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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.

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.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.4: The Singular Value Decomposition
Problem 50EQ
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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.
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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