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| Presentation | 2022-01-21 09:25 Approximate Eigenvalue Decomposition of Fisher Information Matrix for Simple ReLU Networks Yoshinari Takeishi, Masazumi Iida, Jun'ichi Takeuchi (Kyushu Univ.)  IT2021-68 SIP2021-76 RCS2021-236 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (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 $W$. |
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| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | machine learning / neural networks / Fisher information / / / / / | |
| Reference Info. | IEICE Tech. Rep., vol. 121, no. 327, IT2021-68, pp. 225-230, Jan. 2022. | |
| Paper # | IT2021-68 | |
| Date of Issue | 2022-01-13 (IT, SIP, RCS) | |
| ISSN | Online edition: ISSN 2432-6380 | |
| Copyright and reproduction |
All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034) | |
| Download PDF | IT2021-68 SIP2021-76 RCS2021-236 |
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| Conference Information | |
| Committee | RCS SIP IT |
| Conference Date | 2022-01-20 - 2022-01-21 |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Online |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Paper Information | |
| Registration To | IT |
| Conference Code | 2022-01-RCS-SIP-IT |
| Language | English (Japanese title is available) |
| 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 |
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| 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.) |
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| Speaker | Author-1 |
| Date Time | 2022-01-21 09:25:00 |
| Presentation Time | 25 minutes |
| Registration for | IT |
| Paper # | IT2021-68, SIP2021-76, RCS2021-236 |
| Volume (vol) | vol.121 |
| Number (no) | no.327(IT), no.328(SIP), no.329(RCS) |
| Page | pp.225-230 |
| #Pages | 6 |
| Date of Issue | 2022-01-13 (IT, SIP, RCS) |
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