Efficient Training Of Deep Networks Using Guided Spectral Data

Leo Migdal
-
efficient training of deep networks using guided spectral data

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. A collection of research papers on efficient training of DNNs.

If you find some ignored papers, please open issues or pull requests. Scientific Reports volume 14, Article number: 15197 (2024) Cite this article Deep neural networks have achieved remarkable success in various fields. However, training an effective deep neural network still poses challenges. This paper aims to propose a method to optimize the training effectiveness of deep neural networks, with the goal of improving their performance. Firstly, based on the observation that parameters (weights and bias) of deep neural network change in certain rules during training process, the potential of parameters prediction for improving training efficiency is discovered.

Secondly, the potential of parameters prediction to improve the performance of deep neural network by noise injection introduced by prediction errors is revealed. And then, considering the limitations comprehensively, a deep neural network Parameters Linear Prediction method is exploit. Finally, performance and hyperparameter sensitivity validations are carried out on some representative backbones. Experimental results show that by employing proposed Parameters Linear Prediction method, as opposed to SGD, has led to an approximate 1% increase in accuracy for optimal model, along with a reduction of about 0.01... Moreover, it also exhibits stable performance under various hyperparameter settings, shown the effectiveness of the proposed method and validated its capacity in enhancing network’s training efficiency and performance. From epoch-making Convolutional Neural Network (CNN)1 to Deep Belief Network (DBN)2 and various effective and remarkable neural network structures3,4,5,6,7,8,9, Deep-learning Neural Networks (DNN) today has undoubtedly become the mainstream of Machine Learnings, and have...

However, as DNN models grow larger and more complex, training DNN models remains a challenging and time-consuming task, often requiring extensive computational resources and careful hyperparameter tuning. The training effectiveness of DNN models is crucial for their success and widespread adoption. Despite their impressive capabilities, DNN are susceptible to several challenges that can hinder their training and limit their performance. One of the main concerns among these challenges is parameters optimization problem. Lots of remarkable works have been proposed to optimizing this process based on Gradient Descent, among which including the non-adaptive method from SGD to DEMON10,11, and the adaptive method from AdaGrad to AdamW12,13,14,15,16. However, even equipped with the methods above, researchers still have to carefully tuning hyperparameters to struggle for the 1% accuracy improvement, because the better performance of DNN usually comes at the availability of exceptionally...

Moreover, the extensive periods need for DNN model training also prolong the validation cycle of the algorithm, which often result in researchers invest time and effort in vain. Therefore, research on how to improve the training efficiency and performance of DNN is still necessary. R��u��q2�ե.�6���8Ŏɓux�1F�����;���ȭ�Mz�[�pe<\t}�=$��O}�+�Ƶ�wn�P�^w��ñW��2ڲ�7~�7?d �f��#�9���cs$Ԭ]�w ��A�V�)pC�Գ!�Q悩��{u����*<�-ፄ��Bdy�ud��w�AEb�nq )w�}�uՅS������[�w{2W}fz�6˦DF�cg:�t��1ON�/s�;4mu��H��5إ Bp�c��B-1�k������_����v��U�c,c��>D��8�y&�D��P*HM]�%�<�P,�� �"m��&��wq��G7f� ��$�ߊ*S��j_7�i�v�D�B���4�O gjEd?<��t����ym��^�҅d��?�ݔ�� ZKn��j�) ��=����>Nq�H���<�M6���J�N f��s�lѻ�|Ώ?�Dð9i�������FS�W��~��p,Z�JV$�Ȋ�4���H�}D�y��%�|��l�JD8������i'���w���ۜ��2������G�&Q�ꢟ\�-/ �����$�}D �g��X�Y1,h�d#�y cYm��� 5�N5��$��u��Hr'�[j���:���`B%���.�I��Ym~��V�E�U��d_O>�;���T��I ϗ��'Ͻ��~��c�?q9���}8��U�L�ͣ%T~��iT��ܺ�Ւܶ{]���>��+?Ң�q��j�d�ɩ��V�⇼~f��t8m��.{dy � �U��TE�iˑ9�:�^p��`�t���-���,w?� ��Q�҄�/}���O�Yy�6s���)�QRS�m�tD�Ӌ���Qy�U 7�!�l��.�!No8�3�RQ�& ����naҒ��;Ng�����,9ܕD=V���d� ڤv��ƶt"���s���3?�-:$Q߾|��'�,D���[�J6�����kڊL&�N���op=<����8����>��զ ��ӊž��;`��T��)[�� ;�p������O*���C�-�x�I��X�4���cROC�qZ�����e?��b)s���le�~%О:�]�{��1���t�b�t.Xq��J�����$�Fh�+�f}��� z��r�k��j� ��$��U�G��&�Y����n^<��K�A%$�5чW�}QLn�$>W\AbY��?S��7�����~�:�Ըu.�����K"O��;�e6���/~��|�0� ք�ts��{�;Y2:��Ш�aٳ�<���k��jz���+D�n_bPQ^K��a��(�u=�!h;j,?<� B@�-� B�̎�����y#�>lڍ@���;ʭ'X�9����� u[Dg����c�N�l�M�3�ꔺ�U|�_S�/ ��G��FU��钕φ2>��k6��􂄞���竬�1 ����N?=�1���<�ɍj�UK��xgs���I�r=,���#����}r�x���$3� �% �hϻ�Tږ7尗4��^�rx9����... �9�� ?��܁ �?+� u��<�.k��#��`�h�j���g�䯂���g�g�L�sB�N0�sVuiٿ�٘���v?��ճ�%������g�gfvt�@�?�,@K������s�g2'(��2\]������Y�C-�A..�4��n�_}�K��NN�EC���g `� �ފ���9'������g^� .ο햮N���@п.����0?an q��X���9T!��������9���G�������5�/?����wjYW{{Us���{����#�y������Ͼ��Hs������z������[�;�7�����:l\|�<��.�`w��:�X��?_�_vGK��z���}���7L� �s��������x���9�5�%TtY��M�����D��=�@���IOb���*II�;�����6n^��?@�������/��U�aP�;������ �����ӻ��qB,�������y��i�]��g��Zύ������@� ��(l����%��6���B q*m��P�_ ��K_�4{� ao�����m��qK����B{��T�Q�-so!� C��v �I)VƁ^�����!?���Ƙ��I�2�D���ٟ֭���� ��VGЉ��W[����w}�802<4�}�ԻEƒ�F/bN䛲O� �0�^4#ݹ @�/%�ѿ�n���@��o����r���}�����zã�-FI�ݙ�������L͸Y��N��c8}kaBk���ͫ� Q�<�L_���u��^�$��v�oj�nw�X0O��~ϣw��Yx�N'[jp�W� ˎ��]��f�I�ʾ?�� �l��.�a�Q�.��S��/�Θ�v4�H��1�=K�o8���t#{W-H xvZ��R�� �m�K_Ƨo�kN��'��,��Z>�������d/�2B�J$��o����9�W]�����{�-�+R��T�3HUJ�B�< ���}�fN�13Vέ���R>��I��e\q�S /)R���3M*X�F��;�d�(ۧ+E!�ql����כ��n�!!oW[}X� c�4 �ۧ��@ͬ�>L�{o�B�QT?�w 2)e��@�X�<ž��p^�@�PlzY�jU��|����pߘ�'*s�xH���Lҷs����l�3[ ��p@A���|�rXd<||�D��ܧ�`��Rq7I��+��+s��ֿt>"/3if�X���� 11P��5�q�Xnuڅ+<�.V�4�4d�Pg0���O�P6�Ǖ1���A�g��g��N�;�$�*!�W�=� ��� �>1��M���'�b 'y�˥�D9�5���r��B�1Tk��:�f... ��w�@ bG��V�:J�j)ҍ��K����7/�Q�N1�"J=�>��YE1(��V�y��,�������*?�q���j�����8a�v��i�(@�t��O.u�Bf���� ���������R�;>w�$ʯ#��B��� hXs��6�*��R����?z�)?4�X���r�^�� �hN4���t_E0[�T���v�y����_�BIj��GU��g�"�W>��DB�� %�a���{)1c��$��\���Pk��D$��^{}:�R�_B����t*�0jS�D)�]� ?�>�����| ����+ݮ�O$ߋ��Br310���x߲-'���l��F�NΖ�` +x=�#��P�`�$�jl�jbw���m����GB���X� ̾T��8\m"�����`���l�U�p#f�1���*��'�02o�y)�6ith���E=�]�񻛁cM�Lv�!����7�S1�͎X?Z��C��^�(��p�U�T� ��?���!������ ����T�~嘰�x��K����S-��+�@b�A���l��WX�EC��ע�c_=�%:=�s�'򵚅�g�W����;��,��^pZ����k��>���H�W��u�)�z�]/�d7�f/z�|���,�/��ک/���@x�=������m ��߽��]\� 2h�"�Wh��õM��&յ�ڐ�c�i�� ��d��fH�DeY�m���*�sߑh���\����?-5�#��3����Gz��ڐ� �U|y d����� tq&�m���.N��� �~BX���߉�x�����&��������ݲ��ǘU��~�G��ʾw��]��^/�UQ� 8P�;90Г��cK�O. �K�,�W�7�K'���YO�衦 �B�W۝㏿��+ߊ⹐�F���3���+�OkO�����_4���!�ҖN(��Nv��om�K�v3��{�Up���W�4��"o�Og����w;�fG��5�eI���Q�,K�ٽ�֦Oґx��C=sMd����Ax��_�F����՛7��L��"?F���h�Bg��/3��#���Q u�1VT���c��K��kn��1�D�a�>`���9��̟�مV����E/3 &�ޑW����X�9-��G�05���FBh]ѝ��o��4�:x�3�D��\�-�PTS�(����C5Μ}" T��ҵQ>:Q��H_H$j�#)#�`{eqVV��� [���sv�t:޺:Zo&�33Y���M ����\��h{�Ѹ�o��E4��١��O4�/�ʼ� � ".�<�枴w�d��O3/ľ�EY�w�ͼ@j� -, ��b�bȅ�w�j4�qί}�I�b룉B �����5U��a�l\6� B�(ޯr��v�fቹ�@�}e��w7Oܟ$~�/b^��k��������R��.PsV����t� ؤd ^d�1����0�V2�^&b2���q����O�-'��m���jMr^������ �1��ճ�������G�q}_9κ�7J1mmf�MU �\�W;|�R@Y�3Ұد�y|6�QC���߾�$� �yz���Y�|��zCw��J�@�E�ք[el�5 ���B$|@�3}g��/B&k�� �P���1� ��O�em:ڤ4���#�cM�J��{��Y�ER�BhF��ו�$��Bo����BfĀ!1�8]�WJyu�}�Iz׹+�|5e�վ��=��/n��|����m�x�>ບɅM6|�L�������1���4DJ�ۮ.�xV-"��*���`���p�vDQv*� F�<�G�[Қ���4�9�,��C`�*5˒�#͐���5�U��Fl�ԋ�.����}��X��P�I�� > |I�ϰy��-�^ϸ�ld���X��h�ܝ�߼��]eܦ�s��Q�Y,�o�#=2�+��#?^��Cx4u.�"{8�F��}��)�ސ���g���X[���*��1cn=�sBz(�RR�@I/��Q�D��cZ_�n�3>O�3S�֞�)��k�������|��t��'/0�H�O�)��S~�*�]Xٛ�\Z~�Ӏ���"��|2Ӫ��U�:ݧ`����;��M����a�<�: �`(�˲⇹��������7ܓ5B�b�O��(� Tm�\je���y�V��[��|ު�'�R>/W��'3K��Q�A@<����t}�\*�-�5��G2��!����X����7َ�f�gh�1�H(�jvCF��@#��LX��O:X"�8����&�67'�~n�n�^e �#��FM� I뫍w�E^\/Tf�E!�� �f: ��3��[ݫ�?M�cy�ۈ3�hp^mM�\CP�RRz�i E[�\�N��bᱷ�p��S�k���8�*�^�q�o�d�P����Q3ٙ���:Mn��mc�����Lu��cn��$^-�����ϒqߞcsn��c�K�]cZ�te���]��c\�:��}?�w�w%�|s�ޘE"~g_����P��q�;����j��>T �Q5��O�f!��29�%ͨ����N)v�Kv~�� ����6�� ¾zI5+i���\��2ה�v�m?��$�]��...

���)��ҝ���%!��������w�9g��<���u��ֽ�@ZҖ0s������- P�؛;�_���a"@��`kg��]��Q� l�����`Q�.� ���xDDDp�0Gw'�� ���k]66�Z�\���'�� �X;�\�P��=��H�v��0� d5@��ꊀ���o�`��r6�B,@��fX��п ��%�Oip�G.i8� w[@��n`�?;��d���8������ q��:[�I��n�+!G'�� �G� �#�NG�1*HN��<6f�?��G�z�i �p�S�_�#�#�0�8���O,s0�w���?�~$st����3�`�� �N`k3'K(�y��ӝ� �/՛9:B����u�9@p0Ԋ���1��1�5���Ϭ(;X�<��-��s;�ՠ�f��1 3K��` ���R�!C^��T�����o���"�E�������y������� �P�������c�K���g@��E5s�o>f��������u���?�)#��"�`�( �'�0����q[�  ����o��8X����������/�� ����C`���Q��j�eTT������Ђ>� ����.�DZ@h�;��/�����?�2207�'��0��W���5>�&����� ��?�jf'���������ϗ�O���B#�`��3HZ3������l����(�_����<�� �`7���<�B,�69-Q�,�Tΰ���?ȱ�V;?׷��>9tM����2��n\���}n��~S�uk�� �ܙ>ʡ�f`��%\fjb���z[�����y< \E3���Z�|����z��� ���ŗ�%ח�ť#��ERM4iAQU��>S���%�硁���S��MJ��hlF1�g> {t�wS��Z��!x�\z�na�W��yg�Qk�<)�|4ֿ���sK͛G����F���J���Nh���n�W�_�zP#!�l�� �ݮ �WLf�Xy �y)��y6� �����0A���N�� !��璌���RU�C��ץ... �3��d�fܶ)j��s�h��_zz��e(r���ꀂ�"B�,���s��_Hl�[��$c�}��ؤ�!�L��+˞�xb�o��7�޻�ㅲ�:��s��*A�d�RS�\z���R��]ﯿ��D��Zt�;4�]S����:4�H�xy��[�|Lc{�9K�QŃ��������Ʌ�z(xX88է��q >��:��Y����^ 3�k4R�uPjw׾h���֨d�;C� �g �����H�>�yD$ݨ 8a#��y�un{��tq9D5�����u���5{:���${ȸ� ��]"Jβk��j_����ϫ����=SN�r�A�U 3 �y#o���Uꅜ��N��%��Y���qoهu1�,���K��]��j���Li�${P�d3��?�*yF�f����DЀ,֕��N����e��bN9�G;���dW�����I�t����c�4��F9��8��� �LpyC\̊���� �~�μ��.r-?-[����7ö������ISb�K�R�&������iz������^a���F�^��O���g����-谎.;��0҆����*�"���Xw%�@d��8>/��RۣOߜV�"��Ȧ�g��ьxѿ9�b��ܳ�&w�/�\4ʂF:.���F�Pͽ��;EX�N[��3Z��z��d� �?�k}�[�@}�\�Pzǁ%�V�̱l��촧�Lld��D���S�����N��~�I������6�f[>;��� !�E�8�7JxLR�W"����r�(U2�z� �%W���{jn�m4�ʅlj��-�H������6��d��[�R����w/i� ���b���<�`B^WG�|�R�aDi�Ow��(�O����#�&��$o�Z���NP���:-Y��x�^n���>��CB��l#�Ը� �46X�g�(��\��t�Q)� ���1�i��G���^\�S���x�0�|�ҳ�x�Xl�Q�Q�[�n�|�;������_Opܿ$K�^� �ڧ�����破`s���1ژ���p�\ys��G^��ؗ��g�9�h}� B4�LW� ���m�W6���ք<�DLYԀ�oT6u�*[�s��m�$�FXDf�f.�F� }j������i�҆���s[w��P^R+����~]��zV�R�܅��q�6NJ����xcO�� � 1�_0�gcSN�Bzi%s��y��I�3.^b�nL����K��e1�Q������,��=�;=~�)�\ؕ8 �`4� �a"�>����� {2�#~I�ٻ}�M�[���PdL�g g��`��/@�%�����!@K׵[՗����O�O}N������q�s"5��|� sj�r`�d�6�<�X�G$�9�Ot$��S���?C��)���N �,|��d�X�w#uh���?��"�u�V��f@� �%���\K�ˑ��2��2;ZC�� ��Pȃ~��w��0�|=����|ޏڇ��l�O O+�e���b7)�����m}^D�h������b��6��;�_�-7ذ1���n�� [ o�,�J-���|�U���A... �y�F�+�aѫ � 3�#�ܕI�ifn����1��^�L\��=�m����I�ۖ{��5�l��%��(����$֪��(�a���[��b�c�o`~�u?����5�:���;s&�J6R�K]U&hf�v�)�{T擊[`�vi�����/�,{�#�S����P�pn����0*)L�U�eTo�Y�������L�^�E��[H���A����S���~�a�و`���Ȫ-6�U� P�g��.f�o�Y^�.XX�'>Zu��)��/i���n��ͯ��Aε˨ w�vs/b�5��|�A�-o�{9 �2�xT����I����m�b�q���;j��~,���A C����T�z2��~��WI1�^�yIlY��pܫ<=���/:v�8����� f� ������w�b}2\HԞ�Ϲ�\�?�n& ����pj�eP,���� ZI��U\Ǽ��u�fea�'��d�i���>o�dnߑ5~M���~�t��$�ww�4mUG�gh,ܤ(�{�!�U�*��� ŕi���β��OS*�Ppd��9��W�z�<ɠ+�#��k��%���|$F�9�>Th��l=�Ą[�>���his/�f���gÔ��u�a2�VvPj̜}���}X�<ڕ5pfk��g��h� +�?W�4vo(%ƽ>���p�a%4�ln!����ڼm��L�wG�����͍���+�;��7����GQ�^��M��K'�4��W�&1���q�7��:�������P�`�Ɂ�Q@���>��T��X�y���f�=:f�� �_ޫ����e1�Q-��w�6H�أ�'P8I��e4���´��{ (/՘�r�錽Ŵ\�C�zt=/�0:~^��D��H�8�6��ht,���g�v�X��}�a5u}h��� ��^��ZuT���:!1����1η�j:�/Q3��O�*��7p 1������ӅWZ�[lH�:k�ஂ.iFP�qP��c6`��є4R���f�ǯ3<�gc*��v��n��xel��#w��F ��s����/��g�q�����F �vqd�6�O>�.�s1�*^[���tf��z&~#q��_ZR�}�����Նr�aG����G,�W_�*��:�uM�w�㘆�U�P����[qJ譙\�/Ř.ƻ�p�=�p1��rr��^�A�K� #9S���B�Bo˵ݝ�b3lM�"H��d٣ ���Le���M�K#'��ʑ$Q̐�ʄ�x�#�Y<6^voH� ce��5}��&�j��>��c�$?�~�ˬMx��wKI�>��M=�T ��*�� 㸏xPs�=�ɽ&𒫋�e���mN]�1�+DEi�d�݇�KT� w���f�ll[_��J�y��\�*R����ڕN��gU�L���Q)�:JO�*=��NË�`��1�]���j��p�-�T� Y���h��K?a�xᴈg���Ѕ�ͻ}窧Њ`��j��r�>߁ʒmJ��'�Z�.���4<���U��8a���������(~������hM)pr�bbQ-Y8A�W�+��TDw�*�᝟$gU<˒����P����V6�����q�w �U��S�#Pfbl�0�e���%���(З�6y���k�h}�k^���Ȫ��[ γt��H��%I�U ���� "�������M��Hs��|{/(����%�ɫ��띤j����W��� q(�����#�򁶦��ڋ��݁W"Ʀ��X��3 u��?F���A��D曈ww 2����_�p���۩�R�7���8i��;�����x����ÿ�߿��C�͛�J $��ӌ����}--Yv��o�W{a�\c�������5N*���wl��(�M�[�����j16g�"|u]���ٶ�#q��... [1]\orgdivDepartment of Computer Engineering, \orgnameFerdowsi University of Mashhad, \orgaddress\streetAzadi Square, \cityMashhad, \postcode9177948974, \stateKhorasan-Razavi, \countryIran Effective data curation is essential for optimizing neural network training. In this paper, we present the Guided Spectrally Tuned Data Selection (GSTDS) algorithm, which dynamically adjusts the subset of data points used for training using an off-the-shelf pre-trained reference model.

Based on a pre-scheduled filtering ratio, GSTDS effectively reduces the number of data points processed per batch. The proposed method ensures an efficient selection of the most informative data points for training while avoiding redundant or less beneficial computations. Preserving data points in each batch is performed based on spectral analysis. A Fiedler vector-based scoring mechanism removes the filtered portion of the batch, lightening the resource requirements of the learning. The proposed data selection approach not only streamlines the training process but also promotes improved generalization and accuracy. Extensive experiments on standard image classification benchmarks, including CIFAR-10, Oxford-IIIT Pet, and Oxford-Flowers, demonstrate that GSTDS outperforms standard training scenarios and JEST, a recent state-of-the-art data curation method, on several key factors.

It is shown that GSTDS achieves notable reductions in computational requirements, up to four times; without compromising performance. GSTDS exhibits a considerable growth in terms of accuracy under the limited computational resource usage in contrast to other methodologies. These promising results underscore the potential of spectral-based data selection as a scalable solution for resource-efficient deep learning and motivate further exploration into adaptive data curation strategies. You can find the code at https://github.com/rezasharifi82/GSTDS. The quality of training data is a cornerstone of deep learning model performance. While large-scale datasets have propelled advancements in natural language processing ([2]), computer vision ([34]), and multimodal learning ([25, 14]), not all data points contribute equally to model training.

Datasets often contain redundant, irrelevant, or non-informative samples, which increase computational overhead without significantly enhancing learning outcomes. Identifying and selecting the most informative data points is therefore essential to improve the efficiency of the model, reduce resource consumption, and improve generalization capabilities ([16, 29]). Recent advancements in automated data curation, such as active learning, have demonstrated the potential of dynamically selecting valuable data points based on heuristic approaches, which can result in noticeable training efficiency improvement ([28, 4]). Spectral analysis, particularly through the use of the Fiedler vector, has emerged as a robust mechanism for scoring data points within batches. This approach captures the geometric relationships between samples, enabling a principled evaluation of their informativeness ([35, 18]). Furthermore, recent studies have shown that processing data collectively at the batch level, rather than individually, significantly improves the assessment of relative informativeness, outperforming traditional methods ([9]).

A key challenge in data curation lies in balancing the rigor of sample selection with the model’s accuracy. By integrating spectral scoring with a pre-scheduled filtering ratio, we can achieve precise control over computational costs while maintaining model performance. To ensure resource allocation matches the training process dynamics, we smoothly increase filtering ratio to effectively work with larger batch sizes and enhance final stages of learning ([31]).

People Also Search

ArXivLabs Is A Framework That Allows Collaborators To Develop And

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add v...

If You Find Some Ignored Papers, Please Open Issues Or

If you find some ignored papers, please open issues or pull requests. Scientific Reports volume 14, Article number: 15197 (2024) Cite this article Deep neural networks have achieved remarkable success in various fields. However, training an effective deep neural network still poses challenges. This paper aims to propose a method to optimize the training effectiveness of deep neural networks, with ...

Secondly, The Potential Of Parameters Prediction To Improve The Performance

Secondly, the potential of parameters prediction to improve the performance of deep neural network by noise injection introduced by prediction errors is revealed. And then, considering the limitations comprehensively, a deep neural network Parameters Linear Prediction method is exploit. Finally, performance and hyperparameter sensitivity validations are carried out on some representative backbones...

However, As DNN Models Grow Larger And More Complex, Training

However, as DNN models grow larger and more complex, training DNN models remains a challenging and time-consuming task, often requiring extensive computational resources and careful hyperparameter tuning. The training effectiveness of DNN models is crucial for their success and widespread adoption. Despite their impressive capabilities, DNN are susceptible to several challenges that can hinder the...

Moreover, The Extensive Periods Need For DNN Model Training Also

Moreover, the extensive periods need for DNN model training also prolong the validation cycle of the algorithm, which often result in researchers invest time and effort in vain. Therefore, research on how to improve the training efficiency and performance of DNN is still necessary. R��u��q2�ե.�6���8Ŏɓux�1F�����;���ȭ�Mz�[�pe<\t}�=$��O}�+�Ƶ�wn�P�^w��ñW��2ڲ�7~�7?d �f��#�9���cs$Ԭ]�w ��A...