Efficient Language Model Training

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15 papers in the last four weeks, up 67% on the four weeks before. 0.1% of all new papers.

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Latest papers 109

Jul 31, 2026cs.CL

PARALLEL: A Prefrontal-Aligned Reinforcement inspired Approach for Language-Model Learning under Explicit Limits

Recent language models achieve strong performance across a variety of tasks, but conventional adaptation applies updates uniformly across training samples regardless of their local update benefit. We propose PARALLEL, a prefrontal-aligned reinforcement inspired approach for language-model learning. Inspired by the complementary roles of goal-related and uncertainty-related control, PARALLEL represents these forms of information as separate controller signals and combines them with the current model representation. A reinforcement-inspired controller assigns sample-dependent update intensity using immediate utility-cost feedback. PARALLEL therefore learns when and how strongly to adapt to each sample, prioritizing beneficial updates while limiting unnecessary parameter changes. PARALLEL uses available updates more efficiently than selective baselines while retaining 94.1--99.2% of Full-adaptation performance. Beyond multiple-choice reasoning, experiments on XSum and CNN/DailyMail show that PARALLEL retains 96.9--98.6% of the ROUGE-1 and ROUGE-2 scores achieved by Full adaptation and 98.8--98.9% of the corresponding ROUGE-L scores. When compared at the same cumulative adaptation time or GPU energy, PARALLEL achieves higher ARC accuracy and exhibits a more stable late-stage adaptation trajectory than Full adaptation in the representative run. These results show that learning when and how strongly to update each sample supports stable and efficient post-deployment stream adaptation while avoiding unnecessary updates.

Namkyung Yoon, Sanghong Kim, Hwangnam Kim

School of Electrical Engineering, Korea University Seoul 02841, Republic of Korea

Continual Learning for LLMs LLM Fine-Tuning Efficient Language Model Training

Jul 29, 2026cs.LG

SDO: Structure-Aware Data Organization for Efficient LLM Post-Training

Post-training of large language models is expensive, and existing efficiency improvements mainly focus on selecting informative samples or designing training schedules. However, data organization itself is usually treated as a static preprocessing step: embedding-based grouping methods construct fixed partitions before training and cannot adapt to the evolving sample exposure during optimization. As a result, all samples receive similar exposure despite their different optimization needs, leading to redundant updates for some samples while leaving others under-optimized. To address this problem, we propose SDO (Structure-Aware Data Organization), a plug-and-play data organization framework with an exposure-driven feedback mechanism that organizes mini-batch composition and sample exposure according to representation-space structure. SDO operates epoch by epoch on frozen external embeddings, avoiding model warm-up training overhead: within each epoch, locality-aware batching forms coherent mini-batches via KNN neighborhood traversal; across epochs, exposure-balanced scheduling records per-sample participation and reduces the sampling probability of over-exposed samples to preserve long-term coverage. Across SFT, DPO, and GRPO, SDO accelerates convergence, with the largest gains observed in the early-to-mid phase, producing more coherent gradients and more balanced accuracy across question types without permanently excluding training samples.

Jinliang Gao, Ning Yang, Hai Wang +2

Institute of Automation, Chinese Academy of Sciences · National University of Defense Technology

Training Data Curation Efficient Language Model Training LLM Post-Training Data-Efficient Learning

Jul 27, 2026cs.CL

From Data to Device: ELMOD An Efficient German-First 2.7B Language Model for Mobile Inference

We present ELMOD - Efficient Language Model for On-Device Deployment - a compact (2.7B) German language model designed for efficient inference on resource-constrained hardware. ELMOD was trained on a limited computational budget (55k H100 GPU hours) using exclusively publicly available data. We developed a suite of German-specific data pre-processing, which differ from English-oriented counterparts in their handling of morphological variation, compounding, and orthographic conventions. Furthermore, we introduced a quality filtering and rephrasing step, which increased the instructional quality of the data, improved performance during the annealing phase, and reduced overall compute requirements. Thanks to our architectural model and data choices, including prefiltering, our educational-quality filtering and rephrasal to raise the educational-quality, ELMOD is the strongest performer in its size class (<3B), matching the performance of 7B-parameter models in German.

Darina Gold, Alexander Schwirjow, Viktor Haag +4

IIS Fraunhofer

On-Device Language Model Inference Training Data Curation Small Language Models Efficient Language Model Training Language Modeling

Jul 24, 2026cs.LG

DomainPilot: Domain-Level Loss-Guided Two-Stage Data Mixture Optimization for Efficient Language Model Fine-Tuning

The training efficacy of large language models (LLMs) is fundamentally constrained by the quality and composition of training data. Existing dynamic data scheduling methods face critical limitations in industrial-scale pretraining and supervised fine-tuning (SFT): data selection incurs prohibitive O(N) costs on terabyte-scale corpora, mixture optimization schemes introduce severe I/O bottlenecks or require training auxiliary reference models, and sample-level reweighting strategies rely on loss signals that conflate noise, difficulty, and novelty. We present DomainPilot, a domain-level loss-guided two-stage data mixture optimization framework. DomainPilot introduces token-level domain loss monitoring to capture per-domain learning dynamics during training without halting the data pipeline. Building on these signals, we propose a Scaling Law guided coarse optimization stage that fits domain-specific convergence curves and derives a principled prior for mixture adjustment. A subsequent Mixing Law guided fine optimization stage refines the mixture by modeling cross-domain interaction effects through controlled sweep experiments. The entire mechanism is realized via a patch-based architecture that injects domain-aware loss computation into existing training frameworks (e.g., MindSpeed/Megatron-LM) with only ~30 lines of framework-specific adapter code. We validate DomainPilot on the Qwen3-1.7B model during SFT. Compared to the original data mixture, our optimized mixture achieves improvements of +2% on MMLU-Redux, +1.8% on AIME24, +3.8% on LiveCodeBench v5, and +3.6% on BFCL v3, without increasing total data volume or training cost. These results demonstrate that domain-level training signals provide an effective, lightweight alternative to expensive data selection or auxiliary model training for mixture optimization.

He Zhang

Tsinghua University

Supervised Fine-Tuning Large Language Model-Guided Optimization Efficient Language Model Training Data Mixture Optimization

Jul 21, 2026cs.LG

Where Should Optimizer State Live? Tiered State Allocation for Memory-Efficient Mixture-of-Experts Training

Optimizer state is the largest single line item in the memory budget of mixture-of-experts (MoE) training. On a 6.78B-parameter MoE language model AdamW keeps 50.6 GB of first and second moments to update 12.6 GB of bfloat16 weights. We study SkewAdam, an optimizer built on the observation that the three parameter populations of an MoE differ enough in size and gradient statistics that they should not receive the same state. Those populations are the dense backbone, the experts and the router. SkewAdam keeps float32 momentum plus a factored second moment for the backbone (5% of parameters), a factored second moment alone for the experts (95%) and an exact second moment for the router (<0.01%). The resulting state occupies 1.29 GB or 2.6% of AdamW's and peak training memory falls from 81.4 GB to 31.3 GB, within the budget of a 40 GB accelerator. In a controlled comparison from identical initializations over 82M tokens, SkewAdam reaches validation perplexity 108.4, ahead of AdamW (126.8), Muon (120.2) and Lion (393.7), and settles router load balance to within 1% of its uniform floor. The allocation is not what earns that perplexity. A tier ablation reaches the same value while carrying twenty times the state, so the tiers buy memory rather than accuracy. Same-platform runs separate what does earn it. Removing momentum costs 31 perplexity points (tuned Adafactor, 139.7) and replacing the factored second moment and its update clipping with a full second moment costs 10 (tuned AdamW, 118.5), so neither tuned baseline reaches the untuned tiered policy. Where optimizer state lives, these results suggest, matters at least as much as how much of it there is.

Nuemaan Malik

Independent Researcher

Deep Learning Optimization Mixture-of-Experts Language Models Memory-Efficient Optimization Efficient Language Model Training Memory-Efficient Training

Jul 20, 2026cs.CL

PPL-Factory: Task-Aware and Budget-Aware Data Selection from Language Modeling to Reasoning

Not all training samples contribute equally to large language model fine-tuning. Selecting informative training samples can reduce the computational cost while preserving downstream performance. Many existing data selection methods rely on indirect heuristics, such as data quality, diversity or reasoning trace length. However, the effectiveness of these fixed criteria is task-dependent and difficult to generalize across diverse downstream tasks. Perplexity-based data selection provides a simple and model-aware solution to estimate the sample difficulty, but existing approaches typically score the entire training sequence and ignore the difference in learning objectives of language modeling and reasoning tasks. In this paper, we propose PPL-Factory, a simple and interpretable data selection framework that combines task-aware perplexity-based scores and data budget-aware selection criteria. Experiments on GSM8K demonstrate that PPL-Factory outperforms other state-of-the-art data selection methods using only

1\%

of the training set. With

10\%

of the data, PPL-Factory exceeds full-data fine-tuning accuracy by 0.9 on GSM8K and 4.8 on MATH. Overall, our results demonstrate that task-aware and budget-aware perplexity-based selection provides an effective and applicable approach for efficient fine-tuning.

Hang Zhang, Warren J. Gross

Department of Electrical and Computer Engineering, McGill University Montreal, QC, Canada

LLM Fine-Tuning Efficient Language Model Training Training Data Selection Selective Fine-Tuning

Jul 18, 2026cs.CL

OpenLanguageModel: Readable and Composable Small-Language-Model Pretraining for Education and Research

OpenLanguageModel (OLM) is an open-source PyTorch library for building and pretraining small language models while keeping their machinery visible. In OLM, model code reads like the architecture: components are ordinary modules, while Block, Residual, Repeat, and Parallel describe how they are wired. The resulting model can move unchanged from a teaching notebook to a complete pretraining run or a research ablation. OLM connects this readable model layer to tokenizers, local and streaming datasets, optimization, mixed precision, callbacks, checkpoints, and hardware-aware CPU, single-GPU, and single-node multi-GPU execution. We demonstrate the full path by tracing GPT-2 from diagram to code, launching a FineWeb-Edu training script, replacing one attention component, and letting AutoTrainer configure the available machine. The package includes 27 presets across nine familiar model families and documentation that progresses from LM fundamentals to architecture research. Validation shows close agreement with independent reference implementations, 90.6% four-GPU weak-scaling efficiency for a 348M-parameter workload, compact architecture edits, and positive early usability results. OLM is MIT-licensed and available through PyPI, GitHub, and its documentation site.

Tavish Mankash, Vardhaman Kalloli, Keshava Prasad +1

FAIRC · Plaksha University

Language Model Pretraining Small Language Models Efficient Language Model Training

Jul 16, 2026cs.AI

Long-Context Fine-Tuning with Limited VRAM

Parameter-efficient fine-tuning reduces model and optimizer memory, but dense attention still makes long training sequences expensive. We combine Hierarchical Global Attention (HGA) with segment-wise backpropagation and tiered KV storage. Only the active segment remains differentiable in VRAM; older KV is detached into RAM or NVMe, and HGA loads a bounded set of exact historical tokens for each query block. On Qwen3-8B with 4-bit QLoRA and PG19, dense training on a 16 GB Quadro RTX 5000 fits 2,048 tokens but fails at 4,096, whereas HGA reaches 16,384 tokens with 15.28 GB peak VRAM. Under evaluation the same adapter runs through 131,072 tokens on this card; VRAM is not constant but grows gently with the resident chunk summaries, so RAM and NVMe capacity set the practical limit beyond these lengths. At the shared 2K training length, HGA-trained and dense-trained adapters obtain 2.7405 and 2.7383 nat under the same dense-attention readout, while the stock model obtains 2.9541. At this boundary HGA training is already marginally faster (217.75 vs. 207.02 tokens/s), and the HGA-to-dense throughput ratio improves from 1K to 2K; because HGA keeps the attended historical set per token approximately constant while dense work per token grows, we expect this lead to widen as context grows. Dense attention is used for the main quality and retrieval comparisons so that they measure the learned weights and remain compatible with standard generation frameworks. HGA can also be used for retrieval and generation; an optimized production-grade serving implementation is under development.

Vladimir Fedosov, Aleksandr Sazhin, Artemiy Grinenko +1

BMW Group

Fine-Tuning KV-Cache Offloading Memory-Efficient Fine-Tuning Efficient Language Model Training Attention Mechanisms Parameter-Efficient Fine-Tuning

Jul 16, 2026cs.LG

LongStraw: Long-Context RL Beyond 2M Tokens under a Fixed GPU Budget

A growing gap separates inference context lengths from RL post-training: inference systems are approaching million-token contexts, while post-training workloads often remain at 256K tokens or below and rely on length generalization at deployment. The gap is especially important for AI agents, whose observations, tool outputs, documents, and prior decisions accumulate over long trajectories. LongStraw is an architecture-aware execution stack for million-token RL post-training under a fixed GPU budget, instantiated with Group Relative Policy Optimization (GRPO). It evaluates the shared prompt without autograd, retains only model-specific state needed by later tokens, and replays short response branches one at a time, reducing the live training graph at the cost of additional replay time. We implement it for the hybrid recurrent and full-attention Qwen3.6-27B and the compressed-attention mixture-of-experts GLM-5.2. On eight H20 GPUs, LongStraw completes grouped Qwen scoring and response backward at 2.1M positions for groups of 2 and 8; increasing the group size adds only 0.21 GB of peak allocated memory, while a separate stress test reaches 4.46M positions. On 32 H20 GPUs, we validate the end-to-end LongStraw execution path for a 2.1M-token prompt across all 78 layers of GLM-5.2. These experiments establish execution capacity rather than complete training correctness because the captured prompt state is detached and some distributed forward and gradient composition paths remain incomplete.

Changhai Zhou, Kieran Liu, Yuhua Zhou +17

MindLab · Fudan University

Efficient Language Model Training Long-Context Modeling RL Post-Training

Jul 6, 2026cs.LG

Train Smarter, Not Longer: Memorization-Guided Data Reuse for Efficient LLM Training

The training paradigm of large language models has shifted from traditional one-pass training to multi-epoch training, as reasonable reuse of limited high-quality data can improve both model performance and sample efficiency. Meanwhile, excessive repetition introduces the risk of overfitting and diminishing returns. Determining when and how to reuse data effectively thus emerges as a natural but under-explored question. Through a novel observation of model's "Memorization Window" signals derived from loss retention dynamics and downstream evaluation scores, we propose "Memorization-guided Data Reuse", a training paradigm that adaptively determines when and how data should be reused, enabling principled decisions on the number of training epochs and the scheduling of data replays. Our preliminary experiments reveal a consistent memorization-driven regime: performance continues to improve with repetition far beyond current practice (e.g., the commonly cited four-epoch limit). While a full scheduler remains future work, these insights provide a foundation for memorization-aware training schedules, helping to determine reuse budgets and move toward training LLMs smarter rather than longer with limited high-quality data.

Jingwei Zuo, Cong Zeng, Ilyas Chahed +6

Technology Innovation Institute Abu Dhabi, UAE

Memorization in Language Models Neural Network Memorization Efficient Language Model Training LLM Training Data Repetition in Language Model Training

Jul 2, 2026cs.DC

Mixture-of-Parallelisms: Towards Memory-Efficient Training Stack for Mixture-of-Experts Models

This paper showcases a memory-efficient training stack for Mixture-of-Experts (MoE) models. It is a training paradigm that combines and specializes various existing and novel parallelism techniques at different layers and stages of the Mixture-of-Experts (MoE) model training pipeline. It leverages these techniques to achieve maximal efficiency given the physical constraints of CPU, CPU memory, GPU HBM memory, and the CPU-GPU, GPU-GPU, and node-node communication bandwidth of the GPU cluster. It also contains a novel strategy for the optimizer step to achieve high throughput and memory efficiency, enabling practitioners to conduct lossless pre-training/fine-tuning of trillion-parameter scale models, at a million context length, with just under 12 8x H200 GPU nodes, with state-of-the-art throughput and memory efficiency. In our experiments, MoP delivers 4.7x--8.2x higher per-GPU throughput than a strongly-tuned FSDP2 baseline (with the gap widening at larger scale) and sustains training at context lengths up to 1M tokens, where the baseline runs out of memory beyond 64--128K.

Xuan-Phi Nguyen, Shrey Pandit, Yiran Zhao +3

Salesforce AI Research

Communication-Efficient Distributed Training High-Performance Computing Efficient Language Model Training Mixture-of-Experts Models Memory-Efficient Training

Jul 1, 2026cs.CL

Parameter Golf: What Really Works?

How far can a language model improve under a strict artifact budget? Parameter Golf posed this question as an open community challenge in which participants trained the best language model, with the complete artifact (training code + compressed weights) required to fit within 16 MB and be trained in under ten minutes on 8xH100 SXM GPUs. Quality was measured in bits-per-byte (BPB), the average number of bits required to encode each byte of unseen text. We analyze 2,037 pull requests and 1,430 clean scored submissions from the contest, build a taxonomy of 84 optimization techniques, and measure each technique's contribution to BPB. The verified leaderboard score dropped from 1.2244 to 1.058 BPB across three phases -- a 13.6% reduction, despite individual techniques rarely improving BPB by more than 1%. We show that most gains in techniques shrink across competitive submissions, isolating the few methods that improve performance across stacks.

Prashanna Mani Paudel, Shivanand Venkanna Sheshappanavar

Geometric Intelligence Research Lab., Department of Electrical Engineering and Computer Science University of Wyoming

LLM Evaluation LLM Compression Efficient Language Model Training Language Modeling

Jul 1, 2026cs.LG

Token Geometry

Language models learn continuous programs over discrete symbols, with the embedding table and LM-head acting as the read/write interface between them. We show that this interface has gradient geometry distinct from dense hidden weights which can be exploited to improve the Pareto frontier across supervised finetuning, RL, and pretraining, while only utilizing kilobytes of optimizer state. We introduce Ember, a lightweight optimizer for embedding and LM-head matrices that utilizes O(V + D) VRAM, instead of Adam's O(2VD), and forgoes the need to shard both token table optimizer states. We provide empirical evidence that Ember scales effectively across batch size and parameter count. We show that the optimization trajectory of tokens can be well described by a simple 1D ray, counter to the popular belief that neural net parameters navigate a heavily nonconvex landscape. We provide a principled view on the surprisingly narrow space of optimizers that suffice for Transformer training. Finally, we open-source our distributed Ember implementation that merges cleanly with existing ZeRO/FSDP setups to support further research at https://github.com/katop1234/ember

Kathan Shah

Preprint.

Language Model Pretraining LLM Fine-Tuning Memory-Efficient Optimization Efficient Language Model Training Representation Geometry in Language Models

Jun 30, 2026cs.CL

CHERRY: Compressed Hierarchical Experts with Recurrent Representational Yield

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

Dohyeon Kwon, Youngjin Park

AXOps Team, TeamSparta Inc., Seoul, South Korea

Mixture-of-Experts Language Models LLM Compression Efficient Language Model Training Recurrent Transformers

Jun 23, 2026cs.AI

BluTrain: A C++/CUDA Framework for AI Systems

Progress in deep learning is, at scale, more a matter of systems engineering than of modelling: the behaviour of a model in training (its throughput, its memory footprint, and the numerical fidelity of the result) is determined less by the architecture itself than by how that architecture is expressed on the hardware. To achieve absolute control over this hardware expression while abstracting away systems complexity to make modelling seamless and eliminating the need for repetitive orchestration logic, BluTrain was architected from first principles as a robust, lightweight, and architecture-general training framework in standard C++ and the core CUDA programming model. Every layer is implemented natively: a typed tensor module with reverse-mode autograd, a linear-algebra library, a caching allocator, a multi-mode distributed-execution module, and an MLIR-based deep-learning compiler. In formal evaluations training a 124M-parameter GPT-2 baseline in FP32 on an 8-GPU 6000 Ada system, BluTrain outperforms industry-standard baselines in both throughput (sustaining an average of 407K tokens/s versus PyTorch's 395K tokens/s) and memory efficiency (achieving up to a 22% footprint reduction), while strictly preserving numerical fidelity and converging to a marginally lower final validation loss. With every layer explicitly open to native tuning, the performance ceiling is the framework's own to raise.

Adhitya Charan, Adwaid Suresh, Anuj Kumar +19

Blubridge AI

GPU Acceleration High-Performance Computing Efficient 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 20, 2026cs.LG

L20-Edu-135M: An Auditable Single-GPU Study of Data-Efficient Small Language Modeling

Small language models are cheap to serve and feasible on local hardware, but strong public 135M-class systems are commonly trained with hundreds of billions to trillions of tokens on large clusters. We study a sharply resource-constrained regime: a complete 134.5M-parameter language-model pipeline executed on one NVIDIA L20 GPU. The released checkpoint, L20-Edu-135M, receives approximately 13B pretraining tokens: 10B FineWeb-Edu tokens followed by a 3B-token educational, mathematics, code, and reasoning mixture. We document the architecture, data gates, cross-source MinHash/LSH near-deduplication, segment deduplication, benchmark-overlap removal, throughput optimization, supervised fine-tuning (SFT) with weight interpolation, and reinforcement learning from verifiable rewards (RLVR) on GSM8K. In a self-run zero-shot six-task harness, L20-Edu-135M obtains a mean score of 0.4150. It trails SmolLM-135M (0.4767) and SmolLM2-135M (0.4917), but its mean is 87.1% of SmolLM-135M's while its nominal token count is 2.17% as large. This ratio is descriptive, not evidence of statistical equivalence or a controlled scaling law. The model exceeds several older 100M-160M public baselines under the same harness. Direct GRPO-style RLVR decreases GSM8K exact-match accuracy from 1.82% to 1.59% (192-token completions) and 1.21% (320-token completions). These single-run results identify a concrete failure mode rather than establishing a general lower bound on RLVR. The contribution is an auditable resource-constrained case study, not a state-of-the-art claim.

Yin Li

University of Birmingham

Language Model Pretraining Small Language Models Efficient Language Model Training

Jun 13, 2026cs.CL

Ling and Ring 2.6 Technical Report: Efficient and Instant Agentic Intelligence at Trillion-Parameter Scale

Efficient and scalable agentic intelligence requires models that can deliver both low-latency responses and strong reasoning capabilities while remaining practical to train, serve, and deploy. In this report, we present Ling-2.6 and Ring-2.6, a family of models designed to address this challenge at scale. Ling-2.6 is optimized for instant response generation and high capability per output token, whereas Ring-2.6 is tailored for deeper reasoning and more advanced agentic workflows. Instead of training from scratch, we upgrade the Ling-2.0 base model through architectural migration pre-training and large-scale post-training. This upgrade is guided by a unified co-design of model architecture, optimization objectives, serving systems, and agent training environments, enabling improvements in both model capability and deployment efficiency. At the architectural level, we introduce a hybrid linear attention design that integrates Lightning Attention with MLA, improving the efficiency of long-context training and decoding. To further enhance token efficiency, we optimize capability per output token through Evolutionary Chain-of-Thought, Linguistic Unit Policy Optimization, bidirectional preference alignment, and shortest-correct-response distillation. For agentic capabilities, we propose KPop, a reinforcement learning framework designed to support stable training of Ring-2.6-1T on large-scale environment-grounded data. KPop improves training efficiency through asynchronous scheduling across coding, search, tool use, and workflow execution, enabling scalable learning from complex agent-environment interactions. Together, Ling-2.6 and Ring-2.6 provide a practical pathway toward efficient, scalable, and open agentic systems. We open-source all checkpoints in the 2.6 family to support further research and development in practical agentic intelligence.

Ang Li, Ben Liu, Bin Han +215

Efficient Language Model Training Linear Attention LLM Agent Training Efficient Language Model Inference Language Model Post-Training RL for LLM Agents

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.AI

Pythagoras-Prover: Advancing Efficient Formal Proving via Augmented Lean Formalisation

Modern Lean theorem provers achieve strong performance only with substantial training and inference compute, driven in part by scarce verified proof data and the long reasoning traces of formal proof search, making both supervised fine-tuning (SFT) and sampling expensive. We introduce Pythagoras-Prover, a compute-efficient open-source family of Lean theorem provers built for practical compute budgets. The family spans two generation paradigms: autoregressive models at 4B and 32B parameters, and a first proof-of-concept diffusion-based prover (4B) that iteratively refines Lean proofs at inference time. For training efficiency, we build a Lean-verified corpus stratified into easy, medium, and hard problems for curriculum SFT, so models acquire proof skills progressively from shorter, simpler proofs to longer, harder ones. During SFT, a dynamic proof-reasoning filtering scheme preserves informative proof traces while keeping each instance within an 8k-token context budget. We also introduce Augmented Lean Formalisation (ALF), which expands scarce verified corpora into variants of formal statements, populated via self-distillation for extra training signal without formally verifying every mutated instance. By perturbing known problems while preserving their formal character, ALF reduces reliance on any statement's surface form. Empirically, Pythagoras-Prover-4B surpasses DeepSeek-Prover-V2-671B at pass@32 on MiniF2F-Test (86.1% vs 82.4%) with ~167x fewer parameters, while Pythagoras-Prover-32B sets the open-source state of the art at 93.0% on MiniF2F-Test and solves 93 of 672 PutnamBench problems. We release MiniF2F-ALF, an ALF-mutated contamination-sensitive benchmark on which every evaluated model loses accuracy; here our 32B remains strongest and our 4B matches the prior state of the art, Goedel-Prover-V2-32B.

Joshua Ong Jun Leang, Zheng Zhao, Mihaela Cătălina Stoian +5

Imperial College London · University of Edinburgh · Nanyang Technological University +1

Automated Theorem Proving Efficient Language Model Training Lean Theorem Proving

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 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 2, 2026cs.LG

q0: Primitives for Hyper-Epoch Pretraining

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

Bishwas Mandal, Shmuel Berman, Akshay Vegesna +1

Q Labs · Princeton University

Language Model Pretraining Efficient Language Model Training Language Model Ensembles Data-Efficient Learning

Jun 1, 2026cs.CL

PortBERT: Navigating the Depths of Portuguese Language Models

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

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

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

Language Model Pretraining Efficient Language Model Training Language Modeling Efficient Language Model Inference

May 31, 2026cs.LG

When Data Is Scarce: Scaling Sparse Language Models with Repeated Training

Scaling laws for dense LLMs under infinite data are well explored, but how sparsity interacts with limited data is not. In this work, we study sparse training in data-constrained regimes where limited unique tokens require multi-epoch training. Our experiments span models up to 1.92B parameters in the fitting set, sparsity up to 93.75%, unique data budgets up to 2.6B tokens, and total training tokens up to 41.6B over 16 epochs; we further validate extrapolation on held-out dense-equivalent models up to 7.68B parameters. We find that: 1. Sparse scaling in data-limited settings: We introduce a scaling law that models loss as a function of active parameters, unique tokens, data repetition, and sparsity, accurately predicting performance across compute and data budgets. 2. Delayed data saturation: sparse training postpones diminishing returns from repeated data, making multi-epoch training more effective. 3. Resource trade-offs: With fixed data, loss-optimal sparsity is moderate ~ 50%, while compute-optimal sparsity is higher and grows with data scale. Overall, sparsity is not just a tool for efficiency, but a mechanism for improving scaling trade-offs under data scarcity. Our code is available at: https://github.com/boqian333/sparse-dc-scaling.

Boqian Wu, Qiao Xiao, Patrik Okanovic +6

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

Language Model Scaling Laws Efficient Language Model Training Data Repetition in Language Model Training Data-Efficient Learning

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 29, 2026cs.LG

PithTrain: A Compact and Agent-Native MoE Training System

Mixture-of-Experts (MoE) has become the dominant architecture for frontier language models. To meet this demand, production frameworks have built optimized MoE training stacks over years of engineering effort. Yet evolving these stacks for new architectures and system optimizations remains expensive. With the rise of AI coding agents, they could automate parts of training-framework development and accelerate this evolution. But applying them to these existing frameworks carries hidden costs, invisible to today's throughput-only evaluations. We name this missing dimension agent-task efficiency (ATE): the cost of using coding agents to understand, operate, and extend a framework. Grounded in four agent-native design principles, we build PithTrain, a compact, agent-native MoE training framework. We further introduce ATE-Bench, covering real-world training-framework tasks. Our evaluation shows PithTrain matches the throughput of production frameworks, and on ATE-Bench, PithTrain enables higher agent-task efficiency, with up to 62% fewer Agent Turns and 64% less Active GPU Time.

Ruihang Lai, Hao Kang, Haozhan Tang +6

1Carnegie Mellon University · 3NVIDIA · 2Xlue

Mixture-of-Experts Language Models Efficient Language Model Training AI Agent Benchmarks Mixture-of-Experts Models

May 29, 2026cs.CL

Towards Efficient LLMs Annealing with Principled Sample Selection

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

Yuanjian Xu, Jianing Hao, Wanbo Zhang +2

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

Language Model Pretraining Efficient Language Model Training Training Data Selection

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.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