Questions about discriminator attribute models

[yangshuodelove]

In Section 4.3, the paper says, "... we use the distirubtion ~p_(t+1) (instead of a hard sample x_(t+1)), and feed it forward to obtain (a biased) estimate of the next token’s embedding and then update delta_H_t." In the code, I found hard sample x_(t+1) (i.e., model(last, ...)) is feeded into the model and got the probs in the first time,

all_logits, _, all_hidden = model(last, past=perturbed_past)
        hidden = all_hidden[-1]
        new_accumulated_hidden = accumulated_hidden + torch.sum(
            hidden,
            dim=1
        ).detach()
        # TODO: Check the layer-norm consistency of this with trained discriminator (Sumanth)
        logits = all_logits[:, -1, :]
        probs = F.softmax(logits, dim=-1)

and then, the code put the soft distribution ~p_(t+1) (i.e., inputs_embeds) in the model in the second time,

if loss_type == PPLM_DISCRIM or loss_type == PPLM_BOW_DISCRIM:
            ce_loss = torch.nn.CrossEntropyLoss()
            # TODO why we need to do this assignment and not just using unpert_past? (Sumanth)
            curr_unpert_past = unpert_past
            curr_probs = torch.unsqueeze(probs, dim=1)
            wte = model.resize_token_embeddings()
            for _ in range(horizon_length):
                inputs_embeds = torch.matmul(curr_probs, wte.weight.data)
                _, curr_unpert_past, curr_all_hidden = model(
                    past=curr_unpert_past,
                    inputs_embeds=inputs_embeds
                )
                curr_hidden = curr_all_hidden[-1]
                new_accumulated_hidden = new_accumulated_hidden + torch.sum(
                    curr_hidden, dim=1)

My questions are
(1) Why it uses past=curr_unpert_past, instead of past=past, to predict next token in the second time? Because if you predict next token, we need to input GPT2 with current token_id (or embedding) and the past_key_values before current token.
(2) In the second time, the code didn't update logits (i.e., _, curr_unpert_past, curr_all_hidden = model(...), so it cann't update probs, thus it use the probs in the first time (i.e., probs = F.softmax(logits, dim=-1). Why not to update probs at the second time?
Thank you so much. Please correct me if I'm wrong.