How To Choose A Subproblem

Decompose monster problems into a fractal sequence of smaller tasks to maintain momentum and clarity.

Key Points

Junior researchers often struggle with ‘400-hour problems’ because they lack the strategy to decompose them into a sequence of smaller, manageable subproblems (e.g., 20-hour or 1-hour tasks).
Three primary methods for generating subproblems: 1) Ask a simpler question (start small), 2) Ask about a simpler system (toy problems/limits), and 3) Fact-finding/processing.
The most effective form of fact-processing is visualization: ‘PUT IT IN A PICTURE’ to leverage the brain’s visual processing machinery over abstract calculus.
A good subproblem provides one of three payoffs: actionable information (changes the overall strategy), human capital (builds long-term skills), or strategic information (identifies failure points).
Red flags for bad subproblems include vagueness (prevents progress tracking), excessive difficulty (lack of a clear plan of attack), or being too easy (provides negligible insight).
Avoid ‘failuremaxxing’ (prioritizing failure probability per unit time) if the project has a non-linear payoff structure where intermediate infrastructure and skills remain valuable even if the primary approach fails.
Maintaining objectivity regarding a problem’s value and one’s own success probability requires external perspectives from advisors or peers to avoid wasting years on dead ends.

Subproblems should be viewed as a fractal structure, where daily tasks are sub-sub-problems of massive goals like AI Alignment.
The best gauge of a problem’s solvability is the completeness and number of available ‘plans of attack’.
High-information activities, such as generating graphs, are often more valuable than binary yes/no questions, even if the immediate action resulting from that information is not pre-defined.