Natural gradient works efficiently in learning
Neural Computation
Statistically efficient estimation using population coding
Neural Computation
Probabilistic interpretation of population codes
Neural Computation
Neuronal tuning: to sharpen or broaden
Neural Computation
The effect of correlations on the Fisher information of population codes
Proceedings of the 1998 conference on Advances in neural information processing systems II
Algebraic geometrical methods for hierarchical learning machines
Neural Networks
On Density Estimation under Relative Entropy Loss Criterion
Problems of Information Transmission
Population coding and decoding in a neural field: a computational study
Neural Computation
Synchronous firing and higher-order interactions in neuron pool
Neural Computation
Sequential Bayesian decoding with a population of neurons
Neural Computation
Attention Modulation of Neural Tuning Through Peak and Base Rate
Neural Computation
Algebraic Analysis for Nonidentifiable Learning Machines
Neural Computation
Population Coding with Correlation and an Unfaithful Model
Neural Computation
Multidimensional Encoding Strategy of Spiking Neurons
Neural Computation
Singularities Affect Dynamics of Learning in Neuromanifolds
Neural Computation
Dynamics of learning near singularities in layered networks
Neural Computation
BVAI'07 Proceedings of the 2nd international conference on Advances in brain, vision and artificial intelligence
Input identification in the Ornstein-Uhlenbeck neuronal model with signal dependent noise
BVAI'07 Proceedings of the 2nd international conference on Advances in brain, vision and artificial intelligence
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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.