Legends: | Link to a Model | Reference cited by multiple papers |
References and models cited by this paper | References and models that cite this paper | |||
Abeles M (1991) Corticonics: Neural Circuits of the Cerebral Cortex. Amari S (1977) Dynamics of pattern formation in lateral-inhibition type neural fields. Biol Cybern 27:77-87 [PubMed] Amari S (1998) Natural gradient works efficiently in learning Neural Comput 10:251-276 Amari S, Arbib MA (1977) Competition and cooperation in neural nets Systems neuroscience, Metzler J, ed. pp.119 Amari S, Nagaoka H (2000) Methods of information geometry Amari S, Nakahara H, Wu S, Sakai Y (2003) Synchronous firing and higher-order interactions in neuron pool. Neural Comput 15:127-42 [Journal] [PubMed] Amari S, Ozeki T (2001) Differential and algebraic geometry of multilayer perceptrons IEICE Trans 84:31-38 Burnashev MV, Amari S (2002) On some singularities in parameter estimation problems Problems Of Information Transmission 38:328-346 Clarke BS, Barron AR (1990) Information theoretic asymptotics of Bayes methods IEEE Transactions On Information Theory 36:453-471 Dacunha-castelle D, Gassiat E (1997) Testing in locally conic models, and application to mixture models Probability And Statistics 1:285-317 Diesmann M, Gewaltig MO, Aertsen A (1999) Stable propagation of synchronous spiking in cortical neural networks. Nature 402:529-33 [Journal] [PubMed]
Eurich CW, Wilke SD (2000) Multidimensional encoding strategy of spiking neurons. Neural Comput 12:1519-29 [PubMed] Fukumizu K (2003) Likelihood ratio of unidentifiable models and multilayer neural networks Annals Of Statistics 31:833-851 Fukumizu K, Amari S (2000) Local minima and plateaus in hierarchical structures of multilayer perceptrons. Neural Netw 13:317-27 [PubMed] Hotelling H (1939) Tubes and spheres in n-spaces, and a class of statistical problems Amer J Math 61:440-460 Ingle D (1968) Visual releasers of pre-catching behavior in frogs and toads Brain Behavior And Evolution 1:500-518 Komaki F (1996) On asymptotic properties of predictive distributions Biometrika 83:299-313 Liu X, Shao Y (2003) Asymptotics for likelihood ratio tests under loss of identifiability Annals Of Statistics 31:807-832 Martinez-Trujillo JCM, Treue S (2000) Attention modulates tuning curves from two stimuli inside the receptive field of MT-MST cells in the macaque monkey Soc Neurosci Abstr 26:251 Nakahara H, Amari SI (2002) Attention modulation of neural tuning through peak and base rate in correlated firing. Neural Netw 15:41-55 [PubMed] Nakahara H, Wu S, Amari S (2001) Attention modulation of neural tuning through peak and base rate. Neural Comput 13:2031-47 [Journal] [PubMed] Pouget A, Dayan P, Zemel R (2000) Information processing with population codes. Nat Rev Neurosci 1:125-32 [Journal] [PubMed] Pouget A, Zhang K, Deneve S, Latham PE (1998) Statistically efficient estimation using population coding. Neural Comput 10:373-401 [PubMed] Reichardt W, Poggio T (1975) A theory of the pattern induced flight orientation of the fly Musca domestica II. Biol Cybern 18:69-80 [PubMed] Sahani M, Dayan P (2003) Doubly distributional population codes: simultaneous representation of uncertainty and multiplicity. Neural Comput 15:2255-79 [Journal] [PubMed] Seung HS, Sompolinsky H (1993) Simple models for reading neuronal population codes. Proc Natl Acad Sci U S A 90:10749-53 [PubMed] Singer W (1999) Neuronal synchrony: a versatile code for the definition of relations? Neuron 24:49-65, 111-25 [PubMed] Treue S, Hol K, Rauber HJ (2000) Seeing multiple directions of motion-physiology and psychophysics. Nat Neurosci 3:270-6 [Journal] [PubMed] von der Malsburg C (1999) The what and why of binding: the modeler's perspective. Neuron 24:95-104, 111-25 [PubMed] Watanabe S (2001) Algebraic analysis for nonidentifiable learning machines. Neural Comput 13:899-933 [PubMed] Watanabe S (2001) Algebraic geometrical methods for hierarchical learning machines. Neural Netw 14:1049-60 [PubMed] Watanabe S (2001) Algebraic information geometry for learning machines with singularities Advances in neural information processing systems, Leen TK:Dietterich TG:Tresp V, ed. pp.329 Weyl H (1939) On the volume of tubes Amer J Math 61:461-472 Wu S, Amari S, Nakahara H (2002) Population coding and decoding in a neural field: a computational study. Neural Comput 14:999-1026 [Journal] [PubMed] Wu S, Amari S, Nakahara H (2002) Asymptotic behaviors of population codes Neurocomputing 44:697-702 Wu S, Amari S, Nakahara H (2004) Information processing in a neuron ensemble with the multiplicative correlation structure. Neural Netw 17:205-14 [Journal] [PubMed] Wu S, Chen D, Niranjan M, Amari S (2003) Sequential Bayesian decoding with a population of neurons. Neural Comput 15:993-1012 [Journal] [PubMed] Wu S, Nakahara H, Amari S (2001) Population coding with correlation and an unfaithful model. Neural Comput 13:775-97 [PubMed] Yoon H, Sompolinsky H (1998) The effect of correlations on the Fisher information of population codes. Advances In Neural Information Processing Systems. 11:167-173 Zemel RS, Dayan P, Pouget A (1998) Probabilistic interpretation of population codes. Neural Comput 10:403-30 [PubMed] Zemel RS, Pillow J (2002) A probabilistic network model of population responses Probabilistic models of the brain: Perception and neural function, Rao RPN:Olshausen BA:Lewicki MS, ed. pp.223 Zhang K, Sejnowski TJ (1999) Neuronal tuning: To sharpen or broaden? Neural Comput 11:75-84 [PubMed] | Amari S, Park H, Ozeki T (2006) Singularities affect dynamics of learning in neuromanifolds. Neural Comput 18:1007-65 [Journal] [PubMed] |