Consider the following Neural Network model to tackle a binary classification problem:

Which activation function would be plausible for the output layer?

Question

Consider the following Neural Network model to tackle a binary classification problem:

Which activation function would be plausible for the output layer?

BlackTom AI · Accepted Answer

Sigmoid maps any real-valued logit to a probability between 0 and 1, so it is the appropriate choice for a single-output binary classifier.

1) Relevant concepts
- Binary classification with a single output neuron: the network should output a probability p that the example belongs to class 1 (and 1−p for class 0).
- Activation choice: use a function that yields values in (0,1). The sigmoid (logistic) function σ(z)=1/(1+e^(−z)) does exactly this.
- Loss compatibility: binary_crossentropy expects probabilities (or logits with from_logits=True); sigmoid output pairs naturally with binary cross-entropy.

2) Step-by-step reasoning
- The final Dense layer is Dense(1,...), so there is exactly one scalar output z for each input.
- To interpret z as a probability p, apply σ(z) = 1/(1+e^(−z)).
- Example intermediate values: if z=0 → σ(0)=0.5; z=2 → σ(2)≈0.8808; z=−2 → σ(−2)≈0.1192. These show how logits map to [0,1].
- Classification decision: commonly threshold p≥0.5 → class 1, else class 0.

3) Calculations (intermediate)
- σ(0) = 1/(1+e^0) = 1/2 = 0.5
- σ(2) = 1/(1+e^(−2)) ≈ 1/(1+0.1353) ≈ 0.8808
- σ(−2) ≈ 0.1192

4) Why Sigmoid is correct
- It produces a single scalar probability in (0,1), directly usable for binary_crossentropy and thresholding. It is the standard and simplest choice when the network has one output neuron for binary tasks.

5) Why the other options are incorrect
- Softmax: designed to normalize a vector of logits into a probability distribution across multiple classes. With Dense(1) softmax is not meaningful (it would always return 1); for two-class problems softmax is used with Dense(2) instead.
- ReLU: outputs [0, ∞), not a probability; cannot represent class probability directly.
- SELU: also unbounded (negative to positive) and intended for hidden layers to preserve self-normalization, not for outputting probabilities.

Conclusion: The correct activation is Sigmoid, which matches the provided answer.

Consider the following Neural Network model to tackle a binary classification problem: Which activation function would be plausible for the output layer?单项选择题

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