Neural networks and the derivatives of the cost function

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SUMMARY

The discussion focuses on the derivation of the derivatives of the quadratic cost function (CF) in artificial neural networks. The user expresses difficulty in applying the Hadamard product and the dot matrix product correctly when calculating the derivative with respect to the weight matrices. A reference to a relevant derivation from stats.stackexchange is provided, emphasizing the importance of the chain rule in this context. Understanding these concepts is crucial for effective neural network training and optimization.

PREREQUISITES
  • Understanding of artificial neural networks and their architecture
  • Familiarity with quadratic cost functions in machine learning
  • Knowledge of linear algebra, specifically matrix operations
  • Proficiency in calculus, particularly the chain rule for derivatives
NEXT STEPS
  • Study the Hadamard product and its applications in neural networks
  • Learn about the dot product and its role in weight updates
  • Explore detailed derivations of the quadratic cost function in neural networks
  • Investigate resources on the chain rule in multivariable calculus
USEFUL FOR

This discussion is beneficial for machine learning practitioners, data scientists, and students studying artificial neural networks who seek to deepen their understanding of cost function derivatives and optimization techniques.

2sin54
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Hello. I need some guidance on the derivation of the derivatives of the quadratic cost function (CF) in an artificial neural network. I can derive the equations for the forward propagation with no trouble but when it comes to finding the derivative of the CF with respect to the weight matrix (matrices) I struggle to distinguish where to use the Hadamar product, where to use the dot matrix product and the order of the multiples. Does anyone know some good resources where I could see a thorough derivation of this OR linear algebra resource relevant to my question?
 
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