Singularities Affect Dynamics of Learning in Neuromanifolds
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[1] H. Weyl. On the Volume of Tubes , 1939 .
[2] H. Hotelling. Tubes and Spheres in n-Spaces, and a Class of Statistical Problems , 1939 .
[3] A. A. Mullin,et al. Principles of neurodynamics , 1962 .
[4] Shun-ichi Amari,et al. A Theory of Adaptive Pattern Classifiers , 1967, IEEE Trans. Electron. Comput..
[5] H. Akaike. A new look at the statistical model identification , 1974 .
[6] Second-Order Systems. Some Geometric Questions in the Theory of Linear Systems , 1976 .
[7] G. Schwarz. Estimating the Dimension of a Model , 1978 .
[8] J. Hartigan. A failure of likelihood asymptotics for normal mixtures , 1985 .
[9] Geoffrey E. Hinton,et al. Learning internal representations by error propagation , 1986 .
[10] J. Rissanen. Stochastic Complexity and Modeling , 1986 .
[11] Héctor J. Sussmann,et al. Uniqueness of the weights for minimal feedforward nets with a given input-output map , 1992, Neural Networks.
[12] Shun-ichi Amari,et al. Statistical Theory of Learning Curves under Entropic Loss Criterion , 1993, Neural Computation.
[13] Robert Hecht-Nielsen,et al. On the Geometry of Feedforward Neural Network Error Surfaces , 1993, Neural Computation.
[14] Katsuyuki Hagiwara,et al. On the problem of applying AIC to determine the structure of a layered feedforward neural network , 1993, Proceedings of 1993 International Conference on Neural Networks (IJCNN-93-Nagoya, Japan).
[15] Oh,et al. Generalization in a two-layer neural network. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.
[16] Shun-ichi Amari,et al. Network information criterion-determining the number of hidden units for an artificial neural network model , 1994, IEEE Trans. Neural Networks.
[17] Paul C. Kainen,et al. Functionally Equivalent Feedforward Neural Networks , 1994, Neural Computation.
[18] Michael Biehl,et al. On-line backpropagation in two-layered neural networks , 1995 .
[19] Saad,et al. On-line learning in soft committee machines. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.
[20] E. Gassiat,et al. Testing in locally conic models, and application to mixture models , 1997 .
[21] Magnus Rattray,et al. Natural gradient descent for on-line learning , 1998 .
[22] Shun-ichi Amari,et al. Natural Gradient Works Efficiently in Learning , 1998, Neural Computation.
[23] K. Fukumizu. Generalization Error of Linear Neural Networks in Unidentiable Cases , 1999 .
[24] M. Rattray,et al. Analysis of natural gradient descent for multilayer neural networks , 1999, cond-mat/9901212.
[25] Kenji Fukumizu,et al. Adaptive Method of Realizing Natural Gradient Learning for Multilayer Perceptrons , 2000, Neural Computation.
[26] Kenji Fukumizu,et al. Local minima and plateaus in hierarchical structures of multilayer perceptrons , 2000, Neural Networks.
[27] Sumio Watanabe. Algebraic Information Geometry for Learning Machines with Singularities , 2000, NIPS.
[28] Sumio Watanabe. Algebraic Analysis for Non-identifiable Learning Machines , 2000 .
[29] Kenji Fukumizu,et al. Adaptive natural gradient learning algorithms for various stochastic models , 2000, Neural Networks.
[30] Shun-ichi Amari,et al. Methods of information geometry , 2000 .
[31] Hilbert J. Kappen,et al. Nonmonotonic Generalization Bias of Gaussian Mixture Models , 2000, Neural Computation.
[32] Shun-ichi Amari,et al. Geometrical Singularities in the Neuromanifold of Multilayer Perceptrons , 2001, NIPS.
[33] Si Wu,et al. Population Coding with Correlation and an Unfaithful Model , 2001, Neural Computation.
[34] Katsuyuki Hagiwara,et al. Upper bound of the expected training error of neural network regression for a Gaussian noise sequence , 2001, Neural Networks.
[35] S. Amari,et al. Differential and Algebraic Geometry of Multilayer Perceptrons , 2001 .
[36] Sumio Watanabe. Algebraic geometrical methods for hierarchical learning machines , 2001, Neural Networks.
[37] Sumio Watanabe,et al. A Probabilistic Algorithm to Calculate the Learning Curves of Hierarchical Learning Machines with Singularities , 2002 .
[38] Katsuyuki Hagiwara,et al. Regularization learning, early stopping and biased estimator , 2002, Neurocomputing.
[39] Si Wu,et al. Population Coding and Decoding in a Neural Field: A Computational Study , 2002, Neural Computation.
[40] Katsuyuki Hagiwara. On the Problem in Model Selection of Neural Network Regression in Overrealizable Scenario , 2002, Neural Computation.
[41] Sumio Watanabe,et al. Singularities in mixture models and upper bounds of stochastic complexity , 2003, Neural Networks.
[42] Shun-ichi Amari,et al. Learning Coefficients of Layered Models When the True Distribution Mismatches the Singularities , 2003, Neural Computation.
[43] Masato Okada,et al. On-Line Learning Dynamics of Multilayer Perceptrons with Unidentifiable Parameters , 2003 .
[44] K. Fukumizu. Likelihood ratio of unidentifiable models and multilayer neural networks , 2003 .
[45] Shun-ichi Amari. New Consideration on Criteria of Model Selection , 2003 .
[46] Shun-ichi Amari,et al. Learning and inference in hierarchical models with singularities , 2003, Systems and Computers in Japan.
[47] Naohiro Toda,et al. On the Statistical Properties of Least Squares Estimators of Layered Neural Networks , 2003 .
[48] Hyeyoung Park,et al. On-Line Learning Theory of Soft Committee Machines with Correlated Hidden Units : Steepest Gradient Descent and Natural Gradient Descent , 2002, cond-mat/0212006.
[49] Shun-ichi Amari,et al. On Some Singularities in Parameter Estimation Problems , 2003, Probl. Inf. Transm..
[50] Y. Shao,et al. Asymptotics for likelihood ratio tests under loss of identifiability , 2003 .
[51] S. Amari. Dynamics of pattern formation in lateral-inhibition type neural fields , 1977, Biological Cybernetics.
[52] Stefan M. Rüger,et al. The Metric Structure of Weight Space , 1997, Neural Processing Letters.
[53] Shun-ichi Amari,et al. Difficulty of Singularity in Population Coding , 2005, Neural Computation.
[54] Shun-ichi Amari,et al. Differential geometry of a parametric family of invertible linear systems—Riemannian metric, dual affine connections, and divergence , 1987, Mathematical systems theory.