Row 8115

Row ID: 8115 | Dataset Entry | Axioma AXP Content Repository

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This page contains data entry 8115 from the Axioma AXP content repository. The structured data below represents the complete record for this entry.

Consider a neural network shown below.

https://preview.redd.it/p6x5cfq4t71d1.png?width=1114&format=png&auto=webp&s=29e980d9727769e2d89bb374052aabf055e23f39

Consider we have a cross-entropy loss function for binary classification:  L=−\[𝑦 ln(𝑎)+(1−𝑦) ln(1−𝑎)\], where 𝑎 is the probability out from the output layer activation function. We've built a computation graph of the network as shown below. The blue letters below are intermediate variable labels to help you understand the connection between the network architecture graph above and the computation graph.

When 𝑦=1, what is the g\*\*radient of the loss function w.r.t. 𝑊11? \*\*Write your answer to three decimal places. Note: Please use the computation graph method. One can calculate the gradient directly using chain rules, but if the computation graph is not used at all, it will not score properly. Try to fill the red boxes above. This question does not need coding and the answer can be easily obtained analytically.

https://preview.redd.it/1y2d9vgmn81d1.png?width=1172&format=png&auto=webp&s=091d1657110510243e253970dc0e1522f2edeca1

Hint

https://preview.redd.it/3x9bpr6at71d1.png?width=1182&format=png&auto=webp&s=ea220648ee1874a22daadb6dd719c1952516ccba

FieldValue
text Consider a neural network shown below. https://preview.redd.it/p6x5cfq4t71d1.png?width=1114&format=png&auto=webp&s=29e980d9727769e2d89bb374052aabf055e23f39 Consider we have a cross-entropy loss function for binary classification:  L=−\[𝑦 ln(𝑎)+(1−𝑦) ln(1−𝑎)\], where 𝑎 is the probability out from the output layer activation function. We've built a computation graph of the network as shown below. The blue letters below are intermediate variable labels to help you understand the connection b…
label r/neuralnetworks
dataType post
communityName r/neuralnetworks
datetime 2024-05-18
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url_encoded Z0FBQUFBQm5Lak9ITHcwcGUzM1FrVzIybXhrc1BhWjhOTjNJRnV4WUNxNGlKMnYtbWhZdDFPeEtTQlhTVy00ZFFkQTBCcFdDR3RNZmp4X0hWLVVhNEhIZjBFSHllTEpKZjBtOU5FclZxQ2lkWXNUNjdTUHlQTmFlU1p5c01TZ3cxWmhTc3dfMmNjSFF3QndzU3h1WXBaNVdYdmVSNnJ0bHNPZ0doOWhxcWRYVDFoWkpUWGRtQ2liM3pBa0N2b1g5ZXg5R2stanQ5dmJR

Raw Record

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  "text": "Consider a neural network shown below.\n\nhttps://preview.redd.it/p6x5cfq4t71d1.png?width=1114&format=png&auto=webp&s=29e980d9727769e2d89bb374052aabf055e23f39\n\nConsider we have a cross-entropy loss function for binary classification:  L=−\\[𝑦 ln(𝑎)+(1−𝑦) ln(1−𝑎)\\], where 𝑎 is the probability out from the output layer activation function. We've built a computation graph of the network as shown below. The blue letters below are intermediate variable labels to help you understand the connection between the network architecture graph above and the computation graph. \n\nWhen 𝑦=1, what is the g\\*\\*radient of the loss function w.r.t. 𝑊11? \\*\\*Write your answer to three decimal places. Note: Please use the computation graph method. One can calculate the gradient directly using chain rules, but if the computation graph is not used at all, it will not score properly. Try to fill the red boxes above. This question does not need coding and the answer can be easily obtained analytically.\n\nhttps://preview.redd.it/1y2d9vgmn81d1.png?width=1172&format=png&auto=webp&s=091d1657110510243e253970dc0e1522f2edeca1\n\nHint\n\nhttps://preview.redd.it/3x9bpr6at71d1.png?width=1182&format=png&auto=webp&s=ea220648ee1874a22daadb6dd719c1952516ccba",
  "label": "r/neuralnetworks",
  "dataType": "post",
  "communityName": "r/neuralnetworks",
  "datetime": "2024-05-18",
  "username_encoded": "Z0FBQUFBQm5Lakw0bE91ZHhnRE1RZFR1NmJhUGZMLTFjOExXTXhuSDlIMWdLLVZTanFUNHlrX1dKdXc1M3Fvbm5NeWVmTzFtbWJNMkxuNFhfRDB4dlJuTXdPZFBnWktjZmc9PQ==",
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}
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