研究業績 | 高次元ニューラルネットワーク研究所

ニューラルネットワークに関する研究業績をモデル別にまとめました。

複素連想記憶 (Complex-Valued Associative Memory)
Rotor 連想記憶 (Rotor Associative Memory)
双曲連想記憶 (Hyperbolic-Valued Associative Memory)
四元数連想記憶 (Quaternion-Valued Associative Memory)
双複素数連想記憶 (BiComplex-Valued Associative Memory)
その他の高次元連想記憶モデル
高次元 MLP (High-Dimensional MultiLayer Perceptron)
実数型連想記憶
その他

複素連想記憶 (Complex-Valued Associative Memory)

論文

M. Kobayashi: “Complex-valued Hopfield associative memories with hybrid connections”, Nonlinear Theory and Its Applications, Vol.16, No.1, pp.13-29 (2025)
T. Hashimoto, T. Isokawa, M. Kobayashi, N. Kamiura: “Enhancing computational efficiency of gradient descent in complex-valued Hopfield neural network through GPU parallelization”, Nonlinear Theory and Its Applications, Vol.16, No.1, pp.197-207 (2025)
M. Kobayashi: “Two-level complex-valued Hopfield neural networks”, IEEE Transactions on Neural Networks and Learning Systems, Vol.32, No.5, pp.2274-2278 (2021)
M. Kobayashi: “Complex-valued Hopfield neural networks with real weights in synchronous mode”, Neurocomputing, Vol.423, pp.535-540 (2021)
M. Tuji, T. Isokawa, M. Kobayashi, N. Matsui, N. Kamiura: “A projection rule for complex-valued associative memory with partial connections”, IEEJ Transactions on Electrical and Electronic Engineering, Vol.15, No.9, pp.1327-1336 (2020)
M. Kobayashi: “Bicomplex projection rule for complex-valued Hopfield neural networks”, Neural Computation, Vol.32, No.11, pp.2237-2248 (2020)
M. Kobayashi: “Fixed points of symmetric complex-valued Hopfield neural networks”, Neurocomputing, Vol.275, pp.132-136 (2018)
M. Kobayashi: “Chaotic complex-valued bipartite auto-associative memory with a periodic activation function”, IEEJ Transactions on Electrical and Electronic Engineering, Vol.12, No.4, pp.584-588 (2017)
M. Kobayashi: “Fast recall for complex-valued Hopfield neural networks with projection rules”, Computational Intelligence and Neuroscience, Vol.2017, Article ID 4894278, 6 pages (2017)
M. Kobayashi: “Symmetric complex-valued Hopfield neural networks”, IEEE Transactions on Neural Networks and Learning Systems, Vol.28, No.4, pp.1011-1015 (2017)
M. Kobayashi: “Gradient descent learning rule for complex-valued associative memories with large constant terms”, IEEJ Transactions on Electrical and Electronic Engineering, Vol.11, No.3, pp.357-363 (2016)
Y. Suzuki, M. Kobayashi: “Complex-valued bipartite auto-associative memory”, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Vol.E97-A, No.8, pp.1680-1687 (2014)
S. Furusawa, M. Kobayashi: “Chaotic complex-valued bidirectional associative memory with a real-valued context part”, Nonlinear Theory and Its Applications, Vol.4, No.3, pp.299-312 (2013)
M. Kitahara, M. Kobayashi: “Projection rule for complex-valued associative memory with large constant terms”, Nonlinear Theory and Its Applications, Vol.3, No.3, pp.426-435 (2012)
M. Kobayashi, H. Yamada, M. Kitahara: “Noise robust gradient descent learning for complex-valued associative memory”, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Vol.E94-A, No.8, pp.1756-1759 (2011)
M. Kobayashi: “Pseudo-relaxation learning algorithm for complex-valued associative memory”, International Journal of Neural Systems, Vol.18, No.2, pp.147-156 (2008)
小林正樹，山崎晴明: “複素多方向連想メモリ”, 電気学会論文誌C, Vol.125, No.8, pp.1290-1295 (2005)
(英訳)
M. Kobayashi，H. Yamazaki: “Complex-valued multidirectional associative memory”, Electrical Engineering in Japan, Vol.159, No.1, pp.39-45 (2007)
小林正樹，山崎晴明: “複素ボルツマンマシンの情報幾何”, 電子情報通信学会論文誌A, Vol.J87-A, No.8, pp.1093-1101 (2004)

国際会議

T. Minemoto, T. Isokawa, M. Kobayashi, H. Nishimura, N. Matsui: “Retrieval performance of Hopfield associative memory with complex-valued and real-valued neurons”, International Joint Conference on Neural Networks (IJCNN 2016), pp.4133-4138 (2016)
Y. Suzuki, M. Kobayashi: “Complex-valued bidirectional auto-associative memory”, International Joint Conference on Neural Networks (IJCNN 2013), pp.984-990 (2013)
Y. Suzuki, M. Kitahara, M. Kobayashi: “Dynamic complex-valued associative memory with strong bias terms”, International Conference on Neural Information Processing (ICONIP 2011), pp.509-518 (2011)
M. Kitahara, M. Kobayashi: “Complex-valued associative memory with strong thresholds”, 2011 International Symposium on Nonlinear Theory and its Applications (NOLTA 2011), pp.362-365 (2011)

Rotor 連想記憶 (Rotor Associative Memory)

論文

M. Kobayashi: “Noise robust projection rule for rotor and matrix-valued Hopfield neural networks”, IEEE Transactions on Neural Networks and Learning Systems, Vol.33, No.2, pp.567-576 (2022)
M. Kobayashi: “Quaternion projection rule for rotor Hopfield neural networks”, IEEE Transactions on Neural Networks and Learning Systems, Vol.32, No.2, pp.900-908 (2021)
M. Kobayashi: “Diagonal rotor Hopfield neural networks”, Neurocomputing, Vol.415, pp.40-47(2020)
M. Kobayashi: “Storage capacity of rotor Hopfield neural networks”, Neurocomputing, Vol.316, pp.30-33 (2018)
M. Kobayashi: “Decomposition of rotor Hopfield neural networks using complex numbers”, IEEE Transactions on Neural Networks and Learning Systems, Vol.29, No.4, pp.1366-1370 (2018)
M. Kobayashi: “Stability of rotor Hopfield neural networks with synchronous mode”, IEEE Transactions on Neural Networks and Learning Systems, Vol.29, No.3, pp.744-748 (2018)
M. Kobayashi: “Pseudomemories of two-dimensional multistate Hopfield neural networks”, IEEJ Transactions on Electrical and Electronic Engineering, Vol.12, No.2, pp.269-272 (2017)
M. Kobayashi: “Information geometry of rotor boltzmann machines”, Nonlinear Theory and Its Applications, Vol.7, No.2, pp.266-282 (2016)
M. Kobayashi: “Attractors accompanied with a training pattern of multi-valued Hopfield neural networks”, IEEJ Transactions on Electrical and Electronic Engineering, Vol.10, No.2, pp.195-200 (2015)
M. Kitahara, M. Kobayashi: “Projection rule for rotor Hopfield neural networks”, IEEE Transactions on Neural Networks and Learning Systems, Vol.25, No.7, pp.1298-1307 (2014)
北原倫理，小林正樹: “ロータ連想記憶の勾配降下学習”, 電気学会論文誌C, Vol.131, No.1, pp.116-121 (2011)
北原倫理，小林正樹，服部元信: “ロータ連想記憶による偽記憶の削減”, 電気学会論文誌C, Vol.131, No.1, pp.109-115 (2011)

国際会議

Y. Suzuki, M. Kitahara, M. Kobayashi: “Rotor associative memory with a periodic activation function”, 2012 IEEE World Congress on Computational Intelligence (WCCI 2012), pp.720-727 (2012)
M. Kitahara, M. Kobayashi: “Fundamental abilities of rotor associative memory”, 9th IEEE/ACIS International Conference on Computer and Information Science (ICIS 2010), pp.497-502 (2010)
M. Kitahara, M. Kobayashi, M. Hattori: “Chaotic rotor associative memory”, 2009 International Symposium on Nonlinear Theory and its Applications (NOLTA 2009), pp.399-402 (2009)

双曲連想記憶 (Hyperbolic-Valued Associative Memory)

論文

M. Kobayashi: “Hyperbolic-valued Hopfield neural networks in hybrid mode”, Neurocomputing, Vol.440, pp.275-278 (2021)
M. Kobayashi: “Information geometry of hyperbolic-valued boltzmann machines”, Neurocomputing, Vol.431, pp.163-168 (2021)
M. Tuji, T. Isokawa, M. Kobayashi, N. Matsui, N. Kamiura: “Gradient descent learning for hyperbolic Hopfield associative memory”, Transactions of the Institute of Systems, Control and Information Engineers, Vol.34, No.1, pp.11-22 (2021)
M. Kobayashi: “Hyperbolic-valued Hopfield neural networks in synchronous mode”, Neural Computation, Vol.32, No.9, pp.1685-1696 (2020)
M. Kobayashi: “Noise robust projection rule for hyperbolic Hopfield neural networks”, IEEE Transactions on Neural Networks and Learning Systems, Vol.31, No.1, pp.352-356 (2020)
M. Kobayashi: “Storage capacity of hyperbolic Hopfield neural networks”, Neurocomputing, Vol.369, pp.185-190 (2019)
M. Kobayashi: “Hyperbolic Hopfield neural networks with directional multistate activation function”, Neurocomputing, Vol.275, pp.2217-2226 (2018)
M. Kobayashi: “Hyperbolic Hopfield neural networks with four-state neurons”, IEEJ Transactions on Electrical and Electronic Engineering, Vol.12, No.3, pp.428-433 (2017)
M. Kobayashi: “Global hyperbolic Hopfield neural networks”, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Vol.E99-A, No.12, pp.2511-2516 (2016)
M. Kobayashi: “Hyperbolic Hopfield neural networks”, IEEE Transactions on Neural Networks and Learning Systems, Vol.24, No.2, pp.335-341 (2013)

四元数連想記憶 (Quaternion-Valued Associative Memory)

論文

M. Kobayashi: “Storage capacity of quaternion-valued Hopfield neural networks with dual connections”, Neural Computation, Vol.33, No.8, pp.2226-2240 (2021)
M. Kobayashi: “Quaternion-valued twin-multistate Hopfield neural networks with dual connections”, IEEE Transactions on Neural Networks and Learning Systems, Vol.32, No.2, pp.892-899 (2021)
M. Kobayashi: “Storage capacities of twin-multistate quaternion Hopfield neural networks”, Computational Intelligence and Neuroscience, Vol.2018, Article ID 1275290, 5 pages (2018)
M. Kobayashi: “Quaternionic Hopfield neural networks with twin-multistate activation function”, Neurocomputing, Vol.267, pp.304-310 (2017)
M. Kobayashi: “Gradient descent learning for quaternionic Hopfield neural network”, Neurocomputing, Vol.260, pp.174-179 (2017)
M. Kobayashi: “Three-dimensional quaternionic Hopfield neural networks”, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Vol.E100-A, No.7, pp.1575-1577 (2017)
M. Kobayashi: “Fixed points of split quaternionic Hopfield neural networks”, Signal Processing, Vol.136, pp.38-42 (2017)
M. Kobayashi: “Symmetric quaternionic Hopfield neural networks”, Neurocomputing, Vol.240, pp.110-114 (2017)
M. Kobayashi: “Rotational invariance of quaternionic Hopfield neural networks”, IEEJ Transactions on Electrical and Electronic Engineering, Vol.11, No.4, pp.516-520 (2016)
M. Kobayashi: “Hybrid quaternionic Hopfield neural network”, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Vol.E98-A, No.7, pp.1512-1518 (2015)

国際会議

T. Minemoto, T. Isokawa, M. Kobayashi, H. Nishimura, N. Matsui: “Pattern retrieval by quaternionic associative memory with dual connections”, International Conference on Neural Information Processing (ICONIP 2016), pp.317-325 (2016)
T. Minemoto, T. Isokawa, M. Kobayashi, H. Nishimura, N. Matsui: “On the performance of quaternionic bidirectional auto-associative memory”, International Joint Conference on Neural Networks (IJCNN 2015), pp.2910-2915 (2015)

双複素数連想記憶 (BiComplex-Valued Associative Memory)

論文

M. Kobayashi: “Bicomplex-valued twin-hyperbolic Hopfield neural networks”, Neurocomputing, Vol.434, pp.203-210 (2021)
M. Kobayashi: “Stability conditions of bicomplex-valued Hopfield neural networks”, Neural Computation, Vol.33, No.2, pp.552-562(2021)
M. Kobayashi: “Twin-multistate commutative quaternion Hopfield neural networks”, Neurocomputing, Vol.320, pp.150-156 (2018)

その他の高次元連想記憶モデル

論文

M. Kobayashi: “Group ring-valued Hopfield networks”, Nonlinear Theory and Its Applications, Vol.15, No.4, pp.910-919 (2024)
M. Kobayashi: “Noise robust projection rule for Klein Hopfield neural networks”, Neural Computation, Vol.33, No.6, pp.1698-1716 (2021)
M. Kobayashi: “Synthesis of complex- and hyperbolic-valued Hopfield neural networks”, Neurocomputing, Vol.423, pp.80-88 (2021)
M. Kobayashi: “Split quaternion-valued twin-multistate Hopfield neural networks”, Advances in Applied Clifford Algebras, Vol.30, No.3, Article number 30 (2020)
M. Kobayashi: “Matrix-valued twin-multistate Hopfield neural networks”, Neurocomputing, Vol.397, pp.108-113 (2020)
M. Kobayashi: “Hopfield neural networks using Klein four-group”, Neurocomputing, Vol.387, pp.123-128 (2020)
M. Kobayashi: “O(2)-valued Hopfield neural networks”, IEEE Transactions on Neural Networks and Learning Systems, Vol.30, No.12, pp.3833-3838 (2019)
M. Kobayashi: “Dual-numbered Hopfield neural networks”, IEEJ Transactions on Electrical and Electronic Engineering, Vol.13, No.2, pp.280-284 (2018)
M. Kobayashi: “Multistate vector product Hopfield neural networks”, Neurocomputing, Vol.272, pp.425-431 (2018)
小林正樹: “外積を利用した３次元連想記憶”, 電気学会論文誌C, Vol.124, No.1, pp.150-156 (2004)

高次元 MLP (High-Dimensional MultiLayer Perceptron)

論文

M. Kobayashi: “Reducibilities of hyperbolic neural networks”, Neurocomputing, Vol.378, pp.129-141 (2020)
M. Kobayashi: “Singularities of three-layered complex-valued neural networks with split activation function”, IEEE Transactions on Neural Networks and Learning Systems, Vol.29, No.5, pp.1900-1907 (2018)
M. Kobayashi: “Uniqueness theorem for quaternionic neural networks”, Signal Processing, Vol.136, pp.102-106 (2017)
M. Kobayashi: “Uniqueness theorem of complex-valued neural networks with polar-represented activation function”, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Vol.E98-A, No.9, pp.1937-1943 (2015)
M. Kobayashi, A. Nakajima: “Twisted quaternary neural networks”, IEEJ Transactions on Electrical and Electronic Engineering, Vol.7, No.4, pp.397-401 (2012)
M. Kobayashi: “Exceptional reducibility of complex-valued neural networks”, IEEE Transactions on Neural Networks, Vol.21, No.7, pp.1060-1072 (2010)
小林正樹，村松純，山崎晴明: “行列の線形結合による高次元ニューラルネットワーク”, 電子情報通信学会論文誌 A, Vol.J85-A, No.7, pp.763-770 (2002)
(英訳)
M. Kobayashi, J. Muramatsu, H. Yamazaki: “Construction of high-dimensional neural networks by linear connections of matrices”, Electronics and Communications in Japan, Part3, Vol.86, No.11, pp.38-45 (2003)

実数型連想記憶

論文

M. Kobayashi: “Chaotic pseudo-orthogonalized Hopfield associative memory”, Neurocomputing, Vol.241, pp.147-151 (2017)
S. Furusawa, M. Kobayashi: “Multidirectional associative memory with self-connections”, Nonlinear Theory and Its Applications, Vol.5, No.2, pp.222-234 (2014)
M. Kobayashi, A. Nakajima, M. Kitahara: “Multidirectional associative memory with two hidden layers”, IEEJ Transactions on Electrical and Electronic Engineering, Vol.8, No.3, pp.299-300 (2013)
M. Kobayashi: “Boltzmann machines with identified states”, IEICE Transaction on Fundamentals of Electronics, Communications and Computer Sciences, Vol.E91-A, No.3, pp.887-890 (2008)
小林正樹，服部元信，山崎晴明: “隠れ層をもつ多方向連想メモリ”, 電子情報通信学会論文誌 D-II, Vol.J84-D-II, No.7, pp.1495-1502 (2001)
(英訳)
M. Kobayashi, M. Hattori, H. Yamazaki: “Multidirectional associative memory with a hidden layer”, Systems and Computers in Japan, Vol.33, No.6, pp.1-9 (2002)

その他

論文

T. Nitta, M. Kobayashi, D. P. Mandic: “Hypercomplex widely linear estimation through the lens of underpinning geometry”, IEEE Transactions on Signal Processing, Vol.67, No.15, pp.3985-3994 (2019)