Above are papers related to the following paper: [Paper_ID] Paper #1140231. 	[Title] NIPS*97 The Efficiency and The Robustness of Natural Gradient Descent Learning Rule [Abstract] We have discovered a new scheme to represent the Fisher information matrix of a stochastic multi-layer perceptron. Based on this scheme, we have designed an algorithm to compute the inverse of the Fisher information matrix. When the input dimension n is much larger than the number of hidden neurons, the complexity of this algorithm is of order O(n 2 ) while the complexity of conventional algorithms for the same purpose is of order O(n 3 ). The inverse of the Fisher information matrix is used in the natural gradient descent algorithm to train single-layer or multi-layer perceptrons. It is confirmed by simulation that the natural gradient Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #851968. 	[Title] Natural Gradient Descent for Training Multi-Layer Perceptrons [Abstract] The main difficulty in implementing the natural gradient learning rule is to compute the inverse of the Fisher information matrix when the input dimension is large. We have found a new scheme to represent the Fisher information matrix. Based on this scheme, we have designed an algorithm to compute the inverse of the Fisher information matrix. When the input dimension n is much larger than the number of hidden neurons, the complexity of this algorithm is of order O(n 2 ) while the complexity of conventional algorithms for the same purpose is of order O(n 3 ). The simulation has confirmed the efficience and robustness of the natural gradient learning rule. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #278394. 	[Title] Statistical Theory of Overtraining Is Cross-Validation Asymptotically Effective? [Abstract] A statistical theory for overtraining is proposed. The analysis treats realizable stochastic neural networks, trained with Kullback-Leibler loss in the asymptotic case. It is shown that the asymptotic gain in the generalization error is small if we perform early stopping, even if we have access to the optimal stopping time. Considering cross-validation stopping we answer the question: In what ratio the examples should be divided into training and testing sets in order to obtain the optimum performance. In the non-asymptotic region cross-validated early stopping always decreases the generalization error. Our large scale simulations done on a CM5 are in nice agreement with our analytical findings. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #230879. 	[Title] Equivariant adaptive source separation [Abstract] Source separation consists in recovering a set of independent signals when only mixtures with unknown coefficients are observed. This paper introduces a class of adaptive algorithms for source separation which implements an adaptive version of equivariant estimation and is henceforth called EASI (Equivariant Adaptive Separation via Independence). The EASI algorithms are based on the idea of serial updating: this specific form of matrix updates systematically yields algorithms with a simple, parallelizable structure, for both real and complex mixtures. Most importantly, the performance of an EASI algorithm does not depend on the mixing matrix. In particular, convergence rates, stability conditions and interference rejection levels depend only on the (normalized) distributions of the source signals. Close form expressions of these quantities are given via an asymptotic performance analysis. This is completed by some numerical experiments illustrating the effectiveness of the proposed approach. Please summarise all the given information.

Paper #1140231 has the title `NIPS*97 The Efficiency and The Robustness of Natural Gradient Descent Learning Rule  
` and the abstract `We have discovered a new scheme to represent the Fisher information matrix of a stochastic multi-layer perceptron. Based on this scheme, we have designed an algorithm to compute the inverse of the Fisher information matrix. When the input dimension n is much larger than the number of hidden neurons, the complexity of this algorithm is of order O(n 2 ) while the complexity of conventional algorithms for the same purpose is of order O(n 3 ). The inverse of the Fisher information matrix is used in the natural gradient descent algorithm to train single-layer or multi-layer perceptrons. It is confirmed by simulation that the natural gradient 
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Question: Which category should Paper #1140231 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #1140231 has the title `NIPS*97 The Efficiency and The Robustness of Natural Gradient Descent Learning Rule  
` and the abstract `We have discovered a new scheme to represent the Fisher information matrix of a stochastic multi-layer perceptron. Based on this scheme, we have designed an algorithm to compute the inverse of the Fisher information matrix. When the input dimension n is much larger than the number of hidden neurons, the complexity of this algorithm is of order O(n 2 ) while the complexity of conventional algorithms for the same purpose is of order O(n 3 ). The inverse of the Fisher information matrix is used in the natural gradient descent algorithm to train single-layer or multi-layer perceptrons. It is confirmed by simulation that the natural gradient 
`.
Question: Which category should Paper #1140231 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