Dynamic Programming
Abstract
Little has been done in the study of these intriguing questions, and I do not wish to give the impression that any extensive set of ideas exists that could be called a "theory." What is quite surprising, as far as the histories of science and philosophy are concerned, is that the major impetus for the fantastic growth of interest in brain processes, both psychological and physiological, has come from a device, a machine, the digital computer. In dealing with a human being and a human society, we enjoy the luxury of being irrational, illogical, inconsistent, and incomplete, and yet of coping. In operating a computer, we must meet the rigorous requirements for detailed instructions and absolute precision. If we understood the ability of the human mind to make effective decisions when confronted by complexity, uncertainty, and irrationality then we could use computers a million times more effectively than we do. Recognition of this fact has been a motivation for the spurt of research in the field of neurophysiology. The more we study the information processing aspects of the mind, the more perplexed and impressed we become. It will be a very long time before we understand these processes sufficiently to reproduce them. In any case, the mathematician sees hundreds and thousands of formidable new problems in dozens of blossoming areas, puzzles galore, and challenges to his heart's content. He may never resolve some of these, but he will never be bored. What more can he ask?
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Deep learning models can handle the curse of dimensionality by leveraging different degrees of smoothness in compositional function and parallel computations of GPUs.
“The multivariate evaluation shows another benefit of deep learning models, which is the ability to handle the curse of dimensionality (Bellman, 2010; Keogh and Mueen, 2017) by leveraging different degrees of smoothness in compositional function (Poggio et al., 2017) as well as the parallel computations of the GPUs (Lu et al., 2015).”
From Deep learning for time series classification: a review (2019) · cites this paper as Bellman, 2010
Storing intermediate values in memory allows the N-th Fibonacci number to be computed in time linear to N, achieving an exponential speedup over direct recursive computation.
“if we store intermediate values of u1D439 ( u1D45B ) in memory and retrieve them whenever necessary, u1D439 ( u1D441 ) can be computed in time linear to u1D441 , achieving an exponential speedup.”
From Quantum Dynamic Programming (2025) · cites this paper as [3]
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- Authors
- Bellman, R. E.
- Affiliations
- University of Southern California (US)
- Corresponding author
- Bellman, Richard E.
- Venue
- Science
- Publisher
- Princeton University Press
- Published
- 2010-12-31
- Volume
- 153
- Issue
- 3731
- Pages
- 34-37
- ISSN
- 0036-8075 (ISSN-L)
- OpenAlex
- W2341171179
- Cited by
- 14,588
- References
- 0
- Citations by year
- 2026: 227 · 2025: 367 · 2024: 358 · 2023: 345 · 2022: 332 · 2021: 629 · 2020: 582 · 2019: 575 · 2018: 469 · 2017: 429 · 2016: 440 · 2015: 570 · 2014: 616 · 2013: 615 · 2012: 634
- FWCI
- 137.95
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Science (publishedVersion)
- Princeton University Press eBooks (publishedVersion)
- PubMed (publishedVersion)
- Virtual Defense Library (Ministerio de Defensa) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- International Linear Collider (submittedVersion)
- Andalas University Repository (Andalas University) (submittedVersion)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Cognitive Computing and Networks
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Complexity and Algorithms in Graphs
- Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
- Keywords
- dynamic programming, optimization, decision-making, human cognition, information processing, brain processes, neurophysiology
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