Precision Scaling Law

A Precision Scaling Law is a quantization scaling law that characterizes the relationship between numerical precision and model performance across training phases and inference phases.

• AKA: Bit-Precision Scaling Law, Quantization Scaling Law, Numerical Precision Scaling Law.
• Context:
  • It can typically predict Compute-Optimal Precision for precision scaling model training based on precision scaling compute budget.
  • It can typically determine Precision Scaling Trade-offs between precision scaling model accuracy and precision scaling computational efficiency.
  • It can typically characterize Precision Scaling Performance Degradation when reducing from precision scaling full precision to precision scaling low precision.
  • It can typically enable Precision Scaling Hardware Optimization through precision scaling bit width selection.
  • It can typically guide Precision Scaling Model Compression strategies for precision scaling deployment scenarios.
  • ...
  • It can often reveal Precision Scaling Sensitivity Patterns across different precision scaling model layers.
  • It can often identify Precision Scaling Critical Thresholds below which precision scaling performance collapses occur.
  • It can often support Precision Scaling Mixed Strategys combining different precision scaling bit widths.
  • It can often facilitate Precision Scaling Energy Savings through reduced precision scaling memory bandwidth.
  • ...
  • It can range from being a Simple Precision Scaling Law to being a Complex Precision Scaling Law, depending on its precision scaling quantization strategy.
  • It can range from being a Uniform Precision Scaling Law to being a Non-Uniform Precision Scaling Law, depending on its precision scaling bit allocation.
  • It can range from being a Post-Training Precision Scaling Law to being a Quantization-Aware Precision Scaling Law, depending on its precision scaling application timing.
  • It can range from being a Weight-Only Precision Scaling Law to being a Full-Model Precision Scaling Law, depending on its precision scaling component scope.
  • ...
  • It can integrate with Test-Time Scaling Laws for combined precision scaling inference optimization.
  • It can complement Mixed Quantization Scaling Laws in precision scaling heterogeneous systems.
  • It can inform Precision Scaling Hardware Design for precision scaling accelerators.
  • It can validate Precision Scaling Theoretical Models against precision scaling empirical results.
  • ...
• Examples:
  • Precision Scaling Law Implementations, such as:
    • Kumar et al. 2024 Precision Scaling Law demonstrating 7-8 bit precision scaling compute optimality.
    • Mixed Precision Scaling Law combining different precision scaling bit widths across precision scaling layers.
    • INT8 Precision Scaling Law showing near-lossless precision scaling 8-bit quantization.
    • Binary Precision Scaling Law for extreme precision scaling 1-bit compression.
  • Precision Scaling Law Applications, such as:
    • Precision Scaling Post-Training Quantization reducing precision scaling model size.
    • Precision Scaling Training Optimization using precision scaling gradient computation.
    • Precision Scaling Edge Deployment for precision scaling mobile devices.
    • Precision Scaling Inference Acceleration on precision scaling specialized hardware.
  • ...
• Counter-Examples:
  • Pre-Training Scaling Law, which focuses on model size and training data rather than numerical precision.
  • Test-Time Scaling Law, which scales inference compute rather than numerical precision.
  • Data Scaling Law, which relates dataset size to model performance rather than precision level.
• See: Scaling Law, Quantization Scaling Law, Neural Network Quantization, Model Compression Law, Mixed Precision Training, Computational Scaling Law, Scaling Law Trade-off, Post-Training Quantization, Quantization-Aware Training, Deep Learning Scaling Laws Relationship, LLM Scaling Law.

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