Learning internal representations by error propagation
Parallel distributed processing: explorations in the microstructure of cognition, vol. 1
Neural Computation
A universal theorem on learning curves
Neural Networks
A hierarchy of macrodynamical equations for associative memory
Neural Networks
Natural gradient works efficiently in learning
Neural Computation
Synchronous firing and higher-order interactions in neuron pool
Neural Computation
Information-geometric measure for neural spikes
Neural Computation
Information geometry of U-Boost and Bregman divergence
Neural Computation
Stochastic reasoning, free energy, and information geometry
Neural Computation
Singularities Affect Dynamics of Learning in Neuromanifolds
Neural Computation
Estimating Spiking Irregularities Under Changing Environments
Neural Computation
Learning Patterns and Pattern Sequences by Self-Organizing Nets of Threshold Elements
IEEE Transactions on Computers
Measure of correlation orthogonal to change in firing rate
Neural Computation
Blind source separation-semiparametric statistical approach
IEEE Transactions on Signal Processing
Information geometry on hierarchy of probability distributions
IEEE Transactions on Information Theory
Information geometry of Boltzmann machines
IEEE Transactions on Neural Networks
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Theoreticians have been enchanted by the secrets of the brain for many years: how and why does it work so well? There has been a long history of searching for its mechanisms. Theoretical or even mathematical scientists have proposed various models of neural networks which has led to the birth of a new field of research. We can think of the 'pre-historic' period of Rashevski and Wiener, and then the period of perceptrons which is the beginning of learning machines, neurodynamics approaches, and further connectionist approaches. Now is currently the period of computational neuroscience. I have been working in this field for nearly half a century, and have experienced its repeated rise and fall. Now having reached very old age, I would like to state my own endeavors on establishing mathematical neuroscience for half a century, from a personal, even biased, point of view. It would be my pleasure if my experiences could encourage young researchers to participate in mathematical neuroscience.