The Scaling Law

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How to prompt a model to trigger System 2 scaling:

Triggering “System 2” scaling (test-time compute) depends on whether you are using a model with native reasoning (like OpenAI o1/o3 or Gemini 2.0 Thinking) or a standard model (like GPT-4o or Claude 3.5).

Here is how to mathematically and practically force a model to spend more compute on your answer.


1. For Native Reasoning Models (o1, o3, Gemini Thinking)

These models have a “hidden” scratchpad. They are trained to scale their own inference compute based on the difficulty of the prompt.

  • Avoid “Think Step by Step”: Ironically, adding “let’s think step by step” to these models can actually degrade performance because it interferes with their pre-trained internal reasoning traces.
  • The “Nudge” Technique: To make the model spend more time, frame the problem as adversarial or multi-perspective.
    • Example: “Solve this, then look for 3 reasons why your first solution might be wrong, and then provide a final verified version.”
  • Effort Levels: Many APIs in 2026 now include a reasoning_effort parameter (Low, Medium, High). Setting this to High explicitly forces the model to expand more nodes in its search tree.

2. For Standard Models (Manual System 2)

If the model doesn’t “think” natively, you must force it to use sequential compute through your prompt structure.

The “XML Thinking” Block

Encourage the model to separate its internal logic from its final answer. This uses more tokens and thus more compute.

“Before providing the final answer, use a <thinking> tag to:

  1. Break the problem into 5 sub-steps.
  2. Identify potential pitfalls in each step.
  3. Perform a ‘sanity check’ calculation.”

The “Recursive Refinement” Prompt

This mimics the Inference Scaling Law by turning a single turn into a multi-step process.

“Analyze the following problem. First, generate a draft solution. Second, critique your own draft for logical fallacies. Third, rewrite the solution to be 100% accurate based on that critique.”


3. Advanced Strategy: “Tree of Thoughts” (ToT)

To truly scale inference, you can prompt the model to act as a Search Algorithm. This is the most effective way to trigger System 2 thinking for complex tasks like coding or high-level math.

The Prompt Template:

“Imagine three different brilliant experts are solving this problem.

Step 1: Each expert writes down their initial thought process.

Step 2: They review each other’s work and point out one specific flaw.

Step 3: They collaborate to produce a single, corrected final consensus.”


Summary of Techniques

TechniqueHow it Scales ComputeBest For
Direct NudgingIncreases internal search depth.Math, Logic, Physics.
XML ThinkingIncreases token count (Sequential).Summarization, Coding.
Self-CritiqueForces “Backtracking” (Inference Scaling).Legal, Policy, Ethics.
Tree of ThoughtsExplores parallel reasoning paths.Creative Problem Solving.

A Note on “The Data Wall”

As of 2026, the best way to get a “smarter” answer is no longer to write a better prompt, but to allocate more time. If you are using an API, increasing your max_tokens and allowing the model a “thought budget” is the most direct way to trigger these scaling laws.

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