zavelinski least-to-most
Hard problems fail when attempted in one leap. Decompose into ordered subproblems (easiest/foundational first), solve each using the answers from the earlier ones, then assemble. Explicit decomposition, sequential solving.
Why this exists (evidence)
- Least-to-most prompting (Zhou et al., arXiv:2205.10625): decompose-then-solve-in-sequence generalizes to harder problems than chain-of-thought, with large gains on compositional generalization (e.g. SCAN) and multi-step reasoning, precisely because later steps build on solved earlier ones.
- It targets the failure where a model can do each step but botches the leap when forced to do them all at once.
When to use
- Multi-step tasks where step N depends on step N-1 (migrations, multi-file refactors, algorithmic problems, data pipelines).
- A task that keeps failing when attempted whole.
- NOT for simple or already-atomic tasks (decomposition is overhead there).
The method
- Decompose: list the subproblems in dependency order, simplest/foundational first. Make the ordering explicit (each item names what it needs from prior items).
- Solve in sequence: solve subproblem 1; carry its concrete answer into subproblem 2; and so on. Do not skip ahead.
- Assemble: combine the sub-answers into the full solution.
- Check the seams: verify the points where one sub-answer feeds the next (that is where composition errors hide).
How to run it
- Inline: write the ordered subproblem list, then solve down the list.
- For code: decompose into the ordered edits/functions; implement+verify each before the next (composes with TDD/testsmith per step).
- Distinct from orchestrate (which is the plan->spec->build->verify dev cycle with a gate); least-to-most is the reasoning-decomposition technique you can use INSIDE any step.
Composes with
orchestrate: least-to-most is how you fill the PLAN step.reflexion: if a subproblem fails, reflect before retrying that one (not the whole chain).self-consistency: sample the decomposition itself when the right breakdown is unclear.
Honest limits
- A wrong decomposition propagates: if the ordering/breakdown is off, every step inherits it. Sanity-check the decomposition before solving.
- Overhead on simple tasks; scope to genuinely compositional problems.
- Gains are on the paper's benchmarks; measure your own.