#0013

Stable Softmax

MediumML18 min15 XP

Problem

Given a one-dimensional NumPy array of logits, return softmax probabilities. Subtract the maximum logit before exponentiating.

Why This Matters

Softmax is used in multi-class classification, attention, and language models. The stable version prevents large logits from breaking the calculation.

Function Signature

def softmax(logits):

Examples

Example 1

Inputlogits = np.array([1.0, 2.0, 3.0])

Outputarray([0.09, 0.2447, 0.6652])

The largest logit gets the largest probability, but all probabilities sum to 1.

Constraints

Input is a one-dimensional numeric NumPy array.
Return probabilities that sum to 1.
Use max-shifting for numerical stability.

CodePython

import numpy as np

def softmax(logits):
    """
    Input example: logits = np.array([1.0, 2.0, 3.0])
    Return: array([0.09, 0.2447, 0.6652])
    Return the value from the function so the tests can compare it. Do not print unless the prompt asks.
    """
    # write your code here
    return logits

import numpy as np

def softmax(logits):
    """
    Input example: logits = np.array([1.0, 2.0, 3.0])
    Return: array([0.09, 0.2447, 0.6652])
    Return the value from the function so the tests can compare it. Do not print unless the prompt asks.
    """
    # write your code here
    return logits

Visible browser tests run here when available.

Testcases2 visible / 4 hidden categories

Normal logits

Inputnp.array([1.0, 2.0, 3.0])

Expectedprobabilities sum to 1

Class 3 has the largest probability.

Large logits

Inputnp.array([1000.0, 1001.0])

Expectedfinite probabilities

Subtracting the max prevents exp(1001) overflow.

Hidden Test Categories

Equal logitsNegative logitsVery large logitsSingle dominant class