{ "

Evidential Deep Learning to Quantify Classification Uncertainty Experiment

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This trains a model based on Evidential Deep Learning to Quantify Classification Uncertainty on MNIST dataset.

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\u5206\u985e\u4e0d\u78ba\u5b9a\u6027\u5b9f\u9a13\u3092\u5b9a\u91cf\u5316\u3059\u308b\u305f\u3081\u306e\u30a8\u30d3\u30c7\u30f3\u30b7\u30e3\u30eb\u30c7\u30a3\u30fc\u30d7\u30e9\u30fc\u30cb\u30f3\u30b0

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\u3053\u308c\u306b\u3088\u308a\u3001\u30a8\u30d3\u30c7\u30f3\u30b7\u30e3\u30eb\u30c7\u30a3\u30fc\u30d7\u30e9\u30fc\u30cb\u30f3\u30b0\u306b\u57fa\u3065\u304f\u30e2\u30c7\u30eb\u3092\u30c8\u30ec\u30fc\u30cb\u30f3\u30b0\u3057\u3066\u3001MNIST\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306e\u5206\u985e\u306e\u4e0d\u78ba\u5b9f\u6027\u3092\u5b9a\u91cf\u5316\u3057\u307e\u3059\u3002

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Configurations

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We use _^_0_^_ configurations.

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\u30b3\u30f3\u30d5\u30a3\u30ae\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3

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_^_0_^_\u69cb\u6210\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002

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LeNet based model fro MNIST classification

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MINST \u5206\u985e\u7528\u306e Lenet \u30d9\u30fc\u30b9\u306e\u30e2\u30c7\u30eb

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Create model

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\u30e2\u30c7\u30eb\u4f5c\u6210

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Initialization

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\u521d\u671f\u5316

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KL Divergence Loss Coefficient Schedule

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KL \u30c0\u30a4\u30d0\u30fc\u30b8\u30a7\u30f3\u30b9\u640d\u5931\u4fc2\u6570\u30b9\u30b1\u30b8\u30e5\u30fc\u30eb

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Training or validation step

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\u30c8\u30ec\u30fc\u30cb\u30f3\u30b0\u307e\u305f\u306f\u691c\u8a3c\u30b9\u30c6\u30c3\u30d7

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'loss_func': 'max_likelihood_loss', 'loss_func': 'cross_entropy_bayes_risk',

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'loss_func': 'max_likelihood_loss', 'loss_func': 'cross_entropy_bayes_risk',

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Cross Entropy Bayes Risk

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\u30af\u30ed\u30b9\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u30d9\u30a4\u30ba\u30ea\u30b9\u30af

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KL Divergence regularization

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KL \u30c0\u30a4\u30d0\u30fc\u30b8\u30a7\u30f3\u30b9\u6b63\u5247\u5316

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Maximum Likelihood Loss

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\u6700\u5927\u78ba\u7387\u640d\u5931

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Squared Error Bayes Risk

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\u4e8c\u4e57\u8aa4\u5dee\u30d9\u30a4\u30ba\u30ea\u30b9\u30af

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Stats module for tracking

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\u8ffd\u8de1\u7528\u7d71\u8a08\u30e2\u30b8\u30e5\u30fc\u30eb

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_^_0_^_ max-pooling

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_^_0_^_\u30de\u30c3\u30af\u30b9\u30d7\u30fc\u30ea\u30f3\u30b0

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Apply dropout

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\u30c9\u30ed\u30c3\u30d7\u30a2\u30a6\u30c8\u3092\u9069\u7528

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Apply final layer and return

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\u6700\u7d42\u30ec\u30a4\u30e4\u30fc\u3092\u9069\u7528\u3057\u3066\u623b\u308b

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Apply first convolution and max pooling. The result has shape _^_0_^_

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\u6700\u521d\u306e\u30b3\u30f3\u30dc\u30ea\u30e5\u30fc\u30b7\u30e7\u30f3\u3068\u30de\u30c3\u30af\u30b9\u30d7\u30fc\u30ea\u30f3\u30b0\u3092\u9069\u7528\u3057\u307e\u3059\u3002\u7d50\u679c\u306b\u306f\u5f62\u304c\u3042\u308a\u307e\u3059 _^_0_^_

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Apply hidden layer

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\u96a0\u3057\u30ec\u30a4\u30e4\u30fc\u3092\u9069\u7528

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Apply second convolution and max pooling. The result has shape _^_0_^_

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2 \u56de\u76ee\u306e\u30b3\u30f3\u30dc\u30ea\u30e5\u30fc\u30b7\u30e7\u30f3\u3068\u6700\u5927\u30d7\u30fc\u30ea\u30f3\u30b0\u3092\u9069\u7528\u3057\u307e\u3059\u3002\u7d50\u679c\u306b\u306f\u5f62\u304c\u3042\u308a\u307e\u3059 _^_0_^_

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Calculate KL Divergence regularization loss

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KL \u30c0\u30a4\u30d0\u30fc\u30b8\u30a7\u30f3\u30b9\u6b63\u5247\u5316\u640d\u5931\u306e\u8a08\u7b97

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Calculate gradients

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\u52fe\u914d\u306e\u8a08\u7b97

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Calculate loss

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\u640d\u5931\u306e\u8a08\u7b97

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Clear the gradients

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\u30b0\u30e9\u30c7\u30fc\u30b7\u30e7\u30f3\u3092\u30af\u30ea\u30a2

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Create a relative piecewise schedule

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\u76f8\u5bfe\u7684\u306a\u533a\u5206\u7684\u30b9\u30b1\u30b8\u30e5\u30fc\u30eb\u306e\u4f5c\u6210

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Create configurations

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\u69cb\u6210\u306e\u4f5c\u6210

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Create experiment

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\u5b9f\u9a13\u3092\u4f5c\u6210

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Dropout

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\u30c9\u30ed\u30c3\u30d7\u30a2\u30a6\u30c8

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Dropout for the hidden layer

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\u96a0\u3057\u30ec\u30a4\u30e4\u30fc\u306e\u30c9\u30ed\u30c3\u30d7\u30a2\u30a6\u30c8

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Final fully connected layer to output evidence for _^_0_^_ classes. The ReLU or Softplus activation is applied to this outside the model to get the non-negative evidence

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_^_0_^_\u30af\u30e9\u30b9\u306e\u30a8\u30d3\u30c7\u30f3\u30b9\u3092\u51fa\u529b\u3059\u308b\u305f\u3081\u306e\u6700\u5f8c\u306e\u5b8c\u5168\u63a5\u7d9a\u30ec\u30a4\u30e4\u30fc\u3002\u3053\u308c\u306bReLU\u307e\u305f\u306fSoftplus\u30a2\u30af\u30c6\u30a3\u30d9\u30fc\u30b7\u30e7\u30f3\u3092\u30e2\u30c7\u30eb\u5916\u3067\u9069\u7528\u3059\u308b\u3068\u3001\u975e\u9670\u6027\u30a8\u30d3\u30c7\u30f3\u30b9\u304c\u5f97\u3089\u308c\u307e\u3059

\u3002\n", "

First _^_0_^_ convolution layer

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_^_0_^_\u6700\u521d\u306e\u7573\u307f\u8fbc\u307f\u5c64

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First fully-connected layer that maps to _^_0_^_ features

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\u30d5\u30a3\u30fc\u30c1\u30e3\u306b\u30de\u30c3\u30d4\u30f3\u30b0\u3055\u308c\u308b\u6700\u521d\u306e\u5b8c\u5168\u63a5\u7d9a\u30ec\u30a4\u30e4\u30fc _^_0_^_

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Flatten the tensor to shape _^_0_^_

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\u30c6\u30f3\u30bd\u30eb\u3092\u5e73\u3089\u306b\u3057\u3066\u5f62\u3092\u6574\u3048\u308b _^_0_^_

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Get evidences _^_0_^_

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\u8a3c\u62e0\u3092\u53d6\u5f97 _^_0_^_

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Get model outputs

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\u30e2\u30c7\u30eb\u51fa\u529b\u3092\u53d6\u5f97

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KL Divergence loss coefficient _^_0_^_

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KL \u767a\u6563\u640d\u5931\u4fc2\u6570 _^_0_^_

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KL Divergence regularization coefficient schedule

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KL \u30c0\u30a4\u30d0\u30fc\u30b8\u30a7\u30f3\u30b9\u6b63\u5247\u5316\u4fc2\u6570\u30b9\u30b1\u30b8\u30e5\u30fc\u30eb

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Load configurations

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\u69cb\u6210\u3092\u30ed\u30fc\u30c9

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Module to convert the model output to non-zero evidences

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\u30e2\u30c7\u30eb\u51fa\u529b\u3092\u30bc\u30ed\u4ee5\u5916\u306e\u30a8\u30d3\u30c7\u30f3\u30b9\u306b\u5909\u63db\u3059\u308b\u30e2\u30b8\u30e5\u30fc\u30eb

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Move data to the device

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\u30c7\u30fc\u30bf\u3092\u30c7\u30d0\u30a4\u30b9\u306b\u79fb\u52d5

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One-hot coded targets

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\u30ef\u30f3\u30db\u30c3\u30c8\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u30bf\u30fc\u30b2\u30c3\u30c8

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ReLU activation

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ReLU \u30a2\u30af\u30c6\u30a3\u30d9\u30fc\u30b7\u30e7\u30f3

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ReLU to calculate evidence

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\u30a8\u30d3\u30c7\u30f3\u30b9\u306e\u8a08\u7b97\u306b\u306f ReLU

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Save the tracked metrics

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\u8ffd\u8de1\u3057\u305f\u30e1\u30c8\u30ea\u30af\u30b9\u3092\u4fdd\u5b58\u3059\u308b

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Second _^_0_^_ convolution layer

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2 _^_0_^_ \u756a\u76ee\u306e\u7573\u307f\u8fbc\u307f\u5c64

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Set tracker configurations

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\u30c8\u30e9\u30c3\u30ab\u30fc\u69cb\u6210\u3092\u8a2d\u5b9a

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Softplus to calculate evidence

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\u8a3c\u62e0\u8a08\u7b97\u7528\u30bd\u30d5\u30c8\u30d7\u30e9\u30b9

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Start the experiment and run the training loop

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\u5b9f\u9a13\u3092\u958b\u59cb\u3057\u3001\u30c8\u30ec\u30fc\u30cb\u30f3\u30b0\u30eb\u30fc\u30d7\u3092\u5b9f\u884c\u3057\u307e\u3059

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Take optimizer step

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\u6700\u9069\u5316\u306e\u4e00\u6b69\u3092\u8e0f\u307f\u51fa\u3059

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Total loss

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\u7dcf\u640d\u5931

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Track statistics

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\u30c8\u30e9\u30c3\u30af\u7d71\u8a08

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Train the model

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\u30e2\u30c7\u30eb\u306e\u30c8\u30ec\u30fc\u30cb\u30f3\u30b0

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Training/Evaluation mode

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\u30c8\u30ec\u30fc\u30cb\u30f3\u30b0/\u8a55\u4fa1\u30e2\u30fc\u30c9

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Update global step (number of samples processed) when in training mode

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\u30c8\u30ec\u30fc\u30cb\u30f3\u30b0\u30e2\u30fc\u30c9\u6642\u306b\u30b0\u30ed\u30fc\u30d0\u30eb\u30b9\u30c6\u30c3\u30d7 (\u51e6\u7406\u3055\u308c\u305f\u30b5\u30f3\u30d7\u30eb\u6570) \u3092\u66f4\u65b0

\n", "\n": "\n", "Evidential Deep Learning to Quantify Classification Uncertainty Experiment": "\u5206\u985e\u4e0d\u78ba\u5b9a\u6027\u5b9f\u9a13\u3092\u5b9a\u91cf\u5316\u3059\u308b\u305f\u3081\u306e\u30a8\u30d3\u30c7\u30f3\u30b7\u30e3\u30eb\u30c7\u30a3\u30fc\u30d7\u30e9\u30fc\u30cb\u30f3\u30b0", "This trains is EDL model on MNIST": "\u3053\u306e\u5217\u8eca\u306fMNIST\u306eEDL\u30e2\u30c7\u30eb\u3067\u3059" }