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bab0e1f | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 | # 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](allocating-exploration.md) — 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.
[Open in the reader](../index.html#node=adaptive-computational-resolution) · [All problems](../CATALOG.md)
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