Language Model Pretraining

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Overview

Language model pretraining builds general-purpose models by learning from large collections of text, commonly through next-token prediction or masked-token prediction. Researchers study how data curation, filtering, mixing, repetition, and multilingual or domain-specific corpora affect what models learn, alongside changes to tokenization, architecture, training objectives, and optimizers. Work also aims to make training cheaper through methods such as sparse attention, low-precision computation, parameter sharing, and more efficient data selection. A central tension is that lower training loss or greater data volume does not always bring better downstream abilities: data quality, diversity, exposure, and evaluation choices all matter, and their effects can vary with model scale and task.

Latest papers

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448 papers72 papers in the last four weeks, up 57% on the four weeks before. 0.4% of all new papers.

Jun 5, 2026

Data-Constrained Language Model Pretraining: Improved Regularization and Scaling Laws

Classical scaling laws for language model pretraining balance model size against training dataset size under a fixed compute budget, assuming abundant data and a single pass over the corpus. As training compute grows faster than the supply of natural language data, pretraining is likely to enter a data-constrained, compute-rich regime where models train for multiple epochs over a finite dataset. We study data-constrained pretraining along two axes, regularization and scaling. For regularization, we study masked-input regularization (MIR), an auxiliary next-token prediction loss on randomly masked inputs. MIR tests whether the random masking central to diffusion language models can benefit autoregressive pretraining without architectural changes or inference overhead. Across 72M to 1.4B parameter models, we find that MIR added on top of strong weight decay improves validation loss over autoregressive strong-weight-decay-only models, with downstream gains at 1.4B. For scaling, we propose SoftQ, a scaling law that couples model size and data size to capture their interaction under repeated data. Classical alternatives such as the Chinchilla law use an additive form that decouples these terms, making them misspecified in the data-constrained regime. We find that SoftQ fits data-constrained experiments substantially better than these alternatives, and estimates MIR's gains as equivalent to roughly 1.3 times as much unique training data. We release our code at https://github.com/yixinw-lab/dc_pretrain.

Zhiwei Xu, Shihao Wu, Hanseul Cho +2

University of Michigan · KAIST AI

Language Model PretrainingLanguage Model Scaling LawsScaling LawsData Repetition in Language Model Training
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Jun 4, 2026

PC Layer: Polynomial Weight Preconditioning for Improving LLM Pre-Training

We propose a preconditioning (PC) layer, a weight parameterization via polynomial preconditioner that ensures stable weight conditioning throughout LLM training. The PC module reshapes the singular-value spectrum of weight matrices via low-degree polynomial preconditioning. After training, the preconditioned weights can be merged back into the original architecture, incurring no inference overhead. We demonstrate the advantage of the proposed PC layer over standard transformers in Llama-1B pre-training, for both the AdamW and Muon optimizers. Theoretically, we justify this spectrum-control principle by proving that uniformly bounding each layer's singular values ensures geometric convergence of gradient descent to global minima, for certain deep linear networks. Our code is available at https://github.com/Empath-aln/PC-layer.

Senmiao Wang, Tiantian Fang, Haoran Zhang +4

The Chinese University of Hong Kong, Shenzhen, China · Google LLC, Mountain View, CA, United States · Shenzhen International Center for Industrial and Applied Mathematics, Shenzhen2026 Research Institute of Big Data +1

Language Model PretrainingTransformerNeural Network Optimization
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Jun 3, 2026

Arithmetic Pedagogy for Language Models

We investigate whether methods of human mathematics pedagogy can guide the training of language models toward arithmetic reasoning. Building on the GASING method -- an Indonesian pedagogy that solves basic arithmetic through a left-to-right procedure aligned with the causal order of token generation -- we operationalize each operation as a computational procedure whose execution trace is serialized into natural-language Chain-of-Thought (CoT) supervision. A small GPT-2 decoder (86M parameters) with a syllabic-agglutinative TOBA tokenizer for Indonesian is trained from scratch on this data using only a next-token prediction objective, without reinforcement learning or reward-based optimization. Monitoring training reveals three distinct learning phases, and mechanistic analyses -- attention-masking interventions on the CoT information graph, residual-stream probing, and logit-lens inspection -- show that the model first internalizes a procedural pathway and subsequently develops an associative, ``mental-arithmetic'' capacity that retrieves intermediate results without explicit step-by-step computation. The trained model reaches over 80% accuracy on held-out problems and attains competitive performance against substantially larger language models, indicating that targeted, pedagogically grounded training can yield strong and economical arithmetic capability at small scale.

Andhika Bernard Lumbantobing, Hokky Situngkir

Bandung Fe Institute & Adjunct Science Fellow in InaAI · Adjunct Science Fellow in InaAI · AI Research Center IT Del +1

Numerical Reasoning in Language ModelsLanguage Model PretrainingCoT SupervisionLLM Mathematical Reasoning
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Jun 2, 2026

RL Excursions during Pre-Training: Re-examining Policy Optimization for LLM training

The standard LLM training pipeline applies reinforcement learning (RL) only after pre-training and supervised fine-tuning (SFT). We question this status quo by training a LLM from scratch and applying RL, SFT, and SFT followed by RL directly to intermediate pre-training checkpoints. We find that RL is effective very early, and often matches the full SFT→\toRL pipeline early as well. Through experiments on harder problems, we find that targeted pre-training data composition is a strong lever for RL effectiveness, even more so than model scale. Beyond reasoning accuracy, applying RL directly to base checkpoints expands the model's distribution; the sharpening effect reported in recent work arises only when RL follows SFT. The general capabilities of the model remain essentially unchanged by RL, while they degrade following SFT. Finally, we merge RL and SFT objectives by parallel averaging, which outperforms across all other training methods discussed, across metrics, while preserving general capabilities. Together, these results suggest that LLM training might benefit from an expanded use of RL.

Rachit Bansal, Clara Mohri, Tian Qin +2

Harvard University

Language Model PretrainingSupervised Fine-TuningRL for Language ModelsReinforcement LearningRL Post-Training
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Jun 2, 2026

q0: Primitives for Hyper-Epoch Pretraining

Multi-epoch training is becoming the standard now that compute is growing faster than the supply of high-quality text. But pretraining a single model saturates within a few passes, long before the compute budget is exhausted. We argue this calls for a conceptual shift from training a single model toward exploring a population of models and aggregating their predictions. We introduce hyper-epoch pretraining (q0), which turns a multi-epoch budget into a population of diverse models whose combined predictions reach a lower validation loss than a single refined model. q0 reduces to three core primitives. A cyclic schedule with anti-correlated learning rate and weight decay collects diverse models from a few parallel trajectories. Chain distillation trains each model against its predecessor so that model quality compounds across the population. A learned prior, fit on a held out set, selects and weights members for any inference budget. On a 1.8B-parameter model trained on 100M FineWeb tokens, q0 matches a strong 256-epoch ensemble baseline using only ~56 epochs (~4.6x fewer), or ~67 epochs (~3.8x fewer) when matched to the baseline's ensemble size, and continues to improve beyond it. These gains reach cumulative ~12.9x data efficiency under the Slowrun setting and transfer to downstream benchmarks. Crucially, the optimal allocation shifts with the budget, so we give prescriptive recipes for how to spend a given epoch budget to maximize generalization, from a single epoch up to the largest budgets.

Bishwas Mandal, Shmuel Berman, Akshay Vegesna +1

Q Labs · Princeton University

Language Model PretrainingEfficient Language Model TrainingLanguage Model EnsemblesData-Efficient Learning
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Jun 2, 2026

KletterMix: Climbing Toward High-Quality German Pretraining Data

High-quality pretraining data is a central ingredient in modern language models, but German-language resources remain far less developed than their English counterparts: they are often smaller, less carefully curated, weakly documented, and rarely validated through controlled training experiments. We introduce KletterMix, a high-quality German corpus for language model pretraining and annealing, designed as a reusable dataset artifact for the natural language processing and modeling community. KletterMix is built by translating a state-of-the-art English pretraining corpus into German while preserving document boundaries, metadata, source structure, and topical diversity. This construction yields a German corpus with the scale and diversity of a modern pretraining dataset, while enabling direct comparison to its English source. We document the dataset through a broad set of corpus-level analyses, including translation quality, document length distributions, topic coverage, source composition, and geographic metadata. Using COMETKiwi, we show that the translated documents achieve strong quality across diverse domains, suggesting that careful translation can preserve much of the semantic and stylistic richness of the original corpus. Beyond dataset construction, we evaluate KletterMix as training data. Through controlled pretraining and annealing ablations against established German corpora, we show that models trained on KletterMix achieve measurable improvements on German-language downstream evaluations. These results demonstrate that carefully curated translated data can substantially strengthen the German pretraining data ecosystem.

Maurice Kraus, Ruben Härle, Sebastian Sztwiertnia +4

AI & ML Group, TU Darmstadt · Lab1141 · Fraunhofer IAIS +3

Language Model PretrainingSynthetic Data PretrainingLow-Resource Language Processing
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Jun 2, 2026

Regret Pre-training: Bridging Prior and Posterior Views for Enhanced Knowledge Grounding

Causal language models factorize sequence probabilities using only preceding context, leaving future information unexploited during training despite its availability in the training data. This paper introduces Regret Pre-training, a self-supervised framework grounded in the Learning Using Privileged Information (LUPI) paradigm. The framework employs a dual-view architecture in which a single model generates both a causal Student distribution and a future-conditioned Teacher distribution. The training objective augments standard language modeling with a regret loss that minimizes the KL divergence from teacher to student, transferring future-aware signals to the causal representations. We investigate two teacher configurations on the OLMoE-1B-7B architecture:LocalRegret, which extends attention by one future token, andGlobalRegret, which conditions on bidirectional context with the target position masked. Experiments on nine downstream tasks following 4 billion tokens of training demonstrate that both configurations consistently outperform the baseline. On average,GlobalRegret andLocalRegret achieve 33.9% and 32.2% accuracy respectively, surpassing the baseline's 30.2%. Most notably,GlobalRegret improves BoolQ performance by 18.1 percentage points (61.0% vs 42.9%). The framework introduces no additional parameters and requires only one extra inference-mode forward pass per training step.

Mingkuan Zhao, Xiayu Sun, Wentao Hu +5

The School of Computer Science and Technology, Xi’an Jiaotong University, China.

Language Model PretrainingLLM GroundingLanguage Model DistillationLearning Using Privileged Information
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Jun 2, 2026

Pretraining Language Models on Historical Text

We introduce TypewriterLM, a 7.24B History language model (LM) trained exclusively on English text predating 1913. Developing History LMs requires addressing challenges in data quality and availability, preventing temporal leakage, designing temporally consistent post-training pipelines, and constructing reliable evaluations. To address these issues, we construct TypewriterCorpus, a 54B-token historical corpus collected from diverse archival and linguistically annotated sources with extensive data cleaning and leakage mitigation procedures. Furthermore, we introduce lexically grounded instructing tuning, a post-training framework that constraints responses to remain directly grounded in historical source documents. Using this framework we construct two historical instruction tuning datasets: History-LIMA and History-SelfInstruct. To evaluate capability and temporal consistency, we introduce History-Event, a benchmark suite for evaluating competence, temporal grounding and data leakage. We release TypewriterLM and all associated resources to support future research on historical language models.

Xiaoxi Luo, Zachary Shinnick, Niclas Griesshaber +5

University of Waterloo · Vector Institute · AIML, Adelaide University +3

Language Model PretrainingLLM EvaluationLLM GroundingLanguage Modeling
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Jun 2, 2026

EURO-5K: When Does Domain Pretraining Matter? Benchmarking Transformers for EU Reporting Obligation Extraction

Extracting reporting obligations from EU legislation is critical for assessing and reducing regulatory reporting burden. However, distinguishing reporting requirements from structurally similar provisions requires specialised legal understanding. Current legal NLP methods lack specialised datasets with clear guidelines and comparative evaluation of extraction paradigms and domain adaptation strategies. We curate EURO-5K, a corpus of sentence-level reporting obligations and challenging negative examples from 136 EU legislative acts. On this dataset, we train and compare discriminative token-classification models (BERT-style) and generative span-extraction models (LLMs), evaluating both full fine-tuning and parameter-efficient QLoRA against baselines (pattern and dependency-based extraction, few-shot prompting). Results show that fully fine-tuned generic and legal BERT models achieve similar performance (0.89 F1), while fine-tuned LLMs match encoder accuracy for sentence-level extraction. Legal pretraining offers only small gains for generative models. In contrast, it is clearly beneficial when adaptation capacity is constrained, as parameter-efficient tuning of Legal-BERT outperforms its generic counterpart. Learning curve analysis demonstrates that legal pretraining accelerates early learning with minimal data. All approaches converge around 3K samples with diminishing returns thereafter, validating dataset sufficiency. Cross-dataset evaluation on two external regulatory corpora shows that our models behave as specialised reporting obligation extractors rather than generic regulatory classifiers. We release EURO-5K, trained models, and an interactive demo with explainability visualizations and structured RDF export. These demonstrate that both paradigms and parameter-efficient training provide practical tools for regulatory compliance automation.

Marios Koniaris, Vasileios Kotronis, Eugenia Giannini +1

Division of Computer Science, School of Electrical and Computer Engineering, National Technical University of Athens, Iroon Polytechniou 9, Zographou Campus, 15780, Athens, Greece. · Department of Humanities Social Sciences and Law, School of Applied Mathematical and Physical Sciences, National Technical University of Athens, Iroon Polytechniou 9, Zographou Campus, 15780, Athens, Greece.

Language Model PretrainingLegal NLPDocument Information ExtractionLegal Document AnalysisParameter-Efficient Fine-Tuning
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Jun 1, 2026

When Do Attention Circuits Form? Developmental Trajectories of Capability and Attention-Sink Emergence Across Three 1B-ClassArchitectures

We track the developmental trajectory of attention-head circuit formation across three 1B-class language models spanning two architecture families (dense transformer, mixture-of-experts) and two pretraining corpora (The Pile, DCLM): Pythia 1B, OLMo 1B-0724-hf, and OLMoE 1B-7B-0924. At each of 10 log-spaced revisions per model -- 30 mechanistic-interpretability runs in total -- we apply a participation-ratio (PR) spectral signal and an all-head capability-specific selectivity screen to track induction, previous-token, and BOS-attractor heads as they emerge. Five findings. (F1) Layers 0 and 1 produce zero BOS-classified heads at every revision in every model: the L0/L1 zero-BOS floor is an architectural property, not a learned outcome. (F2) The whole-model BOS-attractor fraction follows three distinct emergence shapes -- a gradual ramp in Pythia 1B, a sharp phase transition in OLMo 1B (7% to 70% between adjacent checkpoints), and a gradual ramp in OLMoE 1B-7B. (F3) In DCLM models, induction-circuit formation precedes BOS-attractor formation by 10-20x in tokens; capability-circuit formation and attention-sink formation are two transitions, not one. (F4) The capability-specific screen converges to the final induction circuit within 0.3-2% of total training tokens -- circuit identification does not require the final model. (F5) For every final-checkpoint induction head sampled across all three models, per-head PR is elevated at or before the first revision at which that head crosses its capability-selectivity threshold. The results refine the induction-phase-transition framing: in 1B-class models trained on DCLM, the induction transition and the attention-sink transition are separated by an order of magnitude in tokens and have qualitatively different shapes.

Yongzhong Xu

Language Model PretrainingTransformer InterpretabilityAttention Head AnalysisAttention SinksInduction HeadsMulti-Head Attention
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Jun 1, 2026

PortBERT: Navigating the Depths of Portuguese Language Models

Transformer models dominate modern NLP, but efficient, language-specific models remain scarce. In Portuguese, most focus on scale or accuracy, often neglecting training and deployment efficiency. In the present work, we introduce PortBERT, a family of RoBERTa-based language models for Portuguese, designed to balance performance and efficiency. Trained from scratch on over 450 GB of deduplicated and filtered mC4 and OSCAR23 from CulturaX using fairseq, PortBERT leverages byte-level BPE tokenization and stable pre-training routines across both GPU and TPU processors. We release two variants, PortBERT base and PortBERT large, and evaluate them on ExtraGLUE, a suite of translated GLUE and SuperGLUE tasks. Both models perform competitively, matching or surpassing existing monolingual and multilingual models. Beyond accuracy, we report training and inference times as well as fine-tuning throughput, providing practical insights into model efficiency. PortBERT thus complements prior work by addressing the underexplored dimension of compute-performance tradeoffs in Portuguese NLP. We release all models on Huggingface and provide fairseq checkpoints to support further research and applications.

Raphael Scheible-Schmitt, Henry He, Armando B. Mendes

School of Computation, Information and Technology, Technical University of Munich, Munich, Germany · IS2E - Intelligent Systems, Science and Engineering, LIACC polo on Azores University, Ponta Delgada, Portugal

Language Model PretrainingPortuguese Language ModelsEfficient Language Model TrainingLanguage ModelingEfficient Language Model Inference
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Jun 1, 2026

KliniskVestBERT: BERT Model Specialised to Norwegian Clinical Texts

The increasing application of Natural Language Processing (NLP) in healthcare demands language models specifically attuned to the complexities of clinical language. This work introduces KliniskVestBERT, a suite of three BERT-based encoder models pre-trained on a substantial corpus of real-world, de-identified Norwegian clinical texts from Helse Vest. We continue pretraining existing language models Nb-BERT-large, NorBERT3-large, and ModernBERT on our specialized clinical dataset. This dataset is based on a representative population of Helse Vest patients. The included document types are carefully curated to encompass a broad clinical spectrum in bokmål and nynorsk including discharge summaries, surgical reports, nursing notes etc. ensuring comprehensive representation of the linguistic landscape within Norwegian healthcare settings. Evaluation on three synthtetic Norwegian clinical benchmark datasets and two real-world problems demonstrates that each of our clinically specialized models consistently outperforms their baseline counterparts, highlighting the significant benefit of domain-specific pre-training for NLP tasks within the clinical domain. The project was a joint effort by all Helse Vest entities (Helse Bergen, Helse Fonna, Helse Førde and Helse Stavanger) with DIPS under the project lead of Helse Vest ICT.

Christian Autenried, Cosimo Persia

Helse Vest ICT

Language Model PretrainingDomain-Adaptive PretrainingClinical Language Model EvaluationClinical NLPMedical LLMs
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May 31, 2026

Child-directed speech facilitates production, not comprehension, in BabyLMs

Recent studies suggest that child-directed speech is not conducive to language learning in BabyLMs. However, current evaluations focus predominantly on comprehension and not production, which is central to usage-based theories of language acquisition which argue how CDS facilitates early language use through constructional ''frames'' (frequent lexical patterns with open slots). We introduce a novel generation-based evaluation inspired by such theories in form of a frame-completion task, and compare Llama models trained with CDS, the BabyLM corpus, and web-crawl data (FineWeb-edu) on comprehension benchmarks and our novel framework. Our results reveal a clear dissociation between models' comprehension and production capabilities: while FineWeb-trained models excel at minimal pairs, CDS-trained models produce grammatical completions substantially earlier in training and concentrate probability mass on appropriate slot-fillers. These findings show that comprehension benchmarks underestimate what CDS affords to BabyLMs.

Bastian Bunzeck, Sina Zarrieß

Computational Linguistics, Department of Linguistics Bielefeld University, Germany

Language Model PretrainingLLM EvaluationLanguage Model Generation EvaluationSmall Language ModelsChild Language AcquisitionGenerative AI Evaluation
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May 30, 2026

Memory-Efficient LLM Training with Dynamic Sparsity: From Stability to Practical Scaling

Dynamic Sparse Training (DST) offers a promising paradigm for improving the training and inference efficiency of deep neural networks; however, we find that in large language model training, DST can suffer from optimization instability, manifested as loss spikes after topology updates. In this work, we show that the naive use of standard Adam-based optimizers leads to a cold-start issue for newly regrown parameters, resulting in excessively large updates and disrupted training dynamics. To address this issue, we propose Sparse Memory-Efficient Training (SMET), which stabilizes DST with optimizer warm-up and improves training progress through density-aware learning-rate scaling. SMET further reduces memory consumption by storing gradients and optimizer states only for active parameters. We provide a theoretical analysis of the update behaviors under SMET, showing improved optimization stability. Extensive experiments demonstrate that SMET enables stable, scalable, and memory-efficient sparse pre-training of LLMs, paving the way for sparse training as a practical alternative to dense training. Our code is publicly available at: https://github.com/QiaoXiao7282/SMET.

Qiao Xiao, Boqian Wu, Patrik Okanovic +6

Eindhoven University of Technology · University of Luxembourg · University of Twente +1

Language Model PretrainingEfficient Language Model TrainingDynamic Sparse TrainingLLM TrainingMemory-Efficient Training
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May 29, 2026

A Pre-Training Analogue of Grokking in Language Models: Tracing Delayed Grammatical Generalization

Grokking, the phenomenon in which neural networks generalize long after fitting their training data, has been studied in supervised settings on many epochs. LLM pre-training instead involves next-token prediction over an unlabeled corpus, with limited data repetition and no explicit train/validation split. To address this, we propose an exposure-based framework that enables the study of grokking-like dynamics during LLM pre-training. We ground our evaluation in BLiMP minimal pairs, which provide controlled grammatical contrasts. For every BLiMP minimal pair, we identify a critical phrase, the smallest continuous span that captures the grammatical contrast and the phenomenon-relevant context. Examples whose critical phrase appears in the pre-training window are assigned to the proxy-train split; the remaining examples are assigned to the proxy-validation split. Across five grammatical phenomena, we observe delayed generalization. Analyzing pre-training checkpoints before and after generalization shows that grammatical concept vectors become more predictive of grammatical acceptability and occupy a higher-dimensional subspace after generalization. We also find that attention from the critical token to the relevant context token is concentrated in a small number of heads.

Sherin Muckatira, Namrata Shivagunde, Vijeta Deshpande +1

University of Massachusetts Lowell

Language Model PretrainingNeural Network GeneralizationSyntactic Generalization in Language Models
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May 29, 2026

Towards Efficient LLMs Annealing with Principled Sample Selection

The annealing phase is a pivotal convergence stage in LLM pre-training that ultimately determines final model quality. However, effectively selecting training data during this phase remains a key challenge. Current strategies rely on empirical heuristics, such as domain filtering or context extension, which lack a principled grounding in optimization theory. In this work, we characterize the annealing phase through the lens of the loss landscape's spectral geometry. We argue that optimal convergence requires gradient updates to satisfy heterogeneous constraints across different eigen-directions. Building on this insight, we formulate data selection as a problem of satisfying these directional constraints. To this end, we propose DiReCT (Directionally-Restrained Constrained Training), a novel framework that reformulates sample selection in the annealing stage as a constrained optimization problem. By imposing explicit directional constraints on per-sample gradients based on the spectral properties of the Hessian, DiReCT identifies samples that align with the optimal curvature-aware descent path. Extensive experiments across various model scales demonstrate that DiReCT consistently achieves state-of-the-art performance. For future research, code is available at https://github.com/xuyj233/Direct.

Yuanjian Xu, Jianing Hao, Wanbo Zhang +2

The Hong Kong University of Science and Technology (Guangzhou), Guangzhou, China · Microsoft Research Asia, Beijing, China · Fudan University, Shanghai, China

Language Model PretrainingEfficient Language Model TrainingCurvature-Aware OptimizationTraining Data Selection
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May 29, 2026

Repetition Mismatch: Why Data Mixture Experiments Don't Scale and How to Fix Them

Pre-training data mixtures are commonly tuned by running small-scale experiments and extrapolating to the target training budget. When high-quality data is scarce and must be repeated, this extrapolation frequently fails, but the source of the failure has not been isolated. We show that a primary culprit is a repetition mismatch: because high-quality datasets are small, their repetition rate changes as the training budget grows, shifting the optimal mixture in ways that small-scale proxy experiments do not anticipate. A subsampling procedure that matches the target repetition rate controls for this effect. In a two-source setting combining limited high-quality data with web crawl, a single repetition-controlled experiment using only 1/16 of the target tokens recovers a mixture within 0.10 of the optimum on Wiki-Text for a 1.17B parameter model, compared to an error of 0.85 without repetition control. Achieving comparable accuracy without repetition control requires multiple training horizons, consuming 19%, 44%, and 94% of the target token budget when using the results from two, three, and four horizons respectively. With three data sources, the larger mixture space requires more than a single experiment to constrain, but the approach remains effective: at the 757M scale, just two repetition-controlled horizons recover the optimal mixture, outperforming baselines that instead require the full two-source experiments to construct. Our results reveal that repetition dynamics, not scale alone, shape whether small-scale mixture experiments generalize. More broadly, they suggest that data repetition deserves treatment as a first-class variable in mixture optimization, rather than an inconvenient side effect of limited data.

Kevin Zhou, Lisa Alazraki, Kris Cao +1

Imperial College London · Cohere

Language Model PretrainingData Mixture OptimizationData Repetition in Language Model Training
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May 28, 2026

Demystifying Data Organization for Enhanced LLM Training

Large Language Models (LLMs) have revolutionized various fields, yet their training efficiency is heavily reliant on effective data curation. While data selection has been widely studied, the strategic data organization for enhanced training remains an underexplored area, particularly since current LLMs are often trained for only one or a few epochs. This paper systematically explores the influence of data organization on LLM training by reusing pre-computed sample-level scores originally generated for data efficiency, thereby incurring minimal additional computational overhead. We identify and formalize four key guidelines for optimizing data organization: Boundary Sharpening, Cyclic Scheduling, Curriculum Continuity, and Local Diversity. Guided by them, we introduce two novel data ordering methods termed STR and SAW. Extensive experiments across different model scales and data sizes, encompassing both pre-training and SFT stages, validate the effectiveness of our summarized guidelines. They also demonstrate the robustness of our proposed data ordering methods in enhancing the stability and performance of LLM training. Github Link: https://github.com/microsoft/data-efficacy/

Yalun Dai, Yangyu Huang, Tongshen Yang +8

Nanyang Technological University · Microsoft Research · The Hong Kong University of Science and Technology

Language Model PretrainingTraining Data CurationCurriculum LearningLLM Training
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May 28, 2026

Kronecker Embeddings: Byte-Level Structured Token Representations for Parameter-Efficient Language Models

Large language models route every input through a learned embedding table of shape |V| x d_model, consuming hundreds of millions to billions of trainable parameters at frontier scale. We introduce Kronecker Embeddings, a deterministic byte-level character-position factorization that replaces this table with a fixed encoder and a single learned projection, compatible with standard BPE tokenizers, eliminating 91--94% of input-side trainable parameters at frontier scale. We provide five contributions. First, a cross-model probe across six LMs (135M-671B parameters) shows trained input embeddings cluster typographic variants of the probe word far more than morphological relatives; Kronecker escapes this clustering at the embedding layer. Second, a controlled three-seed comparison on nanoGPT GPT-2 124M over 2.5B tokens of FineWeb-Edu shows Kronecker reaching 2.5 +- 0.2% lower validation loss than the BPE-tied baseline (gap 0.083 +- 0.007 nats, ~9% lower perplexity), needing ~1.43x fewer steps to reach BPE's converged loss. Third, a spelling-robustness probe over 110 clean/typo pairs shows Kronecker preserves the top-1 prediction on 55.5% of pairs vs. 47.3% for BPE (+8.2 pp) and lowers KL by 7.6%, winning or tying in 10 of 11 categories; a generation probe shows Kronecker echoes byte-novel strings and typos through generation where BPE forgets them. Fourth, BPE embedding norm drifts during training while Kronecker projection norm stays near 1.0, consistent with a stable representational target. Fifth, an on-the-fly runtime variant reconstructs embeddings from a 4.5 MB byte buffer rather than a 2.15 GB table at vocabulary 131,072, with 0.01--0.24% step-time overhead. Byte-level locality has a tradeoff: byte-similar but semantically distant pairs (compute/commute, nation/notion) cluster together, shifting disambiguation to early attention layers.

Rohan Shravan

The School of AI Bengaluru, India

Language Model PretrainingLLM CompressionWord EmbeddingsByte-Level Language Model
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May 27, 2026

Parallax: Parameterized Local Linear Attention for Language Modeling

Large Language Models (LLMs) have become the central paradigm in artificial intelligence, yet the core computational primitive of attention has remained structurally unchanged. Local Linear Attention (LLA) is an attention mechanism derived from nonparametric statistics in the test-time regression framework. In contrast to prior research on efficient attention variants, LLA upgrades the local constant estimate in softmax attention to a local linear estimate, yielding provably superior bias-variance tradeoffs for associative memory. However, LLA has not been scaled in LLM pretraining due to computational and numerical stability concerns. We introduce Parallax, a parameterized Local Linear Attention that is scalable for LLMs. Parallax eliminates the numerical solver in LLA and learns an extra query-like projector that probes the KV covariance. We place Parallax within a family of attention mechanisms connected by the bandwidth, the probe construction and the affine structure. We propose a hardware-aware algorithm that increases the arithmetic intensity over FlashAttention, shifting attention into a more compute bound regime. Our prototype decode kernel matches or outperforms FlashAttention 2/3 across diverse batch sizes and context lengths. We pretrain Parallax at 0.6B and 1.7B scales and find consistent perplexity improvements throughout pretraining with gains that transfer to downstream benchmarks. The advantage persists under both parameter-matched and compute-matched controls, demonstrating a Pareto improvement. We perform careful pretraining ablations and identify a novel phenomenon whereby Muon unlocks the capacity of Parallax. To our knowledge, this is the first empirical demonstration of strong architecture-optimizer codesign for attention mechanisms in the architecture research literature.

Yifei Zuo, Dhruv Pai, Zhichen Zeng +3

Northwestern University · Tilde Research · University of Washington

Language Model PretrainingSelf-AttentionLLM Inference AccelerationLinear Attention
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May 27, 2026

Efficient Pre-Training of LLMs through Truncated SVD Representations

LLM pretraining is extremely costly; therefore, parameter-efficient LLM architectures have recently emerged as a compelling research direction. One such promising approach is to represent the parameters as orthonormal low-rank weight matrices. However, maintaining orthonormality during training is computationally expensive, making it impractical. This paper presents the TSVD (Truncated Singular Value Decomposition) framework which efficiently maintains orthonormality through QR decomposition and caching. Furthermore, a spectral energy heuristic is introduced to select the rank of the resulting low-rank weight matrices. Empirical evaluations across model sizes show that TSVD matches or outperforms full-parameter baselines at a fraction of the compute cost. TSVD thus provides a scalable, computationally efficient foundation for LLM pretraining.

Kaivan Kamali, Kajetan Schweighofer, Hormoz Shahrzad +3

Cognizant AI Lab

Language Model PretrainingLow-Rank Matrix DecompositionLow-Rank CompressionLow-Rank ApproximationSingular Value Decomposition
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May 26, 2026

DunbaaBERT: From Sacrifice to Semantics

Large language models have achieved strong performance across many NLP tasks, yet Urdu remains comparatively underexplored due to limited resources and fragmented evaluation settings. To address this gap, we introduce DunbaaBERT, a family of Urdu RoBERTa-base models trained from scratch with Byte-BPE vocabularies of 32k, 52k, and 96k tokens on a deduplicated 17GB Urdu corpus. We evaluate DunbaaBERT across intrinsic and downstream Urdu NLP benchmarks covering linguistic acceptability, news classification, offensive language detection, and sentiment analysis while analyzing vocabulary-size effects on performance and efficiency trade-offs. Across benchmarks, the DunbaaBERT variants achieve competitive performance against strong multilingual baselines while consistently maintaining favorable efficiency trade-offs. Interestingly, larger vocabularies do not consistently improve downstream effectiveness, with DunbaaBERT32k_{\text{32k}} repeatedly providing the strongest overall efficiency profile. Overall, our results demonstrate that carefully curated Urdu-specific encoder models can remain highly competitive despite comparatively compact model and training scales. All models are released under the MIT license.

Iffat Maab, Waleed Jamil, Raphael Schmitt

Research and Development Center for Large Language Models (LLMC), National Institute of Informatics, Tokyo · Independent Researcher, Edinburgh, United Kingdom · School of Computation, Information and Technology, Technical University of Munich, Germany +1

Language Model PretrainingLanguage ModelingLow-Resource Language Processing
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May 26, 2026

Negligible in Size, Significant in Effect: On Scale Vectors in Large Language Models

Normalization layers in modern large language models (LLMs) consist of a deterministic normalization operation and a learnable scale vector. While the normalization operation has been extensively studied, the scale vector remains poorly understood despite its ubiquitous use. In this work, we present a systematic study of scale vectors in LLMs from the perspectives of expressivity, optimization, and architectural structure. First, we show empirically that although scale vectors constitute only a negligible fraction of model parameters, removing them substantially degrades LLM pre-training. Our theory further shows that, in Pre-Norm architectures, scale vectors do not increase expressivity; instead, they improve optimization through a self-amplifying preconditioning effect on subsequent linear mappings. Second, we investigate the role of weight decay for scale vectors. By distinguishing Input-Norm and Output-Norm layers, we theoretically show that weight decay is beneficial for the former but harmful for the latter, due to their distinct roles in optimization and expressivity. Third, motivated by this understanding, we propose three lightweight and complementary improvements to scale vectors: branch-specific heterogeneity, improved placement around linear mappings, and magnitude-direction reparameterization. Both theory and experiments show that each improvement yields consistent gains. Finally, we combine these improvements into a unified scale-vector strategy and evaluate it through extensive LLM pre-training experiments on dense and mixture-of-experts models ranging from 0.12B to 2B parameters, across multiple optimizers and learning rate schedules, under industrial-scale token budgets. The unified strategy consistently achieves lower terminal loss than well-tuned baselines and exhibits more favorable scaling behavior, while adding negligible parameter and computational overhead.

Mingze Wang, Shuchen Zhu, Yuxin Fang +3

ByteDance Seed · Peking University

Language Model PretrainingWeight DecayLLM Training
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May 26, 2026

MONA: Muon Optimizer with Nesterov Acceleration for Scalable Language Model Training

The Muon optimizer has recently offered a promising alternative to AdamW for large language model training, leveraging matrix orthogonalization to produce geometry-aware updates. However, like all first-order methods, Muon can become trapped in sharp local minima. In this work, we present MONA, an optimizer that bridges Muon's orthogonalization framework with curvature-aware acceleration. MONA adds an acceleration term directly into Muon's gradient processing pipeline. This term is calculated from the exponential moving average of gradient differences. We provide a detailed convergence analysis for MONA, showing that the acceleration term introduces curvature-sensitive corrections while preserving Muon's spectral-norm regularization. Empirically, MONA achieves better convergence and downstream task performance compared to both Muon and AdamW across three scales of Mixture-of-Experts pretraining, spanning from 1B to 68B parameters, with the largest model trained on 1 trillion tokens. Furthermore, we conduct supervised fine-tuning on the MOE-68B-A3B model and evaluate it on general capability, mathematical reasoning, and code generation benchmarks, where MONA achieves SOTA performance.

Jiacheng Li, Jianchao Tan, Hongtao Xu +5

Meituan, Beijing, China

Language Model PretrainingGradient DescentMuon OptimizerAccelerated Gradient Methods
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May 26, 2026

Latent Recurrent Transformer: Architecture Exploration, Training Strategies, and Scaling Behavior

We study Latent Recurrent Transformer (LRT), a lightweight augmentation of autoregressive transformers that reuses a high-level source-layer hidden state from the previous token as recurrent memory for the next token. Because this state is already computed during ordinary decoding, LRT introduces a cross-token, cross-layer latent pathway while preserving the standard attention mechanism, KV-cache interface, and one model forward per generated token. To pretrain this recurrence without sequentially unrolling the full sequence, we introduce interleaved parallel training: one full-sequence initialization forward constructs a shared buffer, followed by sequential refinement of disjoint position subsets with parallel computation within each subset. This provides every token with recurrent-memory-aware supervision at approximately 2x ideal token compute. Across 1.3B- and 2.1B-parameter nanochat-style backbones and a wide range of training budgets, LRT improves both BPB and CORE under matched effective compute. Additionally, LRT outperforms two-forward PonderLM-2 and matches a three-loop Transformer in BPB, while retaining one-forward-per-token decoding with 9% latency overhead over the standard Transformer.

Zeyi Huang, Xuehai He, LiLiang Ren +8

Microsoft · University of Washington · University of Wisconsin-Madison

Language Model PretrainingTransformer InferenceAutoregressive Language ModelingRecurrent TransformersAutoregressive Transformer
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May 26, 2026

The Stability of Singular Distribution: A Spectral Perspective on the Two-Phase Dynamics of Language Model Pre-training

Large language model pre-training typically exhibits a two-phase trajectory: a fast initial loss drop followed by a prolonged slow improvement. We identify an underlying spectral phenomenon, Stability of Singular Distribution (SoSD), where the trace-normalized singular value spectrum stabilizes early, even as parameter matrices continue to evolve. We demonstrate that synchronization between SoSD and the slow-descent regime is widely observed across diverse architectures (GPT-2, LLaMA) and settings, including various schedules (Step-wise, WSD, Cosine Decay), weight decays, and optimizers (AdamW, Muon). By analyzing a simplified Transformer, we prove that growing weight norms inevitably precipitate an early SoSD threshold, after which the rate of loss decrease becomes theoretically bounded by the variation in the singular distribution. We further interpret strategies like WSD and Muon through their ability to modulate the SoSD scale, offering a spectral lens for understanding efficient pre-training dynamics.

Hongtao Zhang, Wenjie Zhou, Chenxi Jia +2

State Key Laboratory of AI Safety, Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China · School of Advanced Interdisciplinary Sciences, University of Chinese Academy of Sciences, Beijing, China · University of Chinese Academy of Sciences, Beijing, China +1

Language Model PretrainingDeep Learning OptimizationNeural Network Training Dynamics
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May 26, 2026

Extra-Merge: Tracing the Rank-1 Subspace of Model Merging in Language Model Pre-Training

Model merging has emerged as a lightweight paradigm for enhancing Large Language Models (LLMs), yet its underlying mechanisms remain poorly understood. In this work, we analyze late-stage pre-training trajectories and uncover a Rank-1 Subspace phenomenon: while raw optimization steps oscillate violently, consecutive merged checkpoints collapse onto a stable, approximately one-dimensional linear manifold. We theoretically ground this observation in a river-valley landscape analysis: averaging acts as a geometric low-pass filter that dampens high-curvature noise to reveal the optimal descent direction. Capitalizing on this insight, we propose Extra-Merge, a training-free strategy that extrapolates along this subspace to minimize loss without additional gradient updates. Extensive experiments across GPT-2 and LLaMA families (124M to 2B) demonstrate that Extra-Merge consistently outperforms standard merging baselines. Notably, it yields consistent zero-shot accuracy gains on Pythia-12B downstream tasks and generalizes effectively to the Muon optimizer \citep{jordan2024muon}.

Wenjie Zhou, Bohan Wang, Hongtao Zhang +3

State Key Laboratory of AI Safety, Institute of Computing Technology, Chinese Academy of Sciences, China · University of Chinese Academy of Sciences, China · Alibaba Group, China +2

Language Model PretrainingNeural Network OptimizationWeight-Space AnalysisLanguage Model Merging
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May 25, 2026

On the Limits of Model Merging for Multilinguality in Pre-Training

Endowing models with consistent multilingual performance can be achieved by mixing pre-training data, or post-training approaches such as language-specific model merging. In this work, we test whether merging can be applied to monolingually pre-trained models. We conduct a controlled study on the efficacy of mixed, merged, and monolingual pre-training setups. We find that while monolingual pre-training results in strong in-language performance, merging any combination of monolingual models leads to performance collapse due to interference. Our analysis suggests representational similarity is a prerequisite for model merging. We therefore conclude that the flexibility of merging in fine-tuning does not extend trivially to language-specific pre-training.

Seth Aycock, Fedor Vitiugin, Aleksandr Umnov +2

University of Amsterdam

Language Model PretrainingMultilingual Language ModelsMultilingual Language Model EvaluationLanguage Model MergingModel Merging
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May 25, 2026

PowLU: An Activation Function for Stable Pre-Training of LLMs

In contemporary large language models (LLMs), the swish-gated linear unit (SwiGLU) activation function is widely adopted to regulate the information flow and introduce non-linearity. For large positive inputs, SwiGLU approximates the quadratic function x2x^2, providing strong nonlinearity and expressive capacity. However, this property also causes numerical instability as the input or model scale increases, particularly in low-precision LLM training. The main reason is its approximate quadratic amplification, which enlarges the output range and exacerbates outliers. To address this issue, we propose a stable activation function, Power Linear Unit (PowLU), for large-scale LLM pre-training. Specifically, PowLU employs a rational power function to achieve adaptive nonlinearity, thereby improving representation ability and enabling stable training in spike regions. Moreover, we provide theoretical justification for several key properties of PowLU. Scaling law experiments confirm that the performance is consistent across model sizes, and further experimental results with the Ling architecture (7.9B and 124B total parameters) demonstrate that PowLU achieves competitive results against SwiGLU and SwiGLU-Clip in large-scale training of LLMs. In addition, the experimental results also show that PowLU effectively improves the scalability of the large-scale training of LLMs.

Peijie Jiang, Yuqi Feng, Cunyin Peng +5

Ling Team, Ant Group

Language Model PretrainingNeural Network Activation FunctionsLLM Training
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May 24, 2026

Mimir: Large-scale Multilingual Concept Modeling

Current language modeling approaches are built around tokens. Text corpora are split into tokens, and models are trained by performing computations on these tokens, such as predicting the next token given the preceding ones as context. This paradigm has become the standard in modern language modeling, especially given the outstanding performance obtained by token-based architectures. However, recent works have not only begun to question how language models process and understand meaning from tokens, but also to question whether using higher levels of granularity could advance the research field. This led to the idea of Concept Modeling, that is, to directly train models for next-concept prediction rather than next-token prediction. In this work, we introduce Mimir, a 1.6B Large Concept Model trained for multilingual concept understanding and generation. We leverage a large-scale multilingual pre-training corpus (38,883,987,240 sentences) spanning 46 languages and a large-scale multi-turn, and multilingual instruction-tuning dataset (66,816,428 sentences) covering a total of 35 languages. We extensively evaluate model performance against a language model with a comparable number of parameters.

Elio Musacchio, Lucia Siciliani, Pierpaolo Basile

Department of Computer Science University of Bari Aldo Moro Bari, Italy

Language Model PretrainingMultilingual Language Models
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