S. Amari, H. Park, and T. Ozeki, Singularities Affect Dynamics of Learning in Neuromanifolds, Neural Computation, vol.28, issue.2, pp.1007-1065, 2006.
DOI : 10.1016/S0893-6080(03)00005-4

M. Cottrell, B. Girard, Y. Girard, M. Mangeas, and C. Muller, Neural modeling for time series: A statistical stepwise method for weight elimination, IEEE Transactions on Neural Networks, vol.6, issue.6, pp.1355-1364, 1995.
DOI : 10.1109/72.471372

D. Dacunha-castelle and E. Gassiat, Testing the order of a model using locally conic parametrization: population mixtures and stationary ARMA processes, The Annals of Statistics, vol.27, issue.4, pp.1178-1209, 1999.
DOI : 10.1214/aos/1017938921

K. Fukumizu, A Regularity Condition of the Information Matrix of a Multilayer Perceptron Network, Neural Networks, vol.9, issue.5, pp.871-879, 1996.
DOI : 10.1016/0893-6080(95)00119-0

K. Fukumizu, Likelihood ratio of unidentifiable models and multilayer neural networks, The Annals of Statistics, vol.31, issue.3, pp.833-851, 2003.
DOI : 10.1214/aos/1056562464

E. Gassiat and C. Keribin, The likelihood ratio test for the number of components in a mixture with Markov regime, ESAIM: Probability and Statistics, vol.4, pp.25-52, 2000.
DOI : 10.1051/ps:2000102

E. Gassiat, Likelihood ratio inequalities with applications to various mixtures, Annales de l'Institut Henri Poincare (B) Probability and Statistics, vol.38, issue.6, pp.897-906, 2002.
DOI : 10.1016/S0246-0203(02)01125-1

X. Liu and Y. Shao, asymptotics for likelihood ratio tests under loss of identifiability The Annals of, Statistics, vol.31, pp.807-832, 2003.

H. J. Sussmann, Uniqueness of the weights for minimal feedforward nets with a given input-output map, Artificial Neural Networks: Approximation and Learning Theory, pp.589-593, 1992.
DOI : 10.1016/S0893-6080(05)80037-1