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 #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.

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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 #627024. 	[Title] Early Stopping but when? [Abstract] Validation can be used to detect when overfitting starts during supervised training of a neural network; training is then stopped before convergence to avoid the overfitting ("early stopping"). The exact criterion used for validation-based early stopping, however, is usually chosen in an ad-hoc fashion or training is stopped interactively. This trick describes how to select a stopping criterion in a systematic fashion; it is a trick for either speeding learning procedures or improving generalization, whichever is more important in the particular situation. An empirical investigation on multi-layer perceptrons shows that there exists a tradeoff between training time and generalization: From the given mix of 1296 training runs using different 12 problems and 24 different network architectures I conclude slower stopping criteria allow for small improvements in generalization (here: about 4% on average), but cost much more training time (here: about factor 4 longer on average). Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #35797. 	[Title] Proben1 A Set of Neural Network Benchmark Problems and Benchmarking Rules [Abstract] Proben1 is a collection of problems for neural network learning in the realm of pattern classification and function approximation plus a set of rules and conventions for carrying out benchmark tests with these or similar problems. Proben1 contains 15 data sets from 12 different domains. All datasets represent realistic problems which could be called diagnosis tasks and all but one consist of real world data. The datasets are all presented in the same simple format, using an attribute representation that can directly be used for neural network training. Along with the datasets, Proben1 defines a set of rules for how to conduct and how to document neural network benchmarking. The purpose of the problem and rule collection is to give researchers easy access to data for the evaluation of their algorithms and networks and to make direct comparison of the published results feasible. This report describes the datasets and the benchmarking rules. It also gives some basic performance measures indicating the difficulty of the various problems. These measures can be used as baselines for comparison. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #911198. 	[Title] Centering Neural Network Gradient Factors [Abstract] Technical Report IDSIA-19-97 Abstract. It has long been known that neural networks can learn faster when their input and hidden unit activities are centered about zero; recently we have extended this approach to also encompass the centering of error signals [2]. Here we generalize this notion to all factors involved in the network's gradient, leading us to propose centering the slope of hidden unit activation functions as well. Slope centering removes the linear component of backpropagated error; this improves credit assignment in networks with shortcut connections. Benchmark results show that this can speed up learning significantly without adversely affecting the trained network's generalization ability. 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 #278394 has the title `Statistical Theory of Overtraining Is Cross-Validation Asymptotically Effective?  
` and the 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. 
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Question: Which category should Paper #278394 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #278394 has the title `Statistical Theory of Overtraining Is Cross-Validation Asymptotically Effective?  
` and the 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. 
`.
Question: Which category should Paper #278394 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