Language Model Scaling Laws

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15 papers in the last four weeks, up 200% on the four weeks before. 0.1% of all new papers.

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Latest papers 95

Jul 9, 2026cs.CL

Hidden Decoding at Scale: Latent Computation Scaling for Large Language Models

Scaling Large Language Models (LLMs) has been driven mainly by enlarging the Transformer backbone, but for an already-strong model this requires another round of costly pretraining. We study whether an existing backbone can keep improving by allocating more computation to each token while leaving the Transformer backbone fixed. Depth-recurrent (looped) Transformers pursue this goal but are hard to scale, because looped computation does not fit naturally with the pipeline parallelism used to train the largest models. We add computation along the sequence-length dimension, where the extra computation is simply a longer input and stays compatible with standard large-model training. We propose Hidden Decoding, a sequence-length scaling method applied during continued pretraining (CPT). It expands each token into n streams with independent embedding tables and keeps the intermediate streams' key-value cache as context, so each token performs more internal computation without adding or widening Transformer layers. To keep this affordable at scale, we introduce Stream-Factorized Attention, in which most layers attend only within each stream and only a few layers mix across streams, reducing the attention cost from quadratic to roughly linear in n. Experiments support two scaling results. At frontier scale, we train WeLM-HD4-80B and WeLM-HD4-617B at n=4 and improve their matched non-HD baselines, making Hidden Decoding the first demonstrated sequence-length scaling method at the 100B+ MoE scale. Across expansion factors, the gains grow as n increases, showing that sequence-length expansion is a practical fixed-backbone scaling path for frontier-scale LLMs.

Aiwei Liu, Cheng Shi, Chuhan Wu +45

Language Model Scaling Laws Transformer Attention Language Model Scaling LLM Training

Jul 2, 2026cs.CL

Will Scaling Improve Social Simulation with LLMs?

Large Language Model (LLM) social simulations are a promising research method, but they are not yet faithful enough to be adopted widely. In this work, we investigate whether the current scaling paradigm in language modeling is likely to close these gaps, or whether simulation fidelity is orthogonal to general capabilities and therefore deserving of more research attention. We use scaling laws to study the relationship between LLMs' compute scale, general capability benchmarks, and the fidelity of social simulation in three representative sub-domains: opinion modeling, behavioral simulation, and longitudinal forecasting. Surprisingly, we discover strong compute scaling in all three settings, using a suite of 85 transformer LLMs with the Qwen3 architecture pre-trained on the DCLM web text corpus under fixed-compute budgets from

10^{18}

to

10^{20}

FLOPs. Then we evaluate 35 larger and more capable open-weight models up to 70B parameters, allowing us to predict downstream accuracy from loss. This reveals that the majority of behavioral and opinion simulation tasks will rapidly improve with scale, particularly when they involve populations that are well-represented in English web corpora. Longitudinal forecasting and underrepresented opinions scale more slowly, especially when they are less correlated with general knowledge and reasoning benchmarks like MMLU. In behavior simulation, scaling fails to improve model calibration with human cognitive biases like risk aversion, as well as human heuristics like learning correlated rewards from related tasks. On these tasks, even fine-tuned models fail to noticeably scale up performance from 0.5B to 8B parameters. Taken together, we conclude that scale will improve social simulations in most settings, but outliers exist, and improvements will be less reliable in low-resource domains.

Caleb Ziems, William Held, Su Doga Karaca +3

Stanford University · Open Athena

Opinion Dynamics Language Model Scaling Laws Computational Social Science Language Model Calibration Large Language Model-Based Social Simulation

Jul 2, 2026cs.CL

When Does Generating More Help? Disentangling Fixed-Source Synthesis from Source Expansion in Synthetic Data Scaling

Synthetic data can be scaled along two routes: Source Expansion (SE), which enlarges the source by adding seed materials or generators, and Fixed-Source Synthesis (FSS), which holds the source fixed and scales the generation budget. Existing scaling studies typically expand the source as the data grows, conflating SE with FSS and leaving FSS underexplored. We isolate FSS by holding the seed-question pool and teacher model fixed, varying only the per-question response budget under Rejection Sampling (RS). We adapt the rectified scaling law to FSS, deriving it from how repeated sampling covers a fixed source. Empirically, the derived form, fit on low budgets, predicts performance at the held-out highest budget for every evaluated teacher--student pair. At matched total-sample budgets, SE and FSS are comparable at small budgets; at large budgets, adding seed questions outperforms spending the same budget on more responses. Within FSS, however, neither synthesizing additional questions from the existing seeds nor varying the synthesis protocol outperforms plain RS at matched budgets. FSS is thus a bounded scaling axis and a controlled setting for comparing synthesis protocols. We will release our code and data to facilitate further research.

Xu Guo, Jian Tong, Zhihui Lu +1

Shanghai AI Laboratory · Shanghai Innovation Institute · Fudan University

Synthetic Data Generation Language Model Scaling Laws Synthetic Data Generation for Language Models Rejection Sampling

Jul 1, 2026cs.LG

How to Allocate Your Tokens? Scaling Laws with Training Steps and Batch Size

We propose a scaling law that takes into account model size and training data while explicitly splitting the latter into training steps and batch size (called three-term law). Fitting the proposed law on a large set of training runs, we find that it correctly recovers the scaling of the optimal batch size. Moreover, because it makes use of training runs with suboptimal batch size, our proposed law can be robustly fit with a significantly smaller amount of training runs. We further show that the three-term law can be used to derive scaling laws for suboptimal batch sizes, and that it matches previous empirical findings related to the critical batch size.

Fabian Schaipp

Inria, ´Ecole Normale Sup´erieure, PSL Research University, Paris

Language Model Scaling Laws Scaling Laws Neural Scaling Laws Hyperparameter Optimization

Jul 1, 2026cs.AI

Two AI Metrics Diverged: Will it Make All the Difference?

As exponential compute scaling continues, will the capabilities of frontier AI models outstrip what is accessible to developers on a small fixed budget? Or will capabilities converge, with "meek models inheriting the earth"? Building on Gundlach et al. (2025b), we show that the answer depends on how we value and measure AI capabilities. We discuss conventional performance measures and show that, while validation loss shows a shrinking gap, on other metrics frontier models grow their lead forever. Classifying performance metrics by their functional forms in relation to training (and inference) compute, we provide tight mathematical conditions for determining which metrics favor meek models, and show that bounded performance metrics always do. But careful interpretation of performance metrics is essential: we show that many common bounded metrics have closely-related counterpart metrics that are unbounded (and vice versa). Determining the apt metric in a domain is a prerequisite for policy, since bounded and unbounded metrics may suggest opposing policy responses. If a particular capability -- like software engineering, synthetic biology, or rhetorical persuasiveness -- is unbounded when measured in the terms we care about, frontier-level capability will likely be concentrated in the hands of a few wealthy actors. Conversely, if that capability is instead bounded, frontier-level capabilities proliferate through meek models into the hands of the many.

Alex Fogelson, Zachary A. Brown, Hans Gundlach +2

MIT FutureTech, CSAIL, Cambridge, MA, USA.

Language Model Scaling Laws AI Governance AI Scaling Laws

Jun 29, 2026cs.CL

Smooth Scaling Laws Hide Stepwise Token Learning

Language model loss follows remarkably regular scaling laws over model and data size, yet it remains unclear why the aggregate loss should exhibit a power-law form. Existing explanations often attribute this regularity to a heavy-tailed spectrum of pattern difficulty in natural language, but this view has not been directly validated at token-level granularity in large-scale real-data training. We present a token-level framework that decomposes scaling laws into localized learning events of individual contextualized tokens. By fitting token loss trajectories with sigmoids, we show that token learning is concentrated in localized transitions, giving rise to a learning-time spectrum that dominates the scaling-law shape. Across more than one hundred pre-training runs on large and diverse real-language corpora with modern LLM architectures, scaling up to 6B parameters and 300B training tokens, the measured learning-time spectrum quantitatively reconstructs the validation loss derivative along the training-step

T

, data-scale

D

, and model-scale

M

axes. We further show that the same signal is actionable: by reshaping the training distribution according to when tokens become learnable, we alter the optimization trajectory and achieve 11% faster validation-loss reduction. These results provide direct empirical evidence that scaling laws are governed primarily by the distribution of token-level learning times, and that this distribution can be used not only to explain scaling behavior but also to improve training performance.

Pingjie Wang, Zechen Hu, Peiru Yang +2

Dots Studio, Xiaohongshu Inc. · Shanghai Jiao Tong University · Tsinghua university

Language Model Pretraining Language Model Scaling Laws LLM Training

Jun 28, 2026cs.LG

Representational Depth of Evaluation Awareness Shifts With Scale in Open-Weight Language Models

Do language models know when they are being tested? This question matters for AI safety: a model that recognises an evaluation context could alter its behaviour strategically, making downstream benchmarks harder to interpret. Using 11 models spanning Qwen 2.5, Gemma 2, and Llama 3.2, we find a systematic size-dependent shift in representational depth: in both Qwen 2.5 and Gemma 2, the layer at which evaluation-awareness is most linearly recoverable moves from late layers in smaller models to early layers in larger ones. This suggests that scale changes not only the strength of evaluation-awareness but also where it is most linearly recoverable in the network. This depth shift helps explain why within-family scaling trajectories are non-monotonic or inverse rather than smooth and family-general, showing that a simple universal power-law account is not supported under denser within-family sampling. Finally, white-box probe signals are consistently stronger than black-box behavioural expression, and the relationship between the two varies by family in ways not predicted by probe AUROC alone.

Archit Manek

Independent Researcher.

LLM Interpretability Language Model Scaling Laws Evaluation Awareness in Language Models Metacognition in Language Models Language Model Probing

Jun 28, 2026cs.LG

On the Nonlinearity of Learning Rate Scaling for LLM Training

Learning-rate transfer can reduce the cost of training large language models: instead of sweeping learning rates at target scale, practitioners extrapolate from smaller runs. Existing approaches often assume that the optimal learning rate follows a log-linear scaling law in data scale and model size. We carefully examine and evaluate this scaling law. In our empirical study of GPT-2--style models from 22M to 707M parameters trained on 5B to 100B tokens, the optimal learning rate develops upward curvature at larger scales, leading to inaccurate extrapolation. We find that this curvature largely disappears when learning rates are replaced by effective learning rate (the step size in normalized weight space), and when data

D

extrapolation is used instead of model size

N

extrapolation. Next, we explain nonlinearity in scaling: weight-norm converges to equilibrium slower when optimal learning is small, requiring a larger step size to reduce the transient phase. Experiments with AdamH, which directly controls the effective learning rate, further support this explanation.

Zaiwen Yang, Huaqing Zhang, Jing Xu +1

Tsinghua University · Tsinghua University, Shanghai Qi Zhi Institute

Language Model Scaling Laws Hyperparameter Transfer Neural Network Training Dynamics LLM Training

Jun 26, 2026cond-mat.dis-nn

Scaling limit of the Random Language Model

We develop a quantitative theory of the Random Language Model (RLM), an ensemble of stochastic context-free grammars, in a scaling limit where the number of hidden symbols

N \to \infty

while the grammar temperature

\tildeε_d \to 0

at fixed

x = {\tildeε}_d \log N

. In this limit, the model admits a controlled description based on a large-deviation principle over rule-usage patterns. A semi-annealed approximation maps the problem to a class of Random Energy Models with nontrivial combinatorics. We show that the RLM exhibits a condensation transition at a critical value

x_c=1/8

, below which rule usage concentrates and language statistics acquire a nontrivial dependence on corpus length. A second characteristic scale at

x=1/2

marks the onset of entropy reduction from its maximal value. Across these regimes, we derive explicit scaling laws for the number of distinct rules, entropy, and related observables, identifying distinct scaling, saturation, and critical regimes controlled by the interplay of grammar size, corpus length, and temperature. The theory resolves previous ambiguities regarding the existence of a thermodynamic transition and explains the slow approach to the large-

N

limit as a consequence of the dependence on

\log N

. It further provides a unified framework in which universal statistical properties of language emerge from typical realizations of generative grammars, with implications for both natural language statistics and the behavior of large language models.

Eric De Giuli

Department of Physics, Toronto Metropolitan University, M5B 2K3, Toronto, Canada

Language Model Scaling Laws Language Modeling

Jun 23, 2026cs.LG

Emergent Capabilities Arise Randomly from Learning Sparse Attention Patterns

Neural scaling laws for transformer language models predict smooth improvements in pretraining loss with increasing parameters, but downstream capabilities such as in-context learning are known to emerge abruptly past a certain model scale. In this paper, we show that emergent capabilities arise stochastically throughout training, with larger models acquiring them earlier on average. We demonstrate that the emergence of capabilities such as pattern completion and indirect object identification corresponds to the abrupt learning of task-relevant attention patterns. To isolate this phenomenon, we train transformer models on synthetic linear map and cellular automata datasets, and we show that the difficulty of learning attention patterns depends on context length and pattern sparsity. Moreover, scaling the number of attention heads improves learning efficiency on our synthetic tasks, while increasing the head dimension yields diminishing returns past a minimum capacity. We additionally investigate architectures with alternative attention mechanisms, showing that MLP-Mixer outperforms a transformer on linear map tasks with complex attention patterns. Our findings provide a mechanistic insight into emergence, showing that downstream capabilities arise abruptly due to the intrinsic difficulty of learning sparse attention patterns in transformer models.

Vatsal Baherwani, Zixi Chen, Shikai Qiu +2

New York University

Language Model Scaling Laws Transformer Attention Sparse Attention

Jun 23, 2026cs.LG

Neural Scaling Universality: If Exponents Are Fixed, Time to Understand Coefficients

Neural scaling laws describe how pre-training loss decays as power laws with training time, model size, and compute. This position paper argues that the exponents of these power laws are fixed by generic mechanisms: a one-third time scaling due to the strong nonlinearity of Softmax, an inverse width scaling due to representational superposition, and an inverse depth scaling due to ensemble averaging of Transformer layers. These mechanisms are robust to a wide range of data structures and architectural details, placing current large language models in a universality class with fixed exponents. The coefficients, however, are expected to be sensitive to data and architecture details, and directly determine practical quantities such as the optimal model shape and the compute-optimal frontier. We therefore argue that understanding the coefficients is the key to near-term performance improvements, and that a closer examination of the current universality class may reveal pathways to better universality classes.

Yizhou Liu, Jeff Gore

Massachusetts Institute of Technology Cambridge, MA 02139

Language Model Scaling Laws Neural Scaling Laws

Jun 23, 2026cs.AI

Can Scale Save Us From Plasticity Loss in Large Language Models?

The loss of plasticity - the ability of a network to learn new information after having already learned older information - is a fundamental challenge in creating artificial neural networks capable of continual learning. Although this phenomenon has been known for decades, it has mostly been studied in older, relatively small architectures and rarely in natural-language domains. To determine whether loss of plasticity remains a problem in the modern transformer-based LLM paradigm, we study plasticity loss in GPT-style Transformer models trained on a multilingual continual learning problem. Consistent with prior work, we find evidence of plasticity loss across models ranging from 5M to 314M non-embedding parameters, as measured by deterioration on a held-out Vietnamese probing task. We further find that the onset of plasticity loss follows a predictable scaling law, growing sublinearly with model size. These results suggest that larger models may delay the measurable effects of plasticity loss, but that increasing parameter count alone is likely to be insufficient to completely prevent it. We also find evidence of plasticity loss under stationary multilingual training, challenging the view that the phenomenon is exclusive to continual learning with abrupt task changes. Overall, our results suggest that even large Transformer language models trained on natural-language will eventually lose the ability to efficiently adapt to new data after sufficiently long training, in both continual and stationary settings.

J. Fernando Hernandez-Garcia, Tomás Figliolia, Beren Millidge

Zyphra San Francisco, CA

Continual Learning for LLMs Loss of Plasticity Language Model Scaling Laws

Jun 23, 2026cs.AI

Scaling Laws for Task-Specific LLM Distillation

Large Language Models (LLMs) achieve strong performance across a growing range of domains, yet their scale poses deployment challenges in applications where latency and cost constraints are critical. This paper derives empirical scaling laws for domain-specific LLM compression, quantifying how in-domain and general knowledge performance scale with dataset size, compression ratio, supervision format, and iterative pruning schedule. Using quantitative finance as our application domain, we compare logit-based and LoRA-based distillation under iterative structural pruning, introducing a blended chain-of-thought supervision loss that stabilizes KL-divergence distillation over reasoning traces. In-domain task quality degrades predictably under compression while general-knowledge benchmarks collapse well before the same point; supervision format is the key driver of this tradeoff, with chain-of-thought supervision actively recovering general knowledge that pruning erases. We release the headline dataset FinHeadlineMix, scaling law results, and practical recommendations to provide a reusable framework for domain-specific compression decisions.

Lavinia Ghita, Dhruv Desai, Ioana Boier

NVIDIA

LLM Pruning LLM Compression Language Model Scaling Laws Language Model Distillation

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 23, 2026cs.AI

On the Smallness of the Large Language Models Scaling Exponents

We discuss reasons why the scaling exponents of current Large Language Models (LLMs) applications are indicating an unsustainable regime in terms of energy resources. We further show that attributing the smallness of such exponents to a numerical bias due to the neglect of a non-zero value of the loss function in the limit of infinite data (``pedestal effect") does not remove the unsustainability issue. Finally, the effects of the smoothness (roughness) of the data on the scaling exponents is commented upon based on an analogy with phenomenological models of fluid turbulence.

Sauro Succi, Peter V. Coveney, Alex Hansen

Italian Institute of Technology, Viale Regina Elena, 291, 00161, Rome, Italy · PoreLab, Physics Department, Norwegian University of Science and Technology, 7491 Trondheim, Norway · Centre for Computational Science, Chemistry Department, University College of London, 20 Gordon Street, WC1H 0AJ, London, United Kingdom

Energy-Efficient ML Language Model Scaling Laws

Jun 22, 2026cs.LG

The Energy Consumption of Transformer Fine-Tuning: A Roofline-Inspired Scaling Model

Transformer-based models underpin modern natural language processing but incur rapidly growing computational and energy costs. As training scales in both model size and parallelism, accurately predicting energy consumption has become critical for sustainable and cost-aware system design. We present a framework for modeling the energy consumption of Transformer training on multiple GPUs. Using controlled architectural sweeps of BERT models, we relate measured energy to lightweight proxies for compute, memory traffic, and hardware efficiency. Inspired by roofline models, our approach incorporates a speedup-based hardware-efficiency factor that captures the effects of tensor parallelism and fully sharded data parallelism. We derive a scaling law model that accurately predicts training energy across heterogeneous configurations.

Mansour Zoubeirou a Mayaki

Université Lumière Lyon 2, CNRS, Ecole Centrale de Lyon, INSA Lyon, Universite Claude Bernard Lyon 1, LIRIS, UMR5205, 69007 Lyon, France

Energy-Efficient ML Transformer Language Model Scaling Laws

Jun 20, 2026cs.AI

Human vs Machine Mathematical Difficulty on Project Euler: An Experimental Analysis

We study how the effort and success probability of frontier AI systems scale with human difficulty on problems from Project Euler, an online platform of computational mathematics problems. Our dataset, from the MathArena benchmark, consists of 3840 attempts across 50 problems and 26 model configurations, with problem difficulty measured by the site's public human solve times. Motivated by a proposal of Timothy Gowers, we test a power-law relation

t_{\text{machine}} = a \cdot t_{\text{human}}^b

between generated-token cost per successful answer and human time, and find

b < 1

for 20 of the 25 models with usable fits, including the strongest base models; this operationalization therefore does not support an earlier prediction that machines scale worse than humans with difficulty. We also investigate whether success probability on the tested problems can be modeled by a simple exponential decay

p_{\text{success}} = e^{c t_{\text{human}}}

, predicting a linear relation between

\log p_{\text{success}}

and

t_{\text{human}}

. Using a binning approach for data aggregation we find moderate empirical support (median bin-level

R^2 = 0.92

across the 22 best-covered configurations) for this model. Following METR, we also fit logistic success curves and extract 50% task-length horizons

h_{50}

; the strongest configurations in our 20 April 2026 snapshot reach roughly

2.5

--

4.3

hours on our fastest-five human baseline, with a log-linear fit through the state-of-the-art frontier giving a descriptive doubling time of about

75

~days for the SOTA

h_{50}

.

David Holmes, Johannes Schmitt

Mathematical Reasoning Benchmarks Language Model Scaling Laws LLM Mathematical Reasoning

Jun 5, 2026cs.LG

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

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

Zhiwei Xu, Shihao Wu, Hanseul Cho +2

University of Michigan · KAIST AI

Language Model Pretraining Language Model Scaling Laws Scaling Laws Data Repetition in Language Model Training

Jun 4, 2026cs.CL

Decomposing Factual Sycophancy in Language Models: How Size and Instruction Tuning Shape Robustness

Factual sycophancy occurs when a language model abandons a correct, verifiable answer under social pressure. Because a flip occurs only when pressure toward a false answer exceeds the model's neutral preference for the truth, flip rates conflate two mechanisms: the strength of that baseline preference (truth margin), and how far pressure shifts it (manipulation sensitivity). We decompose factual sycophancy into these channels and use them to separate the effects of size and instruction tuning across 56 open-weight models spanning 0.3B-32B parameters and 13 manipulation types. We find that vulnerability is governed mainly by size, but instruction tuning changes how size acts: small instruction-tuned models can become less robust, whereas large instruction-tuned models usually become more robust. Instruction tuning primarily increases truth margin, but its behavioral effect depends on manipulation type. Scaling also changes the two channels differently: base models gain margin but become mildly more manipulation-sensitive, whereas instruction-tuned models gain margin faster and become less sensitive. Factual sycophancy is therefore not a single scalar property. Evaluations should report channel-specific, manipulation-specific, and size-conditioned robustness rather than flip rates alone.

Victor De Marez, Luna De Bruyne, Walter Daelemans

Centre for Computational Linguistics, Psycholinguistics and Sociolinguistics University of Antwerp Antwerp, Belgium

LLM Evaluation LLM Sycophancy Language Model Scaling Laws LLM Reliability Instruction Tuning Language Model Robustness

Jun 4, 2026cs.CL

Entity tracking emerges in sub-billion parameter language models and exceeds human performance in naturalistic narratives

Understanding language requires tracking entities across discourse - i.e., knowing where things are and how they change, even when not explicitly stated. Whether language models perform such tracking in a human-like fashion remains unclear, in part because existing evaluations rely on artificial tasks, far removed from natural language comprehension, and lack comparisons to humans. Here, we evaluate entity tracking in both language models and humans (N = 48) using naturalistic narratives at multiple levels of complexity. In humans, we find that entity tracking degrades specifically with narrative complexity, not narrative length. In language models, we find that human-level entity tracking is already present at 410 million parameters - well below the multi-billion parameter, code-specialised models identified by prior work - and improves with scale, with contemporary models far exceeding human performance. Together, these results demonstrate that entity tracking, a core component of language understanding, emerges at model scales far smaller than previously thought.

Karolina Drożdż, Micha Heilbron

IDEAS Research Institute; Warsaw, Poland · Max Planck Institute for Psycholinguistics; Nijmegen, Netherlands · University of Amsterdam, Amsterdam Brain and Cognition; Amsterdam, Netherlands

LLM Evaluation Language Model Scaling Laws

Jun 4, 2026cs.CL

Predictable Scaling Laws of Optimal Hyperparameters for LLM Continued Pre-training

The efficacy of continued pre-training for Large Language Models (LLMs) hinges upon hyperparameter configurations, such as learning rate and batch size. However, current practices often rely on heuristics or grid searches, leading to training instability and excessive costs. In this work, we first empirically discover that optimal hyperparameters follow stable and predictable scaling laws throughout the continued pre-training process. Leveraging these insights, we propose a novel framework to establish quantitative relationships between compute budget and optimal hyperparameters for a given checkpoint. Our approach has two stages: (1) \textit{Empirical Law Discovery}, where we train small-scale proxy models to derive functions mapping compute budget to optimal hyperparameters via standard loss-compute scaling laws; and (2) \textit{State-Aware Hyperparameter Prediction}, where we evaluate an initial checkpoint's validation loss and use the inverse scaling law to estimate its \textit{equivalent pre-training compute} -- the compute needed to achieve the same loss from scratch. Combining this with the planned compute budget, we predict optimal hyperparameters for the target run. Empirical results demonstrate that our method reduces the hyperparameter search overhead by up to 90% while achieving comparable or superior performance relative to baselines. This model-agnostic framework generalizes across architectures, providing a principled and efficient methodology for diverse continued pre-training scenarios starting from any given point.

Yongwei Zhou, Juncheng Diao, Junlin Shang +2

MeiTuan · University of Chinese Academy of Sciences · Harbin Institute of Technology

Language Model Scaling Laws Hyperparameter Transfer Continued Pretraining Hyperparameter Optimization

May 31, 2026cs.LG

Structure and Scale in Simplicial Sequence Modelling

Modern large-scale deep learning exhibits two striking empirical phenomena: behavioural scaling laws (predictable performance gains with increasing scale) and emergent mechanisms (structured internal representations and circuits in deep neural networks). We hypothesise that these two phenomena are connected: that predictable changes in behaviour are the result of predictable changes in internal computational structure. In this paper, we report preliminary evidence of such a connection. We find a correlation between scaling patterns in performance and representations in small transformers trained to predict the outputs of a hidden Markov model, for which residual activations are known to linearly encode a belief distribution over latent states in a probability simplex.

Matthew Farrugia-Roberts

Department of Computer Science, University of Oxford

Representation Geometry Transformer Language Model Scaling Laws Neural Network Interpretability Neural Scaling Laws Sequence Modeling

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 29, 2026cs.LG

Item Response Scaling Laws: A Measurement Theory Approach for Efficient and Generalizable Neural Scaling Estimation

Scaling laws provide a fundamental framework for understanding the performance of Language Models (LMs), yet deriving them requires prohibitively expensive evaluations across thousands of checkpoints or millions of inference samples. To address this, we introduce Item Response Scaling Laws (IRSL), a unified framework that integrates Item Response Theory (IRT) within the scaling law framework. Unlike traditional approaches that treat each model-benchmark pair in isolation, IRSL disentangles latent model ability from question characteristics, factorizing the scaling law estimation for

M

models and

N

questions to significantly reduce parameter complexity from

O(M \times N)

to

O(M + N)

. We instantiate IRSL with Beta-IRT, which leverages the empirical probability responses of LMs -- such as token probabilities in pre-training and pass rates in test-time sampling -- to capture richer signals than binary responses. We validate our approach across two prevalent scaling paradigms: (1) pre-training downstream scaling, using 6,612 LM checkpoints and 37,682 questions from 10 benchmarks; and (2) test-time scaling, using 12 LMs and 120 questions from 4 benchmarks with up to 2,500 samples per question. Given a one-time calibration on existing model responses, IRSL yields more reliable scaling estimates using only 50 questions per benchmark (a 99.9% reduction), achieving comparable or superior decision accuracy to traditional approaches. Furthermore, we show that the estimated latent model abilities are generalizable, enabling accurate performance forecasting across benchmarks that share the same measurement objective.

Sang Truong, Yuheng Tu, Rylan Schaeffer +1

1Stanford University · University of California, Los Angeles

Language Model Scaling Laws Test-Time Scaling Item Response Theory

May 28, 2026cs.CL

How LoRA Remembers? A Parametric Memory Law for LLM Finetuning

Large Language Models (LLMs) must continuously learn and update knowledge to remain effective in dynamic real-world environments. While Low-Rank Adaptation (LoRA) is widely used for such memory updates, existing studies mainly rely on qualitative downstream evaluations, leaving the quantitative capacity limits and underlying dynamics of exact parametric memory largely unexplored. To bridge this gap, we employ LoRA as a controlled memory capacity probe within the latent space to systematically quantify exact parametric memory. We introduce the Parametric Memory Law, a robust power law linking loss reduction Delta L to effective parameters and sequence length. At the token level, fine-grained analysis reveals a deterministic phase transition, demonstrating that a prediction probability of p > 0.5 constitutes a sufficient condition for verbatim recall under greedy decoding. Driven by these insights, we introduce MemFT, a threshold-guided optimization strategy that dynamically redistributes the training budget toward sub-threshold tokens. Empirical evaluations demonstrate that MemFT can enhance memory fidelity and efficiency. Code will be released at https://github.com/zjunlp/ParametricMemoryLaw.

Ziwen Xu, Haiwen Hong, Linsong Yu +4

Zhejiang University · Alibaba Group

Memorization in Language Models LLM Fine-Tuning Language Model Scaling Laws LLM Memory Memorization in Generative Models Parameter-Efficient Fine-Tuning

May 28, 2026cs.LG

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

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

Jing Huang, Daniel Wurgaft, Rachit Bansal +6

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

Long-Tail Learning Language Model Scaling Laws LLM Training

May 28, 2026cs.AI

The Curse of Helpfulness: Inverse Scaling Law in Robustness to Distractor Instructions via DistractionIF

Large Language Models (LLMs) are increasingly deployed in agentic and retrieval-augmented generation (RAG) systems, where they must execute user-specified tasks over externally provided reference text. In practice, such context is often unstructured and contaminated with benign but instruction-like semantic noise, such as editorial comments and system traces, which should be treated strictly as data. We introduce DistractionIF, a benchmark designed to evaluate robustness against such distractor instructions in reference text. Across a broad range of models, we observe a consistent inverse scaling phenomenon: larger models are often less robust, with performance dropping by up to 30 points as scale increases. Mechanistically, our perplexity analysis reveals that scaling erodes the probabilistic boundary between robust and distracted behaviors, making models increasingly prone to over-interpreting noise as instructions. To address this, we demonstrate that reinforcement learning, specifically Group Relative Policy Optimization (GRPO), can restore this boundary, improving robustness by up to 15.5% without compromising general instruction-following capability. Our findings highlight a critical instruction-following robustness gap in reference-grounded tasks and establish reinforcement learning as a promising path for enforcing strict data-instruction separation at scale.

Zeli Su, Zhankai Xu, Tianlei Chen +4

Minzu University of China, Beijing, China · Ant Group, Hangzhou, China · Renmin University of China, Beijing, China +1

Language Model Scaling Laws Language Model Robustness

May 27, 2026cs.CL

SuperValid: Capability-Aligned OOD Validation for Generalizable Downstream Scaling

Scaling laws guide large language model training by relating compute to cross-entropy loss, and recent work further extends them to predict downstream benchmark performance. However, prior approaches face generalization limitations from two aspects: focusing on benchmark-level performance introduces scenario-specific artifacts, while relying on IID validation loss fails to track capability improvements when training distributions vary. In this work, we argue that downstream scaling should be studied at the capability level, which captures shared skill factors across related tasks while abstracting away benchmark-specific noise. We propose SuperValid, a framework that synthesizes OOD (out-of-distribution), capability-aligned validation data by distilling core concepts from benchmarks within a capability domain and expanding them into diverse, knowledge-rich texts. Extensive experiments spanning 16 benchmarks grouped into 6 capability domains show that SuperValid loss exhibits strong and stable correlation with downstream performance across models of different architectures, scales, and training data distributions. As a training-free metric computable during training without benchmark evaluation, SuperValid enables effective model selection, early stopping, and scaling decisions.

Quanen Sun, Changxin Tian, Ke Shi +6

Ant Group

LLM Evaluation Language Model Scaling Laws OOD Generalization

May 27, 2026cs.LG

Law of Neural Interaction: Depth-Width Shape, Interaction Efficiency, and Generalization

The guidance of scaling laws has increased the resource demands of modern large language models (LLMs), yet it remains questionable whether these models utilize resources effectively under a fixed budget. Previous research has proved superposition as a key contributor to loss. By leveraging the Neural Feature Ansatz, we extend superposition from parameter space to gradient space and define it as neural interaction. We find that under a fixed budget, good generalization is usually accompanied by efficient neural interactions, and the model can be placed in an efficient interaction interval by adjusting its depth-width ratio (

R_{D/W}

). In addition, as the budget scales up, the efficient interaction interval of the model remains relatively stable. By comparing existing small scale dense LLMs, we observe that models operating near this interval tend to perform better on the MMLU-Pro benchmark. Our findings reveal that the

R_{D/W}

influences resource utilization efficiency and thereby affects generalization, providing insights into model shape initialization and the understanding of model generalization mechanisms. Code for Neural Interaction Law is available at: https://anonymous.4open.science/r/Neural_Interaction_Law-D788

Wenjie Sun, Jinning Yang, Shuai Zhang +1

The Chinese University of Hong Kong, Shenzhen · Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences · New Jersey Institute of Technology

Neural Network Generalization Language Model Scaling Laws

May 25, 2026cs.LG

Unified Neural Scaling Laws

We present a functional form (that we refer to as a Unified Neural Scaling Law (UNSL)) that accurately models and extrapolates the scaling behaviors of deep neural networks as multiple dimensions all vary simultaneously (i.e. how the evaluation metric of interest varies as one simultaneously varies the number of model parameters, training dataset size, number of training steps, number of inference steps, amount of compute, and various hyperparameters) for various architectures and for each of various tasks within a varied set of upstream and downstream tasks. This set includes large-scale vision, language, math, and reinforcement learning. When compared to other functional forms for neural scaling, this functional form yields extrapolations of scaling behavior that are considerably more accurate on this set.

Ethan Caballero, Priyank Jaini, David Krueger +1

Mila, University of Montreal · Google DeepMind

Language Model Scaling Laws Scaling Laws Neural Scaling Laws