Adaptive Control Processes¶
Bellman, R. E. (1961). Adaptive Control Processes: A Guided Tour. Princeton University Press.
Cited by¶
3 citations across 3 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Dimensionality Reduction
- Dimensionality reduction is a primary tool for combating the "curse of dimensionality" — the phenomenon where high-dimensional spaces become increasingly empty (distances between random points converge), statistical methods become increasingly unstable (sample sizes needed grow exponentially), and visualization becomes impossible
This sourceCoins and conceptualizes the 'curse of dimensionality'
- Dimensionality reduction is a primary tool for combating the "curse of dimensionality" — the phenomenon where high-dimensional spaces become increasingly empty (distances between random points converge), statistical methods become increasingly unstable (sample sizes needed grow exponentially), and visualization becomes impossible
- Spatial Indexing
- The pattern supports a tight family of inferences. Query-time versus build-time tradeoff: a spatial index makes range queries fast at the cost of building and maintaining the index, so insertion, deletion, and movement become more expensive than in an unindexed catalogue, with the same arithmetic in R-trees, in shelf reorganization, and in memory-palace updates. Curse of dimensionality: as the embedding dimension grows, the fraction of space within a fixed radius of any point shrinks rapidly, so neighborhood queries become hard to make output-sensitive — a result that holds identically in high-dimensional vector indexes, high-dimensional cognitive embeddings, and high-dimensional GIS-like substrates.
This sourceCoins and analyzes the 'curse of dimensionality' — as dimension grows, the fraction of space within a fixed radius shrinks, undermining output-sensitive neighborhood queries.
- The pattern supports a tight family of inferences. Query-time versus build-time tradeoff: a spatial index makes range queries fast at the cost of building and maintaining the index, so insertion, deletion, and movement become more expensive than in an unindexed catalogue, with the same arithmetic in R-trees, in shelf reorganization, and in memory-palace updates. Curse of dimensionality: as the embedding dimension grows, the fraction of space within a fixed radius of any point shrinks rapidly, so neighborhood queries become hard to make output-sensitive — a result that holds identically in high-dimensional vector indexes, high-dimensional cognitive embeddings, and high-dimensional GIS-like substrates.
Mechanisms¶
- Dynamic Programming Table
- Its failure mode is the curse of dimensionality — the grid's size is the product of its axes, so a handful of state variables at fine resolution yields more cells than can be stored or filled, and the artifact that made small problems trivial becomes impossible for large ones.
This sourceIdentifies the curse of dimensionality in dynamic programming, where discretized state spaces grow multiplicatively with the number of state variables.
- Its failure mode is the curse of dimensionality — the grid's size is the product of its axes, so a handful of state variables at fine resolution yields more cells than can be stored or filled, and the artifact that made small problems trivial becomes impossible for large ones.
Verification¶
Does it exist? Confirmed. This work's DOI resolves to a registered record, which fixes its identity. That is all it fixes.
Does it back the claim? Not recorded. Neither this nor any other of the 3 citations of this work carries a recorded support check.
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Links previously used in the corpus¶
Before the registry existed this work was also linked 2 other ways.
- https://books.google.com/books?id=POAmAAAAMAAJ ×1
- https://press.princeton.edu/books/hardcover/9780691652214/adaptive-control-processes ×1
Registry ID ref:3d91dcc24b48 · see in the full table