In this paper we propose new algorithm to reduce autocorrelation in Markov chain Monte-Carlo algorithms for euclidean field theories on the lattice. Our proposing algorithm is the Hybrid Monte-Carlo algorithm (HMC) with restricted Boltzmann machine. We examine the validity of the algorithm by employing the phi-fourth theory in three dimension. We observe reduction of the autocorrelation both in symmetric and broken phase as well. Our proposing algorithm provides consistent central values of expectation values of the action density and one-point Green's function with ones from the original HMC in both the symmetric phase and broken phase within the statistical error. On the other hand, two-point Green's functions have slight difference between one calculated by the HMC and one by our proposing algorithm in the symmetric phase. Furthermore, near the criticality, the distribution of the one-point Green's function differs from the one from HMC. We discuss the origin of discrepancies and its improvement.

Kukjin Kang and Jong-Hoon Oh Department of Physics Pohang University of Science and Technology Hyoja San 31, Pohang, Kyongbuk 790-784, Korea Email: kkj.jhohOgalaxy.postech.ac.kr Abstract We study generalization capability of the mixture of experts learning fromexamples generated by another network with the same architecture. When the number of examples is smaller than a critical value,the network shows a symmetric phase where the role of the experts is not specialized. Upon crossing the critical point, the system undergoes a continuous phase transition to a symmetry breakingphase where the gating network partitions the input space effectively and each expert is assigned to an appropriate subspace. Wealso find that the mixture of experts with multiple level of hierarchy shows multiple phase transitions. 1 Introduction Recently there has been considerable interest among neural network community in techniques that integrate the collective predictions of a set of networks[l, 2, 3, 4]. The mixture of experts [1, 2] is a well known example which implements the philosophy ofdivide-and-conquer elegantly.

The mixture of experts [1, 2] is a well known example which implements the philosophy of divide-and-conquer elegantly. Whereas this model are gaining more popularity in various applications, there have been little efforts to evaluate generalization capability of these modular approaches theoretically. Here we present the first analytic study of generalization in the mixture of experts from the statistical 184 K. Kang and 1. Oh physics perspective. Use of statistical mechanics formulation have been focused on the study of feedforward neural network architectures close to the multilayer perceptron[5, 6], together with the VC theory[8]. We expect that the statistical mechanics approach can also be effectively used to evaluate more advanced architectures including mixture models.

The mixture of experts [1, 2] is a well known example which implements the philosophy of divide-and-conquer elegantly. Whereas this model are gaining more popularity in various applications, there have been little efforts to evaluate generalization capability of these modular approaches theoretically. Here we present the first analytic study of generalization in the mixture of experts from the statistical 184 K. Kang and 1. Oh physics perspective. Use of statistical mechanics formulation have been focused on the study of feedforward neural network architectures close to the multilayer perceptron[5, 6], together with the VC theory[8]. We expect that the statistical mechanics approach can also be effectively used to evaluate more advanced architectures including mixture models.

We study the effect of noise and regularization in an online gradient-descent learning scenario for a general two-layer student network with an arbitrary number of hidden units. Training examples are randomly drawn input vectors labeled by a two-layer teacher network with an arbitrary number of hidden units; the examples are corrupted by Gaussian noise affecting either the output or the model itself. We examine the effect of both types of noise and that of weight-decay regularization on the dynamical evolution of the order parameters and the generalization error in various phases of the learning process.

We study the effect of noise and regularization in an online gradient-descent learning scenario for a general two-layer student network with an arbitrary number of hidden units. Training examples arerandomly drawn input vectors labeled by a two-layer teacher network with an arbitrary number of hidden units; the examples arecorrupted by Gaussian noise affecting either the output or the model itself. We examine the effect of both types of noise and that of weight-decay regularization on the dynamical evolution ofthe order parameters and the generalization error in various phases of the learning process. 1 Introduction One of the most powerful and commonly used methods for training large layered neural networks is that of online learning, whereby the internal network parameters {J} are modified after the presentation of each training example so as to minimize the corresponding error.

We study the effect of noise and regularization in an online gradient-descent learning scenario for a general two-layer student network with an arbitrary number of hidden units. Training examples are randomly drawn input vectors labeled by a two-layer teacher network with an arbitrary number of hidden units; the examples are corrupted by Gaussian noise affecting either the output or the model itself. We examine the effect of both types of noise and that of weight-decay regularization on the dynamical evolution of the order parameters and the generalization error in various phases of the learning process.

This research has been motivated by the dominance of the suboptimal symmetric phase in online learning of two-layer feedforward networks trained by gradient descent [2]. This trapping is emphasized for inappropriate small learning rates but exists in all training scenarios, effecting the learning process considerably. We Adaptive Back-Propagation in Online Learning of Multilayer Networks 329 proposed an adaptive back-propagation training algorithm [Eq.

This research has been motivated by the dominance of the suboptimal symmetric phase in online learning of two-layer feedforward networks trained by gradient descent [2]. This trapping is emphasized for inappropriate small learning rates but exists in all training scenarios, effecting the learning process considerably. We Adaptive Back-Propagation in Online Learning of Multilayer Networks 329 proposed an adaptive back-propagation training algorithm [Eq.

This research has been motivated by the dominance of the suboptimal symmetric phase in online learning of two-layer feedforward networks trained by gradient descent [2]. This trapping is emphasized for inappropriate small learning rates but exists in all training scenarios, effecting the learning process considerably. We Adaptive Back-Propagation in Online Learning of Multilayer Networks 329 proposed an adaptive back-propagation training algorithm [Eq.