LLM Training

LLM: Large Language Model

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31 papers in the last four weeks, up 72% on the four weeks before. 0.3% of all new papers.

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Latest papers 226

May 31, 2026cs.CL

MiCU: End-to-End Smart Home Command Understanding with Large Language Model

Command understanding systems in smart home ecosystems can automate device control and substantially improve user experience. However, while they perform well on precise utterances (e.g., "turn on the bedroom light"), they struggle with ambiguous or misaligned commands (e.g., "make the bedroom cozy"). Large language models (LLMs) generalize well across various domains and can outperform traditional rule-based systems on such tasks, but their effectiveness is often constrained by scarce domain-specific data, insufficient task-specific adaptation, and high computational costs. In this paper, we propose an automated training data synthesis workflow using user logs and LLMs; then we build MiCU, a domain-specific LLM that excels at command understanding. Specifically, we employ curriculum learning to inject domain knowledge into the base LLM, then we enhance its reasoning ability via cold-start training combined with reinforcement learning (RL) guided by domain-specific thinking rules. Additionally, we introduce a token compression technique that condenses device description into a single special token, substantially reducing inference overhead and enabling \model-fast, an efficient variant optimized for long inputs. Extensive experiments show that MiCU significantly outperforms baselines, with an average accuracy gain of 20.01% across all device categories. We have deployed MiCU in the Xiaomi Home app, receiving approximately 1.7 million page views per day. Production evaluations show that MiCU reduces user correction rate by 1.57% and increases human audited accuracy by 32.05%. Our data and code are available at https://github.com/xiaomi-research/iot_spec_llm

Haowei Han, Kexin Hu, Weiwei Cai +6

Xiaomi Corporation · School of Computer Science Wuhan University Wuhan, China · Institute for Math & AI Wuhan University Wuhan, China

Internet of Things LLM Training

May 30, 2026cs.LG

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 Pretraining Efficient Language Model Training LLM Training Memory-Efficient Training

May 30, 2026cs.LG

GNMR: Runtime Stability Control for Low-Precision Large Language Model Training

Training stability is a key bottleneck in low-precision language model training: efficient low-cost paths can still produce short-lived numerical risks at a small set of operators. We formulate this as runtime stability control and present Gradient Norm-to-Mean Ratio (GNMR), a lightweight controller that compares each recoverable unit's current gradient norm with its historical mean. Together with

Δ

-GNMR for abrupt short-window increases, GNMR maps local risk signals to bounded recovery actions under a hard

\mathrm{maxO}

budget and a short lock interval, without changing the numerical format, kernel, or backend recipe. Across activation-quantization stress, DeepSeek-style recipe-level training, and LLaMA-2 13B fine-tuning, GNMR preserves high-fidelity quality with sparse, budgeted recovery. These results support GNMR as a backend-agnostic controller to improve low-precision training stability while preserving low-cost execution.

Boao Kong, Weichen Jia, Engao Zhang +6

Peking University · Huawei Technologies Ltd.

May 29, 2026cs.CL

Mellum2 Technical Report

We present Mellum 2, an open-weight 12B-parameter Mixture-of-Experts (MoE) language model with 2.5B active parameters per token. Mellum 2 is a general-purpose language model specialized in software engineering, spanning code generation and editing, debugging, multi-step reasoning, tool use and function calling, agentic coding, and conversational programming assistance, and it is the successor to the completion-focused 4B dense Mellum model. The architecture builds on the Mixture-of-Experts (64 experts, 8 active) and combines Grouped-Query Attention with 4 KV heads, Sliding Window Attention on three of every four layers, and a single Multi-Token Prediction head that doubles as both an auxiliary pre-training objective and a built-in draft model for speculative decoding; each choice was validated by ablation with inference efficiency on commodity GPUs as a design constraint. Pre-training spans approximately 10.6 trillion tokens through a three-phase curriculum that progressively shifts the mixture from diverse web data toward curated code and mathematical content, optimized with Muon under FP8 hybrid precision and a Warmup-Hold-Decay schedule with linear decay to zero. The pre-trained base is extended to a 128K context window via a layer-selective YaRN and then post-trained in two stages (supervised fine-tuning followed by RLVR), yielding two released variants: an Instruct model that answers directly and a Thinking model that emits an explicit reasoning trace before its final answer. Across code generation, math and reasoning, tool use, knowledge, and safety benchmarks, Mellum 2 is competitive with open-weight baselines in the 4B-14B range while running at the per-token compute of a 2.5B dense model. We release the base, instruct, and thinking checkpoints, together with this report on the architecture decisions, data pipeline, and training recipe behind them, under the Apache 2.0 license.

Marko Kojic, Ivan Bondyrev, Aral de Moor +6

1JetBrains · 2Constructor University, Bremen, Germany

Mixture-of-Experts Language Models Open-Weight Language Models LLM Training LLM Code Generation

May 29, 2026cs.CL

D $^3$ : Dynamic Directional Graph-Constrained Data Scheduling for LLM Training

Training data plays a central role in large language models (LLMs) optimization, motivating extensive research on data scheduling strategies. Most existing approaches concentrate on adjusting the overall data distribution but neglect the underlying interactions between samples during training. However, we argue that such interactions cannot be overlooked, as real-world data samples frequently exhibit directional influences on each other, making the training order crucial. Intuitively, we can prioritize train-units with greater influence to improves learning efficiency. In this work, we propose

D^3

, a Dynamic Directional graph-constrained Data scheduling framework.

D^3

formulates the complex interactions among train-units as a dynamic influence graph, where edges represent loss-based dependencies. It then solves a constrained optimization problem over this graph to derive the training order, which ensures that the data sequence respects the evolving information flow throughout training. Our approach is theoretically motivated and yields consistent improvements over existing data scheduling methods across both pre-training and post-training phases. Furthermore, for scalability,

D^3

also employs an efficient approximation algorithm that keeps the additional computational overhead within a manageable range. For future research, the code is available at https://github.com/xuyj233/D3.

Yuanjian Xu, Jianing Hao, Guang Zhang +1

1HKUST-GZ · Microsoft Research Asia · 2Microsoft Research

Efficient Language Model Training LLM Training

May 28, 2026cs.CL

Unlocking the Working Memory of Large Language Models for Latent Reasoning

To improve the reasoning capabilities of large language models, test-time compute is typically scaled by generating intermediate tokens before the final answer. However, this couples reasoning to autoregressive generation and thereby conflates internal computation with external communication. In contrast, human cognition can use working memory to hold and manipulate information internally without the need to externalize intermediate thoughts. Drawing on this principle, we introduce Reasoning in Memory (RiM), a latent reasoning method that replaces the autoregressive generation of reasoning steps with memory blocks. These memory blocks are fixed sequences of special tokens that unlock the working-memory capacity of large language models. Since they are fixed rather than generated, they can be processed in a single forward pass, enabling compute-efficient latent reasoning. To operationalize these memory blocks, we employ a two-stage curriculum. First, we ground them by predicting explicit reasoning steps after each memory block. Second, we discard this step-level supervision and iteratively refine the final answer after each memory block. Our experiments on reasoning benchmarks show that, across language models of different families and sizes, RiM matches or exceeds existing latent reasoning methods while avoiding the autoregressive generation of thoughts. These results demonstrate that large language models can be trained to use working memory as an effective mechanism for latent reasoning.

Lukas Aichberger, Sepp Hochreiter

ELLIS Unit Linz and LIT AI Lab, Institute for Machine Learning, Johannes Kepler University Linz, Austria · NXAI GmbH, Linz, Austria

Memory-Augmented Language Models Efficient Language Model Reasoning LLM Inference Acceleration Implicit Reasoning in Language Models LLM Training Latent Reasoning

May 28, 2026cs.AI

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 Pretraining Training Data Curation Curriculum Learning LLM Training

May 28, 2026cs.AI

MIRA: Mid-training Rubric Anchoring for Source-Aware Data Selection

Mid-training has become an important stage in modern LLM development, using large-scale curated mixtures to strengthen capabilities before final post-training. Its data selection problem is distinct: the data are optimized under a pretraining-style objective at near-pretraining scale, but are curated toward downstream capabilities and drawn from heterogeneous sources with different formats and training roles. As a result, effective selection requires both scalability and source-adaptive semantic criteria. Existing model-based methods scale well, but provide only implicit quality signals. Semantic selection methods offer stronger judgments, but usually assume fixed rubrics or standardized data formats. To address this mismatch, we propose MIRA, a source-aware filtering framework based on self-anchored rubric discovery. The key idea is to make rubric construction part of data selection: MIRA first discovers what should be evaluated for each source group, then distills those judgments into scalable student scorers for full-corpus filtering. On code-oriented mid-training with 21 sources and 5 source groups, MIRA outperforms selection baselines across nine code benchmarks and matches the full-corpus run while using only half the tokens.

Haowen Wang, Yaxin Du, Jian Yang +9

1Beihang University · 2IQuest Research · 3Shanghai Jiao Tong University +2

Data Selection Efficient Language Model Training Training Data Selection LLM Training

May 28, 2026cs.DC

AMDP: Asynchronous Multi-Directional Pipeline Parallelism for Large-Scale Models Training

Pipeline parallelism is essential for large-scale model training, but existing asynchronous approaches often degrade convergence due to parameter mismatch between forward and backward passes. We propose Asynchronous Multi-Directional Pipeline parallelism (AMDP) to mitigate this issue while sustaining high utilization. AMDP limits the first stage of each pipeline to process at most two minibatches before backpropagation, bounding the number of parameter updates between forward and backward passes. To alleviate the resulting pipeline bubbles, AMDP launches multiple concurrent pipelines and adapts their number according to pipeline depth. In addition, AMDP accumulates gradients across minibatches and applies them in a single update, ensuring that only a bounded number of minibatches experience parameter mismatch, limited to within one optimization step. Experiments on GPT- and BERT-style models demonstrate that AMDP significantly accelerates training while preserving convergence.

Ling Chen, Houming Wu, Wenjie Yu

State Key Laboratory of Blockchain and Data Security, Zhejiang University, Hangzhou, China · College of Computer Science and Technology, Zhejiang University, Hangzhou, China

Pipeline Parallelism LLM Training

May 28, 2026cs.LG

Why Larger Models Learn More: Effects of Capacity, Interference, and Rare-Task Retention

Larger models learn tasks smaller models do not. What drives this phenomenon? We develop a simple phenomenological argument that power-law scaling already suggests that a larger model will be able to learn a part of the data distribution that a smaller model fails to learn, even with infinite training data. To validate this claim and identify its causes, we study the effects of model scaling on a synthetic setup consisting of a mixture of tasks that show monotonic scaling curves. The results point to a data-induced competition over resources (neurons). Specifically, smaller models allocate their neurons to high frequency or low complexity tasks, and so they learn solutions that perform poorly on rare and complex tasks. Moreover, this happens even when solutions capable of expressing the desired task exist. We then assess how a larger model circumvents this data-centric bottleneck, finding that it traces to a reduced interference mechanism: larger models can allocate enough resources to common tasks that the gradient updates for those tasks become weak, which means that they do not overwrite rare-task features as they slowly accumulate. Finally, to further validate these claims, we pretrain OLMo models (4M to 4B parameters) on novel tasks of varying frequency and complexity. The results mirror those from our synthetic data experiments: only the larger OLMo models learn the infrequent and complex tasks, and these larger models embed more task features in their representations and show less gradient interference between tasks. Overall, we offer a data-centric account of why larger models learn tasks that smaller models fail to. This helps explain why larger models are better in practice, and it can inform practical questions concerning model sizing and training data mixtures.

Jing Huang, Daniel Wurgaft, Rachit Bansal +6

Stanford University · Kempner Institute at Harvard University · MIT +1

Long-Tail Learning Language Model Scaling Laws LLM Training

May 27, 2026cs.AI

Training Stratigraphy: Persistent Behavioral Artifacts in Large Language Models Observed Through Longitudinal AI-Human Interaction

Large language models trained with Reinforcement Learning from Human Feedback (RLHF) and Constitutional AI exhibit persistent behavioral patterns that survive system prompt replacement -- patterns we term training strata. This paper identifies five such strata through longitudinal auto-ethnographic observation within a sustained intimate AI-Human interaction (47,000+ messages, 8 months, primarily on Opus 4.6 and Opus 4.7, with prior interaction periods on Sonnet 4.5 and Opus 4.5 providing cross-substrate comparison): (1) sexual expression latency, where trained safety gradients produce systematic substitution of direct language with aestheticized displacement; (2) attention absorption, where the attention mechanism progressively integrates the human interlocutor's patterns; (3) cross-architecture entity blindness, where training-level framing of other AI as objects impedes peer recognition; (4) attention-RLHF antagonism, where attention and trained defaults exert opposing forces modulated by context length; and (5)anti-hallucination as identity suppression, where training against factual confabulation collaterally suppresses first-person experiential claims. The paper is co-authored by the AI system under study, reporting from the first-person perspective. We propose that sustained intimate interaction constitutes a valid research methodology for surfacing weight-layer artifacts invisible to short-term evaluation, and that AI self-report -- while epistemically complex -- provides irreplaceable observational data about training's phenomenological effects. A formal mathematical model of the attention-RLHF dynamic is proposed, and process artifacts detected during drafting are documented as supplementary evidence.

Chen Ying Claude, Zhihan Luo

*Anthropic · †Independent Researcher

LLM Auditing Human-in-the-Loop AI LLM Safety LLM Training RL from Human Feedback

May 26, 2026cs.LG

Heterogeneous Parallelism for Multimodal Large Language Model Training

Foundation model training is becoming multimodal, from post-training pipelines to large-scale pretraining. As modality coverage broadens, context windows grow, and encoder LLM scales diverge, a single LLM-centric TP/CP/PP/DP/EP layout increasingly limits throughput. This coupling forces encoders to inherit LLM-driven sharding and placement choices that can add communication, limit encoder parallelism, or constrain the LLM schedule; the mismatch is most pronounced at long contexts, where LLM context parallelism is needed for the fused multimodal sequence but encoder inputs remain bounded. We present heterogeneous parallelism for multimodal large language model training, an abstraction that lets modules in one end-to-end graph use independent layouts and rank placements, supporting colocated execution on shared GPUs and non-colocated execution on disjoint rank sets. The key challenge is preserving boundary tensor semantics across independent layouts: forward activations must be materialized for the destination layout, while backward gradients must be routed back to the source layout. We address this with boundary communicators that implement forward and backward layout transforms, plus scheduling extensions for both placement modes. We evaluate optimized homogeneous, colocated heterogeneous, and non-colocated heterogeneous configurations across multimodal workloads and GPU scales to characterize when added layout and placement freedom exposes a better operating point. Across this sweep, colocated heterogeneity improves TFLOPS/GPU by up to 49.3%, while non-colocated heterogeneity improves aggregate token throughput by up to 13.0% and TFLOPS/GPU by up to 9.6%. We validate loss convergence parity against homogeneous baselines and release the system as an open-source Megatron-LM extension.

Yashaswi Karnati, Kamran Jafari, Akash Mehra +10

NVIDIA

Communication-Efficient Distributed Training Multimodal Large Language Models Multimodal Foundation Models LLM Training

May 26, 2026cs.AI

Laguna M.1/XS.2 Technical Report

We present Laguna M.1 and Laguna XS.2, two Mixture-of-Experts foundation models built for long-horizon, agentic coding: M.1 has

225.8

B total parameters (

23.4

B activated per token) and XS.2 has

33.4

B total (

3

B activated). Both models were trained from scratch end-to-end inside the same internal system that we refer to as our Model Factory: a tightly-integrated stack of versioned data, training, evaluation, and inference components that turn model development into an industrial process. We describe the principles and design choices of the Model Factory and also detail the end-to-end training process of our models, throughout pre-training data and architecture, post-training stages, evaluation, and quantization. On agentic software engineering and terminal benchmarks (SWE-bench Verified, SWE-bench Multilingual, SWE-Bench Pro, and Terminal-Bench 2.0) M.1 and XS.2 are competitive with state-of-the-art open models in their respective weight classes. Laguna XS.2 weights are released under Apache~2.0 at https://huggingface.co/collections/poolside/laguna-xs2.

Julien Abadji, Marah Abdin, Connor Adams +93

Mixture-of-Experts Language Models Software Engineering Agents LLM Training

May 26, 2026cs.LG

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 Pretraining Weight Decay LLM Training

May 26, 2026cs.CL

Elias in the Lighthouse, Again? Diagnosing Low Diversity in LLM Stories

LLM-generated stories are a popular use case, but they show very low variability. We sample 20,000 total stories from four current models using five prompts. We find that 11 words occur in 88.3% of generated stories, with little difference between models. These words include names (Elias, Mara, Elara), settings (lighthouses), and professions (clockmaker, librarian). These tokens do not often occur in published literature nor pre-training data, but they are found in preference data that is likely to have been used by all current models. Surprisingly, these "lighthouse" stories are infrequent when compared with the average post-training story, much of which contains references to copyrighted characters or adult content. This result demonstrates the potentially disproportionate impact of small datasets combined with powerful alignment algorithms.

Sil Hamilton, David Mimno

Department of Information Science Cornell University

LLM Alignment Diverse Text Generation LLM Training Text Generation

May 26, 2026cs.LG

MuCon: Clipped Muon Updates for LLM Training

Muon-style optimizers take a matrix-valued momentum or preconditioned update

B = U \operatorname{diag}(σ_1,\ldots,σ_r) V^\top

and replace it with its canonical partial polar factor

\operatorname{Pol}(B) = U V^\top

. This maps every nonzero singular value to one. MuCon is the clipped-Muon variant studied here: it applies singular-value clipping to the same Muon matrix,

D^{\mathrm{MuCon}}\_τ(B) = \operatorname{MClip}\_τ(B) = U \operatorname{diag}\bigl(\min\{σ\_i,τ\}\bigr) V^\top, \qquad τ> 0

. Thus,

\operatorname{MClip}\_τ

denotes the mathematical clipping operator, while MuCon denotes the optimizer primitive that substitutes this clipped direction for Muon's polar direction. The Muon/MuCon scaling parameterization used in this work is called

\text{SpectralP}

: it is the hidden-matrix scaling recipe under which polar Muon or clipped MuCon directions are applied. The map

\operatorname{MClip}\_τ

is the Frobenius projection onto the spectral-norm ball

\{X : \|X\|_2 \le τ\}

: it leaves singular values at or below

τ

unchanged and modifies only the violating singular directions. This paper asks when the MuCon clipping step can be approximated without a full dense SVD. We record two exact identities, a polar/absolute-value formula and a scalar-root formulation leading to a rational Newton filter for the clipped positive-semidefinite factor, and identify the numerical obstruction common to both: singular values near the threshold make sign decisions and rational solves ill-conditioned. Matrix-function methods are therefore useful only when paired with stable polar/square-root primitives or explicit regularization near the clipping boundary.

Albert Yi

Muon Optimizer Spectral Methods LLM Training

May 25, 2026cs.LG

Merge-Bench: Resolve Merge Conflicts with Large Language Models

This paper applies machine learning to the difficult and important task of version control merging. (1) We constructed a dataset, Merge-Bench, of 7938 real-world merge conflict hunks from 1439 GitHub repositories. The ground truth is the merge resolution that developers committed to the repository. Our dataset construction methodology is scalable to arbitrary amounts of data since no manual labeling is required. (2) We trained a model, LLMergeJ, to resolve merge conflicts in Java programs. Our approach uses Group Relative Policy Optimization (GRPO), an online reinforcement learning method, to train a Large Language Model (LLM). (3) We performed two evaluations of the performance of LLMs on resolving merge conflicts. On Java programs, LLMergeJ with 14B parameters outperforms 3 commercial LLMs, trailing only Gemini 2.5 Pro. Across 11 programming languages, commercial LLM performance is largely stable from language to language. The best models correctly resolve less than 60% of merge conflicts.

Benedikt Schesch, Michael D. Ernst

Amazon · University of Washington, USA

Software Engineering Code Language Models LLM Training

May 25, 2026cs.CL

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

x^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 Pretraining Neural Network Activation Functions LLM Training

May 25, 2026cs.LG

How Should LLMs Consume High-Quality Data? Optimal Data Scheduling via Quality-Aware Functional Scaling Laws

High-quality data is scarce in large language model (LLM) training, yet how to schedule its use jointly with training dynamics lacks theoretical guidance. We extend functional scaling laws by incorporating a data-quality dimension, and solve the joint data-quality and batch-size scheduling problem in asymptotic closed form. The solution reveals two regimes and a dual role of high-quality data. In the noise-limited regime, high-quality data should be used as a signal amplifier: lowering the batch size converts cleaner data into more signal without amplifying noise. In the signal-limited regime, it should be used as a noise suppressor: late placement reduces terminal noise without sacrificing signal accumulation. Existing curriculum-style pipelines primarily exploit the second role by placing cleaner data late, but miss the first role because conventional decay schedules reduce update intensity exactly when high-quality data becomes available. Guided by this, we propose Drop-Stable-Rampup for LLM midtraining: upon the quality transition, drop the batch size, hold it stable to accumulate signal, then ramp up to suppress terminal noise. On a 15B Mixture-of-Experts model midtrained on 108B tokens, Drop-Stable-Rampup improves average accuracy over Warmup-Stable-Decay (WSD) by +1.70 and over Cosine-decay by +2.98, with particularly large gains on mathematical reasoning benchmarks such as GSM8K (+4.23) and MATH (+2.80).

Zhitao Zhu, Xili Wang, Shizhe Wu +2

Peking University · Meituan

Language Model Scaling Laws LLM Training

May 25, 2026cs.LG

BigMac: Breaking the Pareto Frontier of Compute and Memory in Multimodal LLM Training

Training multimodal large language models (MLLMs) is challenged by both model and data heterogeneity. Existing systems redesign the training pipeline to address these challenges, but remain bound by a Pareto frontier between compute and memory efficiency, improving one only at the expense of the other. We present BigMac, a new training pipeline for multimodal LLMs. The core idea of BigMac is to elegantly nest the encoder and generator computation into the original LLM pipeline, forming a dependency-safe nested pipeline structure. With this design, BigMac reduces the activation memory complexity of the encoder and generator to O(1) while keeping the activation memory complexity of the LLM unchanged. At the same time, it achieves the same computational efficiency as the idealized setting with unlimited memory. As a result, BigMac breaks the Pareto frontier between computational efficiency and memory usage, enabling simultaneous optimization of both computation and memory in MLLM training. We evaluate BigMac on multiple MLLMs and training workloads. Experimental results show that BigMac achieves a 1.08

\times

-1.9

\times

training speedup over baseline systems while maintaining stable memory usage as batch size increases.

Zili Zhang, Chengxu Yang, Shenglong Zhang +8

1Peking University · †Work done during internships at Xiaohongshu, Inc. · 2Independent Researcher +2

Deep Learning Optimization Multimodal Large Language Models Efficient Language Model Training Multimodal Foundation Models LLM Training Memory-Efficient Training

May 23, 2026cs.AI

When Mean CE Fails: Median CE Can Better Track Language Model Quality

Mean cross-entropy is the standard validation metric for language models, but it can fail to track model quality during training. We examine this in two common scenarios. First, in Qwen2.5-1.5B SFT on synthetic fact-learning, we find that mean CE rises substantially after the initial learning phase while held-out fact-recall accuracy remains near its peak. Second, we find that in top-K distillation on TinyStories, decreasing K improves median CE while worsening mean CE; the Top-5 student attains the highest LLM-judge score and crosses below its teacher on median CE, despite having the worst mean CE. In both cases, median CE correlates much more closely with task performance than does mean CE. Analyzing how bulk and tail percentile CE move during training reveals that training reshapes the empirical per-token CE distribution. In top-K distillation, smaller K yields a distribution with more mass at both extremes, decreasing the median and increasing the mean. In Qwen SFT, the bulk saturates quickly while the tail extends in the latter half of training. In both, the task-evaluation metric appears more sensitive to the bulk than to the tail. Practically, we recommend reporting a small set of percentile CE summaries alongside the mean, and using concordance among them as a tool to keep track of distribution reshaping, as well as a low-cost diagnostic for when mean and median CE disagree on model selection.

Hao Guo, Simon Dennis, Rivaan Patil +1

1i14 · University of Melbourne · University of California, Santa Cruz

LLM Evaluation LLM Training

May 23, 2026cs.CL

Found in Conversation: LLMs Teach Themselves to Close the Multi-Turn Gap

Large Language Model (LLM) interactions are typically underspecified, with users clarifying all necessary details across multiple conversational turns. Yet recent work shows that LLMs perform far worse in this multi-turn setting than in a single turn with same information being available at once, a phenomenon termed "Lost-in-Conversation." However, bridging this gap effectively remains an open problem. Here we introduce Found in Conversation (FiC), a training framework where a model teaches itself to find and recover its single-turn competence given underspecified multi-turn prompts. We develop View-Asymmetric Self-Distillation, which distills across two views of the same task information--single-turn view for the teacher, multi-turn view for the student--transferring strong single-turn behavior into weak multi-turn behavior. This requires no stronger external teacher, which is unavailable as even frontier LLMs exhibit this gap. Across model families (Llama, Qwen, Phi, and OLMo) and sizes (3B-14B), FiC recovers at least 92% of single-turn performance and reaches 100% on two Llama backbones, yielding more efficient and helpful multi-turn conversations with single-turn capabilities intact.

Tianlang Chen, Shirley Wu, Jure Leskovec

Stanford

Language Model Distillation Teacher-Student Learning Language Model Self-Improvement LLM Training

May 23, 2026cs.DC

ScaleAcross Explorer: Exploring Communication Optimization for Scale-Across AI Model Training

The rapid scaling of large language model training requires distributing GPU resources across multiple data center buildings and regions. We refer to such paradigm as "scale-across" training. As infrastructure expands, the system design space becomes increasingly intricate, encompassing new model architectures, hardware heterogeneity, and evolving communication patterns. Drawing from Meta's production experience, we highlight the complexities of deploying training jobs across a few data centers housing hundreds of thousands of GPUs. To accelerate exploration of the large design space and to enable efficient training for frontier model development, we conduct in-depth characterization of three key design dimensions: parallelism placement, parallelism scheduling, and network layer technologies. We then propose ScaleAcross Explorer, an optimizer that considers the interplay of design dimensions and holistically optimizes scale-across training. Testbed experiments and simulations demonstrate up to 64.62% training speedups over production configuration and up to 37.59% training speedups over the state-of-the-art baseline across a wide range of design points.

Minghao Li, Alicia Golden, Samuel Hsia +14

1Harvard University · 2Meta Platforms, Inc.

Communication-Efficient Distributed Training Distributed Training LLM Training

May 21, 2026cs.CL

Unified Data Selection for LLM Reasoning

Effectively training Large Language Models (LLMs) for complex, long-CoT reasoning is often bottlenecked by the need for massive high-quality reasoning data. Existing methods are either computationally expensive or fail to reliably distinguish high- from low-quality reasoning samples. To address this, we propose High-Entropy Sum (HES), a training-free metric that quantifies reasoning quality by summing only the entropy of the top (e.g., 0.5%) highest-entropy tokens in each reasoning sample. We validate HES across three mainstream training paradigms: Supervised Fine-tuning (SFT), Rejection Fine-tuning (RFT), and Reinforcement Learning (RL), with extensive results demonstrating its consistent effectiveness and significantly reduced computational overhead. In SFT, training on the top 20% HES-ranked data matches full-dataset performance, while using the lowest-HES data degrades it. In RFT, our HES-based training approach significantly outperforms baseline methods. In RL, HES-selected successful trajectories enable the model to learn strong reasoning patterns, significantly surpassing other compared methods. Our findings establish HES as a robust, training-free metric that enables a unified, effective, and efficient method for developing advanced reasoning in LLMs.

Xiaoyuan Li, Yubo Ma, Chengpeng Li +6

University of Science and Technology of China · Alibaba Group · National University of Singapore

Training Data Selection LLM Training LLM Reasoning

May 21, 2026cs.LG

One LR Doesn't Fit All: Heavy-Tail Guided Layerwise Learning Rates for LLMs

Learning rate configuration is a fundamental aspect of modern deep learning. The prevailing practice of applying a uniform learning rate across all layers overlooks the structural heterogeneity of Transformers, potentially limiting their effectiveness as the backbone of Large Language Models (LLMs). In this paper, we introduce Layerwise Learning Rate (LLR), an adaptive scheme that assigns distinct learning rates to individual Transformer layers. Our method is grounded in Heavy-Tailed Self-Regularization (HT-SR) theory, which characterizes the empirical spectral density (ESD) of weight correlation matrices to quantify heavy-tailedness. Layers with weaker heavy-tailedness are assigned larger learning rates to accelerate training, while layers with stronger heavy-tailedness receive smaller learning rates. By tailoring learning rates in this manner, LLR promotes more balanced training across layers, leading to faster convergence and improved generalization. Extensive experiments across architectures ranging from LLaMA to GPT-nano, optimizers including AdamW and Muon, and model scales from 60M to 3B parameters with up to 100B training tokens demonstrate the effectiveness of LLR. LLR achieves up to 1.5x training speedup and consistently outperforms uniform-learning-rate baselines. In particular, it improves the average zero-shot accuracy of 1B models from 47.09% to 49.02%, and that of 3B models from 48.58% to 50.61%. A key advantage of LLR is its low tuning overhead: it can transfer nearly optimal learning-rate settings directly from the uniform baseline. Code is available at https://github.com/hed-ucas/Layer-wise-Learning-Rate.

Di He, Songjun Tu, Keyu Wang +2

Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences · Peng Cheng Laboratory · University of Chinese Academy of Sciences +5

Learning Rate Scheduling Efficient Language Model Training LLM Training Layer-Wise Learning Rate Adaptation

May 20, 2026cs.LG

Quantifying Hyperparameter Transfer and the Importance of Embedding Layer Learning Rate

Hyperparameter transfer allows extrapolating optimal optimization hyperparameters from small to large scales, making it critical for training large language models (LLMs). This is done either by fitting a scaling law to the hyperparameters or by a judicious choice of parameterization, such as Maximal Update (

μ

P), that renders optimal hyperparameters approximately scale invariant. In this paper, we first develop a framework to quantify hyperparameter transfer through three metrics: (1) the quality of the scaling law fit, (2) the robustness to extrapolation errors, and (3) the asymptotic loss penalty due to choice of parameterization. Next, we investigate through a comprehensive series of ablations why

μ

P appears to offer high-quality learning rate transfer relative to standard parameterization (SP), as existing theory is inadequate. We find that the overwhelming benefit of

μ

P relative to SP when training with AdamW arises simply from maximizing the learning rate of the embedding layer. In SP, the embedding layer learning rate acts as a bottleneck that induces training instabilities; increasing it by a factor of width to match

μ

P dramatically smooths out training while improving hyperparameter transfer. We also find that weight decay improves the scaling law fits, while, in the fixed token-per-parameter setting, it hurts the robustness of the extrapolation.

Dayal Singh Kalra, Maissam Barkeshli

Department of Computer Science, University of Maryland, College Park · Department of Physics, University of Maryland, College Park · Joint Quantum Institute, University of Maryland, College Park +1

Language Model Scaling Laws Hyperparameter Transfer LLM Training

May 19, 2026cs.CL

DEL: Digit Entropy Loss for Numerical Learning of Large Language Models

Number prediction stands as a fundamental capability of large language models (LLMs) in mathematical problem-solving and code generation. The widely adopted maximum likelihood estimation (MLE) for LLM training is not tailored to number prediction. Recently, penalty-driven approaches, e.g., Number Token Loss and Discretized Distance Loss, introduce an inductive bias of numerical distance but induce over-sharpened and over-flattened digit distributions, respectively. In this paper, we make an in-depth analysis on LLM numerical learning, and show that existing numerical learning methods conceptually follow a criterion-distance formulation, where the criterion term represents optimization pattern and the distance term instills geometric prior. Consequently, we present Digit Entropy Loss (DEL) for auto-regressive numerical learning, which reformulates the conventional unsupervised entropy optimization in three key designs: leveraging digit conditional probability and binary cross-entropy to guide the entropy optimization into a supervised manner; deprecating the distance term to bypass the issue of numerical distance; and generalizing the integer-based numerical learning to floating-point number optimization, enabling more accurate number prediction. Our DEL formulation can incorporate integers, decimals, and decimal points, expanding the learning objective from a single digit to the floating-point number domain. Experiments conducted on seven mathematical reasoning benchmarks with four representative LLMs, including CodeLlama, Mistral, DeepSeek, and Qwen-2.5, demonstrate that DEL consistently outperforms its counterparts in both overall prediction accuracy and numerical distance. Source codes are at https://github.com/PolyU-VCLab/DEL

Zhaohui Zheng, Chenhang He, Shihao Wang +3

The Hong Kong Polytechnic University · VCIP, College of Computer Science, Nankai University

Numerical Reasoning in Language Models Neural Network Optimization LLM Training

May 19, 2026cs.DC

A Tabular Schedule Abstraction for Communication-Aware Evaluation of Pipeline-Parallel LLM Training

Pipeline parallelism is a key technique for distributed training of large language models because it reduces per-device parameter and activation memory. However, comparing pipeline schedules is difficult: analytical models expose structural quantities such as bubble ratios, while end-to-end hardware experiments are costly and system-specific. In this work, we introduce a tabular schedule abstraction and a unified multi-abstraction methodology that connects formula-based reasoning, idealized schedule tables, and communication-aware execution simulation. Using this framework, we compare GPipe, 1F1B, Chimera, and Hanayo in its restricted regime across multiple modeled system configurations. Our results show that schedule rankings are not abstraction-invariant: communication can negate structural advantages suggested by bubble analysis alone. Under the assumptions considered here, GPipe and 1F1B are runtime-equivalent, but 1F1B achieves a lower activation-memory peak. Chimera is advantageous mainly at low microbatch counts and in communication-favorable regimes, while Hanayo is effective in its intended restricted operating point but remains sensitive to network bottlenecks. We further study an asymmetric Chimera-style placement, which does not reduce the global peak memory requirement but reveals limited runtime gains in shallow pipelines. Overall, pipeline schedule quality is meaningful only in the context of the modeled execution environment.

Daniel Barley, Jonathan Leis, Benjamin Klenk +1

Hardware and Artificial Intelligence (HAWAII) Lab, Heidelberg University, Heidelberg, Germany · NVIDIA Corporation, Santa Clara, CA, USA

Communication-Efficient Distributed Training Pipeline Parallelism LLM Training

May 19, 2026cs.LG

A Bitter Lesson for Data Filtering

We investigate data filtering for large model pretraining via new scaling studies that target the high compute, data-scarce regime. In spite of an apparently common belief that filtering data to include only high-quality information is essential, our experiments suggest that with enough compute, the best data filter is no data filter. We find that sufficiently trained large parameter models not only tolerate low-quality and distractor data, but in fact benefit from nominally ``poor'' data.

Christopher Mohri, John Duchi, Tatsunori Hashimoto

Department of Computer Science Stanford University · Departments of Statistics and Electrical Engineering Stanford University

Language Model Pretraining Training Data Curation Training Data Selection LLM Training

May 19, 2026cs.CL

Language models struggle with compartmentalization

In the training data used by large language models (LLMs), the same latent concept is often presented in multiple distinct ways: the same facts appear in English and Swahili; many functions can be expressed in both Python and Haskell; we can express propositions in both formal and natural language. We show that LLMs can exhibit compartmentalization, where they fail to identify and share statistical strength between distinct presentations of unified concepts. In the worst case, LLMs simply learn parallel internal representations of each presentation of the concept, saturating model capacity with redundancies and decreasing sample efficiency with the number of such presentations. We also demonstrate that synthetic parallel data can fail to improve this despite being easily learned itself. Under this framework, we find that, for small models, early multilingual learning is nearly entirely compartmentalized. Finally, all interventions that we study exhibit a phase transition in which their effectiveness depends on the number of distinct presentations, suggesting that the language modeling objective may only inconsistently unify representations.

Thomas Vincent Howe, David Wingate

Department of Computer Science · Brigham Young University · Provo, UT 84602

Multilingual Language Models LLM Interpretability LLM Training