Chain-of-thought prompting, by including intermediate reasoning steps in few-shot examples, elicits strong reasoning abilities in large language models on arithmetic, commonsense, and symbolic tasks.
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Scaling Laws for Neural Language Models
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abstract
We study empirical scaling laws for language model performance on the cross-entropy loss. The loss scales as a power-law with model size, dataset size, and the amount of compute used for training, with some trends spanning more than seven orders of magnitude. Other architectural details such as network width or depth have minimal effects within a wide range. Simple equations govern the dependence of overfitting on model/dataset size and the dependence of training speed on model size. These relationships allow us to determine the optimal allocation of a fixed compute budget. Larger models are significantly more sample-efficient, such that optimally compute-efficient training involves training very large models on a relatively modest amount of data and stopping significantly before convergence.
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- abstract We study empirical scaling laws for language model performance on the cross-entropy loss. The loss scales as a power-law with model size, dataset size, and the amount of compute used for training, with some trends spanning more than seven orders of magnitude. Other architectural details such as network width or depth have minimal effects within a wide range. Simple equations govern the dependence of overfitting on model/dataset size and the dependence of training speed on model size. These relationships allow us to determine the optimal allocation of a fixed compute budget. Larger models are s
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representative citing papers
BBO-Pile is the first large-scale open dataset of real optimization trajectories used to train and scale foundation models that imitate black-box optimization methods.
Introduces the Synthetic Data Contamination Equilibrium and derives closed-form optimal provenance subsidies s* = KL(q||p)/(2 kappa) plus watermark strengths to mitigate model collapse, validated by OLS matching structural predictions on C4 data.
Cayley unitary adapters executed on real quantum hardware improve LLM perplexity by 1.4% on Llama 3.1 8B with 6000 parameters and recover 83% of compression-induced degradation on SmolLM2.
ε-coresets for attention exist of size O(√d e^{ρ+o(ρ)}/ε) for unit-norm keys/values and queries of norm ≤ρ, nearly matching the Ω(√d e^ρ/ε) lower bound.
RoundPipe achieves near-zero-bubble pipeline parallelism for LLM training on consumer GPUs by dynamically dispatching computation stages round-robin, yielding 1.48-2.16x speedups and enabling 235B model fine-tuning on 8x RTX 4090.
Transformer weight spectra exhibit transient compression waves that propagate layer-wise, persistent non-monotonic depth gradients in power-law exponents, and Q/K-V asymmetry, with the spectral exponent alpha predicting layer importance and enabling pruning gains of 1.1x-3.6x over Last-N baselines.
Grokking reflects escape from a metastable low-dimensional regime where transverse curvature accumulates before generalization, with subspace motion necessary but curvature boost insufficient.
The SDE benchmark shows LLMs lag on scientific discovery tasks relative to general science tests, with diminishing scaling returns and shared weaknesses across models.
Transformers perform kernel-based prediction for Hölder regression on manifolds and achieve intrinsic-dimension-dependent minimax rates with sufficient training tasks.
Introduces hybrid noise and novel coupling analysis to achieve the first convergent hidden-state DP bound for zeroth-order optimization.
LLaDA is a scalable diffusion-based language model that matches autoregressive LLMs like LLaMA3 8B on tasks and surpasses GPT-4o on reversal poem completion.
ErrorRadar is a new benchmark of 2,500 multimodal K-12 math problems for MLLM error step identification and categorization, where GPT-4o trails human experts by ~10%.
TTT layers treat the hidden state as a trainable model updated at test time, allowing linear-complexity sequence models to scale perplexity reduction with context length unlike Mamba.
KANs with learnable univariate spline activations on edges achieve better accuracy than MLPs with fewer parameters, faster scaling, and direct visualization for scientific discovery.
Tiny language models under 10M parameters trained on a synthetic children's story dataset generate fluent, consistent, multi-paragraph English text with near-perfect grammar and reasoning.
Pythia releases 16 identically trained LLMs with full checkpoints and data tools to study training dynamics, scaling, memorization, and bias in language models.
Language models can automatically generate high-quality evaluation datasets that reveal new cases of inverse scaling, sycophancy, and concerning goal-seeking behaviors, including some worsened by RLHF.
The Pile is a newly constructed 825 GiB dataset from 22 diverse sources that enables language models to achieve better performance on academic, professional, and cross-domain tasks than models trained on Common Crawl variants.
A compute-aware framework using cumulative FLOPs shows alignment training has non-monotonic effects on robustness and attack costs vary up to 5x across harm categories.
A novel complexity minimization meta-learning framework provably demonstrates that few-shot adaptation error decreases as meta-training data volume increases.
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D³ introduces a dynamic directional graph-constrained framework that models sample interactions via loss dependencies to derive an optimized training sequence for LLMs.
The study links three LVLM architectural dimensions to three hallucination types via a new benchmark, finding that language foundation quality reduces co-occurrence errors, visual encoder strength reduces similarity errors, alignment reduces uncertainty errors, and joint visual-alignment improvement
citing papers explorer
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Chain-of-Thought Prompting Elicits Reasoning in Large Language Models
Chain-of-thought prompting, by including intermediate reasoning steps in few-shot examples, elicits strong reasoning abilities in large language models on arithmetic, commonsense, and symbolic tasks.
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An Open-Source Training Dataset for Foundation Models for Black-box Optimization
BBO-Pile is the first large-scale open dataset of real optimization trajectories used to train and scale foundation models that imitate black-box optimization methods.
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The Economics of Model Collapse: Equilibrium, Welfare, and Optimal Provenance Subsidies in Synthetic Data Markets
Introduces the Synthetic Data Contamination Equilibrium and derives closed-form optimal provenance subsidies s* = KL(q||p)/(2 kappa) plus watermark strengths to mitigate model collapse, validated by OLS matching structural predictions on C4 data.
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Quantum-enhanced Large Language Models on Quantum Hardware via Cayley Unitary Adapters
Cayley unitary adapters executed on real quantum hardware improve LLM perplexity by 1.4% on Llama 3.1 8B with 6000 parameters and recover 83% of compression-induced degradation on SmolLM2.
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Nearly Optimal Attention Coresets
ε-coresets for attention exist of size O(√d e^{ρ+o(ρ)}/ε) for unit-norm keys/values and queries of norm ≤ρ, nearly matching the Ω(√d e^ρ/ε) lower bound.
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Efficient Training on Multiple Consumer GPUs with RoundPipe
RoundPipe achieves near-zero-bubble pipeline parallelism for LLM training on consumer GPUs by dynamically dispatching computation stages round-robin, yielding 1.48-2.16x speedups and enabling 235B model fine-tuning on 8x RTX 4090.
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The Spectral Lifecycle of Transformer Training: Transient Compression Waves, Persistent Spectral Gradients, and the Q/K--V Asymmetry
Transformer weight spectra exhibit transient compression waves that propagate layer-wise, persistent non-monotonic depth gradients in power-law exponents, and Q/K-V asymmetry, with the spectral exponent alpha predicting layer importance and enabling pruning gains of 1.1x-3.6x over Last-N baselines.
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Low-Dimensional and Transversely Curved Optimization Dynamics in Grokking
Grokking reflects escape from a metastable low-dimensional regime where transverse curvature accumulates before generalization, with subspace motion necessary but curvature boost insufficient.
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Evaluating Large Language Models in Scientific Discovery
The SDE benchmark shows LLMs lag on scientific discovery tasks relative to general science tests, with diminishing scaling returns and shared weaknesses across models.
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Understanding In-Context Learning on Structured Manifolds: Bridging Attention to Kernel Methods
Transformers perform kernel-based prediction for Hölder regression on manifolds and achieve intrinsic-dimension-dependent minimax rates with sufficient training tasks.
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Privacy Amplification in Differentially Private Zeroth-Order Optimization with Hidden States
Introduces hybrid noise and novel coupling analysis to achieve the first convergent hidden-state DP bound for zeroth-order optimization.
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Large Language Diffusion Models
LLaDA is a scalable diffusion-based language model that matches autoregressive LLMs like LLaMA3 8B on tasks and surpasses GPT-4o on reversal poem completion.
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ErrorRadar: Benchmarking Complex Mathematical Reasoning of Multimodal Large Language Models Via Error Detection
ErrorRadar is a new benchmark of 2,500 multimodal K-12 math problems for MLLM error step identification and categorization, where GPT-4o trails human experts by ~10%.
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Learning to (Learn at Test Time): RNNs with Expressive Hidden States
TTT layers treat the hidden state as a trainable model updated at test time, allowing linear-complexity sequence models to scale perplexity reduction with context length unlike Mamba.
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KAN: Kolmogorov-Arnold Networks
KANs with learnable univariate spline activations on edges achieve better accuracy than MLPs with fewer parameters, faster scaling, and direct visualization for scientific discovery.
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TinyStories: How Small Can Language Models Be and Still Speak Coherent English?
Tiny language models under 10M parameters trained on a synthetic children's story dataset generate fluent, consistent, multi-paragraph English text with near-perfect grammar and reasoning.
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Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling
Pythia releases 16 identically trained LLMs with full checkpoints and data tools to study training dynamics, scaling, memorization, and bias in language models.
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Discovering Language Model Behaviors with Model-Written Evaluations
Language models can automatically generate high-quality evaluation datasets that reveal new cases of inverse scaling, sycophancy, and concerning goal-seeking behaviors, including some worsened by RLHF.
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The Pile: An 800GB Dataset of Diverse Text for Language Modeling
The Pile is a newly constructed 825 GiB dataset from 22 diverse sources that enables language models to achieve better performance on academic, professional, and cross-domain tasks than models trained on Common Crawl variants.
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Risk Under Pressure: Compute-Aware Evaluation of Adversarial Robustness in Language Models
A compute-aware framework using cumulative FLOPs shows alignment training has non-monotonic effects on robustness and attack costs vary up to 5x across harm categories.
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Provable Data Scaling Law for Meta Learning via Complexity Minimization
A novel complexity minimization meta-learning framework provably demonstrates that few-shot adaptation error decreases as meta-training data volume increases.
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LLMs Need Encoders for Semantic IDs Too
PrefixMem encoder for Semantic IDs improves deepest-level accuracy by up to 46% relative and full-SID retrieval recall by up to 22% relative on Pinterest data across LLM families.
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D$^3$: Dynamic Directional Graph-Constrained Data Scheduling for LLM Training
D³ introduces a dynamic directional graph-constrained framework that models sample interactions via loss dependencies to derive an optimized training sequence for LLMs.
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What Makes LVLMs Hallucinate Less? Unveiling the Architectural Factors Behind Hallucination Robustness
The study links three LVLM architectural dimensions to three hallucination types via a new benchmark, finding that language foundation quality reduces co-occurrence errors, visual encoder strength reduces similarity errors, alignment reduces uncertainty errors, and joint visual-alignment improvement
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Repetition Mismatch: Why Data Mixture Experiments Don't Scale and How to Fix Them
Repetition rate mismatch between small-scale proxies and target budgets is the main reason data mixture experiments do not scale; a subsampling procedure that equalizes repetition rates recovers optimal mixtures from 1/16-scale experiments.
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YoCausal: How Far is Video Generation from World Model? A Causality Perspective
YoCausal benchmark shows video diffusion models detect the arrow of time but lack genuine causal understanding relative to humans.
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Latent Performance Profiling of Large Language Models
Introduces Latent Performance Profiling (LPP) as a task-agnostic framework deriving scalar metrics from LLM latent representations and dynamics to complement benchmark evaluations.
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How Much Is a Dataset Worth? Scaling Laws, the Vendi Score, and Matrix Spectral Functions
Vendi Score and scaling-law objectives belong to the class of matrix spectral functions, which are submodular, enabling efficient greedy selection of training data that outperforms random subsets in predicting held-out performance.
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Tokenisation via Convex Relaxations
ConvexTok uses convex relaxation of tokenization to a linear program, improving intrinsic metrics, bits-per-byte, and some downstream tasks while certifying near-optimality within 1% at typical vocabulary sizes.
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Forecasting Scientific Progress with Artificial Intelligence
Introduces the CUSP benchmark across 4760 events and finds frontier AI models can pick plausible directions but fail to predict whether or when scientific advances will occur, with performance varying by domain and insensitive to training cutoffs.
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Is Capability a Liability? More Capable Language Models Make Worse Forecasts When It Matters Most
More capable LLMs produce worse distributional forecasts on superlinear growth time series with tail risks of regime change, with the error concentrated in the upper tail; this reverses on conventional threshold metrics.
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Uniform-in-Time Weak Propagation-of-Chaos in Shallow Neural Networks
Finite-width shallow networks remain within poly(d) m^{-min(1,c/6)} of their mean-field limit uniformly in time when mean-field excess loss decays as t^{-c} under standard regularity and an integral condition on the loss.
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Closed Loop Dynamic Driving Data Mixture for Real-Synthetic Co-Training
AutoScale is a closed-loop data engine using Graph-RAE for scene representation and Cluster-GA for importance-based retrieval to improve real-synthetic co-training for autonomous driving.
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RankE: End-to-End Post-Training for Discrete Text-to-Image Generation with Decoder Co-Evolution
RankE co-evolves AR policy and decoder via alternating ranking optimization, improving both FID and CLIP scores on LlamaGen-XL and Janus-Pro where policy-only RL degrades FID.
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Provable Joint Decontamination for Benchmarking Multiple Large Language Models
JECS aggregates per-model conformal p-values via their maximum and reconstructs a conservative envelope of the max-p null distribution to select benchmarks with global contamination rate control.
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LOSCAR-SGD: Local SGD with Communication-Computation Overlap and Delay-Corrected Sparse Model Averaging
LOSCAR-SGD combines local updates, sparse model averaging, and communication-computation overlap with a delay-corrected merge rule, providing convergence rates for smooth non-convex objectives under worker heterogeneity.
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Trusted Weights, Treacherous Optimizations? Optimization-Triggered Backdoor Attacks on LLMs
Compilation optimizations can be exploited to create stealthy backdoors in LLMs that remain dormant without optimization but achieve ~90% attack success while preserving clean accuracy near 100%.
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PilotWiMAE: Pilot-Native Representation Learning for Wireless Channels
PilotWiMAE pretrains an encoder on noisy pilots with factorized attention, 99% masking, patch-normalized reconstruction, scale loss, and AWGN curriculum to outperform supervised baselines in cross-frequency beam selection and channel tasks from 3.5 GHz pretraining to 28 GHz evaluation.
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The Economics of AI Inference: Inflation Dynamics, Welfare Costs, and Optimal Monetary Policy under the Inference-Cost Phillips Curve
Develops the Inference-Cost Phillips Curve linking AI inference costs to inflation dynamics, derives structural slopes and optimal monetary policy, and reports empirical estimates from US and G7 data that align with theoretical predictions.
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JanusPipe: Efficient Pipeline Parallel Training for Machine Learning Interatomic Potentials
JanusPipe introduces SymFold and WaveK to enable efficient 3D-parallel training for conservative MLIPs, reporting 1.51x and 1.45x average throughput gains over 1F1B and Hanayo baselines on 32 GPUs.
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Ringmaster LMO: Asynchronous Linear Minimization Oracle Momentum Method
Ringmaster LMO extends delay-thresholding from ASGD to LMO-based momentum updates, providing convergence guarantees under (L0, L1)-smoothness and time-complexity bounds that recover optimal rates in the Euclidean case.
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A Data-Efficient Path to Multilingual LLMs: Language Expansion via Post-training PARAM$\Delta$ Integration into Upcycled MoE
PARAMΔ upcycles dense models to MoE for per-language experts and grafts post-training deltas to enable data-efficient language expansion while preserving original capabilities.
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PEIRA: Learning Predictive Encoders through Inter-View Regressor Alignment
PEIRA learns predictive encoders by optimizing the trace of the optimal inter-view linear regressor, with only nontrivial global minimizers as stable equilibria that recover leading nonlinear canonical correlation subspaces.
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Scale-Dependent Collective Adaptation in Self-Amending LLM Societies: A Cross-Family Study of Emergent Governance
LLM societies in Nomic show non-monotonic collective adaptation peaking at mid-scales, with smaller models rule-inert and larger ones restrictive.
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Olivia: Harmonizing Time Series Foundation Models with Power Spectral Density
Olivia harmonizes time series datasets via normalized power spectral density using a Harmonizer module and resonator-based HarmonicAttention, achieving state-of-the-art zero-shot, few-shot, and full-shot forecasting on TSLib, GIFT-Eval, and GluonTS benchmarks.
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Characterizing Learning in Deep Neural Networks using Tractable Algorithmic Complexity Analysis
QuBD extends algorithmic complexity estimation to quantized DNN weights, revealing that complexity decreases during learning, increases with overfitting, follows grokking patterns, and correlates with generalization.
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How to Scale Mixture-of-Experts: From muP to the Maximally Scale-Stable Parameterization
The authors derive a Maximally Scale-Stable Parameterization (MSSP) for MoE models that achieves robust learning-rate transfer and monotonic performance gains with scale across co-scaling regimes of width, experts, and sparsity.
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Do Language Models Align with Brains? Prediction Scores Are Not Enough
Language model representations fail all L-PACT alignment gates once controls explain the apparent predictive and relational effects.
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Uniform Scaling Limits in AdamW-Trained Transformers
AdamW-trained transformer hidden states and backpropagated variables converge uniformly in L2 to a forward-backward ODE system (McKean-Vlasov when non-causal) at rate O(L^{-1}+L^{-1/3}H^{-1/2}) as depth L and heads H increase, with bounds independent of token number.
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Learning Less Is More: Premature Upper-Layer Attention Specialization Hurts Language Model Pretraining
Temporarily reducing the learning rate on upper-layer query and key projections during early GPT pretraining prevents premature attention specialization and improves model performance.