Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Transcribed Image Text:Problem 4: Generalization Bounds for Deep Neural Networks via
Rademacher Complexity
Statement: Derive generalization bounds for deep neural networks by computing the Rademacher
complexity of the hypothesis class defined by networks with bounded weights and specific
architectural constraints. Show how these bounds scale with the depth and width of the network.
Key Points for the Proof:
•
•
•
Define the hypothesis class of neural networks under consideration.
Calculate or bound the Rademacher complexity for this class, considering factors like depth,
width, and weight constraints.
Apply concentration inequalities to relate Rademacher complexity to generalization error.
Analyze how the derived bounds behave as the network's depth and width increase.
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