Language Model Scaling Law

A Language Model Scaling Law is an deep learning scaling law that describes how language model performance relates to language model size, language model training data, or language model computational resources.

• AKA: Neural Language Scaling Law, Language Model Power Law, LLM Performance Law, Language Model Growth Pattern.
• Context:
  • It can (typically) reveal LLM Trade-offs between model size, training data, and compute resources through scaling laws.
  • It can (typically) demonstrate LLM Sample Efficiency improvements through scaling laws, showing larger models need less training data.
  • It can (typically) optimize LLM Batch Size based on gradient noise and scaling relationships.
  • It can (often) show that LLM Architecture factors like model depth have minimal impact compared to scaling parameters.
  • ...
  • It can range from being a Empirical Language Model Scaling Law to being a Theoretical Language Model Scaling Law.
  • It can range from being a Simple Language Model Scaling Law focusing on a single variable (e.g., parameter count) to being a Complex Language Model Scaling Law incorporating multiple factors (e.g., parameters, data, compute).
  • It can range from being a Task Specific Scaling Law to being a General Purpose Scaling Law, depending on its application scope.
  • It can range from being a Short Term Prediction Law to being a Long Term Extrapolation Law, depending on its prediction horizon.
  • It can range from being a Model Architecture Dependent Law to being a Architecture Invariant Law, depending on its generalizability.
  • It can range from being an Inference Time Scaling Law to being an Inference Quality Scaling Law, depending on its inference aspect.
  • ...
  • It can optimize Training Strategy for LLM scaling laws by combining large models with modest datasets and early stopping.
  • It can guide Resource Allocation for LLM development and scaling research.
  • It can improve LLM Generalization through training data increases following scaling law patterns.
  • It can predict LLM Performance Ceiling based on resource requirements and scaling patterns.
  • It can forecast Future LLM Capability through scaling law extrapolation.
  • It can demonstrate LLM Compute Efficiency advantages with optimal budgets through scaling laws.
  • It can reveal LLM Performance Gain diminishing returns at extreme scales.
  • It can model LLM Resource Scaling effects on training time and computational cost.
  • It can inform LLM Design decisions through scaling law analysis.
  • It can identify LLM Emergent Property patterns like in-context learning abilities.
  • It can compare LLM Architecture Efficiency across different transformer variants.
  • It can support LLM Task Performance analysis across text generation, machine translation, and question answering.
  • It can exhibit LLM Scaling Behavior changes at extreme scales requiring new theoretical models.
  • It can guide LLM Safety Assessment through scaling law prediction.
  • ...
• Example(s):
  • GPT-3 Scaling Law: relating model size to language model performance in the GPT-3 family of models, where:
    • Model Performance (measured by test loss or perplexity) improves as a power law of the number of model parameters.
    • The relationship follows the form: Loss ∝ (Number of Parameters)^(-0.076), showing consistent improvement across several orders of magnitude of model size.
    • This scaling law predicted the performance of the full GPT-3 model (175 billion parameters) based on smaller variants.
  • Chinchilla Scaling Law: relating model size and training tokens to language model performance, where:
    • Optimal Model Size for a given compute budget is determined by balancing model size and training dataset size.
    • The law suggests that many language models are overparameterized and undertrained relative to the optimal allocation of compute.
    • It proposes that for each doubling of compute, model size and training tokens should both increase by approximately 20%.
  • PaLM Scaling Law: demonstrating few-shot learning improvements in the Pathways Language Model (PaLM), where:
    • Few-shot performance on various tasks improves smoothly with model scale, following a power law.
    • The scaling behavior holds across a wide range of model sizes, from 8 billion to 540 billion parameters.
    • Some tasks show a discontinuous jump in performance at certain model sizes, suggesting emergent abilities.
  • Multilingual Scaling Law: describing how language model performance scales across multiple languages, where:
    • Cross-lingual transfer improves with model size, allowing larger models to perform better on low-resource languages.
    • The scaling behavior varies across languages, with some benefiting more from increased model size than others.
    • Language-specific performance gaps tend to narrow as models become larger, but some disparities persist.
  • Kaplan et al. Scaling Laws: encompassing multiple aspects of language model scaling, where:
    • Performance scales smoothly as a power-law with model size, dataset size, and amount of compute used for training.
    • The power-law exponent for performance improvement with compute is around 0.050–0.057 for large models.
    • Optimal allocation of a fixed compute budget suggests training very large models and stopping significantly short of convergence.
    • The relationship between model size and optimal compute budget follows: Optimal compute ∝ (Number of Parameters)^(0.73–0.9).
  • LLM Inference-Time Scaling Laws, such as:
    • LLM Inference Time Laws, such as:
      • Token Generation Scaling Law showing how generation speed scales with model size.
      • Batch Processing Law relating batch size to inference throughput.
    • LLM Inference Quality Laws, such as:
      • Temperature Scaling Law relating sampling temperature to output quality.
      • Chain of Thought Law showing how reasoning step count affects task performance.
    • LLM Inference Resource Laws, such as:
      • Memory Usage Law relating model size to inference memory requirements.
      • Compute Utilization Law showing hardware efficiency patterns during inference.
  • ...
• Counter-Examples:
  • Task-Specific Performance Laws, which lack cross-task generalization.
  • Fixed Architecture Scaling Laws, which lack architecture flexibility.
  • Data-Limited Scaling Laws, which lack sufficient training data.
  • Non-Autoregressive Model Laws, which follow different scaling patterns.
  • Efficiency-Focused Scaling Laws, which prioritize model compression over raw size.
    • Arithmetic Reasoning tasks, where performance may plateau despite increasing model size.
    • Common Sense Reasoning tasks, which may require different scaling approaches or architectural changes.
  • Data-Limited Scenarios: situations where the available training data becomes a limiting factor, including:
    • Low-Resource Languages, where the scarcity of high-quality training data may limit the benefits of model scaling.
    • Specialized Domains with limited available text corpora, where increasing model size may lead to overfitting.
  • Efficiency-Focused Approaches: methods that achieve comparable performance with smaller models, such as:
    • Distillation Techniques, where smaller models are trained to mimic larger ones, potentially breaking the usual scaling laws.
    • Sparse Models, which may exhibit different scaling behaviors compared to dense models of similar parameter counts.
  • Non-Autoregressive Models: language models with different architectures that may not follow the same scaling laws, like:
    • BERT-style Bidirectional Encoder models, which may have different scaling properties compared to autoregressive models like GPT.
    • T5-style Encoder-Decoder models, which might exhibit unique scaling behaviors due to their architecture.
• See: AI System Scaling Law, Model Size Scaling, Training Data Scaling, Computational Scaling in NLP, Language Model Evaluation Metrics, Emergent Abilities in Language Models, Resource-Performance Trade-offs in NLP, Cross-Lingual Transfer Learning

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References

2024-01-04

• Perplexity.ai
  • Question: Please formally define language model scaling laws in detail.
  • Answer: Scaling laws for language models describe the mathematical relationships between model performance and three key factors: model size, dataset size, and computational resources used during training.
    • Core Scaling Relationships:
      • Model Size Scaling:
        • The model's performance (measured by cross-entropy loss) follows a power-law relationship with the number of parameters.
        • As models grow larger, they become significantly more sample-efficient, meaning they can learn more effectively from a given amount of training data.
      • Dataset Size Scaling:
        • Performance improves as a power-law function of the training dataset size.
        • There are diminishing returns after certain thresholds due to factors like data quality and availability.
      • Compute Scaling:
        • The amount of computation (measured in FLOPs) used for training follows a power-law relationship with model performance.
        • This relationship spans multiple orders of magnitude.
    • Mathematical Formulation:
      • The general form of the scaling law can be expressed as:
        • $$ L(N,D) = \left(\frac{N_c}{N}\right)^{\alpha_N} + \left(\frac{D_c}{D}\right)^{\alpha_D} + L_{\min} $$
        • Where:
          • $$L$$ is the loss
          • $$N$$ is the number of parameters
          • $$D$$ is the dataset size
          • $$\alpha_N$$ and $$\alpha_D$$ are power-law exponents
          • $$N_c$$ and $$D_c$$ are critical values
          • $$L_{\min}$$ is the irreducible loss
    • Key Implications:
      • Optimal Resource Allocation:
        • The most compute-efficient training strategy involves using very large models with relatively modest amounts of data and stopping training before full convergence.
      • Architectural Independence:
        • Network architecture details like width or depth have minimal impact on scaling behavior within a wide range.
      • Sample Efficiency:
        • Larger models demonstrate superior sample efficiency, requiring proportionally less data to achieve the same level of performance.
  • Citations:

[1] https://klu.ai/glossary/scaling-laws
[2] https://arxiv.org/abs/2410.12883
[3] https://huggingface.co/papers/2402.04177
[4] https://www.larksuite.com/en_us/topics/ai-glossary/scaling-laws-for-large-language-models
[5] https://arxiv.org/abs/2001.08361?context=cs.LG
[6] https://proceedings.neurips.cc/paper_files/paper/2022/hash/8c22e5e918198702765ecff4b20d0a90-Abstract-Conference.html
[7] https://openreview.net/forum?id=FxNNiUgtfa
[8] https://www.semanticscholar.org/paper/Scaling-Laws-for-Neural-Language-Models-Kaplan-McCandlish/e6c561d02500b2596a230b341a8eb8b921ca5bf2
[9] https://towardsdatascience.com/scaling-law-of-language-models-5759de7f830c

2024

• Ethan Mollick. (2024). "Scaling: The State of Play in AI A brief intergenerational pause...".
  • NOTES:
    • Scaling Laws in AI: Increasing the size of language models leads to enhanced capabilities, a principle known as the scaling laws in AI.
    • Exponential Resource Increases: The benefits of scaling are exponential; each new generation of models demands an order-of-magnitude increase in data, compute power, and financial investments.
    • Inference compute scaling: Beyond training, scaling laws also apply to inference compute—the computational effort the model uses during its "thinking" process after training.
    • Chain-of-Thought Reasoning: Encouraging models to perform internal reasoning steps (chain-of-thought) enhances accuracy and problem-solving abilities.
    • Dual Scaling Laws Implications: The combination of training scaling and inference compute scaling suggests that AI capabilities will continue to advance dramatically in the coming years.

2024

• (Schaeffer et al., 2024) ⇒ Rylan Schaeffer, Brando Miranda, and Sanmi Koyejo. (2024). “Are Emergent Abilities of Large Language Models a Mirage?.” In: Advances in Neural Information Processing Systems, 36.
  • NOTES:
    • Emergent Abilities in Large Language Models: The paper serves as a key reference for understanding and questioning the notion of emergent abilities that purportedly arise in large language models as they scale in parameter count.
    • Scaling Laws Revisited: This work situates its findings within the broader context of neural scaling laws, reinforcing the idea that smooth performance trends can appear abrupt if measured incorrectly.

2021

• (Jones, 2021) ⇒ Andy L. Jones. (2021). “Scaling Scaling Laws with Board Games.” doi:10.48550/arXiv.2104.03113
  • NOTES: Introduction to Scaling Laws in Reinforcement Learning: Offers a lucid explanation of how scaling laws (originally prominent in NLP and vision) can apply to RL settings. This approach demonstrates the potential for scaling laws to unify multiple aspects of training, including the size of the model, the data, and even the complexity of the environment. The authors highlight how smaller-scale experiments can reliably inform predictions about more expensive or larger-scale tasks.

2023

• (Wei et al., 2023) ⇒ Jason Wei, Yi Tay, Rishi Bommasani, Colin Raffel, Barret Zoph, Sebastian Borgeaud, Dani Yogatama, Maarten Bosma, Denny Zhou, Donald Metzler, Ed H. Chi, Tatsunori Hashimoto, Oriol Vinyals, Percy Liang, Jeff Dean, William Fedus. (2023). "Emergent Abilities of Large Language Models." In: Transactions on Machine Learning Research. arXiv:2206.07682
  • NOTE: This paper discusses how language model scaling laws relate to emergent abilities, providing insights into unexpected behaviors that arise as models become larger.

2022

• (Hoffmann et al., 2022) ⇒ Jordan Hoffmann, Sebastian Borgeaud, Arthur Mensch, Elena Buchatskaya, Trevor Cai, Eliza Rutherford, Diego de Las Casas, Lisa Anne Hendricks, Johannes Welbl, Aidan Clark, Tom Hennigan, Eric Sigler, Mia Xu Chen, Sharan Narang, Saffron Huang, Colin Hubert, Steven Kapturowski, John Aslanides, George van den Driessche, Dani Yogatama, Jared Kaplan, Aaron Goyal, Geoffrey Irving, Oriol Vinyals, Simon Osindero, Karen Simonyan, Jack W. Rae, Demis Hassabis, Laurent Sifre. (2022). "Training Compute-Optimal Large Language Models." In: arXiv preprint arXiv:2203.15556. arXiv:2203.15556
  • NOTE: This paper introduces the Chinchilla scaling law, which provides insights into the optimal balance between model size and training data for language models.

2020

• (Kaplan et al., 2020) ⇒ Jared Kaplan, Sam McCandlish, Tom Henighan, Tom B. Brown, Benjamin Chess, Rewon Child, Scott Gray, Alec Radford, Jeffrey Wu, Dario Amodei. (2020). "Scaling Laws for Neural Language Models." In: arXiv preprint arXiv:2001.08361. arXiv:2001.08361
  • NOTES:
    • The paper identifies power-law relationships between model size, dataset size, and compute, showing that performance improves predictably with scale across these factors.
    • The paper demonstrates that model architecture, such as depth or width, has a minimal effect on performance compared to scaling parameters like model size, data, and compute.
    • The paper reveals that larger models are more sample-efficient, achieving similar or better performance with fewer data and training steps than smaller models.
    • The paper suggests that optimal training efficiency is achieved by training large models on modest datasets and halting training well before full convergence.
    • The paper finds that overfitting can be predicted and mitigated by maintaining a balance between model size and dataset size, using a simple ratio to avoid diminishing returns.
    • The paper emphasizes that training curves follow predictable patterns, enabling researchers to forecast final performance based on early training data.
    • The paper highlights that larger models, when trained with the appropriate compute budget, can be significantly more compute-efficient than smaller models trained to convergence.
    • The paper shows that performance scales smoothly across multiple orders of magnitude, with no significant deviation in trends, even as model size increases dramatically.
    • The paper advocates for the use of larger batch sizes for training large models, with the ideal batch size scaling with the gradient noise of the model.
    • The paper concludes that scaling model size is more impactful than increasing data size or training time, recommending a focus on larger models for future improvements.

2018

• (Hestness et al., 2018) ⇒ Joel Hestness, Sharan Narang, Newsha Ardalani, Gregory Diamos, Heewoo Jun, Hassan Kianinejad, Md Mostofa Ali Patwary, Yang Yang, Yanqi Zhou. (2018). "Deep Learning Scaling is Predictable, Empirically." In: arXiv preprint arXiv:1712.00409. arXiv:1712.00409
  • NOTE: While not specifically focused on language models, this paper provides early evidence of power-law scaling in deep learning, which laid the groundwork for later language model scaling laws.

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