Medium

Dense Layer Forward Pass

Medium

~18 min

code completion

A single dense (fully connected) layer computes:

output = ReLU (X W + b)

where:

X

is the input matrix of shape (m, n_in)

W

is the weight matrix of shape (n_in, n_out)

b

is the bias vector of shape (n_out,)

ReLU is applied element-wise to the result

This combines a linear transformation (the matrix multiply + bias) with a nonlinearity (ReLU) — the building block of deep networks.

Your task:

Implement dense_forward(X, W, b) that returns relu(X @ W + b).

Example Tests

Negative pre-activation clipped to 0

Input: {"W":[[1,-1],[2,-2]],"X":[[1,2]],"b":[0,0]}

Expected: [[5,0]]

Identity-like weights with bias

Input: {"W":[[1],[1]],"X":[[1,0],[0,1]],"b":[0]}

Expected: [[1],[1]]

Output shape is (m, n_out)

Input: {"W":[[1,0],[0,1],[1,1]],"X":[[1,2,3],[4,5,6]],"b":[0,0]}

Expected: [2,2]

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