In contrast to the OLS, which of the following is NOT true about neural networks?

Question

BlackTom AI · Accepted Answer

We start by restating the question and listing all given answer options to frame the comparison clearly.
Question: In contrast to the OLS, which of the following is NOT true about neural networks?
Options:
1) It relies on the central limit theorem to compute parameter standard errors.
2) It can capture both nonlinear and interaction effects.
3) It requires training/tuning to find the # of layers and model parameters.
4) It requires the use of hidden layers and activation functions.

Now, evaluate each option on its own merits and in relation to how ordinary least squares (OLS) differs from neural networks.

Option 1: It relies on the central limit theorem to compute parameter standard errors.
- This statement is typically false for neural networks. OLS standard errors rely on assumptions that yield asymptotic normality and often invoke central limit theorem arguments under certain conditions. Neural networks, especially complex, high-parameter models trained by gradient methods, do not generally provide standard errors derived from the CLT in the same straightforward way; uncertainty quantification is more indirect (e.g., via bootstrap, Bayesian methods, or other approximations). Therefore, as a property of neural networks, this claim is not true.

Option 2: It can capture both nonlinear and interaction effects.
- This is true for neural networks. One of the primary strengths of NN models is their ability to approximate nonlinear functions and to capture interactions between inputs automatically through layers and nonlinear activation functions, without needing explicit feature engineering. This aligns with how NNs differ from linear OLS models.

Option 3: It requires training/tuning to find the # of layers and model parameters.
- This is also true. Neural networks rely on a training process to optimize weights, and model architecture choices—such as the number of layers and neurons per layer—significantly affect performance. Selecting and tuning these hyperparameters is a standard part of deploying NN models.

Option 4: It requires the use of hidden layers and activation functions.
- This statement is generally true for standard feedforward neural networks, where hidden layers and nonlinear activation functions enable the network to model complex patterns. While some very simple neural network variants may be linear, the typical neural network framework emphasizes hidden layers and activations to achieve nonlinearity.

In summary, when comparing to OLS, the distinct and not-true aspect among these statements is the reliance on the central limit theorem to compute parameter standard errors, which does not characterize neural networks in the usual practice. The remaining items describe common, accurate features of neural networks relative to OLS.

Fall 2025.FIN.5321.02 Final Exam

In contrast to the OLS, which of the following is NOT true about neural networks?

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