| Presentation | 2022-01-21 Approximate Eigenvalue Decomposition of Fisher Information Matrix for Simple ReLU Networks Yoshinari Takeishi, Masazumi Iida, Jun'ichi Takeuchi, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | We argue the Fisher information matrix (FIM) of one hidden layer networks with the ReLU activation function. Let $W$ denote the $d times p$ weight matrix from the $d$-dimensional input to the inner layer consisting of $p$ neurons, and $v$ the $p$-dimensional weight vector from the inner layer to the scalar output. We focus on the FIM of $v$, which we denote as $I$. Then, under certain conditions, the following approximately holds. 1) There are three major clusters in the eigenvalue distribution. 2) Since $I$ is non-negative owing to the ReLU, the first eigenvalue is the Perron-Frobenius eigenvalue. 3) For the cluster of the next maximum values, the eigenspace is spanned by the row vectors of $W$. 4) For the third cluster of the eigenvalues, the direct sum of the eigenspace of the cluster and the eigenspace of the first eigenvalue is spanned by the set of each Hadamard product of a pair of row vectors of $W$. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | machine learning / neural networks / Fisher information |
| Paper # | IT2021-68,SIP2021-76,RCS2021-236 |
| Date of Issue | 2022-01-13 (IT, SIP, RCS) |
| Conference Information | |
| Committee | RCS / SIP / IT |
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| Conference Date | 2022/1/20(2days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Online |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Chair | Eiji Okamoto(Nagoya Inst. of Tech.) / Yukihiro Bandou(NTT) / Tadashi Wadayama(Nagoya Inst. of Tech.) |
| Vice Chair | Toshihiko Nishimura(Hokkaido Univ.) / Tomoya Tandai(Toshiba) / Fumihide Kojima(NICT) / Toshihisa Tanaka(Tokyo Univ. Agri.&Tech.) / Takayuki Nakachi(Ryukyu Univ.) / Tetsuya Kojima(Tokyo Kosen) |
| Secretary | Toshihiko Nishimura(NEC) / Tomoya Tandai(Panasonic) / Fumihide Kojima(Xiaomi) / Toshihisa Tanaka(Takushoku Univ.) / Takayuki Nakachi(Tokyo Univ. Agri.&Tech.) / Tetsuya Kojima(Saitamai Univ.) |
| Assistant | Koichi Adachi(Univ. of Electro-Comm.) / Osamu Nakamura(Sharp) / Manabu Sakai(Mitsubishi Electric) / Masashi Iwabuchi(NTT) / Tatsuki Okuyama(NTT DOCOMO) / Taichi Yoshida(UEC) / Seisuke Kyochi(Univ. of Kitakyushu) / Masanori Hirotomo(Saga Univ.) |
| Paper Information | |
| Registration To | Technical Committee on Radio Communication Systems / Technical Committee on Signal Processing / Technical Committee on Information Theory |
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| Language | ENG-JTITLE |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Approximate Eigenvalue Decomposition of Fisher Information Matrix for Simple ReLU Networks |
| Sub Title (in English) | |
| Keyword(1) | machine learning |
| Keyword(2) | neural networks |
| Keyword(3) | Fisher information |
| 1st Author's Name | Yoshinari Takeishi |
| 1st Author's Affiliation | Kyushu University(Kyushu Univ.) |
| 2nd Author's Name | Masazumi Iida |
| 2nd Author's Affiliation | Kyushu University(Kyushu Univ.) |
| 3rd Author's Name | Jun'ichi Takeuchi |
| 3rd Author's Affiliation | Kyushu University(Kyushu Univ.) |
| Date | 2022-01-21 |
| Paper # | IT2021-68,SIP2021-76,RCS2021-236 |
| Volume (vol) | vol.121 |
| Number (no) | IT-327,SIP-328,RCS-329 |
| Page | pp.pp.225-230(IT), pp.225-230(SIP), pp.225-230(RCS), |
| #Pages | 6 |
| Date of Issue | 2022-01-13 (IT, SIP, RCS) |