Test-Time Scaling Law

A Test-Time Scaling Law is a computational scaling law that governs performance improvements through increased inference-time compute allocation during model reasoning tasks.

• AKA: Inference-Time Scaling Law, Test-Time Compute Scaling Law, Reasoning-Time Scaling Law, Long-Thinking Scaling Law.
• Context:
  • It can typically enable Test-Time Performance Improvement through test-time compute scaling without test-time model retraining.
  • It can typically leverage Test-Time Search Algorithms to explore multiple test-time reasoning paths.
  • It can typically generate Test-Time Solution Candidates through test-time Monte Carlo sampling.
  • It can typically implement Test-Time Reasoning Chains using test-time chain-of-thought methods.
  • It can typically optimize Test-Time Resource Allocation between test-time solution generation and test-time solution verification.
  • ...
  • It can often demonstrate Test-Time Scaling Efficiency superior to test-time pre-training scaling for test-time reasoning tasks.
  • It can often exhibit Test-Time Emergent Capabilitys at certain test-time compute thresholds.
  • It can often achieve Test-Time Performance Saturation at extreme test-time compute levels.
  • It can often require Test-Time Verification Mechanisms for test-time solution selection.
  • ...
  • It can range from being a Simple Test-Time Scaling Law to being a Complex Test-Time Scaling Law, depending on its test-time search complexity.
  • It can range from being a Linear Test-Time Scaling Law to being a Logarithmic Test-Time Scaling Law, depending on its test-time performance curve.
  • It can range from being a Single-Path Test-Time Scaling Law to being a Multi-Path Test-Time Scaling Law, depending on its test-time exploration strategy.
  • It can range from being a Greedy Test-Time Scaling Law to being a Exhaustive Test-Time Scaling Law, depending on its test-time search depth.
  • ...
  • It can integrate with Chain-of-Thought Prompting for test-time reasoning enhancement.
  • It can combine with Monte Carlo Tree Search (MCTS) Algorithm for test-time solution exploration.
  • It can support Test-Time Compute Techniques like test-time best-of-N sampling.
  • It can enable Test-Time Adaptive Computation based on test-time problem complexity.
  • ...
• Examples:
  • Test-Time Scaling Law Models, such as:
    • OpenAI o1 Test-Time Scaling using extended test-time reasoning chains.
    • OpenAI o3 Test-Time Scaling with adaptive test-time compute allocation.
    • DeepSeek R1 Test-Time Scaling implementing test-time reinforcement learning.
    • Best-of-N Test-Time Scaling generating multiple test-time candidate solutions.
  • Test-Time Scaling Law Methods, such as:
    • Test-Time Monte Carlo Tree Search for test-time solution exploration.
    • Test-Time Chain-of-Thought Scaling extending test-time reasoning length.
    • Test-Time Self-Consistency Scaling using test-time voting mechanisms.
    • Test-Time Tree-of-Thoughts Scaling with test-time parallel exploration.
  • ...
• Counter-Examples:
  • Pre-Training Scaling Law, which scales training compute rather than inference compute.
  • Data Scaling Law, which increases training data rather than test-time compute.
  • Parameter Scaling Law, which grows model size rather than inference computation.
• See: Scaling Law, Computational Scaling Law, Inference-Time Optimization Method, LLM Inference-Time Scaling Law, Test-Time Compute Technique, Chain-of-Thought Prompting, Monte Carlo Tree Search (MCTS) Algorithm, Reasoning Task, Reasoning LLM-based AI Model, Language Model Scaling Law, Scaling Law Trade-off.

---