Solutions

LM-C10-C-001

The model produces one logit per vocabulary item, so it produces 6 logits.

LM-C10-C-002

There is one target token per prediction position, so 12 positions give 12 targets.

LM-C10-C-003

Softmax over 4 items returns 4 probabilities.

LM-C10-C-004

One token id selects one embedding row.

LM-C10-C-005

Yes. Cross-entropy produces gradients, and the optimizer uses those gradients to update parameters.