dense-forward-pass — NVIDIA case

NVIDIA-inspired GPU-scheduler team is testing a lightweight neural score used to estimate whether a workload will fit a device profile. You need to implement the dense forward pass exactly, because a shape or bias error here would make every downstream score unreliable.

Compute a fully connected layer $Y=X{W}^{\mathrm{\top }}+bY=XW^\backslash top+b$ for a batch. X has shape (n, d_in), W has shape (d_out, d_in) (one row of weights per output unit, as in PyTorch's nn.Linear) and b has length d_out.

Implement solve(X,W,b).

Returns. Return an array of shape (n, d_out).

Examples

Example 1

Input:

solve([[1, 2]], [[1, 0], [0, 1]], [1, 2])

Output:

[[2, 4]]

Example 2

Input:

solve([[1.0, 1.0], [2.0, 0.0]], [[1.0, 2.0]], [0.5])

Output:

[[3.5], [2.5]]