Temperature and Top-K Sampling

Language models pick the next token from a probability distribution. Two settings shape it:

Top-k: keep only the k tokens with the highest logits (if logits tie, the lower index ranks higher).
Temperature T: divide the kept logits by T before softmax. Low T makes the choice more predictable; high T makes it more random.

To make sampling testable, the random number is given:

Keep the top k tokens, then list them by their original index (ascending).
Compute softmax(logit / T) over the kept tokens (subtract the largest before taking e^x).
Walk through the list adding probabilities; return the index of the first token where the running total becomes greater than random_value. If none does (rounding), return the last kept token.

With k = 1 this is greedy decoding: always the most likely token.

Implement sample_token(logits, temperature, k, random_value).

Input

logits: One score per token in the vocabulary.

temperature: T, greater than 0.

k: How many top tokens to keep.

random_value: A random number in [0, 1).

Output

Return the index of the chosen token.

Constraints

1 ≤ k ≤ number of logits ≤ 1,000

0 < temperature ≤ 100, 0 ≤ random_value < 1

-100 ≤ each logit ≤ 100

Examples

Example 1

Input:
k = 1
logits = [1.0, 3.0, 2.0, 0.5]
temperature = 1.0
random_value = 0.99

Expected output:
1

Explanation

k = 1 keeps only the highest logit, 3.0 at index 1. Its probability is 1, so it is chosen whatever the random value: greedy decoding.

Example 2

Input:
k = 2
logits = [2.0, 1.0, 0.0]
temperature = 1.0
random_value = 0.8

Expected output:
1

Explanation

Top-2 keeps indices 0 and 1 (logits 2 and 1). softmax gives about 0.731 and 0.269. The running total is 0.731 after index 0 (not above 0.8) and 1 after index 1, so index 1 is chosen.

References

Run the sample tests to check your code without submitting.

Example 1 Not run

Input:

k = 1
logits = [1.0, 3.0, 2.0, 0.5]
temperature = 1.0
random_value = 0.99

Expected output:

Your output

Example 2 Not run

Input:

k = 2
logits = [2.0, 1.0, 0.0]
temperature = 1.0
random_value = 0.8

Expected output:

Your output

4 hidden tests also run when you submit.

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💡 C# Basics & Examples You Can Try Above

1. Declaring Variables and Constants

C# uses strongly-typed variable declarations. Use const for compile-time constants and readonly for runtime constants.

int age = 30;
double pi = 3.14159;
char grade = 'A';
string name = "Alice";
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