Above are papers related to the following paper: [Paper_ID] Paper #35335. 	[Title] Parallel Gradient Distribution in Unconstrained Optimization [Abstract] A parallel version is proposed for a fundamental theorem of serial unconstrained optimization. The parallel theorem allows each of k parallel processors to use simultaneously a different algorithm, such as a descent, Newton, quasi-Newton or a conjugate gradient algorithm. Each processor can perform one or many steps of a serial algorithm on a portion of the gradient of the objective function assigned to it, independently of the other processors. Eventually a synchronization step is performed which, for differentiable convex functions, consists of taking a strong convex combination of the k points found by the k processors. For nonconvex, as well as convex, differentiable functions, the best point found by the k processors is taken, or any better point. The fundamental result that we establish is that any accumulation point of the parallel algorithm is stationary for the nonconvex case, and is a global solution for the convex case. Computational testing on the Thinking Machines CM-5 multiprocessor indicate a speedup of the order of the number of processors employed. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #27174. 	[Title] Mathematical Programming in Neural Networks [Abstract] This paper highlights the role of mathematical programming, particularly linear programming, in training neural networks. A neural network description is given in terms of separating planes in the input space that suggests the use of linear programming for determining these planes. A more standard description in terms of a mean square error in the output space is also given, which leads to the use of unconstrained minimization techniques for training a neural network. The linear programming approach is demonstrated by a brief description of a system for breast cancer diagnosis that has been in use for the last four years at a major medical facility. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #35343. 	[Title] Backpropagation Convergence Via Deterministic Nonmonotone Perturbed Minimization [Abstract] The fundamental backpropagation (BP) algorithm for training artificial neural networks is cast as a deterministic nonmonotone perturbed gradient method . Under certain natural assumptions, such as the series of learning rates diverging while the series of their squares converging, it is established that every accumulation point of the online BP iterates is a stationary point of the BP error function. The results presented cover serial and parallel online BP, modified BP with a momentum term, and BP with weight decay. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #258259. 	[Title] ERROR STABILITY PROPERTIES OF GENERALIZED GRADIENT-TYPE ALGORITHMS [Abstract] We present a unified framework for convergence analysis of the generalized subgradient-type algorithms in the presence of perturbations. One of the principal novel features of our analysis is that perturbations need not tend to zero in the limit. It is established that the iterates of the algorithms are attracted, in a certain sense, to an "-stationary set of the problem, where " depends on the magnitude of perturbations. Characterization of those attraction sets is given in the general (nonsmooth and nonconvex) case. The results are further strengthened for convex, weakly sharp and strongly convex problems. Our analysis extends and unifies previously known results on convergence and stability properties of gradient and subgradient methods, including their incremental, parallel and "heavy ball" modifications. fl The first author is supported in part by CNPq grant 300734/95-6. Research of the second author was supported in part by the International Science Foundation Grant NBY000, the International Science Foundation and Russian Goverment Grant NBY300 and the Russian Foundation for Fundamental Research Grant N 95-01-01448. y Instituto de Matematica Pura e Aplicada, Estrada Dona Castorina 110, Jardim Bot^anico, Rio de Janeiro, RJ, CEP 22460-320, Brazil. Email : solodov@impa.br. z Operations Research Department, Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia, 119899. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #59772. 	[Title] Serial and Parallel Multicategory Discrimination [Abstract] A parallel algorithm is proposed for a fundamental problem of machine learning, that of mul-ticategory discrimination. The algorithm is based on minimizing an error function associated with a set of highly structured linear inequalities. These inequalities characterize piecewise-linear separation of k sets by the maximum of k affine functions. The error function has a Lipschitz continuous gradient that allows the use of fast serial and parallel unconstrained minimization algorithms. A serial quasi-Newton algorithm is considerably faster than previous linear programming formulations. A parallel gradient distribution algorithm is used to parallelize the error-minimization problem. Preliminary computational results are given for both a DECstation Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1118332. 	[Title] June 1994 T o app ear in Neural Computation A Coun terexample to T emp [Abstract] Sutton's TD( ) metho d aims to provide a represen tation of the cost function in an absorbing Mark ov chain with transition costs. A simple example is given where the represen tation obtained dep ends on . For = 1 the represen tation is optimal with resp ect to a least squares error criterion, but as decreases towards 0 the represen tation becomes progressiv ely worse and, in some cases, very poor. The example suggests a need to understand better the circumstances under which TD(0) and Q-learning obtain satisfactory neural net work-based compact represen tations of the cost function. A variation of TD(0) is also prop osed, which performs b etter on the example. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #3229. 	[Title] Book Review  Introduction to the Theory of Neural Computation Reviewed by: 2 [Abstract] Neural computation, also called connectionism, parallel distributed processing, neural network modeling or brain-style computation, has grown rapidly in the last decade. Despite this explosion, and ultimately because of impressive applications, there has been a dire need for a concise introduction from a theoretical perspective, analyzing the strengths and weaknesses of connectionist approaches and establishing links to other disciplines, such as statistics or control theory. The Introduction to the Theory of Neural Computation by Hertz, Krogh and Palmer (subsequently referred to as HKP) is written from the perspective of physics, the home discipline of the authors. The book fulfills its mission as an introduction for neural network novices, provided that they have some background in calculus, linear algebra, and statistics. It covers a number of models that are often viewed as disjoint. Critical analyses and fruitful comparisons between these models Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #168958. 	[Title] New Inexact Parallel Variable Distribution Algorithms  Editor: [Abstract] We consider the recently proposed parallel variable distribution (PVD) algorithm of Ferris and Mangasarian [4] for solving optimization problems in which the variables are distributed among p processors. Each processor has the primary responsibility for updating its block of variables while allowing the remaining "secondary" variables to change in a restricted fashion along some easily computable directions. We propose useful generalizations that consist, for the general unconstrained case, of replacing exact global solution of the subproblems by a certain natural sufficient descent condition, and, for the convex case, of inexact subproblem solution in the PVD algorithm. These modifications are the key features of the algorithm that has not been analyzed before. The proposed modified algorithms are more practical and make it easier to achieve good load balancing among the parallel processors. We present a general framework for the analysis of this class of algorithms and derive some new and improved linear convergence results for problems with weak sharp minima of order 2 and strongly convex problems. We also show that nonmonotone synchronization schemes are admissible, which further improves flexibility of PVD approach. Please summarise all the given information.

Paper #35335 has the title `Parallel Gradient Distribution in Unconstrained Optimization  
` and the abstract `A parallel version is proposed for a fundamental theorem of serial unconstrained optimization. The parallel theorem allows each of k parallel processors to use simultaneously a different algorithm, such as a descent, Newton, quasi-Newton or a conjugate gradient algorithm. Each processor can perform one or many steps of a serial algorithm on a portion of the gradient of the objective function assigned to it, independently of the other processors. Eventually a synchronization step is performed which, for differentiable convex functions, consists of taking a strong convex combination of the k points found by the k processors. For nonconvex, as well as convex, differentiable functions, the best point found by the k processors is taken, or any better point. The fundamental result that we establish is that any accumulation point of the parallel algorithm is stationary for the nonconvex case, and is a global solution for the convex case. Computational testing on the Thinking Machines CM-5 multiprocessor indicate a speedup of the order of the number of processors employed. 
`.
Question: Which category should Paper #35335 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #35335 has the title `Parallel Gradient Distribution in Unconstrained Optimization  
` and the abstract `A parallel version is proposed for a fundamental theorem of serial unconstrained optimization. The parallel theorem allows each of k parallel processors to use simultaneously a different algorithm, such as a descent, Newton, quasi-Newton or a conjugate gradient algorithm. Each processor can perform one or many steps of a serial algorithm on a portion of the gradient of the objective function assigned to it, independently of the other processors. Eventually a synchronization step is performed which, for differentiable convex functions, consists of taking a strong convex combination of the k points found by the k processors. For nonconvex, as well as convex, differentiable functions, the best point found by the k processors is taken, or any better point. The fundamental result that we establish is that any accumulation point of the parallel algorithm is stationary for the nonconvex case, and is a global solution for the convex case. Computational testing on the Thinking Machines CM-5 multiprocessor indicate a speedup of the order of the number of processors employed. 
`.
Question: Which category should Paper #35335 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