Dense Layer Forward Pass

A dense layer is a group of neurons that all receive the same inputs. Neuron j has its own weights weights[j] and bias biases[j]:

z_j = inputs · weights[j] + biases[j]

Then the layer's activation is applied to each z_j:

"linear": output z_j unchanged
"relu": max(0, z_j)
"sigmoid": 1 / (1 + e^(-z_j))

Implement dense_forward(inputs, weights, biases, activation).

Input

inputs: The n input values.

weights: One row per neuron; each row has n weights.

biases: One bias per neuron.

activation: "linear", "relu" or "sigmoid".

Output

Return the list of outputs, one per neuron, in order.

Constraints

1 ≤ n ≤ 100, 1 ≤ number of neurons ≤ 100

-10 ≤ each value ≤ 10

Examples

Example 1

Input:
inputs = [1.0, 2.0]
weights = [
    [0.5, -1.0],
    [1.5, 0.5]
]
biases = [0.0, -1.0]
activation = "relu"

Expected output:
[0.0, 1.5]

Explanation

Neuron 1: 1×0.5 + 2×(-1) + 0 = -1.5, and ReLU gives 0. Neuron 2: 1×1.5 + 2×0.5 - 1 = 1.5, which ReLU keeps. Result: [0, 1.5].

Example 2

Input:
inputs = [3.0]
weights = [
    [2.0],
    [-1.0],
    [0.5]
]
biases = [1.0, 0.0, -1.5]
activation = "linear"

Expected output:
[7.0, -3.0, 0.0]

Explanation

With a linear activation the outputs are just 3×2 + 1 = 7, 3×(-1) + 0 = -3 and 3×0.5 - 1.5 = 0.

References

Run the sample tests to check your code without submitting.

Example 1 Not run

Input:

inputs = [1.0, 2.0]
weights = [
    [0.5, -1.0],
    [1.5, 0.5]
]
biases = [0.0, -1.0]
activation = "relu"

Expected output:

[0.0, 1.5]

Your output

Example 2 Not run

Input:

inputs = [3.0]
weights = [
    [2.0],
    [-1.0],
    [0.5]
]
biases = [1.0, 0.0, -1.5]
activation = "linear"

Expected output:

[7.0, -3.0, 0.0]

Your output

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💡 Rust Basics & Examples You Can Try Above

1. Declaring Variables and Constants

Use let to declare variables. Use const for constants and mut for mutable variables.

let x = 10;
let pi: f64 = 3.14;
let name = "Alice";
let is_active = true;

const MAX_USERS: u32 = 100;

2. Conditionals (if / match)

Rust uses if for conditions and match for pattern matching.

let x = 2;
if x == 1 {
    println!("One");
} else if x == 2 {
    println!("Two");
} else {
    println!("Other");
}

match x {
    1 => println!("One"),
    2 => println!("Two"),
    _ => println!("Other"),
}

3. Loops

Rust supports for, while, and infinite loop.

for i in 0..3 {
    println!("{}", i);
}

let mut n = 3;
while n > 0 {
    println!("{}", n);
    n -= 1;
}

4. Arrays

Fixed-size arrays in Rust use square brackets. Use slices for views.

let nums = [10, 20, 30];
println!("{}", nums[1]);

5. Vectors (Dynamic Arrays)

Vec is used for dynamic arrays.

let mut fruits = vec!["apple", "banana"];
fruits.push("cherry");
fruits.pop();

for fruit in &fruits {
    println!("{}", fruit);
}

6. Console Input/Output

Use println! for output and std::io for input.

use std::io;

let mut name = String::new();
println!("Enter your name:");
io::stdin().read_line(&mut name).unwrap();
println!("Hello, {}", name.trim());

7. Functions

Functions use fn and can return values using ->.

fn greet(name: &str) -> String {
    format!("Hello, {}", name)
}

println!("{}", greet("Alice"));

8. HashMaps

Use std::collections::HashMap for key-value data.

use std::collections::HashMap;

let mut person = HashMap::new();
person.insert("name", "Bob");
println!("{}", person["name"])

9. Error Handling

Rust handles errors using Result and match or unwrap().

fn fail() -> Result<(), String> {
    Err("Something went wrong".to_string())
}

match fail() {
    Ok(_) => println!("Success"),
    Err(e) => println!("{}", e),
}

10. File I/O

Use std::fs to read and write files.

use std::fs;

fs::write("file.txt", "Hello File").unwrap();
let content = fs::read_to_string("file.txt").unwrap();
println!("{}", content);

11. String Manipulation

Strings in Rust are heap-allocated and support many methods.

let mut text = String::from(" Hello Rust ");
println!("{}", text.trim());
println!("{}", text.to_uppercase());
text = text.replace("Hello", "Hi");
println!("{}", text);

12. Structs & Methods

Rust uses struct for data types and impl for methods.

struct Person {
    name: String,
}

impl Person {
    fn greet(&self) -> String {
        format!("Hi, I'm {}", self.name)
    }
}

let p = Person { name: "Alice".to_string() };
println!("{}", p.greet());

13. References & Borrowing

Rust uses & to borrow values and &mut for mutable references.

fn update(x: &mut i32) {
    *x += 1;
}

let mut value = 10;
update(&mut value);
println!("{}", value);