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Theory To Toy Cases

Turn abstract math or ML ideas into minimal examples, counterexamples, sanity checks, and tiny simulations. Use for theorem intuition, debugging derivations, constructing stress tests, converting a research idea into small checkable cases, or when a concept is too abstract or a claim needs intuition or falsification.

jurgendn Updated
Research & Search

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Theory to Toy Cases

Make the idea concrete before scaling it up.

Workflow

  1. Restate the abstract claim in the smallest possible setting.
  2. Build 2-5 minimal cases:
    • a friendly case where the idea should work
    • a boundary case
    • a failure case
    • a misleading case that appears to work for the wrong reason
  3. If useful, write a tiny simulation or symbolic example.
  4. Compare predicted behavior vs actual behavior.
  5. Extract what the toy case teaches about the full problem.

Good toy cases

Prefer cases that are:

  • low-dimensional
  • analytically tractable
  • numerically checkable
  • likely to expose hidden assumptions

Rules

  • Do not use toy cases as proof.
  • Say what scales and what does not.
  • If a toy case fails, treat that as signal, not annoyance.

Output shape

Return:

  • Abstract idea
  • Minimal setup
  • Cases
  • What each case shows
  • Implication for the full research question
  • What the toy cases cannot establish

jurgendn/agent-skills/tree/main/skills/research-reasoning/theory-to-toy-cases commit 1a2f0a1ae5

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