Categorical Cross-Entropy Loss

A multi-class classifier outputs one probability per class (for example from softmax). Categorical cross-entropy punishes it for giving the correct class a low probability:

loss = -(ln(p₁) + ln(p₂) + … + ln(pₙ)) / n

where pᵢ is the probability the model gave to the correct class of sample i. To avoid ln(0), first raise any probability below 0.0000001 to 0.0000001.

Implement categorical_cross_entropy(probabilities, labels).

Input

probabilities: One row per sample, with one probability per class.

labels: The index of the correct class for each sample (0-based).

Output

Return the average loss as a decimal number.

Constraints

1 ≤ samples ≤ 1,000, 2 ≤ classes ≤ 100

0 ≤ each probability ≤ 1

0 ≤ labels[i] < number of classes

Examples

Example 1

Input:
probabilities = [
    [0.7, 0.2, 0.1],
    [0.1, 0.8, 0.1]
]
labels = [0, 1]

Expected output:
0.289909

Explanation

The correct classes got 0.7 and 0.8: -(ln(0.7) + ln(0.8)) / 2 = -(-0.356675 - 0.223144) / 2 ≈ 0.289909.

Example 2

Input:
probabilities = [
    [1.0, 0.0]
]
labels = [1]

Expected output:
16.118096

Explanation

The correct class got probability 0, which is raised to 0.0000001, so the loss is -ln(0.0000001) ≈ 16.118096: a confident wrong answer is punished hard.

References

Run the sample tests to check your code without submitting.

Example 1 Not run

Input:

probabilities = [
    [0.7, 0.2, 0.1],
    [0.1, 0.8, 0.1]
]
labels = [0, 1]

Expected output:

0.289909

Your output

Example 2 Not run

Input:

probabilities = [
    [1.0, 0.0]
]
labels = [1]

Expected output:

16.118096

Your output

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💡 Node.js Basics Guide for Beginners

1. Declaring Variables and Constants

Use let or const for block-scoped variables. const is used for constants.

let x = 10;
const PI = 3.14;
let name = "Alice";
let isActive = true;

2. Conditionals (if / switch)

Use if, else if, else or switch for control flow.

let x = 2;
if (x === 1) {
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} else if (x === 2) {
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} else {
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}

switch (x) {
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    break;
  case 2:
    console.log("Two");
    break;
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    console.log("Other");
}

3. Loops

Use for, while, and forEach to iterate over data.

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4. Arrays

Use arrays to store ordered lists of values. Access them with indexes.

let fruits = ["apple", "banana", "cherry"];
console.log(fruits[0]);
console.log(fruits.length);

5. Array Manipulation

Use methods like push, pop, slice, and reverse.

fruits.push("kiwi");
fruits.pop();
console.log(fruits.slice(0, 2));
console.log(fruits.reverse());

let squares = [1, 2, 3, 4, 5].map(x => x * x);
console.log(squares);

6. Console Input/Output

Use console.log for output and readline module for input.

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const rl = readline.createInterface({
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  output: process.stdout
});

rl.question("What's your name? ", name => {
  console.log(`Hello, ${name}`);
  rl.close();
});

7. Functions

Functions can be declared or expressed. Arrow functions are often used in modern JavaScript.

function greet(name) {
  return `Hello, ${name}`;
}

const add = (a, b) => a + b;

console.log(greet("Alice"));
console.log(add(2, 3));

8. Objects (Maps)

Objects store key-value pairs. They are similar to dictionaries or maps.

let person = { name: "Bob", age: 25 };
console.log(person.name);
console.log(person["age"]);

// ES6 Map
const map = new Map();
map.set("a", 1);
console.log(map.get("a"));

9. Exception Handling

Use try, catch, and finally to handle errors safely.

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fs.writeFileSync("test.txt", "Hello File");
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class Person {
  constructor(name) {
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  }
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    return `Hi, I'm ${this.name}`;
  }
}

const p = new Person("Alice");
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13. References

Objects and arrays in JavaScript are passed by reference.

function update(arr) {
  arr.push("changed");
}

let data = ["original"];
update(data);
console.log(data);  // ["original", "changed"]