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Attention lets each position in a sequence look at every other position and mix their information. It is the core of the Transformer architecture used by large language models:
Attention(Q, K, V) = softmax(Q × Kᵀ / √d) × V
For each query row q:
- Score every key row k: score = (q · k) / √d, where d is the number of columns of K.
- Turn the scores into weights with softmax (subtract the largest score before taking e^x).
- The output row is the weighted sum of the value rows: Σ weight_j × values[j].
Implement attention(queries, keys, values).
Input
queries: n rows, each with d numbers.
keys: m rows, each with d numbers.
values: m rows (one per key), each with v numbers.
Output
Return the n × v output matrix.
Constraints
1 ≤ n, m ≤ 50, 1 ≤ d, v ≤ 32
-10 ≤ each value ≤ 10
Examples
Example 1
Input:
keys = [
[1.0, 0.0],
[1.0, 0.0]
]
values = [
[2.0, 4.0],
[6.0, 8.0]
]
queries = [
[1.0, 0.0]
]
Expected output:
[
[4.0, 6.0]
]
Explanation
Both keys give the same score, so the softmax weights are 0.5 and 0.5. The output is the average of the value rows: [(2 + 6) / 2, (4 + 8) / 2] = [4, 6].
Example 2
Input:
keys = [
[3.0, 1.0],
[-2.0, 5.0],
[7.0, 7.0]
]
values = [
[1.0],
[2.0],
[6.0]
]
queries = [
[0.0, 0.0]
]
Expected output:
[
[3.0]
]
Explanation
A zero query scores 0 against every key, so attention is spread evenly: (1 + 2 + 6) / 3 = 3.
References
-
Example 1 Not runInput:
keys = [ [1.0, 0.0], [1.0, 0.0] ] values = [ [2.0, 4.0], [6.0, 8.0] ] queries = [ [1.0, 0.0] ]Expected output:[ [4.0, 6.0] ]Your output -
Example 2 Not runInput:
keys = [ [3.0, 1.0], [-2.0, 5.0], [7.0, 7.0] ] values = [ [1.0], [2.0], [6.0] ] queries = [ [0.0, 0.0] ]Expected output:[ [3.0] ]Your output
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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";
bool isActive = true;
// Constants
const int MaxUsers = 100;
const string Company = "CodeUtility";
2. Conditionals (if / switch)
Use if, else if, and switch for control flow.
int x = 2;
if (x == 1)
{
Console.WriteLine("One");
}
else if (x == 2)
{
Console.WriteLine("Two");
}
else
{
Console.WriteLine("Other");
}
switch (x)
{
case 1:
Console.WriteLine("One");
break;
case 2:
Console.WriteLine("Two");
break;
default:
Console.WriteLine("Other");
break;
}
3. Loops
C# supports for, while, and foreach loops.
for (int i = 0; i < 3; i++)
{
Console.WriteLine(i);
}
int n = 3;
while (n > 0)
{
Console.WriteLine(n);
n--;
}
4. Arrays
Arrays store fixed-size collections of elements of the same type.
int[] numbers = { 10, 20, 30 };
Console.WriteLine(numbers[1]);
5. List Manipulation
Use List<T> for dynamic collections.
List<int> nums = new List<int> { 1, 2, 3 };
nums.Add(4);
nums.Remove(2);
foreach (int n in nums)
{
Console.Write(n + " ");
}
6. Console Input/Output
Use Console.WriteLine and Console.ReadLine for basic I/O.
Console.Write("Enter your name: ");
string name = Console.ReadLine();
Console.WriteLine($"Hello, {name}!");
7. Functions
Define methods using a return type, name, and parameters.
int Add(int a, int b)
{
return a + b;
}
Console.WriteLine(Add(3, 4));
8. Dictionaries
Dictionary<TKey, TValue> stores key-value pairs.
Dictionary<string, int> ages = new Dictionary<string, int>();
ages["Alice"] = 30;
Console.WriteLine(ages["Alice"]);
9. Exception Handling
Handle runtime errors using try, catch, and finally.
try
{
throw new Exception("Something went wrong");
}
catch (Exception ex)
{
Console.WriteLine(ex.Message);
}
10. File I/O
Use File and StreamReader/StreamWriter for file operations.
File.WriteAllText("file.txt", "Hello File");
string text = File.ReadAllText("file.txt");
Console.WriteLine(text);
11. String Manipulation
C# strings support methods like Length, Substring, Contains.
string message = "Hello World";
Console.WriteLine(message.Length);
Console.WriteLine(message.Substring(0, 5));
Console.WriteLine(message.Contains("World"));
12. Classes & Objects
C# supports object-oriented programming through classes and objects.
class Person
{
public string Name;
public Person(string name) => Name = name;
public void Greet() => Console.WriteLine($"Hi, I'm {Name}");
}
Person p = new Person("Alice");
p.Greet();