Question at position 13 What activation function should we use for the output layer for the MNIST dataset?SoftmaxReLUSingle choice
A
Softmax
B
ReLU

Question

Question at position 13 What activation function should we use for the output layer for the MNIST dataset?SoftmaxReLU

BlackTom AI · Accepted Answer

Softmax is used because MNIST is a 10-class, single-label classification problem and softmax converts raw network scores (logits) into a probability distribution over those classes.

1) Relevant knowledge points and concepts
- MNIST requires predicting one of 10 digits (0–9): a single categorical label per input.
- Softmax: for a vector of logits z = [z1,...,zK], softmax_i = exp(zi) / sum_j exp(zj). Outputs are nonnegative and sum to 1 — interpretable probabilities.
- ReLU (rectified linear unit): f(x)=max(0,x) — used as a hidden-layer activation, not a probability output.
- Loss pairing: softmax + categorical cross-entropy yields proper probabilistic loss and stable gradients.

2) Step-by-step reasoning
- The output layer should have 10 units (one per digit). The network produces logits z1..z10.
- Apply softmax to these logits to obtain P(class=i | input) = exp(zi) / sum_j exp(zj).
- During inference, predict argmax_i P(class=i).
- During training, minimize categorical cross-entropy between predicted probabilities and one-hot true label.

3) Example calculation (intermediate steps)
- Suppose logits = [2.0, 1.0, 0.1, …].
- exp(2.0)=7.389, exp(1.0)=2.718, exp(0.1)=1.105. If these were the only three, sum ≈ 11.212.
- Softmax probabilities ≈ [7.389/11.212=0.659, 2.718/11.212=0.242, 1.105/11.212=0.099].
- These values are valid probabilities and can be compared to the one-hot label.

4) Why the correct answer is correct
- Softmax produces a normalized probability distribution required for single-label multiclass classification and pairs naturally with cross-entropy loss to train the model effectively.

5) Why the other option is incorrect
- ReLU does not normalize outputs, cannot produce probabilities that sum to 1, and can produce arbitrary positive magnitudes or zeros. It’s appropriate for hidden layers but not for the final layer when you need class probabilities.

6) Conclusion
Softmax is the appropriate activation for the MNIST output layer. This matches the provided correct answer: Softmax.

Question at position 13 What activation function should we use for the output layer for the MNIST dataset?SoftmaxReLUSingle choice

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