Softmax Function

Implement the softmax function for multi-class classification.

Given a list of logits (raw scores) $z = [z_1, z_2, ..., z_k]$ , compute the softmax probabilities:

$\text{softmax}(z_i) = \frac{e^{z_i}}{\sum_{j=1}^{k} e^{z_j}}$

For numerical stability, subtract the maximum value from all logits before exponentiating: $\text{softmax}(z_i) = \frac{e^{z_i - \max(z)}}{\sum_{j=1}^{k} e^{z_j - \max(z)}}$

Return the probability distribution as a list, rounded to 4 decimal places.

Example:

Input:

logits = [2.0, 1.0, 0.1]

Output:

[0.6590, 0.2424, 0.0986]

Reasoning:

First, we find the maximum value in the input list: $\max(z) = 2.0$
Then, we subtract this maximum value from all logits to ensure numerical stability: $z' = [2.0-2.0, 1.0-2.0, 0.1-2.0] = [0.0, -1.0, -1.9]$
Next, we compute the exponentials of these stabilized logits: $e^{z'} = [e^{0.0}, e^{-1.0}, e^{-1.9}] \approx [1.0, 0.368, 0.149]$
Finally, we calculate the softmax probabilities by dividing each exponential by their sum: $\text{softmax}(z_i) = \frac{e^{z_i}}{\sum_{j=1}^{k} e^{z_j}} \approx \frac{[1.0, 0.368, 0.149]}{1.0 + 0.368 + 0.149} \approx [0.6590, 0.2424, 0.0986]$

Constraints:

Input is a list of floats (logits)
Return a list of probabilities that sum to 1 (approximately)
Round each value to 4 decimal places
Use the numerical stability trick (subtract max)

Editor

Python 3.13.1

Test Results

0/0

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