modeling_pure_bert.py

import torch
import torch.nn as nn
import numpy as np
from torch.autograd import Function
from transformers import (
    BertModel,
    PreTrainedModel,
)
from typing import Union, Tuple, Optional
from transformers.modeling_outputs import (
    SequenceClassifierOutput, 
    MultipleChoiceModelOutput, 
    QuestionAnsweringModelOutput
)
from transformers.utils import ModelOutput

from .configuration_pure_bert import PureBertConfig

PureBertModel = BertModel


class CovarianceFunction(Function):

    @staticmethod
    def forward(ctx, inputs):
        x = inputs
        b, c, h, w = x.data.shape
        m = h * w
        x = x.view(b, c, m)
        I_hat = (-1.0 / m / m) * torch.ones(m, m, device=x.device) + (
            1.0 / m
        ) * torch.eye(m, m, device=x.device)
        I_hat = I_hat.view(1, m, m).repeat(b, 1, 1).type(x.dtype)
        y = x @ I_hat @ x.transpose(-1, -2)
        ctx.save_for_backward(inputs, I_hat)
        return y

    @staticmethod
    def backward(ctx, grad_output):
        inputs, I_hat = ctx.saved_tensors
        x = inputs
        b, c, h, w = x.data.shape
        m = h * w
        x = x.view(b, c, m)
        grad_input = grad_output + grad_output.transpose(1, 2)
        grad_input = grad_input @ x @ I_hat
        grad_input = grad_input.reshape(b, c, h, w)
        return grad_input


class Covariance(nn.Module):

    def __init__(self):
        super(Covariance, self).__init__()
        
    def _covariance(self, x):
        return CovarianceFunction.apply(x)

    def forward(self, x):
        # x should be [batch_size, seq_len, embed_dim]
        if x.dim() == 2:
            x = x.transpose(-1, -2)
            C = self._covariance(x[None, :, :, None])
        C = C.squeeze(dim=0)
        return C


class PFSA(torch.nn.Module):
    """
    https://openreview.net/pdf?id=isodM5jTA7h
    """
    def __init__(self, input_dim, alpha=1):
        super(PFSA, self).__init__()
        self.input_dim = input_dim
        self.alpha = alpha

    def forward_one_sample(self, x):
        x = x.transpose(1, 2)[..., None]
        k = torch.mean(x, dim=[-1, -2], keepdim=True)
        kd = torch.sqrt((k - k.mean(dim=1, keepdim=True)).pow(2).sum(dim=1, keepdim=True)) # [B, 1, 1, 1]
        qd = torch.sqrt((x - x.mean(dim=1, keepdim=True)).pow(2).sum(dim=1, keepdim=True)) # [B, 1, T, 1]
        C_qk = (((x - x.mean(dim=1, keepdim=True)) * (k - k.mean(dim=1, keepdim=True))).sum(dim=1, keepdim=True)) / (qd * kd)
        A = (1 - torch.sigmoid(C_qk)) ** self.alpha
        out = x * A
        out = out.squeeze(dim=-1).transpose(1, 2)
        return out

    def forward(self, input_values, attention_mask=None):
        """
        x: [B, T, F]
        """
        out = []
        b, t, f = input_values.shape
        for x, mask in zip(input_values, attention_mask):
            x = x.view(1, t, f)
            # x_in = x[:, :sum(mask), :]
            x_in = x[:, :int(mask.sum().item()), :]
            x_out = self.forward_one_sample(x_in)
            x_expanded = torch.zeros_like(x, device=x.device)
            x_expanded[:, :x_out.shape[-2], :x_out.shape[-1]] = x_out
            out.append(x_expanded)
        out = torch.vstack(out)
        out = out.view(b, t, f)
        return out


class PURE(torch.nn.Module):

    def __init__(
        self, 
        in_dim, 
        svd_rank=16, 
        num_pc_to_remove=1, 
        center=False, 
        num_iters=2, 
        alpha=1, 
        disable_pcr=False, 
        disable_pfsa=False, 
        disable_covariance=True, 
        *args, **kwargs
    ):
        super().__init__()
        self.in_dim = in_dim
        self.svd_rank = svd_rank
        self.num_pc_to_remove = num_pc_to_remove
        self.center = center
        self.num_iters = num_iters
        self.do_pcr = not disable_pcr
        self.do_pfsa = not disable_pfsa
        self.do_covariance = not disable_covariance
        self.attention = PFSA(in_dim, alpha=alpha)
    
    def _compute_pc(self, X, attention_mask):
        """
        x: (B, T, F)
        """
        pcs = []
        bs, seqlen, dim = X.shape
        for x, mask in zip(X, attention_mask):
            rank = int(mask.sum().item())
            x = x[:rank, :]
            if self.do_covariance:
                x = Covariance()(x)
                q = self.svd_rank
            else:
                q = min(self.svd_rank, rank)
            _, _, V = torch.pca_lowrank(x, q=q, center=self.center, niter=self.num_iters)
            # _, _, Vh = torch.linalg.svd(x_, full_matrices=False)
            # V = Vh.mH
            pc = V.transpose(0, 1)[:self.num_pc_to_remove, :] # pc: [K, F]
            pcs.append(pc)
        # pcs = torch.vstack(pcs)
        # pcs = pcs.view(bs, self.num_pc_to_remove, dim)
        return pcs

    def _remove_pc(self, X, pcs):
        """
        [B, T, F], [B, ..., F]
        """
        b, t, f = X.shape
        out = []
        for i, (x, pc) in enumerate(zip(X, pcs)):
            # v = []
            # for j, t in enumerate(x):
            #     t_ = t
            #     for c_ in c:
            #         t_ = t_.view(f, 1) - c_.view(f, 1) @ c_.view(1, f) @ t.view(f, 1)
            #     v.append(t_.transpose(-1, -2))
            # v = torch.vstack(v)
            v = x - x @ pc.transpose(0, 1) @ pc
            out.append(v[None, ...])
        out = torch.vstack(out)
        return out

    def forward(self, input_values, attention_mask=None, *args, **kwargs):
        """
        PCR -> Attention
        x: (B, T, F)
        """
        x = input_values
        if self.do_pcr:
            pc = self._compute_pc(x, attention_mask) # pc: [B, K, F]
            xx = self._remove_pc(x, pc)
            # xx = xt - xt @ pc.transpose(1, 2) @ pc # [B, T, F] * [B, F, K] * [B, K, F] = [B, T, F]
        else:
            xx = x
        if self.do_pfsa:
            xx = self.attention(xx, attention_mask)
        return xx


class StatisticsPooling(torch.nn.Module):

    def __init__(self, return_mean=True, return_std=True):
        super().__init__()

        # Small value for GaussNoise
        self.eps = 1e-5
        self.return_mean = return_mean
        self.return_std = return_std
        if not (self.return_mean or self.return_std):
            raise ValueError(
                "both of statistics are equal to False \n"
                "consider enabling mean and/or std statistic pooling"
            )

    def forward(self, input_values, attention_mask=None):
        """Calculates mean and std for a batch (input tensor).

        Arguments
        ---------
        x : torch.Tensor
            It represents a tensor for a mini-batch.
        """
        x = input_values
        if attention_mask is None:
            if self.return_mean:
                mean = x.mean(dim=1)
            if self.return_std:
                std = x.std(dim=1)
        else:
            mean = []
            std = []
            for snt_id in range(x.shape[0]):
                # Avoiding padded time steps
                lengths = torch.sum(attention_mask, dim=1)
                relative_lengths = lengths / torch.max(lengths)
                actual_size = torch.round(relative_lengths[snt_id] * x.shape[1]).int()
                # actual_size = int(torch.round(lengths[snt_id] * x.shape[1]))

                # computing statistics
                if self.return_mean:
                    mean.append(
                        torch.mean(x[snt_id, 0:actual_size, ...], dim=0)
                    )
                if self.return_std:
                    std.append(torch.std(x[snt_id, 0:actual_size, ...], dim=0))
            if self.return_mean:
                mean = torch.stack(mean)
            if self.return_std:
                std = torch.stack(std)

        if self.return_mean:
            gnoise = self._get_gauss_noise(mean.size(), device=mean.device)
            gnoise = gnoise
            mean += gnoise
        if self.return_std:
            std = std + self.eps

        # Append mean and std of the batch
        if self.return_mean and self.return_std:
            pooled_stats = torch.cat((mean, std), dim=1)
            pooled_stats = pooled_stats.unsqueeze(1)
        elif self.return_mean:
            pooled_stats = mean.unsqueeze(1)
        elif self.return_std:
            pooled_stats = std.unsqueeze(1)

        return pooled_stats

    def _get_gauss_noise(self, shape_of_tensor, device="cpu"):
        """Returns a tensor of epsilon Gaussian noise.

        Arguments
        ---------
        shape_of_tensor : tensor
            It represents the size of tensor for generating Gaussian noise.
        """
        gnoise = torch.randn(shape_of_tensor, device=device)
        gnoise -= torch.min(gnoise)
        gnoise /= torch.max(gnoise)
        gnoise = self.eps * ((1 - 9) * gnoise + 9)

        return gnoise


class PureBertPreTrainedModel(PreTrainedModel):
    """
    An abstract class to handle weights initialization and a simple interface for downloading and loading pretrained
    models.
    """

    config_class = PureBertConfig
    base_model_prefix = "bert"
    supports_gradient_checkpointing = True
    _supports_sdpa = True

    def _init_weights(self, module):
        """Initialize the weights"""
        if isinstance(module, nn.Linear):
            # Slightly different from the TF version which uses truncated_normal for initialization
            # cf https://github.com/pytorch/pytorch/pull/5617
            module.weight.data.normal_(mean=0.0, std=self.config.initializer_range)
            if module.bias is not None:
                module.bias.data.zero_()
        elif isinstance(module, nn.Embedding):
            module.weight.data.normal_(mean=0.0, std=self.config.initializer_range)
            if module.padding_idx is not None:
                module.weight.data[module.padding_idx].zero_()
        elif isinstance(module, nn.LayerNorm):
            module.bias.data.zero_()
            module.weight.data.fill_(1.0)


class BertClsForSequenceClassification(PureBertPreTrainedModel):

    def __init__(self, config, add_pooling_layer=True):
        super().__init__(config)
        self.num_labels = config.num_labels
        self.config = config

        self.bert = PureBertModel(config, add_pooling_layer=add_pooling_layer)
        classifier_dropout = (
            config.classifier_dropout if config.classifier_dropout is not None else config.hidden_dropout_prob
        )
        self.dropout = nn.Dropout(classifier_dropout)
        self.classifier = nn.Linear(config.hidden_size, config.num_labels)

        # Initialize weights and apply final processing
        self.post_init()

    def forward(
        self,
        input_ids: Optional[torch.Tensor] = None,
        attention_mask: Optional[torch.Tensor] = None,
        token_type_ids: Optional[torch.Tensor] = None,
        position_ids: Optional[torch.Tensor] = None,
        head_mask: Optional[torch.Tensor] = None,
        inputs_embeds: Optional[torch.Tensor] = None,
        labels: Optional[torch.Tensor] = None,
        output_attentions: Optional[bool] = None,
        output_hidden_states: Optional[bool] = None,
        return_dict: Optional[bool] = None,
    ) -> Union[Tuple[torch.Tensor], SequenceClassifierOutput]:
        r"""
        labels (`torch.LongTensor` of shape `(batch_size,)`, *optional*):
            Labels for computing the sequence classification/regression loss. Indices should be in `[0, ...,
            config.num_labels - 1]`. If `config.num_labels == 1` a regression loss is computed (Mean-Square loss), If
            `config.num_labels > 1` a classification loss is computed (Cross-Entropy).
        """
        return_dict = return_dict if return_dict is not None else self.config.use_return_dict

        outputs = self.bert(
            input_ids,
            attention_mask=attention_mask,
            token_type_ids=token_type_ids,
            position_ids=position_ids,
            head_mask=head_mask,
            inputs_embeds=inputs_embeds,
            output_attentions=output_attentions,
            output_hidden_states=output_hidden_states,
            return_dict=return_dict,
        )

        pooled_output = outputs.pooler_output
        if pooled_output is None:
            pooled_output = outputs.last_hidden_state[:, 0, :]

        pooled_output = self.dropout(pooled_output)
        logits = self.classifier(pooled_output)

        loss = None
        if labels is not None:
            if self.config.problem_type is None:
                if self.num_labels == 1:
                    self.config.problem_type = "regression"
                elif self.num_labels > 1 and (labels.dtype == torch.long or labels.dtype == torch.int):
                    self.config.problem_type = "single_label_classification"
                else:
                    self.config.problem_type = "multi_label_classification"

            if self.config.problem_type == "regression":
                loss_fct = nn.MSELoss()
                if self.num_labels == 1:
                    loss = loss_fct(logits.squeeze(), labels.squeeze())
                else:
                    loss = loss_fct(logits, labels)
            elif self.config.problem_type == "single_label_classification":
                loss_fct = nn.CrossEntropyLoss()
                loss = loss_fct(logits.view(-1, self.num_labels), labels.view(-1))
            elif self.config.problem_type == "multi_label_classification":
                loss_fct = nn.BCEWithLogitsLoss()
                loss = loss_fct(logits, labels)
        if not return_dict:
            output = (logits,) + outputs[2:]
            return ((loss,) + output) if loss is not None else output

        return SequenceClassifierOutput(
            loss=loss,
            logits=logits,
            hidden_states=outputs.hidden_states,
            attentions=outputs.attentions,
        )


class BertMixupForSequenceClassification(PureBertPreTrainedModel):

    def __init__(self, config, alpha=1.0, label_smoothing=0.0):
        super().__init__(config)
        self.num_labels = config.num_labels
        self.alpha = alpha
        self.label_smoothing = label_smoothing
        self.config = config

        self.bert = PureBertModel(config)
        classifier_dropout = (
            config.classifier_dropout if config.classifier_dropout is not None else config.hidden_dropout_prob
        )
        self.dropout = nn.Dropout(classifier_dropout)
        self.classifier = nn.Linear(config.hidden_size, config.num_labels)

        # Initialize weights and apply final processing
        self.post_init()

    def mixup_data(self, embeddings, labels, alpha=1.0):
        """Compute the mixup data. Returns mixed inputs, pairs of targets, and lambda"""
        if alpha > 0:
            lam = np.random.beta(alpha, alpha)
        else:
            lam = 1

        batch_size = embeddings.size()[0]
        index = torch.randperm(batch_size).to(embeddings.device)

        mixed_x = lam * embeddings + (1 - lam) * embeddings[index, :]
        y_a, y_b = labels, labels[index]
        return mixed_x, y_a, y_b, lam

    def forward(
        self,
        input_ids: Optional[torch.Tensor] = None,
        attention_mask: Optional[torch.Tensor] = None,
        token_type_ids: Optional[torch.Tensor] = None,
        position_ids: Optional[torch.Tensor] = None,
        head_mask: Optional[torch.Tensor] = None,
        inputs_embeds: Optional[torch.Tensor] = None,
        labels: Optional[torch.Tensor] = None,
        output_attentions: Optional[bool] = None,
        output_hidden_states: Optional[bool] = None,
        return_dict: Optional[bool] = None,
    ) -> Union[Tuple[torch.Tensor], SequenceClassifierOutput]:
        r"""
        labels (`torch.LongTensor` of shape `(batch_size,)`, *optional*):
            Labels for computing the sequence classification/regression loss. Indices should be in `[0, ...,
            config.num_labels - 1]`. If `config.num_labels == 1` a regression loss is computed (Mean-Square loss), If
            `config.num_labels > 1` a classification loss is computed (Cross-Entropy).
        """
        return_dict = return_dict if return_dict is not None else self.config.use_return_dict

        outputs = self.bert(
            input_ids,
            attention_mask=attention_mask,
            token_type_ids=token_type_ids,
            position_ids=position_ids,
            head_mask=head_mask,
            inputs_embeds=inputs_embeds,
            output_attentions=output_attentions,
            output_hidden_states=output_hidden_states,
            return_dict=return_dict,
        )

        if self.training:
            mixed_embeddings, targets_a, targets_b, lam = self.mixup_data(outputs.pooler_output, labels, self.alpha)
            mixed_embeddings = self.dropout(mixed_embeddings)
            logits = self.classifier(mixed_embeddings)
        else:
            pooler_output = self.dropout(outputs.pooler_output)
            logits = self.classifier(pooler_output)

        loss = None
        if labels is not None:
            if self.config.problem_type is None:
                if self.num_labels == 1:
                    self.config.problem_type = "regression"
                elif self.num_labels > 1 and (labels.dtype == torch.long or labels.dtype == torch.int):
                    self.config.problem_type = "single_label_classification"
                else:
                    self.config.problem_type = "multi_label_classification"

            if self.config.problem_type == "regression":
                loss_fct = nn.MSELoss()
                if self.num_labels == 1:
                    loss = loss_fct(logits.squeeze(), labels.squeeze())
                else:
                    loss = loss_fct(logits, labels)
            elif self.config.problem_type == "single_label_classification":
                loss_fct = nn.CrossEntropyLoss(label_smoothing=self.label_smoothing)
                logits = logits.view(-1, self.num_labels)
                if self.training:
                    targets_a = targets_a.view(-1)
                    targets_b = targets_b.view(-1)
                    loss = lam * loss_fct(logits, targets_a) + (1 - lam) * loss_fct(logits, targets_b)
                else:
                    loss = loss_fct(logits, labels.view(-1))
            elif self.config.problem_type == "multi_label_classification":
                loss_fct = nn.BCEWithLogitsLoss()
                loss = loss_fct(logits, labels)
        if not return_dict:
            output = (logits,) + outputs[2:]
            return ((loss,) + output) if loss is not None else output

        return SequenceClassifierOutput(
            loss=loss,
            logits=logits,
            hidden_states=outputs.hidden_states,
            attentions=outputs.attentions,
        )


class PureBertForSequenceClassification(PureBertPreTrainedModel):

    def __init__(
        self, 
        config, 
        label_smoothing=0.0, 
    ):
        super().__init__(config)
        self.label_smoothing = label_smoothing
        self.num_labels = config.num_labels
        self.config = config

        self.bert = PureBertModel(config, add_pooling_layer=False)
        classifier_dropout = (
            config.classifier_dropout if config.classifier_dropout is not None else config.hidden_dropout_prob
        )
        self.pure = PURE(
            in_dim=config.hidden_size, 
            svd_rank=config.svd_rank, 
            num_pc_to_remove=config.num_pc_to_remove, 
            center=config.center, 
            num_iters=config.num_iters, 
            alpha=config.alpha, 
            disable_pcr=config.disable_pcr, 
            disable_pfsa=config.disable_pfsa, 
            disable_covariance=config.disable_covariance
        )
        self.mean = StatisticsPooling(return_mean=True, return_std=False)
        self.dropout = nn.Dropout(classifier_dropout)
        self.classifier = nn.Linear(config.hidden_size, config.num_labels)

        # Initialize weights and apply final processing
        self.post_init()

    def forward_pure_embeddings(
        self,
        input_ids: Optional[torch.Tensor] = None,
        attention_mask: Optional[torch.Tensor] = None,
        token_type_ids: Optional[torch.Tensor] = None,
        position_ids: Optional[torch.Tensor] = None,
        head_mask: Optional[torch.Tensor] = None,
        inputs_embeds: Optional[torch.Tensor] = None,
        labels: Optional[torch.Tensor] = None,
        output_attentions: Optional[bool] = None,
        output_hidden_states: Optional[bool] = None,
        return_dict: Optional[bool] = None,
    ) -> Union[Tuple[torch.Tensor], SequenceClassifierOutput]:
        r"""
        labels (`torch.LongTensor` of shape `(batch_size,)`, *optional*):
            Labels for computing the sequence classification/regression loss. Indices should be in `[0, ...,
            config.num_labels - 1]`. If `config.num_labels == 1` a regression loss is computed (Mean-Square loss), If
            `config.num_labels > 1` a classification loss is computed (Cross-Entropy).
        """
        return_dict = return_dict if return_dict is not None else self.config.use_return_dict

        outputs = self.bert(
            input_ids,
            attention_mask=attention_mask,
            token_type_ids=token_type_ids,
            position_ids=position_ids,
            head_mask=head_mask,
            inputs_embeds=inputs_embeds,
            output_attentions=output_attentions,
            output_hidden_states=output_hidden_states,
            return_dict=return_dict,
        )

        token_embeddings = outputs.last_hidden_state
        token_embeddings = self.pure(token_embeddings, attention_mask)

        return ModelOutput(
            last_hidden_state=token_embeddings,
        )

    def forward(
        self,
        input_ids: Optional[torch.Tensor] = None,
        attention_mask: Optional[torch.Tensor] = None,
        token_type_ids: Optional[torch.Tensor] = None,
        position_ids: Optional[torch.Tensor] = None,
        head_mask: Optional[torch.Tensor] = None,
        inputs_embeds: Optional[torch.Tensor] = None,
        labels: Optional[torch.Tensor] = None,
        output_attentions: Optional[bool] = None,
        output_hidden_states: Optional[bool] = None,
        return_dict: Optional[bool] = None,
    ) -> Union[Tuple[torch.Tensor], SequenceClassifierOutput]:
        r"""
        labels (`torch.LongTensor` of shape `(batch_size,)`, *optional*):
            Labels for computing the sequence classification/regression loss. Indices should be in `[0, ...,
            config.num_labels - 1]`. If `config.num_labels == 1` a regression loss is computed (Mean-Square loss), If
            `config.num_labels > 1` a classification loss is computed (Cross-Entropy).
        """
        return_dict = return_dict if return_dict is not None else self.config.use_return_dict

        outputs = self.bert(
            input_ids,
            attention_mask=attention_mask,
            token_type_ids=token_type_ids,
            position_ids=position_ids,
            head_mask=head_mask,
            inputs_embeds=inputs_embeds,
            output_attentions=output_attentions,
            output_hidden_states=output_hidden_states,
            return_dict=return_dict,
        )

        token_embeddings = outputs.last_hidden_state
        token_embeddings = self.pure(token_embeddings, attention_mask)
        pooled_output = self.mean(token_embeddings).squeeze(1)
        pooled_output = self.dropout(pooled_output)
        logits = self.classifier(pooled_output)

        loss = None
        if labels is not None:
            if self.config.problem_type is None:
                if self.num_labels == 1:
                    self.config.problem_type = "regression"
                elif self.num_labels > 1 and (labels.dtype == torch.long or labels.dtype == torch.int):
                    self.config.problem_type = "single_label_classification"
                else:
                    self.config.problem_type = "multi_label_classification"

            if self.config.problem_type == "regression":
                loss_fct = nn.MSELoss()
                if self.num_labels == 1:
                    loss = loss_fct(logits.squeeze(), labels.squeeze())
                else:
                    loss = loss_fct(logits, labels)
            elif self.config.problem_type == "single_label_classification":
                loss_fct = nn.CrossEntropyLoss(label_smoothing=self.label_smoothing)
                loss = loss_fct(logits.view(-1, self.num_labels), labels.view(-1))
            elif self.config.problem_type == "multi_label_classification":
                loss_fct = nn.BCEWithLogitsLoss()
                loss = loss_fct(logits, labels)
        if not return_dict:
            output = (logits,) + outputs[2:]
            return ((loss,) + output) if loss is not None else output

        return SequenceClassifierOutput(
            loss=loss,
            logits=logits,
            hidden_states=outputs.hidden_states,
            attentions=outputs.attentions,
        )


class PureBertForMultipleChoice(PureBertPreTrainedModel):

    def __init__(
        self, 
        config, 
        label_smoothing=0.0, 
    ):
        super().__init__(config)
        self.label_smoothing = label_smoothing

        self.bert = PureBertModel(config)
        self.pure = PURE(
            in_dim=config.hidden_size, 
            svd_rank=config.svd_rank, 
            num_pc_to_remove=config.num_pc_to_remove, 
            center=config.center, 
            num_iters=config.num_iters, 
            alpha=config.alpha, 
            disable_pcr=config.disable_pcr, 
            disable_pfsa=config.disable_pfsa, 
            disable_covariance=config.disable_covariance
        )
        self.mean = StatisticsPooling(return_mean=True, return_std=False)
        classifier_dropout = (
            config.classifier_dropout if config.classifier_dropout is not None else config.hidden_dropout_prob
        )
        self.dropout = nn.Dropout(classifier_dropout)
        self.classifier = nn.Linear(config.hidden_size, 1)

        # Initialize weights and apply final processing
        self.post_init()

    def forward(
        self,
        input_ids: Optional[torch.Tensor] = None,
        attention_mask: Optional[torch.Tensor] = None,
        token_type_ids: Optional[torch.Tensor] = None,
        position_ids: Optional[torch.Tensor] = None,
        head_mask: Optional[torch.Tensor] = None,
        inputs_embeds: Optional[torch.Tensor] = None,
        labels: Optional[torch.Tensor] = None,
        output_attentions: Optional[bool] = None,
        output_hidden_states: Optional[bool] = None,
        return_dict: Optional[bool] = None,
    ) -> Union[Tuple[torch.Tensor], MultipleChoiceModelOutput]:
        r"""
        labels (`torch.LongTensor` of shape `(batch_size,)`, *optional*):
            Labels for computing the multiple choice classification loss. Indices should be in `[0, ...,
            num_choices-1]` where `num_choices` is the size of the second dimension of the input tensors. (See
            `input_ids` above)
        """
        return_dict = return_dict if return_dict is not None else self.config.use_return_dict
        num_choices = input_ids.shape[1] if input_ids is not None else inputs_embeds.shape[1]

        input_ids = input_ids.view(-1, input_ids.size(-1)) if input_ids is not None else None
        attention_mask = attention_mask.view(-1, attention_mask.size(-1)) if attention_mask is not None else None
        token_type_ids = token_type_ids.view(-1, token_type_ids.size(-1)) if token_type_ids is not None else None
        position_ids = position_ids.view(-1, position_ids.size(-1)) if position_ids is not None else None
        inputs_embeds = (
            inputs_embeds.view(-1, inputs_embeds.size(-2), inputs_embeds.size(-1))
            if inputs_embeds is not None
            else None
        )

        outputs = self.bert(
            input_ids,
            attention_mask=attention_mask,
            token_type_ids=token_type_ids,
            position_ids=position_ids,
            head_mask=head_mask,
            inputs_embeds=inputs_embeds,
            output_attentions=output_attentions,
            output_hidden_states=output_hidden_states,
            return_dict=return_dict,
        )

        token_embeddings = outputs.last_hidden_state
        token_embeddings = self.pure(token_embeddings, attention_mask)
        pooled_output = self.mean(token_embeddings).squeeze(1)
        pooled_output = self.dropout(pooled_output)

        logits = self.classifier(pooled_output)
        reshaped_logits = logits.view(-1, num_choices)

        loss = None
        if labels is not None:
            loss_fct = nn.CrossEntropyLoss(label_smoothing=self.label_smoothing)
            loss = loss_fct(reshaped_logits, labels)

        if not return_dict:
            output = (reshaped_logits,) + outputs[2:]
            return ((loss,) + output) if loss is not None else output

        return MultipleChoiceModelOutput(
            loss=loss,
            logits=reshaped_logits,
            hidden_states=outputs.hidden_states,
            attentions=outputs.attentions,
        )


class PureBertForQuestionAnswering(PureBertPreTrainedModel):

    def __init__(
        self, 
        config, 
        label_smoothing=0.0, 
    ):
        super().__init__(config)
        self.num_labels = config.num_labels
        self.label_smoothing = label_smoothing

        self.bert = PureBertModel(config, add_pooling_layer=False)
        self.pure = PURE(
            in_dim=config.hidden_size, 
            svd_rank=config.svd_rank, 
            num_pc_to_remove=config.num_pc_to_remove, 
            center=config.center, 
            num_iters=config.num_iters, 
            alpha=config.alpha, 
            disable_pcr=config.disable_pcr, 
            disable_pfsa=config.disable_pfsa, 
            disable_covariance=config.disable_covariance
        )
        self.qa_outputs = nn.Linear(config.hidden_size, config.num_labels)

        # Initialize weights and apply final processing
        self.post_init()

    def forward(
        self,
        input_ids: Optional[torch.Tensor] = None,
        attention_mask: Optional[torch.Tensor] = None,
        token_type_ids: Optional[torch.Tensor] = None,
        position_ids: Optional[torch.Tensor] = None,
        head_mask: Optional[torch.Tensor] = None,
        inputs_embeds: Optional[torch.Tensor] = None,
        start_positions: Optional[torch.Tensor] = None,
        end_positions: Optional[torch.Tensor] = None,
        output_attentions: Optional[bool] = None,
        output_hidden_states: Optional[bool] = None,
        return_dict: Optional[bool] = None,
    ) -> Union[Tuple[torch.Tensor], QuestionAnsweringModelOutput]:
        r"""
        start_positions (`torch.LongTensor` of shape `(batch_size,)`, *optional*):
            Labels for position (index) of the start of the labelled span for computing the token classification loss.
            Positions are clamped to the length of the sequence (`sequence_length`). Position outside of the sequence
            are not taken into account for computing the loss.
        end_positions (`torch.LongTensor` of shape `(batch_size,)`, *optional*):
            Labels for position (index) of the end of the labelled span for computing the token classification loss.
            Positions are clamped to the length of the sequence (`sequence_length`). Position outside of the sequence
            are not taken into account for computing the loss.
        """
        return_dict = return_dict if return_dict is not None else self.config.use_return_dict

        outputs = self.bert(
            input_ids,
            attention_mask=attention_mask,
            token_type_ids=token_type_ids,
            position_ids=position_ids,
            head_mask=head_mask,
            inputs_embeds=inputs_embeds,
            output_attentions=output_attentions,
            output_hidden_states=output_hidden_states,
            return_dict=return_dict,
        )

        token_embeddings = outputs.last_hidden_state
        sequence_output = self.pure(token_embeddings, attention_mask)

        logits = self.qa_outputs(sequence_output)
        start_logits, end_logits = logits.split(1, dim=-1)
        start_logits = start_logits.squeeze(-1).contiguous()
        end_logits = end_logits.squeeze(-1).contiguous()

        total_loss = None
        if start_positions is not None and end_positions is not None:
            # If we are on multi-GPU, split add a dimension
            if len(start_positions.size()) > 1:
                start_positions = start_positions.squeeze(-1)
            if len(end_positions.size()) > 1:
                end_positions = end_positions.squeeze(-1)
            # sometimes the start/end positions are outside our model inputs, we ignore these terms
            ignored_index = start_logits.size(1)
            start_positions = start_positions.clamp(0, ignored_index)
            end_positions = end_positions.clamp(0, ignored_index)

            loss_fct = nn.CrossEntropyLoss(ignore_index=ignored_index)
            start_loss = loss_fct(start_logits, start_positions)
            end_loss = loss_fct(end_logits, end_positions)
            total_loss = (start_loss + end_loss) / 2

        if not return_dict:
            output = (start_logits, end_logits) + outputs[2:]
            return ((total_loss,) + output) if total_loss is not None else output

        return QuestionAnsweringModelOutput(
            loss=total_loss,
            start_logits=start_logits,
            end_logits=end_logits,
            hidden_states=outputs.hidden_states,
            attentions=outputs.attentions,
        )