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

Jun 25, 2026cs.CL

CARVE: Content-Aware Recurrent with Value Efficiency for Chunk-Parallel Linear Attention

Recurrent delta-rule models keep a fixed-size state matrix S (d_v x d_k) that compresses all past context. The state of the art (GDN-2) gates this update with element-wise matrix erase/write masks. This is powerful but has two defects. First, both gates are computed from the incoming token alone, making the model memory-blind: it decides what to erase without seeing what it has stored. Second, value-axis coupling in the erase gate blocks the WY-form triangular chunk solver that drives efficient training -- the intra-chunk system splits into d_v independent solves, collapsing throughput to serial-recurrence cost. We introduce CARVE (Content-Aware Recurrent with Value Efficiency), which fixes both and, via a single-launch "megakernel" scheduling of the same WY-form math, trains faster than the matrix-gated baseline it replaces. The key idea is architectural: restricting all gating to the key axis makes the intra-chunk coupling independent of the value index, restoring one unmodified WY-form solve. Within this constraint, CARVE conditions both gates on a content signal read once per chunk from the chunk-boundary state and folded algebraically into each gate's low-rank projection (by associativity, U(Sq)=(US)q), giving memory-aware gating at negligible extra traffic. At init the content projections are zero, so CARVE is bit-identical to the baseline; we prove the one-chunk staleness perturbs gates by only O(1/sqrt(L)), matching a measured 0.18% deviation flat up to L=128. At 1.3B parameters / 100B FineWeb-Edu tokens on H100 (three seeds), CARVE improves every axis: WikiText perplexity 15.72 vs 15.90 (hybrid 15.41 vs 15.62), +0.63 pp average common-sense accuracy, and state-of-the-art RULER and real-world recall -- while training +1.4% faster at matched depth and +19.3% at iso-quality depth, at +13% peak memory. Backed by six formal guarantees.

Sayak Dutta

Linear Attention Delta-Rule Linear Attention Attention Mechanisms LLM Training

Jun 23, 2026cs.LG

Training for the Model You Return: Improving Optimization for Iterate-Averaged Language Models

Many modern Language Model (LM) pipelines return an averaged model, such as an exponential moving average of the training iterates, rather than the final iterate itself. This raises a fundamental question: given that we will return an iterate average, how should we change training to improve the performance of this average? We study this question by formulating optimizer design for the iterate-average estimator as an optimal-control problem. In a continuous-time stochastic quadratic model, we solve for the control strategy that minimizes the error of the returned average subject to a penalty on the size of the intervention. A practical approximation to this controller yields PACE, a lightweight wrapper around AdamW that pulls the live weights toward their exponential moving average with a clipped, per-coordinate control strength. We prove that a stylized version of PACE converges at the standard stochastic convex optimization rate, up to a factor depending on the averaging rule, while in the quadratic setting it can strictly improve the limiting squared error of the iterate-average estimator and can do so by an arbitrarily large factor on some instances. Empirically, our results suggest that PACE improves over AdamW and EMA-evaluated AdamW in supervised fine-tuning of 1-2B parameter LMs and in GPT-2 pretraining on FineWeb for a wide range of learning rates, decay schedules, and other hyperparameters.

Kwok Chun Au, Adam Block

Department of Computer Science, Columbia University · Department of Electrical Engineering, Columbia University

Deep Learning Optimization LLM Training

Jun 23, 2026cs.LG

Internal Data Repetition Destroys Language Models

Language models are running out of high-quality training data, and even aggressively deduplicated corpora retain some amount of repetition. Earlier controlled studies predated Chinchilla-style scaling laws and could only measure the cost of repetition indirectly. We revisit repetition in the Chinchilla era, using a fitted no-repetition scaling law to report Compute-Equivalent Gain and Compute-Equivalent Loss. We show that under this modernized paradigm, repetition damage is systematic in three ways. First, holding compute allocated to repeated data constant, eval loss peaks at an intermediate repeat count

\Rep

; repeating a moderately sized subset a moderate number of times damages performance more than repeating a large subset a few times or a small subset many times. Second, the location of this peak is well-fit by a power law in model size; this scaling law reveals that the most damaging number of repeated data grows more quickly than compute. Finally, when repeated documents consume 10% of the FLOPs budget in a controlled exact-document repetition setting, the compute-equivalent loss can be large: on FineWeb-Edu-Dedup, the most damaging repeat count for a Qwen3-style 344M-parameter model at

\OT=1

matches the loss of a no-repetition run using 67% of the FLOPs. We demonstrate that these phenomena are not language-model-specific, and can be analytically understood in a simple statistical model: a misspecified linear regression with verbatim duplicates reproduces the same qualitative loss peak, quantifying how such peaks can arise from a statistical tradeoff between memorization and generalization. Our findings add precision to the study of duplication in language models, allowing practitioners to quantify the wasted compute incurred by the presence and repeat structure of duplicates in pretraining corpora.

Jessica Chudnovsky, Joshua Kazdan, Noam Levi +6

1Stanford Computer Science. · 2Stanford Statistics. · 3Tel Aviv University. +1

Memorization in Language Models Language Model Scaling Laws LLM Training Data Repetition in Language Model Training

Jun 22, 2026cs.LG

FORGE: Fused On-Register Gradient Elimination for Memory-Efficient LLM Training

Reverse-mode differentiation computes every weight gradient, writes it to memory, and only then lets the optimizer read it back. This two-phase schedule sets the memory ceiling of modern training: at the seam between the phases, every layer's gradient is live at once. We argue that this materialized gradient is an artifact of how differentiation is staged, not a quantity that learning requires -- and we eliminate it. FORGE folds the optimizer step into the backward pass and applies it one tile at a time, entirely in registers, so each gradient tile is consumed the instant it is produced and never becomes a tensor. The fusion changes only when the update happens, not what it computes: in full precision the fused step is provably exact -- the identical optimizer update, for every element-wise rule -- and that exactness survives tensor- and sequence-parallel sharding; in the bf16 and 8-bit regimes used in practice it is faithful rather than bit-identical, its deviation bounded and, for the weight store, rendered unbiased by stochastic rounding. Because each gradient tile is born and consumed in the same registers, it is never converted down to bf16 to be stored and read back; FORGE thus preserves the full-precision fidelity that both bf16 and 8-bit optimizers lose to that conversion. Nor is the method tied to one architecture or one optimizer: linear layers are ubiquitous, and FORGE reclaims the gradient memory of any of them under any element-wise rule. Empirically FORGE more than halves the memory of an optimizer step and, at the small batch sizes typical of fine-tuning and continued pretraining, runs about 1.5x faster; integrated into tensor-parallel Megatron-LM it fits 8B training at four times the micro-batch a standard optimizer allows on the same GPUs.

Dikshant Kukreja, Kritarth Prasad, Avinash Anand +6

Puch AI · Singapore Institute of Technology · Nanyang Technological University +2

Automatic Differentiation Backpropagation Memory-Efficient Optimization Efficient Language Model Training LLM Training Memory-Efficient Training

Jun 21, 2026cs.CL

Words as Difference Makers: How Large Language Models Determine Causal Structure in Text

Because large language models (LLMs) are impressively successful in predicting text, it appears that they must have access to a 'world model' representing causal and definitional structure. However, the dominant formalisms of modern causal inference -- Judea Pearl's interventionist approach and the Neyman-Rubin potential outcomes framework -- struggle to illuminate how LLMs learn causal structure. I resolve this puzzle by arguing that LLMs employ a specific inductive approach based on a difference-making logic -- sometimes called variational induction. I demonstrate how central aspects of this logic are realized during training, where LLMs require enormous amounts of text data from a wide range of contexts to identify difference- and indifference-makers within word sequences. Furthermore, I analyze specific architectural features of LLMs -- such as token embeddings and self-attention -- to determine their roles in variational induction. The difference-making logic of LLMs fundamentally parallels the experimental method, where causal relations are derived by systematically varying individual circumstances to determine their influence on a phenomenon.

Wolfgang Pietsch

tum

Causal World Models LLM Interpretability Causal Structure Learning Causal Reasoning in Language Models LLM Training

Jun 19, 2026cs.LG

Towards Understanding the Power and Limits of the Muon Optimizer: A River-Valley Perspective

Recently, Muon has gained substantial attention as an appealing alternative to Adam-like optimizers, with many works highlighting its advantages through spectral normalization and improved conditioning. Yet this positive theoretical narrative contrasts with its empirical performance in large language model (LLM) training, where Muon's gains over Adam/AdamW are often mixed, schedule-sensitive, and not uniformly superior. To address this gap, we develop a trajectory-level theory characterizing both the strengths and limitations of Muon. We introduce a mixed-spiked matrix sensing model whose sensing operator decomposes into signal, spike, and bulk components, capturing a mixture of anisotropic structure and long-tail information reminiscent of LLM training. On top of it, we adopted a river-valley perspective in which we view the landscape as composed of a river direction flowing to the desired solution and hill directions encoding nuisance or task-irrelevant information. In the momentum-free setting, we show that Muon moves faster along the information-bearing river direction during early optimization, but can converge much more slowly near the river bottom than gradient descent. We then extend the river-valley perspective to general nonconvex objectives with momentum by studying points on the spectral river. There, while Muon converges faster early on, its orthogonalized update removes residual scale information, making it prone to overshooting and oscillation near the target solution. Together, these results suggest that our characterizations extend beyond spiked matrix sensing and motivate switching to GD-like refinement optimizers in the final phase, rather than relying only on a fixed learning-rate schedule for Muon. We also provide preliminary evidence supporting this two-stage approach in language model training experiments.

Tianqi Shen, Jinji Yang, Runze Shi +3

Department of Computer Science City University of Hong Kong (CityUHK) · Department of Statistics and Data Science University of Pennsylvania · School of Statistics and Data Science Shanghai University of Finance and Economics

Deep Learning Optimization Muon Optimizer LLM Training

Jun 18, 2026cs.DC

Online Dynamic Batching with Formal Guarantees for LLM Training

Modern LLM training breaks a core assumption behind offline batch samplers: the true training cost of a sample is only observable after preprocessing, augmentation, templating, tokenization, and multimodal visual-token expansion. Unless one pays for a preprocessing- and augmentation-dependent length cache, batch construction is therefore blind to the quantity that determines padding, memory use, and GPU saturation. We introduce Online Dynamic Batching (ODB), a DataLoader-side drop-in system that moves batch formation to this point of accurate observability while preserving DDP step alignment. We formalize this synchronization requirement as the Distributed Group Alignment Problem and prove deadlock-free bounded termination with default join-mode identity coverage and opt-in non-join sample-quota closure. ODB requires no model, optimizer, or attention-kernel changes and is released as online-dynamic-batching with lightweight trainer adapters. Across public 2B/8B Qwen3-VL runs on UltraChat/LLaVA/ShareGPT4o, ODB improves literal emitted-sample throughput vs. fixed-batch Standard by 1.58-2.51x on single-node Full FT/LoRA and 1.71-3.78x on two-node Full FT, with Standard-comparable quality; production MM-Mix reaches 4.43x. Against GMT/BMT offline token-budget oracles, ODB is within 15% on UltraChat/LLaVA and faster on high-CV ShareGPT4o: 2.24-2.39x single-node Full FT/LoRA and 3.06-3.69x two-node Full FT. Together, ODB occupies the online/drop-in regime for high-heterogeneity LLM fine-tuning: large throughput gains at Standard-comparable quality, formal DGAP guarantees, and no length-cache precompute or kernel rewrites.

Dian Li, Zekun Wang, Yaoru Wang +1

Tencent

LLM Fine-Tuning Distributed Training LLM Training

Jun 17, 2026cs.CL

RegMix-D: Dynamic Data Mixing via Proxy Training Trajectories

Data mixture selection is critical for Large Language Model pretraining. Existing methods such as RegMix select a single static mixture by fitting a regression model on small-scale proxy runs. We propose RegMix-D, a simple extension of RegMix to dynamic mixing. Our key observation is that proxy runs produce not only endpoint losses, but also full loss trajectories, which can be used to further improve data mixture. By training regression model on these trajectories, we can predict optimal mixtures at multiple training stages. RegMix-D supports two deployment modes: an offline variant that generates a complete mixture schedule before target training, and an online variant that adapts the mixture during training using observed loss. Experiments on 25B tokens of the Pile dataset with a 1B parameter target model show that RegMix-D consistently improves over RegMix and DoReMi across 13 downstream tasks while remaining proxy-efficient: it surpasses RegMix even with only 128 proxy models (25% of RegMix's proxy compute budget).

Kaiyan Zhao, Zhongtao Miao, Akiko Aizawa +1

The University of Tokyo · National Institute of Informatics

Language Model Pretraining Training Data Selection LLM Training

Jun 17, 2026cs.LG

BLADE: Scalable Bi-level Adaptive Data Selection for LLM Training

As Large Language Model (LLM) datasets scale to trillions of tokens, data selection has emerged as a critical frontier to filter out uninformative noise and construct adaptive learning trajectories. Beyond static heuristic filtering, advanced data selection methods for LLM training largely follow two paradigms, each with fundamental limitations. Influence-based methods provide principled bi-level objectives but require intractable inverse-Hessian computations, while excess-loss methods are computationally efficient but rely on a static reference model that becomes misaligned with the evolving proxy model during training. We propose BLADE (Bi-Level Adaptive Data sElection), a Hessian-free framework for data selection. BLADE reformulates the bi-level optimization problem underlying influence-based methods as a penalized single-level objective via Lagrange multipliers, avoiding inverse-Hessian computation while revealing a principled connection to excess-loss based data selection. The resulting objective recovers an excess-loss form but replaces the static reference model with a dynamic one that stays synchronized with training. Theoretically, we prove that this penalized formulation guarantees first-order convergence. For efficient online batch selection, we instantiate BLADE as a memoryless randomized block-coordinate Frank-Wolfe algorithm. Extensive experiments show that BLADE consistently outperforms state-of-the-art data selection baselines, providing a practical recipe for LLM training.

Jiaxing Wang, Deping Xiang, Jin Xu +9

Training Data Selection Bilevel Optimization LLM Training

Jun 16, 2026cs.AI

The Stanford EDGAR Filings Dataset: Reconstructing U.S. Corporate and Financial Disclosures into Layout-Faithful and Token-Efficient Pretraining Data

As high-quality public web corpora become increasingly exhausted, clean long-context documents have become a scarce and expensive source of training data for large language models (LLMs). Existing long-context corpora are often proprietary and costly to acquire, synthetically generated, or concentrated in narrow domains such as programming. We introduce the Stanford EDGAR Filings Dataset (SEFD), an open reconstruction of SEC filings into layout-faithful MultiMarkdown for financial language modeling and evaluation. SEFD makes audited financial statements, risk disclosures, ownership reports, accounting notes, and market-moving event filings usable as long-context pretraining data and as a basis for financial reasoning, forecasting, compliance, and document understanding. The resulting corpus is token-efficient, model-ready, and has less than 0.1% overlap with Common Crawl-derived corpora. We release SEFD-v1, a 152B-token initial public snapshot, and provide corpus-level analyses of a larger 18.5M-filing archive estimated at 550B tokens. We further introduce two SEFD-derived benchmarks: EDGAR-Forecast, which evaluates filing-grounded numerical forecasting after model knowledge cutoffs, and EDGAR-OCR, which evaluates transcription of complex financial tables.

Nick Bettencourt, Xiaowei Ding, Kay Giesecke

Department of Applied Statistics and Data Science University of California, Los Angeles · School of Information Management Nanjing University · Advanced Financial Technologies Lab Stanford University

Document Understanding Long-Context Language Modeling Financial Forecasting Language Modeling LLM Training Finance

Jun 16, 2026cs.AI

Small Initialization Matters for Large Language Models

Large language models provide a tractable system for asking how intelligence itself emerges, rather than only how LLMs can be engineered. Although progress is usually attributed to scale, data and architecture, we show that parameter initialization is a gene-like determinant of training and, in particular, of model capacity. Reducing the initialization scale consistently improves pretraining, with the largest gains on reasoning-demanding tasks. We identify two widely used empirical settings that restrain the advantage of small initialization, and show how relaxing them restores favorable scaling. We further uncover a critical initialization that balances the reasoning and training. Mechanistically, small initialization drives a distinct developmental trajectory: parameters first condense into low-complexity structures and later expand into richer representations, giving concrete form to the idea that compression is intelligence. Token-level analyses show that the gains concentrate on non-trivial, context-constrained predictions rather than all tokens uniformly. These results motivate a simple

γ

-initialization rule: expose initialization rage as an explicit knob and use small initialization by default, an almost cost-free intervention that improves pretraining and strengthens reasoning across model scales.

Liangkai Hang, Junjie Yao, Zhiyu Li +3

School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, 200240, China. · MemTensor (Shanghai) Technology Co., Ltd.. for Advanced Algorithms Research, Shanghai, China. · Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, 200240, China.

Language Model Pretraining Neural Network Initialization LLM Training LLM Reasoning

Jun 15, 2026cs.CL

Tying the Loop -- Tied Expert Layers in Mixture-of-Experts Language Models

Mixture-of-Experts (MoE) architectures efficiently scale Large Language Models (LLMs) by activating only a small fraction of their experts per token, yet the full parameter count - dominated by the expert parameters - must be held in training and inference memory. To address this, we introduce Expert Tying, an architectural modification that shares expert parameters across consecutive transformer layers while preserving independent, layer-wise routing and attention. We evaluate this approach across common, state-of-the-art architectures, including OLMoE, Qwen3, and DeepSeek-style MoEs. Our pretraining experiments demonstrate that tying experts can reduce memory footprint by almost 2x at virtually no degradation in perplexity or downstream quality. By exploiting the parameter redundancy inherent in MoE pathways, our method provides a highly favorable compute-to-memory trade-off, advancing efficient training and scaling of next-generation LLMs.

Martin Jaggi

EPFL

Mixture-of-Experts Language Models LLM Compression LLM Training

Jun 12, 2026cs.CR

From Prompts to Responses: Dual-Sided Data Leakage and Defense in Split Large Language Models

Large language models (LLMs) are increasingly deployed in privacy-sensitive domains, where users must balance the risk of data exposure through external APIs against the high computational cost of local deployment. Split learning has therefore emerged as a promising paradigm for LLM fine-tuning and inference under limited local resources. However, it introduces new privacy risks. Prior work primarily studies leakage of private input prompts, typically via inversion attacks on intermediate representations, while the potential for sensitive information leakage through generative response outputs remains largely unexplored. In this work, we unveil novel vulnerabilities of Split-LLM by presenting Patched Model Inversion with Dual-Sided Initialization (PIDI), a two-stage attack that simultaneously targets both private input prompts and output responses in Split-LLM settings. It combines dual-sided initialization with a patched inversion strategy to tackle long sequences, substantially outperforming prior inversion methods. To counter threats from both sides, we further propose the Adapter-based DualGuard with Mutual Information Defense (ADMI), which integrates an adapter-based local warmup strategy and mutual information regularization to provide a strong empirical privacy protection with minimal impact on task performance. Extensive experiments across diverse tasks and models demonstrate that ADMI effectively defends against PIDI and other state-of-the-art inversion attacks. Our code is publicly available at https://github.com/FLAIR-THU/VFLAIR-LLM.

Zixuan Gu, Xiaojun Ye, Yang Liu

School of Software, Tsinghua University, Beijing, China · the Hong Kong Polytechnic University, Hongkong, China

Privacy-Preserving Language Models Privacy Leakage in Language Models Model Inversion Attacks LLM Training

Jun 12, 2026cs.LG

Small LLMs: Pruning vs. Training from Scratch

Pruning promises a shortcut to strong small language models. In this work, we examine this promise by pruning Llama-3.1-8B at pruning ratios of 0.5--0.8 with six methods spanning depth, width, and sparse granularities, under two controlled token-matched settings. (1) With the same training token budget, pruned initialization consistently outperforms random initialization. This shows that the parent model provides a strong starting point, although the advantage narrows as the training token budget grows and as the pruning ratio rises, nearly vanishing at the highest pruning ratio we study. (2) When training from scratch is instead given the full token budget consumed by the whole pipeline, pruning at finer granularities still retains an advantage, while coarser structured pruning can be matched or surpassed. This suggests that the parent model transfers knowledge that additional training tokens alone cannot fully recover, but only at fine granularity. Taken together, our results yield a clear recommendation: with a large pretrained model in hand and a limited training token budget, pruning is better than training from scratch; when the training budget is not limited, training from scratch can be competitive for coarser pruning, so a large pretrained parent is not always necessary.

Yufeng Xu, Taiming Lu, Kunjun Li +3

Princeton University · New York University · Carnegie Mellon University

Language Model Pretraining LLM Pruning Small Language Models Structured Pruning LLM Training

Jun 11, 2026cs.LG

Natively Unlearnable Large Language Models

Unlearning aims to remove the influence of specific training data sources, but this has proved challenging because the contributions of different sources are entangled within the model. Isolating source contributions to disjoint parameters makes removal easier, though it obstructs joint learning across sources. We propose NULLs (Natively Unlearnable LLMs), a model class that satisfies the two opposing goals of isolating source-specific contributions and learning jointly across sources, by training a set of shared backbone neurons alongside a pool of sparsely activated sinks. During training, information specific to a source naturally concentrates in its sinks while information shared across sources accumulates in the backbone. A source is then unlearned at deployment by disabling its corresponding sinks, with no gradient updates and no access to the retained data. We show that NULLs scales to Wikipedia's ~6M articles, isolating each as an independent source. Unlearning a single article removes knowledge specific to it while preserving facts shared with semantically related articles, closely matching retraining from scratch. We note that unlearning with NULLs is also robust: in a case study of unlearning the Harry Potter books, NULLs resists both adversarial extraction and relearning that reverses post-hoc unlearning. Finally, NULLs preserves general language capabilities, matching a standard transformer on downstream benchmarks. Together, these results suggest that source-level unlearning need not be an afterthought. It can be built natively into LLM training while retaining the benefits of shared representation learning.

Gaurav R. Ghosal, Pratyush Maini, Aditi Raghunathan

Carnegie Mellon University · DatologyAI

Activation Sparsity Machine Unlearning LLM Unlearning LLM Training

Jun 11, 2026cs.AI

A Quantitative Experimental Repeated Measures Study of Training Dynamics in a Small Llama Style Language Model Under a Compute-Aware Token Budget

This study examines training dynamics in a small Llama-style language model trained under a fixed, compute-constrained token budget. Rather than evaluating efficiency solely through endpoint performance, the study uses a quantitative experimental repeated measures design to analyze how validation loss, validation perplexity, rolling volatility, backslide behavior, spike behavior, and between-seed variability change across token-based training intervals. Six independent training runs were conducted on a 4.26-million-parameter model using the TinyStories corpus, CPU-based full-precision training, and a target budget of approximately 20 million cumulative training tokens. Metrics were collected across 21 intervals, producing 126 seed-by-interval observations. Repeated measures ANOVA showed statistically significant interval effects for validation loss, validation perplexity, and rolling volatility. Descriptive trajectories revealed rapid early improvement followed by non-monotonic degradation during later training intervals. Mean validation loss decreased from 8.3552 at initialization to 2.7996 near 4 million tokens, but increased to 3.9010 by the final checkpoint. Validation perplexity followed the same pattern, falling sharply early in training before rising later. Derived telemetry further showed recurrent validation-loss backslides and no interval-summary evidence of a stable phase under the predefined criteria. These findings suggest that compute-aware language model evaluation should examine training trajectories rather than endpoint metrics alone. In constrained compute settings, additional token exposure may increase computational cost without producing proportional generalization gains, and interval-level telemetry can reveal instability, regression, and diminishing returns that final metrics may obscure.

Joe Dwyer

Department of Computer Information Science ECPI University Virginia Beach, VA 23462

LLM Evaluation Efficient Language Model Training LLM Training

Jun 10, 2026cs.CV

Ouroboros-Spatial: Closing the Data-Model Loop for Spatial Reasoning

Spatial reasoning remains a persistent challenge for multimodal large language models (MLLMs). Existing approaches largely rely on large-scale, statically curated datasets, where all training samples are treated uniformly regardless of the model's evolving capabilities. This static paradigm is inherently data-inefficient: training capacity is often spent on samples that are either trivial or overly difficult for the model at its current stage. To address this limitation, we propose Ouroboros-Spatial, a self-evolving training framework in which the model plays dual roles as a proposer and a solver. In each iteration, a frozen proposer generates spatial question-answer (QA) pairs from 3D scene metadata and raw video frames, together with executable code for deriving reliable ground truth. A learnable solver is then fine-tuned on the accepted samples, and its per-sample prediction confidence is used as a difficulty signal. This signal is fed back to the proposer in the next iteration, guiding it to generate questions better matched to the solver's current capabilities. Through this closed-loop design, the training distribution co-evolves with model ability, reducing redundant trivial examples while filtering out ambiguous or uninformative samples with limited learning value. Across six spatial reasoning benchmarks, Ouroboros-Spatial substantially improves Qwen3-VL-4B and Qwen3-VL-8B while using an order of magnitude fewer training examples than recent large-scale curated datasets. On VSI-Bench, it yields absolute gains of 9.9 and 6.8 points for the 4B and 8B models, respectively, enabling both to outperform a wide range of strong open-source and proprietary baselines.

Enhan Zhao, Wei Wu, Yuanrui Zhang +2

1Peking University · 2Ant International · 3The University of Hong Kong

3D Spatial Reasoning Synthetic Data Generation Multimodal Large Language Models Curriculum Learning LLM Training

Jun 10, 2026cs.CL

Improving Cross-Format Robustness in Language Models with Multi-Format Training

Large language models often remain sensitive to answer format: a question solved correctly in one form may fail in another semantically equivalent form. To study this gap, we define cross-format robustness as the extent to which a model answers the same underlying question consistently across formats. We then compare full-format training with FormatMix, which expands only a subset of training items into multiple equivalent formats using either random or targeted selection. Across GLM4 and Llama-3.1, multi-format supervision consistently improves both task performance and cross-format robustness, whereas Multiple-choice question (MCQ)-only supervision alone brings little benefit and can even reduce robustness. We further find that expanding only about 30% of the training set into multiple formats often recovers most of the gain from full-format training, and this effect appears across the model families and sizes we study. These results suggest that format diversity, rather than additional supervision alone, is the key driver of robustness. That lightweight multi-format augmentation is a practical way to make LLMs less sensitive to answer format without changing the base model.

June M. Liu, Shaomian Zheng, He Cao +3

Ant Group · International Digital Economy Academy (IDEA)

Language Model Robustness LLM Training

Jun 9, 2026cs.CY

Life Cycle Assessment of Pre-training the Lucie 7B Open-Source Large Language Model on the Jean Zay Supercomputer

The environmental impact of training large language models (LLMs) is increasingly scrutinised, yet most published estimates focus on operational energy and disclose little about manufacturing (embodied) emissions, water consumption, or the underlying highperformance computing (HPC) infrastructure. We present a life cycle assessment (LCA) of the pre-training of Lucie 7B, an open-source multilingual Foundation Model developed by the OpenLLM-France consortium and trained on the NVIDIA H100 partition of the Jean Zay supercomputer operated by IDRIS (CNRS). The assessment is framed by the AFNOR SPEC 2314 "Frugal AI" reference and applies the Labos 1point5 methodology for greenhouse gas(GHG) accounting in computing. The study scope extends from data preparation to model validation, and integrates the full life cycle of the hardware infrastructure: manufacturing (including raw-material extraction), use (compute, temporary storage, system administration, cooling), and end-of-life. We report (i) an annual footprint of 417.5 tCO2eq for the Jean Zay H100 partition, split almost equally between manufacturing and operation; (ii) an effective intensity of 36.7 gCO2eq per H100 GPU-hour; (iii) a total training footprint of 21 tCO2eq for Lucie 7B (574 564 H100 GPU-hours), inclusive of amortised hardware manufacturing; (iv) on-site water consumption of approximately 76m3 for the training campaign and an annual Water Usage Effectiveness (WUE) of 0.07 L/kWh for IDRIS; (v) a heat-reuse factor (ERF) of 0.37 thanks to waste-heat recovery into the urban heating network. The study contributes one of the few publicly documented LCAs of an LLM training campaign that explicitly couples operational data with embodied emissions decomposed by subsystem (compute, storage, power chain, cooling), and discusses the implications for the design of frugal-by-construction AI systems in Europe.

Marc Léobet, Pierre-François Lavallée, Jean-Pierre Lorré

Mens Data · CNRS / IDRIS · LINAGORA

Energy-Efficient ML LLM Training

Jun 9, 2026cs.LG

Unifying Data, Memory, and Compute Efficiency in LLM training: A Survey

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

Vanessa Schmidt, Huy Hoang Nguyen, Cédric Jung +2

Chair of Information Theory and Data Analytics (INDA), RWTH Aachen University, 52074 Aachen, Germany · AIT Austrian Institute of Technology GmbH, 1210 Vienna, Austria · Automation and Control Institute, Technische Universität Wien (TUW), 1040 Vienna, Austria

Efficient Language Model Training LLM Training Memory-Efficient Training Data-Efficient Learning

Jun 8, 2026cs.CL

IS-CoT: Breaking the Long-form Generation Collapse via Interleaved Structural Thinking

Generating coherent and controllable long-form content remains a persistent challenge for Large Language Models (LLMs). While reasoning-enhanced models have demonstrated success in logic-intensive domains, our evaluation reveals that they suffer from a severe length collapse in open-ended writing, where performance degrades sharply as target lengths exceed 2,000 words. We attribute this failure to the limitation of static hierarchical planning, which struggles to provide dynamic guidance over extended contexts. To bridge this gap, we introduce the Interleaved Structural Chain-of-Thought (IS-CoT) framework. Unlike external agentic workflows, IS-CoT embeds a dynamic Plan-Write-Reflect cycle into the generation process, enabling continuous strategy adaptation and global alignment without additional assistance. Based on this framework, we construct a high-quality dataset of interleaved reasoning traces via a multi-teacher pipeline and train IS-Writer-8B. Experiments demonstrate that IS-Writer-8B achieves state-of-the-art performance on challenging long-form benchmarks (e.g., +3.08 vs. DeepSeek-V3.2 on LongBench-Write), exhibiting robust length compliance and coherence competitive with significantly larger proprietary models.

Zechen Sun, Yuyang Sun, Zecheng Tang +6

Institute of Computer Science and Technology, Soochow University · 2Information Research Center of Military Science, PLA Academy of Military Science

Open-Ended Generation Long-Form Document Generation CoT Reasoning LLM Training Text Generation

Jun 7, 2026cs.DC

FlashCP: Load-Balanced Communication-Efficient Context Parallelism for LLM Training

Context parallelism (CP) is essential for training large-scale, long-context language models, as it partitions sequences to reduce memory overhead. However, existing CP methods suffer from workload imbalance, inefficient kernels, and redundant communication due to static sequence sharding and key-value (KV) tensor communication. We present FlashCP, a load-balanced and communication-efficient framework for CP training. FlashCP introduces a sharding-aware communication mechanism to eliminate redundant KV communication and proposes a novel Whole-Doc sharding strategy that maximizes communication savings while maintaining balanced workloads. To efficiently combine Whole-Doc and Per-Doc sharding, FlashCP further designs a heuristic algorithm to search for near-optimal sharding plans. Extensive experiments show that FlashCP achieves up to 1.63x speedup over state-of-the-art CP frameworks across diverse datasets.

Zheng Wang, Eric Liu, Linan Jiang +5

University of California San Diego, La Jolla, USA · University of Southern California, Los Angeles, USA · Rice University, Houston, USA.

Communication-Efficient Distributed Training Long-Context Language Modeling LLM Training

Jun 6, 2026cs.LG

Minibatch Selection for Language Models via Partition Matroid Constrained Gradient Matching

Training large language models (LLMs) on heterogeneous data requires selecting minibatches that balance convergence speed with coverage across domains. Existing methods either select samples independently within each domain or rely on computationally expensive proxy models to learn continuous domain weights. We propose PartitionSel, a cross-domain minibatch selection approach that maximizes a validation-guided gradient-matching utility under per-domain budgets encoded as a partition-matroid constraint. By coupling the per-domain budgets through a single utility, PartitionSel is designed to reduce redundancy in selections across domains. The proposed objective is weakly submodular and admits an orthogonal matching pursuit algorithm with provable approximation guarantees. Empirically, we evaluate PartitionSel for minibatch selection during the fine-tuning of Qwen2.5 and Llama-3 on MetaMathQA and Mol-Instructions. PartitionSel achieves robust gains over per-domain and domain-agnostic baselines on both benchmarks. It also reduces the number of conflicting gradient pairs within each batch, indicating that the cross-domain coupling translates into more compatible training updates.

Prayas Agrawal, Prateek Chanda, Ishita Khatri +3

Department of Computer Science and Engineering, Indian Institute of Technology Bombay · Microsoft Research India · Centre for Machine Intelligence and Data Science, Indian Institute of Technology Bombay +1

Submodular Optimization LLM Fine-Tuning Combinatorial Optimization LLM Training

Jun 5, 2026cs.LG

Reversible Foundations: Training a 120B Sparse MoE through State-Preserving Scaling

This paper reports on training a hundred-billion-parameter sparse mixture of experts on a single eight-GPU node, end to end. LightningLM 0.1V is a recurrence-backbone language model family grown in four stages from a small dense seed, through a 5B and a 9B mixture of experts, to a 120B model with 460 routed experts under top-12 routing. Each larger model is grown from the trained weights of the smaller one; active parameters rise monotonically from 1.78B at the dense seed to 5.93B at 120B (about 5% of the 118.67B stored). The full lineage runs on single nodes, the larger stages at 8K context, reaching a released training loss of 1.78 at 120B scale. This is a systems and experience report. It is organized around three disciplines. Reversibility: a reversible recurrence stack reconstructs activations in the backward pass instead of storing them, holding activation memory flat as the model grows. State-preserving growth: each expansion (dense to MoE, shallow to deep, few experts to many) is given as a reproducible principle paired with the failure that results from getting it wrong; several failures are silent. Single-node economics: the 120B trains through TQP, a strategy of quantized base expert weights and trained low-rank adapters that carries optimizer state on 2.26B adapter parameters rather than 100B+ resident in routed experts, cutting expert-path optimizer state by a factor of ~45. What is new is the integration of known primitives, not any primitive in isolation: one grown lineage running end to end on a single node, documented at practitioner level, with per-domain held-out loss as evidence that targeted capabilities (multilingual Indic competence, code) were learned by construction. Model family, tokenizer, and training code are released.

Rohan Shravan

The School of AI Bengaluru, India

Mixture-of-Experts Language Models Efficient Language Model Training Language Model Scaling LLM Training

Jun 5, 2026cs.DB

DataEvolver: Automatic Data Preparation for Large Language Models through Multi-Level Self-Evolving

High-quality training data is essential to large language models (LLMs) and typically requires extensive and costly manual curation. Existing automatic data preparation methods rely on predefined pipelines or customized human instructions, which limits their adaptability to diverse data distributions and lacks principled guidance from high-quality examples. In this paper, we introduce DataEvolver, the first self-evolving data preparation system that automatically constructs pipelines to transform raw data into high-quality data. DataEvolver employs a multi-level mechanism to ensure both pipeline executability and effectiveness. At the operator level, it incrementally expands the operator set to construct a logical plan while resolving dependency conflicts. At the pipeline level, it instantiates logical plans into executable code and iteratively refines pipeline orchestration through a feedback loop that reduces the distribution gap between prepared data and high-quality examples. Experiments on seven benchmarks show that DataEvolver substantially improves data quality and achieves an average 10% gain in downstream LLM performance compared with training on original data, highlighting new opportunities for the iterative co-evolution of LLMs and data.

Chao Deng, Shaolei Zhang, Ju Fan +1

Renmin University of China, Beijing, China

Training Data Curation LLM Training

Jun 4, 2026cs.IT

Automated Proving of Shannon-Type Entropy Inequalities via Fine-Tuned Language Models and Guided Tree Search

Proving Shannon-type entropy inequalities is a fundamental task in information theory that often requires constructing non-trivial linear combinations of known constraints, which is a combinatorial search problem that scales poorly with the number of random variables. We investigate whether small-scale large language models (0.6B--1.7B parameters), fine-tuned on atomic proof steps and combined with guided beam search, can automate this process. On a held-out test set of 60 inequalities spanning n=10 to 15 variables, our 0.6B fine-tuned model achieves an 85% proof success rate with tree search. GPT-5.5 solves 1.7% samples under zero-shot prompting while Psitip solves 33.3% samples. A systematic ablation study across training context length (4096 vs.\ 8192 tokens) and data distribution (n=9-skewed vs not skewed) reveals that a 4096-token not skewed training distribution yields the best performance, with extended context and skewed data providing no marginal benefit. We further identify two dominant failure modes -- format failures and step quality degradation -- and verify that the beam-scoring heuristic is essential via a controlled ablation (random scoring reduces success from 83% to 23%).

Shing Yin Wong, Shaocheng Liu, Linqi Song +2

Department of Computer Science, City University of Hong Kong · Department of Information Engineering, The Chinese University of Hong Kong

Automated Theorem Proving LLM Training

Jun 2, 2026cs.LG

Spectral Scaling Laws of Muon

Orthonormalized update rules have rapidly become a leading choice of optimizer for training large language models, with recent open-source state-of-the-art models adopting Muon. To keep these updates tractable, Muon performs the orthonormalization with the Newton--Schulz (NS) iteration. Since NS is only approximate, directions with small singular values fail to be orthonormalized. In Muon, NS is applied to the momentum matrix at every step, yet little is known about how the singular value spectrum of these momentum matrices behaves during training, or how that behavior changes with model size. We present the first systematic study of this question. Tracking singular value quantiles of the momentum buffer across layers in models ranging from 77M to 2.8B parameters, we observe a consistent picture: after a short burn-in, the quantiles stabilize at a value determined by the layer type and model size. These stabilization values follow remarkably clean power laws in model size, with layer-dependent exponents. Layers up to mid-late depth scale very mildly with model size

M

(around

M^{-0.25}

), so the standard 5-step NS configuration used at academic scale will continue to orthonormalize them at much larger scales. Some of the late layers, however, scale much more aggressively (up to

M^{-0.96}

) and will fall into the NS failure regime at frontier scale unless one uses more NS iterations or better-tuned coefficients. NS iterations are computationally expensive at scale; our laws give practitioners a principled, layer-aware recipe for choosing the minimum NS configuration that still orthonormalizes the directions that matter -- avoiding unnecessary computation without sacrificing update quality.

Gagik Magakyan, Pablo Parrilo, Asuman Ozdaglar

MIT

Newton-Schulz Iteration Momentum Methods Muon Optimizer Second-Order Optimization Neural Network Training Dynamics LLM Training

Jun 2, 2026cs.LG

Unlocking Feature Learning in Gated Delta Networks at Scale

Training and scaling Large Language Models demand enormous computational resources, motivating both efficient sub-quadratic architectures and principled hyperparameter tuning methods. While the Maximal Update Parametrization (

μ

P) has enabled zero-shot hyperparameter transfer for standard Transformers, its extension to linear models, particularly those with structured state transitions and complicated architectures, remains largely unexplored. By rigorously propagating coordinate-size estimates through the forward pass, gating mechanisms, and recurrent state dynamics, we derive the scaling rules for Gated Delta Network. Experiments on language-model pre-training confirm that our configurations enable stable learning-rate transfer across model widths under both AdamW and SGD, whereas standard parametrization fails to transfer, validating the correctness and practical utility of our analysis.

Yifeng Liu, Quanquan Gu

University of California, Los Angeles

Neural Network Optimization Hyperparameter Transfer Gated Delta Networks LLM Training

May 31, 2026cs.CL

Learning from Saturated Data: Signals Beyond Correctness for LLM Training

The growing capabilities of large language models (LLMs) have led to the saturation of many benchmarks and training datasets used to improve them. Motivated by this, we investigate whether questions solved with perfect empirical accuracy can nevertheless be used to improve downstream performance. To do so, we replace binary correctness with two sources of more fine-grained quality signals: (1) pairwise LLM self-judgments, in which the model evaluates the relative quality of its own solutions, and (2) token-level entropy, where token-level uncertainty is used as a proxy for solution quality. We incorporate these signals into several training algorithms and evaluate them on Qwen3-1.7B-Base. When training exclusively on a simple arithmetic task, quality-based signals improve performance by up to

18.6\%

over the base model, substantially outperforming SFT. On GSM8K, however, gains are more modest and depend strongly on the quality signal. For instance, self-judgments show poor agreement with a stronger external judge and can even degrade performance below the base model. Overall, our results suggest that quality-based training can extract useful signal from saturated questions for base models, but that applying such signals to more complex tasks requires careful calibration and further study.

Hanno Hiss, Jasper Dekoninck, Martin Vechev

ETH Zurich

Language Model Self-Improvement LLM Training

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