#0018

Dense Layer Forward Pass

MediumML18 min15 XP

Problem

Given input matrix X, weight matrix W, and bias vector b, return X @ W + b.

Why This Matters

A dense layer is just matrix multiplication plus bias. Once this clicks, neural networks become less like magic and more like repeated linear algebra.

Function Signature

def dense_forward(X, W, b):

Examples

Example 1

InputX shape (2, 3), W shape (3, 2), b shape (2,)

Outputoutput shape (2, 2)

Each input row becomes one output row, and each output unit has one bias.

Constraints

X is a 2D NumPy array of shape (batch, input_features).
W is a 2D NumPy array of shape (input_features, output_units).
b is a 1D NumPy array of shape (output_units,).

CodePython

import numpy as np

def dense_forward(X, W, b):
    """
    Input example: X shape (2, 3), W shape (3, 2), b shape (2,)
    Return: output shape (2, 2)
    Return the value from the function so the tests can compare it. Do not print unless the prompt asks.
    """
    # write your code here
    return X

import numpy as np

def dense_forward(X, W, b):
    """
    Input example: X shape (2, 3), W shape (3, 2), b shape (2,)
    Return: output shape (2, 2)
    Return the value from the function so the tests can compare it. Do not print unless the prompt asks.
    """
    # write your code here
    return X

Visible browser tests run here when available.

Testcases1 visible / 4 hidden categories

Two samples, two output units

InputX = [[1,2,3],[4,5,6]]

Expected[[5, 7], [11, 13]]

The bias is added to every row after matrix multiplication.

Hidden Test Categories

Single sample batchOne output unitNegative weightsFloating point inputs