Computational Scaling Law

A Computational Scaling Law is a scaling law that describes how computational resource allocation affects model performance across different computing phases and optimization objectives.

• AKA: Compute Scaling Law, Resource Scaling Law, Computational Resource Law.
• Context:
  • It can typically characterize Computational Performance Relationships between computational resource input and computational model output.
  • It can typically predict Computational Efficiency Frontiers for given computational hardware constraints.
  • It can typically guide Computational Resource Allocation across computational training phases and computational inference phases.
  • It can typically identify Computational Bottleneck Patterns in computational system architectures.
  • It can typically optimize Computational Cost-Benefit Ratios for computational deployment decisions.
  • ...
  • It can often reveal Computational Phase Transitions where computational scaling behavior changes fundamentally.
  • It can often demonstrate Computational Diminishing Returns at extreme computational scale levels.
  • It can often support Computational Adaptive Strategys based on computational workload characteristics.
  • It can often enable Computational Multi-Objective Optimization balancing computational performance metrics.
  • ...
  • It can range from being a Training Computational Scaling Law to being an Inference Computational Scaling Law, depending on its computational phase focus.
  • It can range from being a Linear Computational Scaling Law to being a Power-Law Computational Scaling Law, depending on its computational growth pattern.
  • It can range from being a Hardware-Agnostic Computational Scaling Law to being a Hardware-Specific Computational Scaling Law, depending on its computational platform dependency.
  • It can range from being a Deterministic Computational Scaling Law to being a Stochastic Computational Scaling Law, depending on its computational prediction certainty.
  • ...
  • It can integrate with Scaling Law Trade-offs for computational optimization decisions.
  • It can combine with Inference-Time Optimization Methods for computational efficiency improvement.
  • It can inform Computational Architecture Design through computational scaling analysis.
  • It can validate Computational Theoretical Models using computational empirical measurements.
  • ...
• Examples:
  • Computational Scaling Law Categorys, such as:
    • Test-Time Scaling Law for computational inference optimization.
    • Training-Time Scaling Law for computational learning efficiency.
    • Memory Scaling Law for computational storage requirement.
    • Bandwidth Scaling Law for computational communication cost.
  • Computational Scaling Law Implementations, such as:
    • FLOPs Scaling Law measuring computational floating-point operations.
    • Token-per-Second Scaling Law for computational throughput measurement.
    • Latency Scaling Law for computational response time.
    • Energy Scaling Law for computational power consumption.
  • ...
• Counter-Examples:
  • Data Scaling Law, which focuses on dataset size rather than compute resources.
  • Parameter Scaling Law, which addresses model size rather than computational allocation.
  • Network Scaling Law, which relates to connectivity rather than computation.
• See: Scaling Law, Test-Time Scaling Law, Computational Complexity, Inference-Time Optimization Method, Scaling Law Trade-off, Moore's Law, Amdahl's Law, Deep Learning Scaling Laws Relationship.

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