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 #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 #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.

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.

Paper #59772 has the title `Serial and Parallel Multicategory Discrimination  
` and the 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 
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Question: Which category should Paper #59772 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #59772 has the title `Serial and Parallel Multicategory Discrimination  
` and the 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 
`.
Question: Which category should Paper #59772 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