Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: Neural networks are capable of approximating any continuous function to an arbitrary degree of accuracy. Reason R: This is explained by the universal approximation theorem. In the light of the above statements, choose the most appropriate answer from the options given below
Assertion A: Approximation Capability
Assertion A states that neural networks can approximate any continuous function to an arbitrary degree of accuracy. This is a fundamental concept in neural network theory and is considered correct.
Reason R: Universal Approximation Theorem
Reason R attributes this capability to the universal approximation theorem. This theorem mathematically proves that feedforward neural networks, under certain conditions (like having a single hidden layer with a finite number of neurons and a non-linear activation function), can approximate any given continuous function.
Explanation Evaluation
The universal approximation theorem provides the theoretical basis for the approximation capabilities of neural networks. Therefore, Reason R is not just correct but also serves as the direct and accurate explanation for Assertion A.
Conclusion
Since both Assertion A and Reason R are correct, and Reason R correctly explains Assertion A, the most appropriate answer is that both statements are correct and R is the correct explanation of A.
Correct Answer: Both A and R are correct and R is the correct explanation of A
