to enable efficient computation, we exploit the spectral equivalence of dual Gram matrices, reducing the complexity of entropy computation and yielding up to a 64x theoretical speedup. Extensive experiments on diverse multimodal benchmarks demonstrate that EntropyPrune consistently outperforms state-of-the-art pruning methods in both accuracy and efficiency. On LLaVA-1.5-7B, our method achieves a 68.2% reduction in FLOPs while preserving 96.0% of the original performance. Furthermore, EntropyPrune generalizes effectively to high-resolution and video-based models, highlighting the strong robustness and scalability in practical MLLM acceleration. The code will be publicly available at https://github.com/YahongWang1/EntropyPrune.

The recent success of LLMs has been predominantly driven by curating the training dataset composition, scaling of model architectures and dataset sizes and advancements in pretraining objectives, leaving tokenizer influence as a blind spot. Shedding light on this underexplored area, we conduct a comprehensive study on the influence of tokenizer choice on LLM downstream performance by training 24 mono- and multilingual LLMs at a 2.6B parameter scale, ablating different tokenizer algorithms and parameterizations. Our studies highlight that the tokenizer choice can significantly impact the model's downstream performance, training and inference costs. In particular, we find that the common tokenizer evaluation metrics fertility and parity are not always predictive of model downstream performance, rendering these metrics a questionable proxy for the model's downstream performance. Furthermore, we show that multilingual tokenizers trained on the five most frequent European languages require vocabulary size increases of factor three in comparison to English. While English-only tokenizers have been applied to the training of multi-lingual LLMs, we find that this approach results in a severe downstream performance degradation and additional training costs of up to 68%, due to an inefficient tokenization vocabulary.

Post-training of language models is commonly framed as a sample-score-update loop implemented by gradient descent. A recent line of work, exemplified by RandOpt, relocates this loop to weight space, sampling Gaussian perturbations around a pretrained model and ensembling the top-K rewarded specialists at inference. While competitive with PPO and GRPO under matched training compute, this prediction-level ensemble incurs K forward passes per test example and does not extend cleanly to free-form generation. We ask whether the rewarded population can instead be folded into a single deployable model, replacing the inference-time ensemble with one consolidated update. A split-half analysis over 25 model-task pairs reveals reproducible low-rank structure in every case. We turn this geometry into CoRP (Consolidating Rewarded Perturbations), a gradient-free operator that combines reward-weighted aggregation, compatibility-aware reweighting, and a held-out validation gate, with no gradient flowing through the language model. Across five language models from 0.5B to 8B and five tasks covering math, code, and creative writing, CoRP improves the base model by 8.1 points on average. Using one tenth of RandOpt's perturbation budget, CoRP exceeds single-inference RandOpt by 6.5 points and recovers more than half of the gain of the 50-pass majority-vote ensemble, at one forward pass per test example.

Pre-pretraining (PPT) on synthetic non-natural language data improves token efficiency during language model pre-training (PT). Prior work attributes this gain to a grammatical prior, i.e., a structural inductive bias learned during PPT that transfers to natural language grammar. However, PPT has only been tested on models of at most 1B parameters and PT budgets below 2B tokens on predominantly web text. It is unknown whether PPT is effective at larger scales and under more realistic PT data mixtures that combine diverse sources (e.g., code and math). We therefore present a comprehensive study on PPT spanning five PPT tasks, four PT data mixtures, four parameter scales (500M to 7B), and PT budgets of up to 100B tokens. Our results demonstrate that the downstream performance and token efficiency gains of PPT persist at scale, e.g., saving at least 21B PT tokens at the 3B scale. However, in contrast to prior work, we find no consistent evidence that these gains stem from a grammatical prior. Downstream performance does not consistently align with grammatical acceptability across model sizes. Instead, we find that downstream gains arise from PPT tasks that improve long-range retrieval. Finally, PPT performance gains are robust to how PT data mixtures are composed and diminish only when web text is absent. Overall, PPT is a low-cost addition to PT, and future PPT task design should target long-range retrieval rather than natural language grammar.

As Large Language Models (LLMs) grow dramatically in size, there is an increasing trend in compressing and speeding up these models. Previous studies have highlighted the usefulness of gradients for importance scoring in neural network compressing, especially in pruning medium-size networks. However, the substantial memory requirements involved in calculating gradients with backpropagation impede the utilization of gradients in guiding LLM pruning. As a result, most pruning strategies for LLMs rely on gradient-free criteria, such as weight magnitudes or a mix of magnitudes and activations. In this paper, we devise a hybrid pruning criterion, which appropriately integrates magnitude, activation, and gradient to capitalize on feature map sensitivity for pruning LLMs. To overcome memory requirement barriers, we estimate gradients using only forward passes. Based on this, we propose a Memory-effIcieNt structured prunIng procedure for LLMs (MINI-LLM) to remove no-critical channels and multi-attention heads. Experimental results demonstrate the superior performance of MINI-LLM over existing gradient-free methods on three LLMs: LLaMA, BLOOM, and OPT across various downstream tasks (classification, multiple-choice, and generation), while MINI-LLM maintains a GPU memory footprint akin to gradient-free methods.

The open-ended nature of language generation makes the evaluation of autoregressive large language models (LLMs) challenging. One common evaluation approach uses multiple-choice questions (MCQ) to limit the response space. The model is then evaluated by ranking the candidate answers by the log probability of the first token prediction. However, first-tokens may not consistently reflect the final response output, due to model's diverse response styles such as starting with "Sure" or refusing to answer. Consequently, MCQ evaluation is not indicative of model behaviour when interacting with users. But by how much? We evaluate how aligned first-token evaluation is with the text output along several dimensions, namely final option choice, refusal rate, choice distribution and robustness under prompt perturbation. Our results show that the two approaches are severely misaligned on all dimensions, reaching mismatch rates over 60%. Models heavily fine-tuned on conversational or safety data are especially impacted. Crucially, models remain misaligned even when we increasingly constrain prompts, i.e., force them to start with an option letter or example template. Our findings i) underscore the importance of inspecting the text output as well and ii) caution against relying solely on first-token evaluation.

Language models contain ranking-based knowledge and are powerful solvers of in-context ranking tasks. For instance, they may have parametric knowledge about the ordering of countries by size or may be able to rank reviews by sentiment. Recent work focuses on pairwise, pointwise, and listwise prompting techniques to elicit a language model's ranking knowledge. However, we find that even with careful calibration and constrained decoding, prompting-based techniques may not always be self-consistent in the rankings they produce. This motivates us to explore an alternative approach that is inspired by an unsupervised probing method called Contrast-Consistent Search (CCS). The idea is to train a probing model guided by a logical constraint: a model's representation of a statement and its negation must be mapped to contrastive true-false poles consistently across multiple statements. We hypothesize that similar constraints apply to ranking tasks where all items are related via consistent pairwise or listwise comparisons. To this end, we extend the binary CCS method to Contrast-Consistent Ranking (CCR) by adapting existing ranking methods such as the Max-Margin Loss, Triplet Loss, and Ordinal Regression objective. Our results confirm that, for the same language model, CCR probing outperforms prompting and even performs on a par with prompting much larger language models.

Large language models (LLMs) exhibit latent multi-token prediction (MTP) capabilities despite being trained solely for next-token generation. We propose a simple, training-free MTP approach that probes an LLM using on-the-fly mask tokens drawn from its embedding space, enabling parallel prediction of future tokens without modifying model weights or relying on auxiliary draft models. Our method constructs a speculative token tree by sampling top-K candidates from mask-token logits and applies a lightweight pruning strategy to retain high-probability continuations. During decoding, candidate predictions are verified in parallel, resulting in lossless generation while substantially reducing the number of model calls and improving token throughput. Across benchmarks, our probing-based MTP consistently outperforms existing training-free baselines, increasing acceptance length by approximately 12\% on LLaMA3 and 8--12\% on Qwen3, and achieving throughput gains of up to 15--19\%. Finally, we provide theoretical insights and empirical evidence showing that decoder layers naturally align mask-token representations with next-token states, enabling accurate multi-step prediction without retraining or auxiliary models.

Recent studies have determined that the learned token embeddings of large-scale neural language models are degenerated to be anisotropic with a narrow-cone shape. This phenomenon, called the representation degeneration problem, facilitates an increase in the overall similarity between token embeddings that negatively affect the performance of the models. Although the existing methods that address the degeneration problem based on observations of the phenomenon triggered by the problem improves the performance of the text generation, the training dynamics of token embeddings behind the degeneration problem are still not explored. In this study, we analyze the training dynamics of the token embeddings focusing on rare token embedding. We demonstrate that the specific part of the gradient for rare token embeddings is the key cause of the degeneration problem for all tokens during training stage. Based on the analysis, we propose a novel method called, adaptive gradient gating (AGG). AGG addresses the degeneration problem by gating the specific part of the gradient for rare token embeddings. Experimental results from language modeling, word similarity, and machine translation tasks quantitatively and qualitatively verify the effectiveness of AGG.

Can we localize the weights and mechanisms used by a language model to memorize and recite entire paragraphs of its training data? In this paper, we show that while memorization is spread across multiple layers and model components, gradients of memorized paragraphs have a distinguishable spatial pattern, being larger in lower model layers than gradients of non-memorized examples. Moreover, the memorized examples can be unlearned by fine-tuning only the high-gradient weights. We localize a low-layer attention head that appears to be especially involved in paragraph memorization. This head is predominantly focusing its attention on distinctive, rare tokens that are least frequent in a corpus-level unigram distribution. Next, we study how localized memorization is across the tokens in the prefix by perturbing tokens and measuring the caused change in the decoding. A few distinctive tokens early in a prefix can often corrupt the entire continuation. Overall, memorized continuations are not only harder to unlearn, but also to corrupt than non-memorized ones.

Current pre-trained language models rely on large datasets for achieving state-of-the-art performance. However, past research has shown that not all examples in a dataset are equally important during training. In fact, it is sometimes possible to prune a considerable fraction of the training set while maintaining the test performance. Established on standard vision benchmarks, two gradient-based scoring metrics for finding important examples are GraNd and its estimated version, EL2N. In this work, we employ these two metrics for the first time in NLP. We demonstrate that these metrics need to be computed after at least one epoch of fine-tuning and they are not reliable in early steps. Furthermore, we show that by pruning a small portion of the examples with the highest GraNd/EL2N scores, we can not only preserve the test accuracy, but also surpass it. This paper details adjustments and implementation choices which enable GraNd and EL2N to be applied to NLP.