Spending computation where approximation fails
Can a cheap local approximation identify where expensive computation is actually needed?
Use regularity-sensitive approximation to allocate fine computation to difficult regions of a fractal visualization.
Status: open problem. Formulation and comparisons: reconstruction. Development: historical branch.
Alternative representations
Uniform high-resolution computation
Affords: Provides a consistent baseline.
Limits or losses: Spends work in regions where a simpler estimate may suffice.
Local approximation with refinement
Affords: Allocates work using an estimated error.
Limits or losses: An incorrect error estimator may miss precisely the difficult regions.
Tension
A cheap indicator must detect its own failure well enough to justify skipping expensive work.
Challenge
How are missed difficult regions counted alongside runtime savings?
This challenge is an editorial prompt, not a claim that the evidence already resolved it.
Proposed next move
Benchmark against a high-resolution reference and report both false refinement decisions and final error.
Status: new model-proposed experiment or extension; not a reported result.
Related problems
- When to deepen, branch, pause, or return — offers an error-guided allocation analogue (retrospective_connection). Local numerical error and research importance both guide where to spend effort, but they are different criteria.
Evidence anchors
- basis-adaptive-computational-resolution: A proposed experiment uses Taylor approximation in regular regions of a fractal visualization and more detailed computation in regions identified as difficult. The material asks what optimization this might provide and includes reported execution errors while attempting it. [Editorial paraphrase; presence of a proposal does not verify its truth.]
Root evidence and private recovery mappings are not part of this public release.