I mean mathematically you need at least one vector to propagate through the network, don't you? That would be a one hot encoding of the starting token. Actually interesting to think about what happens if you make that vector zero everywhere.

In the matmul, it'd just zero out all parameters. In older models, you'd still have bias vectors but I think recent models don't use those anymore. So the output would be zero probability for each token, if I'm not mistaken.