Pruning — standard (10m)

L₂-norm sampling of rows

Procedure L2NormSample(A ∈ ℝ^{n×d}, s)

1. For each row \( i = 1 \ldots n \): \( \ell_i \gets \lVert A_{i,*} \rVert_2^2 \)
2. Let \( P \gets \sum_{j=1}^n \ell_j \)
3. For each \( i \): \( p_i \gets \ell_i / P \)
4. Initialize \( \tilde A \gets [\,] \)
5. Repeat \( s \) times: draw \( i_t \sim p \), set \( \mathbf r \gets A_{i_t,*} \), rescale \( \mathbf r \gets \mathbf r/\sqrt{s p_{i_t}} \), stack.
6. Return \( \tilde A \).

Leverage-score sampling

Procedure LeverageSample(A ∈ ℝ^{n×d}, s)

1. Thin SVD: \( A = U\Sigma V^\top \)
2. \( \ell_i \gets \lVert U_{i,*} \rVert_2^2 \), normalize to probabilities, then sample like above.

These give principled alternatives to plain magnitude pruning.