Laboratory for Mathematical Neuroscience
Laboratory Head
Shun-ichi AMARI (D.Eng.)
Amari Research Laboratory aims at elucidation of the principles of information processing in the brain mathematically, thus establishing foundations of mathematical neuroscience. Information is represented in the brain by spatio-temporal patterns of excitation in ensembles of neurons, and processed by dynamics of parallel interactions of neurons. It is a learning system which modifies its structures, equipped with memory and self-organizing ability. Through mathematical analysis of various parts and functions of the brain, we establish principles of the brain mathematically, and also we search for the performances of brain-style information processing systems. We further develop mathematical tools and methods such as information geometry. We are currently studying information geometry of learning machines and analysis of neuronal spike sequences.
- Information geometry of neuro manifolds
- Mathematical model of higher-order functions in cerebrum
- Mathematical analysis of spatio-temporal spiking pluse sequences
- July 05, 2006
- Elucidating principles of the brain mathematically
- Amari, S.:
"Measure of correlation orthogonal to change in firing rate"
Neural Computation, 21, 960-972 (2009). - Amari, S.:
"α-divergence is unique, belonging to both f-divergence and bregman divergence classes"
IEEE Transactions on Information Theory, 55, 4925-4931 (2009). - Tatsuno, M., Fellous, J-M., and Amari, S.:
"Information-geometric measures as robust estimators of connection strengths and external inputs"
Neural Computation, 21, 2309-2335 (2009). - Yukawa, M.:
"Krylov-proportionate adaptive filtering techniques not limited to sparse systems"
IEEE Transactions on Signal Processing, 57, 927-943 (2009). - Cousseau, F., Ozeki, T., and Amari, S.:
"Dynamics of learning in multilayer perceptrons near singularities"
IEEE Transactions on Neural Networks, 19, 1313-1328 (2008). - Masuda, N., and Amari, S.:
"A computational study of synaptic mechanisms of partial memory transfer in cerebellar vestibulo-ocular-reflex learning"
Journal of Computational Neuroscience, 24, 137-156 (2008). - Wei, H., Zhang, J., Cousseau, F., Ozeki, T., and Amari, S.:
"Dynamics of learning near singularities layered networks"
Neural Computation, 20, 813-843 (2008). - Amari, S.:
"Integration of stochastic models by minimizing α-divergence"
Neural Computation, 19, 2780-2796 (2007). - Miura, K., Okada, M., and Amari, S.:
"Estimating spiking irregularities under changing environments"
Neural Computation, 18, 2359-2386 (2006). - Toyoizumi, T., Aihara, K., and Amari, S.:
"Fisher information for spike-based population decoding"
Physical Review Letters, 97, 098102-1-098102-4 (2006).