title: Difficulty of singularity in population coding.
abstract: Fisher information has been used to analyze the accuracy of neural population coding. This works well when the Fisher information does not degenerate, but when two stimuli are presented to a population of neurons, a singular structure emerges by their mutual interactions. In this case, the Fisher information matrix degenerates, and the regularity condition ensuring the Cramér-Rao paradigm of statistics is violated. An animal shows pathological behavior in such a situation. We present a novel method of statistical analysis to understand information in population coding in which algebraic singularity plays a major role. The method elucidates the nature of the pathological case by calculating the Fisher information. We then suggest that synchronous firing can resolve singularity and show a method of analyzing the binding problem in terms of the Fisher information. Our method integrates a variety of disciplines in population coding, such as nonregular statistics, Bayesian statistics, singularity in algebraic geometry, and synchronous firing, under the theme of Fisher information.
authors.affiliation: Laboratory for Mathematical Neuroscience, RIKEN Brain Science Institute, Wako, Saitama, 351-0198 Japan. amari@brain.riken.jp
authors.forename: Shun-ichi
authors.initials: S
authors.lastname: Amari
authors.forename: Hiroyuki
authors.initials: H
authors.lastname: Nakahara
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D000818:Animals; D001499:Bayes Theorem; D001921:Brain / Q000502:physiology; D006801:Humans; D007257:Information Theory; D008959:Models, Neurological; D009434:Neural Pathways / Q000502:physiology*; D009475:Neurons, Afferent / Q000502:physiology*; D012677:Sensation / Q000502:physiology*; D009435:Synaptic Transmission / Q000502:physiology