Wolfram Language

Neural Networks

Object Classification

Using the CIFAR-10 database of labeled images, train a convolutional net to predict the class of each object.

First obtain the training data.

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obj = ResourceObject["CIFAR-10"]; trainingData = ResourceData[obj, "TrainingData"]; RandomSample[trainingData, 5]
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Extract the unique classes.

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classes = Union@Values[trainingData]
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Create a convolutional net that predicts the class given an image.

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lenet = NetChain[ {ConvolutionLayer[20, 5], Ramp, PoolingLayer[2, 2], ConvolutionLayer[50, 5], Ramp, PoolingLayer[2, 2], FlattenLayer[], 500, Ramp, 10, SoftmaxLayer[]}, "Output" -> NetDecoder[{"Class", classes}], "Input" -> NetEncoder[{"Image", {32, 32}}] ]
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Train the net on the training data.

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trained = NetTrain[lenet, trainingData, MaxTrainingRounds -> 4]
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Predict the most likely classes for a set of images.

In[6]:=
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Out[6]=

For a specific example, give the probabilities of the most likely label assignments.

In[7]:=
Click for copyable input
trained[\!\(\* GraphicsBox[ TagBox[RasterBox[CompressedData[" 1:eJyVlllzE1cWgGHmJTVPgdQUAa8YhrHBBowkLNmyrNWyZe371i2p1d1qdatb +756lRdZMrbBgA1eMMasBoYtLAFMErJMVVIzU5WqecwvmUvIzNO8pOv0rXu7 ur+z9LnnnsNIUI//Yc+ePdFPwKD3JEWRiCdt+BQsTEzU72MwdJCJYT4swkX+ CB42/3Z/mO/du3fP778+fPRR/rf8/6/t3b9/f1dXF5fL7ericDjsjzeLw2ax WGw2m8vj9vTyBcI+IHx+D4/HZbNZ7R0n2o4fO37iryfaW4GA+bHWo61tfwGT 1uMfxvaOtlOdJ9kc1v7PPmtubqYoKhaLxBOhaCyUSCRSmUwylw1FwpFoNJ3L jpTHZ2rV2bna5NTE6GgpFKYh2KbTK/TGISA649CAUiIZECi1/RqjAoyDKonG OIT6PbFU9PCRlvr6erPZYnfYUAyiAr5YNJYvlgpjI/F0KpaIx1LJVCGXHxku jo2UhvPpTJzwo07IrNHJ1FqpQimUDfL5Ek6vhDOoEWnNg2pjv1wlVOqlHp8z nAg2tjTX1dcZjHqL1eRBHD7CEwzSmVw+nc9FE7FQmAnHIrFUIpXL5kvFfCEb iQYJArPa9Eq1cFDZK5FzBVJ2t+h0j/j0gJqvs8j0ln61QaIzy924lY74mw43 1TXUma1GB2RDvLAXhTDcGwyFw7EoRZMY7iH8Pj9FBRga+BJPRGiG9BGo0aSW K/gi2Vm+uLNb3MkTneIJO2QKjsYo0Bj71Hqh1iS1wGoEdzY21dc31NmdVtjt RDE34nV6PDAVoCOJmJ8igEYUQ3DChxM4UMcEyQBNAKUGo0om7+4VsXh9nT1i TreY3SM6I5GfHVR3K7W9Kp1IY5BqTAMmq7a+4RDgA+PdCEQQKO5zYxjCBEPx VBIA3R6nG4FRHPFiHsznJSncT6IeBNLqBgFfoRIbrJq+/l6BtFvY3yORd8sG uQOqHsDXGuVGu8bqNAL4Rz7idQVDVCzOxOLhVDoNoh2OhoBHrg8qIMhlBxMU cwEHQfBVatngUF8giK9uruZHCyiJBUKk0aIeUPYOKHuUWpHBMgQhDjcKNzSC +NRDLgfuR7P59Hh5ZKI8PjlTmaxWM/kMReEejwPwnbDNCVlcbividUCQ2WbX BRj0/sM7P//753/+/K9vvvv6ze6rq2uXCco1oASJKrI6NF4C8fmxxqYGoMKN uuhIYGxqvDo/V5mbm7+0vLC6OloeCzEE7rURBEIHyWiYwDEnw/jyueSFC3PP nz/+6acff/j7t9++f/v9+7fv3r549/bl+sZVyG3WGCQ2p9ZHonSQAvkD+C4v zESZ8emJ2sK52vzC8sa1levXx8uj+XSkPJIaLiaXzle3N5erM+PnF2v37tz8 5uvd7394//r16wcPd7ZvXNm5s35z68rW5tVXX76ozU87XQaHy+insFAkCPgg Pi4EJoP+0kh+ujK9eOH8pasrEzPlYjG9UC3f3lzeuHzuyc71Jztbt29sPP3b /W+/2n3+7PH2za21tfWlixfOzU2sXK4sX5xdvjT/6NHOvQe3A4zPi8MEiTGh wK/8OhgkD+2LxUPFUm6mMl2eHE+lo8Ds87Xy+sXa2uLUvfXzW1cW7t3aePPy 8ZOHd6uVyUI+l0pmgsEg5ffGo+TYcGphrgz8fvb86Xh5DCe8gP8xPvX1dQ6X 3evzgNxLJMOJRDQUplDMiaOOQio4Vy7MjcSXJjOXa2NPHm7du7VaSIdIwoP7 8H75ICiAvT08p9WcSQYvL1Vu3d788vXrtfVroQgDVFC0/zf73TYPYsdwiImS JI2jGCzt5wt72R6nKRX0xSjXaIZcquSWz4+WIniCQIrpmMmgbWisO/Dn/Z2n OpxWYz5Bba0vvnr16M2bNzv3H+WLBbANvagL5E9jYwPh9/pJDw74EcJPIZBN b1T2d3ee6GOddNm1NGYbSxAzBTqG26KQZbFUWpiYxGyOzva2tqPNAzIRApsm 8uFrV+ZePn+wu/vm+YtXtbkaTiAwbK+vP9Tc3BQO0+FwgKLQeJyOhH12vQLS K2X8rrPHj5i00mwAWR1OTYawmNuWI32TuWy1PEkTpEmvlYv4uiEZ6bVVRuLX VxdefnH/h+++evfV2/WNNbBbEcQFinNLS0s6nU6lErEoQxMe2gd5HBoENtot OlHXyZDLeG0sv5GIXqHIVZy8HAhOYr4FMrSEhycoxmHUWI1DNGqdKoZBfO7d Xn/7+vHu7ssvnj0tlfIEgTc2NgF+qTQ8OjY2NlpMhUjKY8VhHWRVWXWqgEX7 eGbiCk1lpNIndOyVP7zigNJy6YzesGR3lTEUtRk1g0LEopgZDq8sTV9bPf/o weaL5w/e7b6Zna0EAlRT0+HDLS2xRCzAkKjL5jarHVqpXSM0DQkjsHP3woV/ LF7cppgdin4fjD+FkRm1MqiSZ7zOCOoMeCHEadENiglIN5EPVCbi1cropYuz 2zdXXr54Mn+uSgeDTc0f+JgfFUr4XHa7gNuhELOsWmGadr1cW/pl5+4vG1s/ zi8+SMQWTbphqZjo63bKgME6HHUGaZwJ4JjLGiKgVNgzkiPHR1K12tily5Vn T+6urV5KpNPNLS1NzY0kQ5jsepVK7rDrCcxB+aCVauHdRuXLpenVaDCpUxn4 bAn7uIDdKuC19/eyNLJuvVbosCkxxAZOS8JjjQTcmRg2WghWJlMLteGnD7dv 39osjo4cPnIE1B8v4abCBEkTuUJ6eno8lQwFEf0UY4y7hrQSjqznpITfKZd0 qxTiIZVIr+/XqYX9kjNDgzyTXua0qlCXiSaggM8RD8HpCDI1HN/ZvrJz98Zo eeLD+d5wyGTXORELqHjZbGJiYjgeDRiGBIhRqlfwNJpeg6ZPJeMpxFxNv1Ax ILTYtG6XyWoY0Kv6dKpeh3WAwMw+1IwhxiDloHB7OkasLlfu3N4sjoyA33vw 0AGFWmq0qjxeeyRKFfKJXCYU8LtBYfF4LGatGNaKIHUfZJLBdo3TocdRiCG8 MZrA3WazTmwzS2BIATtViMfgw2we2EQHXLVqcWNjJZXNgN37+ecHxLKzaq3E bFURJJxMB7JZUIICyVS0WMoSXithlTOO/hCmiVDOKOVO0GiS8RVS0VwyhCEW h01hNfVbjErIaXW7rYQPjoSJanX87r2bxVIe7K/PDx4QSTvlCq5WL0VxRyIV yuaSoNHKZJOz1elkgvbD6qBLHsVVCcqWZuB82BslnKUkPTWeCQQQFLVCdo1e N2SxmFwuB00T6XRs/tzsg4d3C8XcoUMHD/7Kl8rZKo0Yw2GgdLZaGR4tpTLJ mdnpsYlhErOS8GDIq4oSpjQDZYPuJAWVEv6ZcjYcIXEcxrwOECmn0wG7YIoi s9lMuTxxY/taLpcG9Lq6QzI5T9bfo9UpaMY/NVVeXVudv7BYGCmBnrA6V4uE SNJr8bsNNGqJBdwxCslHyeEUMzmaTSYjfj9GBwiv1w25YA8CTlKmWCpNTk1e 31qfnplsaGj49NN9x/56+Nixo8ePt7LYnT09PJFEJBCLurp5/D6BoFfIYbHO nDrR2d7KOtnGOd3OOdXBZZ3md7HUg/JeHvcsh8Xjdp3tOtt+sgN0xZwuDl/A 7xMK+uUSgYC/b9++/zbZv69L/9Mnn/T1Ajzgcxrq61tbW48cPQKk80wnkI6O 9lOnTra1tQH+fwAN6ImN "], {{0, 32}, {32, 0}}, {0, 255}, ColorFunction->RGBColor], BoxForm`ImageTag["Byte", ColorSpace -> "RGB", Interleaving -> True], Selectable->False], DefaultBaseStyle->"ImageGraphics", ImageSizeRaw->{32, 32}, PlotRange->{{0, 32}, {0, 32}}]\), {"TopProbabilities", 3}]
Out[7]=

From a random sample, select the images for which the net produces highest and lowest entropy predictions. High-entropy inputs can be interpreted as those for which the net is most uncertain about the correct class.

In[8]:=
Click for copyable input
images = RandomSample[Keys[trainingData], 5000];
In[9]:=
Click for copyable input
entropies = trained[images, "Entropy"];
In[10]:=
Click for copyable input
Labeled[images[[Ordering[entropies, -10]]], "high entropy"] Labeled[images[[Ordering[entropies, 10]]], "low entropy"]
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Out[10]=

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