Adaptive Control Processes¶
Bellman, R. E. (1961). Adaptive Control Processes: A Guided Tour. Princeton University Press.
Cited by¶
2 citations across 2 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'; supports marker 069 (high-dimensional spaces become empty, sample needs grow, visualization impossible).
- 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.
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Links previously used in the corpus¶
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