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models2018-10-18T04:40:33+00:00monthlyhttps://calculatedcontent.com/2018/06/05/self-regularization-in-deep-neural-networks-a-preview/https://calculatedcontent.com/wp-content/uploads/2018/06/alexnet-small.pngalexnet-smallhttps://calculatedcontent.com/wp-content/uploads/2018/06/screen-shot-2018-06-05-at-4-43-18-pm.pngRMT applied to AlexNethttps://calculatedcontent.com/wp-content/uploads/2018/06/screen-shot-2018-06-05-at-4-41-01-pm.pngLeNet5: Bulk+Spikeshttps://calculatedcontent.com/wp-content/uploads/2018/06/screen-shot-2018-06-05-at-4-39-46-pm-e1528242481295.pngHeavy Tailed Self RegularizationEmpirical Spectral Density for AlexNet, FC2https://calculatedcontent.com/wp-content/uploads/2018/06/5-phases.png5+1 Phases of Learninghttps://calculatedcontent.com/wp-content/uploads/2018/06/5-phases.jpg5-phases2018-10-04T16:32:55+00:00monthlyhttps://calculatedcontent.com/2018/09/09/power-laws-in-deep-learning/https://calculatedcontent.com/wp-content/uploads/2018/09/even-more-alphas.pngeven-more-alphashttps://calculatedcontent.com/wp-content/uploads/2018/09/screen-shot-2018-09-13-at-12-37-26-pm.pngScreen Shot 2018-09-13 at 12.37.26 PMhttps://calculatedcontent.com/wp-content/uploads/2018/09/screen-shot-2018-09-09-at-8-58-26-pm1.pngScreen Shot 2018-09-09 at 8.58.26 PMhttps://calculatedcontent.com/wp-content/uploads/2018/09/screen-shot-2018-09-09-at-8-58-26-pm.pngScreen Shot 2018-09-09 at 8.58.26 PMhttps://calculatedcontent.com/wp-content/uploads/2018/09/screen-shot-2018-09-02-at-9-08-03-pm.pngScreen Shot 2018-09-02 at 9.08.03 PMhttps://calculatedcontent.com/wp-content/uploads/2018/09/inception-l1.pnginception-l1https://calculatedcontent.com/wp-content/uploads/2018/09/screen-shot-2018-09-01-at-9-50-07-am.pngScreen Shot 2018-09-01 at 9.50.07 AMhttps://calculatedcontent.com/wp-content/uploads/2018/09/alexnet-log-log-fc31.pngalexnet-log-log-fc3https://calculatedcontent.com/wp-content/uploads/2018/09/alexnet-log-log-fc3.pngalexnet-log-log-fc3https://calculatedcontent.com/wp-content/uploads/2018/09/power-law-exponents.pngpower-law-exponents2019-04-22T20:57:01+00:00monthlyhttps://calculatedcontent.com/2018/09/14/power-laws-in-deep-learning-2-universality/https://calculatedcontent.com/wp-content/uploads/2018/09/alpha-mu-plot-m-fixed1.pngalpha-mu-plot-M-fixedhttps://calculatedcontent.com/wp-content/uploads/2018/09/alpha-mu-plot-n-fixed.pngalpha-mu-plot-N-fixedhttps://calculatedcontent.com/wp-content/uploads/2018/09/alpha-mu-plot-m-fixed.pnghttps://calculatedcontent.com/wp-content/uploads/2018/09/screen-shot-2018-09-06-at-11-10-53-am.pngFInite Size Effects on Fat Tailed ESDhttps://calculatedcontent.com/wp-content/uploads/2018/09/screen-shot-2018-09-11-at-1-08-15-pm.pngAlexNet FC3 Log-Log Histogram of ESDhttps://calculatedcontent.com/wp-content/uploads/2018/09/screen-shot-2018-09-11-at-1-06-45-pm.pngAlexNet FC3 Log-Log Histogram of the ESDhttps://calculatedcontent.com/wp-content/uploads/2018/09/screen-shot-2018-09-11-at-1-01-41-pm.pngAlexNet FC3 Empirical Spectral Densityhttps://calculatedcontent.com/wp-content/uploads/2018/09/guassian_random_mats.pngGaussian Random MatricesDifferent Q valueshttps://calculatedcontent.com/wp-content/uploads/2018/09/alexnet-log-log-fc3-overlay.pngalexnet-log-log-fc3-overlayhttps://calculatedcontent.com/wp-content/uploads/2018/09/screen-shot-2018-09-02-at-9-55-29-pm.pngScreen Shot 2018-09-02 at 9.55.29 PM2018-10-04T16:27:41+00:00monthlyhttps://calculatedcontent.com/2018/09/21/rank-collapse-in-deep-learning/https://calculatedcontent.com/wp-content/uploads/2018/09/even-more-rank-loss.pngeven-more-rank-losshttps://calculatedcontent.com/wp-content/uploads/2018/09/log-min-nu-pytorch-conv2d2.pnglog-min-nu-pytorch-conv2dhttps://calculatedcontent.com/wp-content/uploads/2018/09/log-min-nu-pytorch-conv2d1.pnglog-min-nu-pytorch-conv2dhttps://calculatedcontent.com/wp-content/uploads/2018/09/log-min-nu-pytorch-conv2d.pnglog-min-nu-pytorch-conv2dhttps://calculatedcontent.com/wp-content/uploads/2018/09/screen-shot-2018-09-22-at-10-17-40-am-e1537639395972.pngEffect of L2 Regularization on the eigenvalues of FC1https://calculatedcontent.com/wp-content/uploads/2018/09/screen-shot-2018-09-22-at-10-17-45-am.pngEffect of L2 Regularization on the eigenvalues of FC1https://calculatedcontent.com/wp-content/uploads/2018/09/screen-shot-2018-09-21-at-1-53-47-pm.pngMini AlexNetA Mini version of AlexNet, trained on CIFAR10, used to explore regularization and rank collapse in DNNs.https://calculatedcontent.com/wp-content/uploads/2018/09/fc1-rank-collapse2.pngRank Collapse in Mini AlexNet FC1Rank Collapse Induced in a Mini AlexNet model, caused by adding weight norm constraints of 0.001https://calculatedcontent.com/wp-content/uploads/2018/09/fc1-rank-collapse1.pnghttps://calculatedcontent.com/wp-content/uploads/2018/09/fc1-rank-collapse.png2018-10-04T16:26:20+00:00monthlyhttps://calculatedcontent.com/2015/01/16/the-bitcoin-crash-and-how-nature-works/https://calculatedcontent.com/wp-content/uploads/2015/01/nikkei.pngnikkeihttps://calculatedcontent.com/wp-content/uploads/2015/01/sp500_rg.pngsp500_rgDiscrete Scale Invariance in the SP500 Crash of 1987https://calculatedcontent.com/wp-content/uploads/2015/01/rg1.pngrghttps://calculatedcontent.com/wp-content/uploads/2015/01/rg.pngrghttps://calculatedcontent.com/wp-content/uploads/2015/01/power_law1.pngpower_lawhttps://calculatedcontent.com/wp-content/uploads/2015/01/power_law.pngpower_lawhttps://calculatedcontent.com/wp-content/uploads/2015/01/power_law.pngpower_lawhttps://calculatedcontent.com/wp-content/uploads/2015/01/coindesk-bpi-chart.pngcoindesk-bpi-chart2018-04-02T00:22:45+00:00monthlyhttps://calculatedcontent.com/2017/12/24/capsule-networks-a-video-presentation/https://calculatedcontent.com/wp-content/uploads/2017/12/screen-shot-2017-12-24-at-10-43-47-pm.pngScreen Shot 2017-12-24 at 10.43.47 PM2017-12-25T06:48:25+00:00monthlyhttps://calculatedcontent.com/2015/12/28/when-regularization-fails/https://calculatedcontent.com/wp-content/uploads/2015/12/4418437-glass-saucepan-on-the-gas-stove-close-up-stock-photo-water-boiling-pot.jpg4418437-Glass-saucepan-on-the-gas-stove-close-up-Stock-Photo-water-boiling-pothttps://calculatedcontent.com/wp-content/uploads/2015/12/screen-shot-2015-12-27-at-11-16-54-pm.pngScreen Shot 2015-12-27 at 11.16.54 PMhttps://calculatedcontent.com/wp-content/uploads/2015/12/screen-shot-2015-12-27-at-10-02-54-pm.pngScreen Shot 2015-12-27 at 10.02.54 PMhttps://calculatedcontent.com/wp-content/uploads/2015/12/screen-shot-2015-12-21-at-1-58-00-pm.pngScreen Shot 2015-12-21 at 1.58.00 PMhttps://calculatedcontent.com/wp-content/uploads/2015/12/matrix.jpgmatrixhttps://calculatedcontent.com/wp-content/uploads/2015/12/luke_and_yoda1.jpegluke_and_yodahttps://calculatedcontent.com/wp-content/uploads/2015/12/luke_and_yoda.jpegluke_and_yodais stablehttps://calculatedcontent.com/wp-content/uploads/2015/12/snowflake.jpegsnowflakehttps://calculatedcontent.com/wp-content/uploads/2015/12/bigfoot.jpegbigfoothttps://calculatedcontent.com/wp-content/uploads/2015/12/it_exists1.jpgit_exists2017-12-06T07:51:57+00:00monthlyhttps://calculatedcontent.com/2016/10/21/improving-rbms-with-physical-chemistry/https://calculatedcontent.com/wp-content/uploads/2016/10/screen-shot-2016-10-21-at-11-15-50-pm.pngscreen-shot-2016-10-21-at-11-15-50-pmOmniglot Datasethttps://calculatedcontent.com/wp-content/uploads/2016/10/screen-shot-2016-10-21-at-8-43-19-am.pngscreen-shot-2016-10-21-at-8-43-19-amAll RPA-like Diagrams, to infinite orderhttps://calculatedcontent.com/wp-content/uploads/2016/10/screen-shot-2016-10-21-at-8-42-41-am.pngscreen-shot-2016-10-21-at-8-42-41-amFourth Order Correctionshttps://calculatedcontent.com/wp-content/uploads/2016/10/screen-shot-2016-10-21-at-8-41-56-am.pngscreen-shot-2016-10-21-at-8-41-56-amFourth Order Correctionshttps://calculatedcontent.com/wp-content/uploads/2016/10/screen-shot-2016-10-21-at-8-39-56-am.pngscreen-shot-2016-10-21-at-8-39-56-amThird Order Correctionshttps://calculatedcontent.com/wp-content/uploads/2016/10/vortices.gifvorticeshttps://calculatedcontent.com/wp-content/uploads/2016/10/g35.gifg35https://calculatedcontent.com/wp-content/uploads/2016/10/rbm-nodes.pngrbm-nodeshttps://calculatedcontent.com/wp-content/uploads/2016/10/screen-shot-2016-10-07-at-11-18-29-pm.pngscreen-shot-2016-10-07-at-11-18-29-pm2017-11-12T01:16:51+00:00monthlyhttps://calculatedcontent.com/2017/06/16/normalization-in-deep-learning/https://calculatedcontent.com/wp-content/uploads/2017/06/screen-shot-2017-06-16-at-8-08-30-pm.pngScreen Shot 2017-06-16 at 8.08.30 PMTensorFlow implementation of Weight Initializationhttps://calculatedcontent.com/wp-content/uploads/2017/06/screen-shot-2017-06-16-at-7-40-40-pm.pngScreen Shot 2017-06-16 at 7.40.40 PMhttps://calculatedcontent.com/wp-content/uploads/2017/06/screen-shot-2017-06-16-at-7-39-49-pm.pngScreen Shot 2017-06-16 at 7.39.49 PMhttps://calculatedcontent.com/wp-content/uploads/2017/06/batchnorm2-e1497643748774.pngBatch Normalizationhttps://calculatedcontent.com/wp-content/uploads/2017/06/screen-shot-2017-06-16-at-12-52-57-pm.pngScreen Shot 2017-06-16 at 12.52.57 PMhttps://calculatedcontent.com/wp-content/uploads/2017/06/mlp1.pngMLPhttps://calculatedcontent.com/wp-content/uploads/2017/06/mlp.pngMLPhttps://calculatedcontent.com/wp-content/uploads/2017/06/screen-shot-2017-06-14-at-11-31-33-pm.pngScreen Shot 2017-06-14 at 11.31.33 PMhttps://calculatedcontent.com/wp-content/uploads/2017/06/screen-shot-2017-06-14-at-10-57-33-am1.pngScreen Shot 2017-06-14 at 10.57.33 AMhttps://calculatedcontent.com/wp-content/uploads/2017/06/screen-shot-2017-06-14-at-5-05-10-pm.pngScreen Shot 2017-06-14 at 5.05.10 PM2018-03-30T09:49:10+00:00monthlyhttps://calculatedcontent.com/2017/07/04/what-is-free-energy-part-i-hinton-helmholtz-and-legendre/https://calculatedcontent.com/wp-content/uploads/2017/07/legendre-transform2.pnglegendre-transformhttps://calculatedcontent.com/wp-content/uploads/2017/07/legendre-transform1.pnglegendre-transformhttps://calculatedcontent.com/wp-content/uploads/2017/07/4theagle.png4thEaglehttps://calculatedcontent.com/wp-content/uploads/2017/07/legendre-transform.pnglegendre-transformhttps://calculatedcontent.com/wp-content/uploads/2017/07/440px-thermodynamic_square-svg.png440px-Thermodynamic_square.svghttps://calculatedcontent.com/wp-content/uploads/2017/07/auto-encoder1.pngauto-encoderhttps://calculatedcontent.com/wp-content/uploads/2017/07/auto-encoder.pngauto-encoderhttps://calculatedcontent.com/wp-content/uploads/2017/07/vae-algo.pngVAE-algohttps://calculatedcontent.com/wp-content/uploads/2017/07/screen-shot-2017-07-02-at-8-24-50-pm.pngScreen Shot 2017-07-02 at 8.24.50 PMhttps://calculatedcontent.com/wp-content/uploads/2017/07/k-ldivergencethekullbacklieblerdivergenceisameasureofdisparitybetween.jpgK-L+Divergence+The+Kullback+Liebler+Divergence+is+a+measure+of+disparity+between.P: the true model (the probability density function that the data are drawn from) and. Q:the approximating model(s) ie. the candidate models. The AIC is derived from the KL-divergence. It tries to select for the model Q that minimizes the KL-divergence. Because the P is fixed (ie. it is dependant on actual data) the AIC is derived only from the component of the KL-divergence relating to q (ie. integral of -p(x) log q(x)) As the KL divergence can’t be less than zero, maximizing this will minimize the KL-divergence. Taken from Wikipedia page ‘Kullback-Liebler Divergence.2017-10-02T08:16:14+00:00monthlyhttps://calculatedcontent.com/2012/12/28/foundations-theory-of-compressed-sensing/https://calculatedcontent.com/wp-content/uploads/2012/12/o_30.pngSpectrum of a Gaussian Random Matrixhttps://www.wolfram.com/language/11/random-matrices/spectral-density-of-a-matrix.html?product=mathematicahttps://calculatedcontent.com/wp-content/uploads/2012/12/obama-and-mckayla.jpgObama-and-McKaylahttps://calculatedcontent.com/wp-content/uploads/2012/12/signal-domain.pngsignal-domainhttps://calculatedcontent.com/wp-content/uploads/2012/12/l1-minimization.jpgNoisy Time Series III: Theoretical Foundations of Compressed Sensinghttps://calculatedcontent.com/wp-content/uploads/2012/12/chirps-ex.pngchirps-exhttps://calculatedcontent.com/wp-content/uploads/2012/12/chirps-real.pngchirps-realhttps://calculatedcontent.com/wp-content/uploads/2012/12/chirps1.pngchirpshttps://calculatedcontent.com/wp-content/uploads/2012/12/chirps.pngchirpshttps://calculatedcontent.com/wp-content/uploads/2012/12/chirplet-b2.pngchirplet-bhttps://calculatedcontent.com/wp-content/uploads/2012/12/chirplet-b1.pngchirplet-b2019-10-29T19:40:45+00:00monthlyhttps://calculatedcontent.com/2017/06/26/interview-with-a-data-scientist/https://calculatedcontent.com/wp-content/uploads/2017/06/screen-shot-2017-06-26-at-8-50-39-am.pngScreen Shot 2017-06-26 at 8.50.39 AM2017-06-28T06:50:57+00:00monthlyhttps://calculatedcontent.com/2017/02/24/why-deep-learning-works-3-backprop-minimizes-the-free-energy/https://calculatedcontent.com/wp-content/uploads/2017/02/screen-shot-2017-02-05-at-8-26-58-pm.pngscreen-shot-2017-02-05-at-8-26-58-pm2017-06-25T00:23:02+00:00monthlyhttps://calculatedcontent.com/2017/01/05/foundations-mean-field-boltzmann-machines-1987/2017-01-20T16:34:52+00:00monthlyhttps://calculatedcontent.com/2016/09/10/on-cheap-learning-partition-functions-and-rbms/2016-10-28T23:39:05+00:00monthlyhttps://calculatedcontent.com/2016/09/24/mmds-video-presentation/2021-10-03T13:29:06+00:00monthlyhttps://calculatedcontent.com/2015/03/14/convex-relaxations-of-transductive-learning/https://calculatedcontent.com/wp-content/uploads/2015/03/screen-shot-2015-03-15-at-1-20-41-am.pngScreen Shot 2015-03-15 at 1.20.41 AMhttps://calculatedcontent.com/wp-content/uploads/2015/03/642f3-backsquat.jpg642f3-backsquat2016-07-31T08:50:31+00:00monthlyhttps://calculatedcontent.com/2016/06/20/why-deep-learning-works-iii-a-preview/2016-09-03T14:43:32+00:00monthlyhttps://calculatedcontent.com/2016/06/08/tensorflow-reproductions-big-deep-simple-mnist/2016-06-14T16:38:32+00:00monthlyhttps://calculatedcontent.com/2016/02/17/ask-me-anything-about-machine-learning/https://calculatedcontent.com/wp-content/uploads/2016/02/ask-me2.jpgask-me2https://calculatedcontent.com/wp-content/uploads/2016/02/ask-me1.jpgask-me1https://calculatedcontent.com/wp-content/uploads/2016/02/ask-me.jpgask-me2017-06-24T18:46:03+00:00monthlyhttps://calculatedcontent.com/2014/11/01/machine-learning-with-missing-labels-part-3-experiments/https://calculatedcontent.com/wp-content/uploads/2014/11/screen-shot-2014-10-31-at-11-32-54-pm.pngScreen Shot 2014-10-31 at 11.32.54 PMhttps://calculatedcontent.com/wp-content/uploads/2014/11/screen-shot-2014-10-31-at-11-31-29-pm.pngScreen Shot 2014-10-31 at 11.31.29 PMhttps://calculatedcontent.com/wp-content/uploads/2014/11/screen-shot-2014-10-31-at-11-15-22-pm.pngScreen Shot 2014-10-31 at 11.15.22 PMhttps://calculatedcontent.com/wp-content/uploads/2014/11/screen-shot-2014-10-31-at-10-55-26-pm.pngScreen Shot 2014-10-31 at 10.55.26 PMhttps://calculatedcontent.com/wp-content/uploads/2014/11/screen-shot-2014-10-31-at-10-53-09-pm.pngScreen Shot 2014-10-31 at 10.53.09 PMhttps://calculatedcontent.com/wp-content/uploads/2014/11/screen-shot-2014-10-31-at-9-45-18-pm.pngScreen Shot 2014-10-31 at 9.45.18 PMhttps://calculatedcontent.com/wp-content/uploads/2014/11/screen-shot-2014-10-31-at-8-54-24-pm.pngScreen Shot 2014-10-31 at 8.54.24 PMhttps://calculatedcontent.com/wp-content/uploads/2014/11/screen-shot-2014-10-31-at-8-52-20-pm.pngScreen Shot 2014-10-31 at 8.52.20 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