Apply a shared base linear layer plus a per-row LoRA adapter in one batched call. This is the serving primitive behind Punica and S-LoRA: many requests, one weight matrix $W$, different adapters.

Inputs

• x: (batch, in_features)
• W: (in_features, out_features) — base weights, used as $x W$
• A: (n_lora, rank, in_features)
• B: (n_lora, out_features, rank)
• lora_ids: length batch ints; lora_ids[i] selects the adapter for row $i$. Use -1 for "base only" (no adapter on that row)
• scales: (n_lora,) — usually $\alpha / r$ for each adapter

Output y of shape (batch, out_features):

$y_i = x_i W + s_{id}\, (x_i A_{id}^\top)\, B_{id}^\top$

when id = lora_ids[i] >= 0, and $y_i = x_i W$ when id == -1.

Here $A_{id}$ has shape (rank, in_features) and $B_{id}$ has shape (out_features, rank), so $x_i A_{id}^\top$ is (rank,) and the second multiply lands in out_features.

Rows may share an adapter. Unused adapters in A/B are ignored.