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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💡 Kotlin Basics Guide for Beginners

1. Declaring Variables and Constants

Kotlin uses val for immutable variables and var for mutable ones.

val name: String = "Alice"
var age: Int = 30
val pi = 3.14  // type inferred

// Constants
const val MAX_USERS = 100

2. Conditionals (if / when)

Use if expressions or when for multiple branches.

val x = 2
if (x == 1) {
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} else if (x == 2) {
    println("Two")
} else {
    println("Other")
}

when (x) {
    1 -> println("One")
    2 -> println("Two")
    else -> println("Other")
}

3. Loops

Use for, while, and do-while for iteration.

for (i in 0..2) {
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}

var n = 3
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}

4. Arrays

Kotlin supports arrays using the arrayOf() function.

val numbers = arrayOf(10, 20, 30)
println(numbers[1])

5. List Manipulation

Use mutableListOf for dynamic lists.

val nums = mutableListOf(1, 2, 3)
nums.add(4)
nums.removeAt(0)

for (n in nums) {
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}

6. Console Input/Output

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print("Enter your name: ")
val name = readLine()
println("Hello, $name")

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fun add(a: Int, b: Int): Int {
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}

println(add(3, 4))

8. Maps

mutableMapOf stores key-value pairs.

val ages = mutableMapOf("Alice" to 30)
println(ages["Alice"])

9. Exception Handling

Use try, catch, and finally to handle errors.

try {
    val result = 10 / 0
} catch (e: ArithmeticException) {
    println("Error: ${e.message}")
}

10. File I/O

Use File from java.io for file operations.

import java.io.File

File("file.txt").writeText("Hello File")
val text = File("file.txt").readText()
println(text)

11. String Manipulation

Kotlin strings support many methods and interpolation.

val text = "Hello World"
println(text.length)
println(text.substring(0, 5))
println(text.contains("World"))

12. Classes & Objects

Kotlin classes are concise and support default constructors.

class Person(val name: String) {
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}

val p = Person("Alice")
p.greet()

13. Null Safety

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val name: String? = null
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