Softmax Function

The softmax function turns a list of scores (logits) into probabilities. Language models use it to choose the next word:

softmax(x)_i = e^(x_i) / (e^(x_1) + e^(x_2) + … + e^(x_n))

Large scores make e^x overflow, so first subtract the largest score from every score. The result is mathematically the same.

Implement softmax(logits).

Input

logits: A list of scores.

Output

Return the list of probabilities, in the same order. They are all between 0 and 1 and add up to 1.

सीमाएँ

1 ≤ length ≤ 1,000

-1,000 ≤ each score ≤ 1,000

उदाहरण

इनपुट:
logits = [1.0, 2.0, 3.0]

अपेक्षित आउटपुट:
expected = [0.090031, 0.244728, 0.665241]

इनपुट:
std::vector<double> logits = {1.0, 2.0, 3.0};

अपेक्षित आउटपुट:
std::vector<double> expected = {0.090031, 0.244728, 0.665241};

इनपुट:
double[] logits = new double[] {1.0, 2.0, 3.0};

अपेक्षित आउटपुट:
double[] expected = new double[] {0.090031, 0.244728, 0.665241};

इनपुट:
logits = [1000.0, 1000.0]

अपेक्षित आउटपुट:
expected = [0.5, 0.5]

इनपुट:
std::vector<double> logits = {1000.0, 1000.0};

अपेक्षित आउटपुट:
std::vector<double> expected = {0.5, 0.5};

इनपुट:
double[] logits = new double[] {1000.0, 1000.0};

अपेक्षित आउटपुट:
double[] expected = new double[] {0.5, 0.5};

संदर्भ

यह चुनौती CodeUtility के लिए अनुकूलित की गई है। ऊपर दिए गए स्टेटमेंट और सीमाओं का पालन करें।

• Goodfellow, Bengio and Courville, Deep Learning
• Stanford CS231n, Neural Networks Part 1