Above are papers related to the following paper: [Paper_ID] Paper #85324. 	[Title] The optimal number of learning samples and hidden units in function approximation with a feedforward network [Abstract] This paper presents a methodology to estimate the optimal number of learning samples and the number of hidden units needed to obtain a desired accuracy of a function approximation by a feedforward network. The representation error and the generalization error, components of the total approximation error are analyzed and the approximation accuracy of a feedforward network is investigated as a function of the number of hidden units and the number of learning samples. Based on the asymptotical behavior of the approximation error, an asymptotical model of the error function (AMEF) is introduced of which the parameters can be determined experimentally. An alternative model of the error function, which include theoretical results about general bounds of approximation, is also analyzed. In combination with knowledge about the computational complexity of the learning rule an optimal learning set size and number of hidden units can be found resulting in a minimum computation time for a given desired precision of the approximation. This approach was applied to optimize the learning of the camera-robot mapping of a visually guided robot arm and a complex logarithm function approximation. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #6213. 	[Title] Machine Learning Learning to Predict by the Methods of Temporal Differences Keywords: Incremental learning, prediction, [Abstract] This article introduces a class of incremental learning procedures specialized for prediction|that is, for using past experience with an incompletely known system to predict its future behavior. Whereas conventional prediction-learning methods assign credit by means of the difference between predicted and actual outcomes, the new methods assign credit by means of the difference between temporally successive predictions. Although such temporal-difference methods have been used in Samuel's checker player, Holland's bucket brigade, and the author's Adaptive Heuristic Critic, they have remained poorly understood. Here we prove their convergence and optimality for special cases and relate them to supervised-learning methods. For most real-world prediction problems, temporal-difference methods require less memory and less peak computation than conventional methods; and they produce more accurate predictions. We argue that most problems to which supervised learning is currently applied are really prediction problems of the sort to which temporal-difference methods can be applied to advantage. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #950986. 	[Title] The locally linear Nested Network for robot manipulation [Abstract] We present a method for accurate representation of high-dimensional unknown functions from random samples drawn from its input space. The method builds representations of the function by recursively splitting the input space in smaller subspaces, while in each of these subspaces a linear approximation is computed. The representations of the function at all levels (i.e., depths in the tree) are retained during the learning process, such that a good generalisation is available as well as more accurate representations in some subareas. Therefore, fast and accurate learning are combined in this method. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #4330. 	[Title] Hierarchical Mixtures of Experts and the EM Algorithm [Abstract] We present a tree-structured architecture for supervised learning. The statistical model underlying the architecture is a hierarchical mixture model in which both the mixture coefficients and the mixture components are generalized linear models (GLIM's). Learning is treated as a maximum likelihood problem; in particular, we present an Expectation-Maximization (EM) algorithm for adjusting the parameters of the architecture. We also develop an on-line learning algorithm in which the parameters are updated incrementally. Comparative simulation results are presented in the robot dynamics domain. This report describes research done at the Dept. of Brain and Cognitive Sciences, the Center for Biological and Computational Learning, and the Artificial Intelligence Laboratory of the Massachusetts Institute of Technology. Support for CBCL is provided in part by a grant from the NSF (ASC-9217041). Support for the laboratory's artificial intelligence research is provided in part by the Advanced Research Projects Agency of the Dept. of Defense. The authors were supported by a grant from the McDonnell-Pew Foundation, by a grant from ATR Human Information Processing Research Laboratories, by a grant from Siemens Corporation, by by grant IRI-9013991 from the National Science Foundation, by grant N00014-90-J-1942 from the Office of Naval Research, and by NSF grant ECS-9216531 to support an Initiative in Intelligent Control at MIT. Michael I. Jordan is a NSF Presidential Young Investigator. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #205196. 	[Title] Constructive Training Methods for Feedforward Neural Networks with Binary Weights [Abstract] DIMACS Technical Report 95-35 August 1995 Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #628751. 	[Title] NESTED NETWORKS FOR ROBOT CONTROL [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #85299. 	[Title] LEARNING BY ERROR-DRIVEN DECOMPOSITION [Abstract] In this paper we describe a new selforganizing decomposition technique for learning high-dimensional mappings. Problem decomposition is performed in an error-driven manner, such that the resulting subtasks (patches) are equally well approximated. Our method combines an unsupervised learning scheme (Feature Maps [Koh84]) with a nonlinear approximator (Backpropagation [RHW86]). The resulting learning system is more stable and effective in changing environments than plain backpropagation and much more powerful than extended feature maps as proposed by [RS88, RMS89]. Extensions of our method give rise to active exploration strategies for autonomous agents facing unknown environments. The appropriateness of our general purpose method will be demonstrated with an ex ample from mathematical function approximation. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #887. 	[Title] Some studies in machine learning using the game of checkers. IBM Journal, 3(3):211-229, 1959. Some [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #628764. 	[Title] Approximation with neural networks: Between local and global approximation [Abstract] We investigate neural network based approximation methods. These methods depend on the locality of the basis functions. After discussing local and global basis functions, we propose a a multi-resolution hierarchical method. The various resolutions are stored at various levels in a tree. At the root of the tree, a global approximation is kept; the leafs store the learning samples themselves. Intermediate nodes store intermediate representations. In order to find an optimal partitioning of the input space, self-organising maps (SOM's) are used. The proposed method has implementational problems reminiscent of those encountered in many-particle simulations. We will investigate the parallel implementation of this method, using parallel hierarchical meth ods for many-particle simulations as a starting point. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #299197. 	[Title] TD Learning of Game Evaluation Functions with Hierarchical Neural Architectures [Abstract]  Please summarise all the given information.

Paper #85324 has the title `The optimal number of learning samples and hidden units in function approximation with a feedforward network  
` and the abstract `This paper presents a methodology to estimate the optimal number of learning samples and the number of hidden units needed to obtain a desired accuracy of a function approximation by a feedforward network. The representation error and the generalization error, components of the total approximation error are analyzed and the approximation accuracy of a feedforward network is investigated as a function of the number of hidden units and the number of learning samples. Based on the asymptotical behavior of the approximation error, an asymptotical model of the error function (AMEF) is introduced of which the parameters can be determined experimentally. An alternative model of the error function, which include theoretical results about general bounds of approximation, is also analyzed. In combination with knowledge about the computational complexity of the learning rule an optimal learning set size and number of hidden units can be found resulting in a minimum computation time for a given desired precision of the approximation. This approach was applied to optimize the learning of the camera-robot mapping of a visually guided robot arm and a complex logarithm function approximation. 
`.
Question: Which category should Paper #85324 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #85324 has the title `The optimal number of learning samples and hidden units in function approximation with a feedforward network  
` and the abstract `This paper presents a methodology to estimate the optimal number of learning samples and the number of hidden units needed to obtain a desired accuracy of a function approximation by a feedforward network. The representation error and the generalization error, components of the total approximation error are analyzed and the approximation accuracy of a feedforward network is investigated as a function of the number of hidden units and the number of learning samples. Based on the asymptotical behavior of the approximation error, an asymptotical model of the error function (AMEF) is introduced of which the parameters can be determined experimentally. An alternative model of the error function, which include theoretical results about general bounds of approximation, is also analyzed. In combination with knowledge about the computational complexity of the learning rule an optimal learning set size and number of hidden units can be found resulting in a minimum computation time for a given desired precision of the approximation. This approach was applied to optimize the learning of the camera-robot mapping of a visually guided robot arm and a complex logarithm function approximation. 
`.
Question: Which category should Paper #85324 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].

This paper should be classified into: Neural_Networks