text: import torch
  import torch.nn as nn
  import torch.nn.functional as F
  from mmcv.cnn import bias_init_with_prob, normal_init
  from mmcv.runner import force_fp32
  
  from mmdet.core import distance2bbox, multi_apply
  from mmdet.core.bbox import bbox_overlaps
  from mmdet.models import HEADS
  from mmdet.models.dense_heads.atss_head import reduce_mean
  from mmdet.models.dense_heads.fcos_head import FCOSHead
  from mmdet.models.dense_heads.paa_head import levels_to_images
  
  EPS = 1e-12
  
  
  class CenterPrior(nn.Module):
      """Center Weighting module to adjust the category-specific prior
      distributions.
  
      Args:
          force_topk (bool): When no point falls into gt_bbox, forcibly
              select the k points closest to the center to calculate
              the center prior. Defaults to False.
          topk (int): The number of points used to calculate the
              center prior when no point falls in gt_bbox. Only work when
              force_topk if True. Defaults to 9.
          num_classes (int): The class number of dataset. Defaults to 80.
          strides (tuple[int]): The stride of each input feature map. Defaults
              to (8, 16, 32, 64, 128).
      """
  
      def __init__(self,
                   force_topk=False,
                   topk=9,
                   num_classes=80,
                   strides=(8, 16, 32, 64, 128)):
          super(CenterPrior, self).__init__()
          self.mean = nn.Parameter(torch.zeros(num_classes, 2))
          self.sigma = nn.Parameter(torch.ones(num_classes, 2))
          self.strides = strides
          self.force_topk = force_topk
          self.topk = topk
  
      def forward(self, anchor_points_list, gt_bboxes, labels,
                  inside_gt_bbox_mask):
          """Get the center prior of each point on the feature map for each
          instance.
  
          Args:
              anchor_points_list (list[Tensor]): list of coordinate
                  of points on feature map. Each with shape
                  (num_points, 2).
              gt_bboxes (Tensor): The gt_bboxes with shape of
                  (num_gt, 4).
              labels (Tensor): The gt_labels with shape of (num_gt).
              inside_gt_bbox_mask (Tensor): Tensor of bool type,
                  with shape of (num_points, num_gt), each
                  value is used to mark whether this point falls
                  within a certain gt.
  
          Returns:
              tuple(Tensor):
  
                  - center_prior_weights(Tensor): Float tensor with shape \
                      of (num_points, num_gt). Each value represents \
                      the center weighting coefficient.
                  - inside_gt_bbox_mask (Tensor): Tensor of bool type, \
                      with shape of (num_points, num_gt), each \
                      value is used to mark whether this point falls \
                      within a certain gt or is the topk nearest points for \
                      a specific gt_bbox.
          """
          inside_gt_bbox_mask = inside_gt_bbox_mask.clone()
          num_gts = len(labels)
          num_points = sum([len(item) for item in anchor_points_list])
          if num_gts == 0:
              return gt_bboxes.new_zeros(num_points,
                                         num_gts), inside_gt_bbox_mask
          center_prior_list = []
          for slvl_points, stride in zip(anchor_points_list, self.strides):
              # slvl_points: points from single level in FPN, has shape (h*w, 2)
              # single_level_points has shape (h*w, num_gt, 2)
              single_level_points = slvl_points[:, None, :].expand(
                  (slvl_points.size(0), len(gt_bboxes), 2))
              gt_center_x = ((gt_bboxes[:, 0] + gt_bboxes[:, 2]) / 2)
              gt_center_y = ((gt_bboxes[:, 1] + gt_bboxes[:, 3]) / 2)
              gt_center = torch.stack((gt_center_x, gt_center_y), dim=1)
              gt_center = gt_center[None]
              # instance_center has shape (1, num_gt, 2)
              instance_center = self.mean[labels][None]
              # instance_sigma has shape (1, num_gt, 2)
              instance_sigma = self.sigma[labels][None]
              # distance has shape (num_points, num_gt, 2)
              distance = (((single_level_points - gt_center) / float(stride) -
                           instance_center)**2)
              center_prior = torch.exp(-distance /
                                       (2 * instance_sigma**2)).prod(dim=-1)
              center_prior_list.append(center_prior)
          center_prior_weights = torch.cat(center_prior_list, dim=0)
  
          if self.force_topk:
              gt_inds_no_points_inside = torch.nonzero(
                  inside_gt_bbox_mask.sum(0) == 0).reshape(-1)
              if gt_inds_no_points_inside.numel():
                  topk_center_index = \
                      center_prior_weights[:, gt_inds_no_points_inside].topk(
                                                               self.topk,
                                                               dim=0)[1]
                  temp_mask = inside_gt_bbox_mask[:, gt_inds_no_points_inside]
                  inside_gt_bbox_mask[:, gt_inds_no_points_inside] = \
                      torch.scatter(temp_mask,
                                    dim=0,
                                    index=topk_center_index,
                                    src=torch.ones_like(
                                      topk_center_index,
                                      dtype=torch.bool))
  
          center_prior_weights[~inside_gt_bbox_mask] = 0
          return center_prior_weights, inside_gt_bbox_mask
  
  
  @HEADS.register_module()
  class AutoAssignHead(FCOSHead):
      """AutoAssignHead head used in AutoAssign.
  
      More details can be found in the `paper
      <https://arxiv.org/abs/2007.03496>`_ .
  
      Args:
          force_topk (bool): Used in center prior initialization to
              handle extremely small gt. Default is False.
          topk (int): The number of points used to calculate the
              center prior when no point falls in gt_bbox. Only work when
              force_topk if True. Defaults to 9.
          pos_loss_weight (float): The loss weight of positive loss
              and with default value 0.25.
          neg_loss_weight (float): The loss weight of negative loss
              and with default value 0.75.
          center_loss_weight (float): The loss weight of center prior
              loss and with default value 0.75.
      """
  
      def __init__(self,
                   *args,
                   force_topk=False,
                   topk=9,
                   pos_loss_weight=0.25,
                   neg_loss_weight=0.75,
                   center_loss_weight=0.75,
                   **kwargs):
          super().__init__(*args, conv_bias=True, **kwargs)
          self.center_prior = CenterPrior(
              force_topk=force_topk,
              topk=topk,
              num_classes=self.num_classes,
              strides=self.strides)
          self.pos_loss_weight = pos_loss_weight
          self.neg_loss_weight = neg_loss_weight
          self.center_loss_weight = center_loss_weight
  
      def init_weights(self):
          """Initialize weights of the head.
  
          In particular, we have special initialization for classified conv's and
          regression conv's bias
          """
  
          super(AutoAssignHead, self).init_weights()
          bias_cls = bias_init_with_prob(0.02)
          normal_init(self.conv_cls, std=0.01, bias=bias_cls)
          normal_init(self.conv_reg, std=0.01, bias=4.0)
  
      def _get_points_single(self,
                             featmap_size,
                             stride,
                             dtype,
                             device,
                             flatten=False):
          """Almost the same as the implementation in fcos, we remove half stride
          offset to align with the original implementation."""
  
          y, x = super(FCOSHead,
                       self)._get_points_single(featmap_size, stride, dtype,
                                                device)
          points = torch.stack((x.reshape(-1) * stride, y.reshape(-1) * stride),
                               dim=-1)
          return points
  
      def forward_single(self, x, scale, stride):
          """Forward features of a single scale level.
  
          Args:
              x (Tensor): FPN feature maps of the specified stride.
              scale (:obj: `mmcv.cnn.Scale`): Learnable scale module to resize
                  the bbox prediction.
              stride (int): The corresponding stride for feature maps, only
                  used to normalize the bbox prediction when self.norm_on_bbox
                  is True.
  
          Returns:
              tuple: scores for each class, bbox predictions and centerness \
                  predictions of input feature maps.
          """
          cls_score, bbox_pred, cls_feat, reg_feat = super(
              FCOSHead, self).forward_single(x)
          centerness = self.conv_centerness(reg_feat)
          # scale the bbox_pred of different level
          # float to avoid overflow when enabling FP16
          bbox_pred = scale(bbox_pred).float()
          bbox_pred = F.relu(bbox_pred)
          bbox_pred *= stride
          return cls_score, bbox_pred, centerness
  
      def get_pos_loss_single(self, cls_score, objectness, reg_loss, gt_labels,
                              center_prior_weights):
          """Calculate the positive loss of all points in gt_bboxes.
  
          Args:
              cls_score (Tensor): All category scores for each point on
                  the feature map. The shape is (num_points, num_class).
              objectness (Tensor): Foreground probability of all points,
                  has shape (num_points, 1).
              reg_loss (Tensor): The regression loss of each gt_bbox and each
                  prediction box, has shape of (num_points, num_gt).
              gt_labels (Tensor): The zeros based gt_labels of all gt
                  with shape of (num_gt,).
              center_prior_weights (Tensor): Float tensor with shape
                  of (num_points, num_gt). Each value represents
                  the center weighting coefficient.
  
          Returns:
              tuple[Tensor]:
  
                  - pos_loss (Tensor): The positive loss of all points
                    in the gt_bboxes.
          """
          # p_loc: localization confidence
          p_loc = torch.exp(-reg_loss)
          # p_cls: classification confidence
          p_cls = (cls_score * objectness)[:, gt_labels]
          # p_pos: joint confidence indicator
          p_pos = p_cls * p_loc
  
          # 3 is a hyper-parameter to control the contributions of high and
          # low confidence locations towards positive losses.
          confidence_weight = torch.exp(p_pos * 3)
          p_pos_weight = (confidence_weight * center_prior_weights) / (
              (confidence_weight * center_prior_weights).sum(
                  0, keepdim=True)).clamp(min=EPS)
          reweighted_p_pos = (p_pos * p_pos_weight).sum(0)
          pos_loss = F.binary_cross_entropy(
              reweighted_p_pos,
              torch.ones_like(reweighted_p_pos),
              reduction='none')
          pos_loss = pos_loss.sum() * self.pos_loss_weight
          return pos_loss,
  
      def get_neg_loss_single(self, cls_score, objectness, gt_labels, ious,
                              inside_gt_bbox_mask):
          """Calculate the negative loss of all points in feature map.
  
          Args:
              cls_score (Tensor): All category scores for each point on
                  the feature map. The shape is (num_points, num_class).
              objectness (Tensor): Foreground probability of all points
                  and is shape of (num_points, 1).
              gt_labels (Tensor): The zeros based label of all gt with shape of
                  (num_gt).
              ious (Tensor): Float tensor with shape of (num_points, num_gt).
                  Each value represent the iou of pred_bbox and gt_bboxes.
              inside_gt_bbox_mask (Tensor): Tensor of bool type,
                  with shape of (num_points, num_gt), each
                  value is used to mark whether this point falls
                  within a certain gt.
  
          Returns:
              tuple[Tensor]:
  
                  - neg_loss (Tensor): The negative loss of all points
                    in the feature map.
          """
          num_gts = len(gt_labels)
          joint_conf = (cls_score * objectness)
          p_neg_weight = torch.ones_like(joint_conf)
          if num_gts > 0:
              # the order of dinmension would affect the value of
              # p_neg_weight, we strictly follow the original
              # implementation.
              inside_gt_bbox_mask = inside_gt_bbox_mask.permute(1, 0)
              ious = ious.permute(1, 0)
  
              foreground_idxs = torch.nonzero(inside_gt_bbox_mask, as_tuple=True)
              temp_weight = (1 / (1 - ious[foreground_idxs]).clamp_(EPS))
  
              def normalize(x):
                  return (x - x.min() + EPS) / (x.max() - x.min() + EPS)
  
              for instance_idx in range(num_gts):
                  idxs = foreground_idxs[0] == instance_idx
                  if idxs.any():
                      temp_weight[idxs] = normalize(temp_weight[idxs])
  
              p_neg_weight[foreground_idxs[1],
                           gt_labels[foreground_idxs[0]]] = 1 - temp_weight
  
          logits = (joint_conf * p_neg_weight)
          neg_loss = (
              logits**2 * F.binary_cross_entropy(
                  logits, torch.zeros_like(logits), reduction='none'))
          neg_loss = neg_loss.sum() * self.neg_loss_weight
          return neg_loss,
  
      @force_fp32(apply_to=('cls_scores', 'bbox_preds', 'objectnesses'))
      def loss(self,
               cls_scores,
               bbox_preds,
               objectnesses,
               gt_bboxes,
               gt_labels,
               img_metas,
               gt_bboxes_ignore=None):
          """Compute loss of the head.
  
          Args:
              cls_scores (list[Tensor]): Box scores for each scale level,
                  each is a 4D-tensor, the channel number is
                  num_points * num_classes.
              bbox_preds (list[Tensor]): Box energies / deltas for each scale
                  level, each is a 4D-tensor, the channel number is
                  num_points * 4.
              objectnesses (list[Tensor]): objectness for each scale level, each
                  is a 4D-tensor, the channel number is num_points * 1.
              gt_bboxes (list[Tensor]): Ground truth bboxes for each image with
                  shape (num_gts, 4) in [tl_x, tl_y, br_x, br_y] format.
              gt_labels (list[Tensor]): class indices corresponding to each box
              img_metas (list[dict]): Meta information of each image, e.g.,
                  image size, scaling factor, etc.
              gt_bboxes_ignore (None | list[Tensor]): specify which bounding
                  boxes can be ignored when computing the loss.
  
          Returns:
              dict[str, Tensor]: A dictionary of loss components.
          """
  
          assert len(cls_scores) == len(bbox_preds) == len(objectnesses)
          all_num_gt = sum([len(item) for item in gt_bboxes])
          featmap_sizes = [featmap.size()[-2:] for featmap in cls_scores]
          all_level_points = self.get_points(featmap_sizes, bbox_preds[0].dtype,
                                             bbox_preds[0].device)
          inside_gt_bbox_mask_list, bbox_targets_list = self.get_targets(
              all_level_points, gt_bboxes)
  
          center_prior_weight_list = []
          temp_inside_gt_bbox_mask_list = []
          for gt_bboxe, gt_label, inside_gt_bbox_mask in zip(
                  gt_bboxes, gt_labels, inside_gt_bbox_mask_list):
              center_prior_weight, inside_gt_bbox_mask = \
                  self.center_prior(all_level_points, gt_bboxe, gt_label,
                                    inside_gt_bbox_mask)
              center_prior_weight_list.append(center_prior_weight)
              temp_inside_gt_bbox_mask_list.append(inside_gt_bbox_mask)
          inside_gt_bbox_mask_list = temp_inside_gt_bbox_mask_list
  
          mlvl_points = torch.cat(all_level_points, dim=0)
          bbox_preds = levels_to_images(bbox_preds)
          cls_scores = levels_to_images(cls_scores)
          objectnesses = levels_to_images(objectnesses)
  
          reg_loss_list = []
          ious_list = []
          num_points = len(mlvl_points)
  
          for bbox_pred, gt_bboxe, inside_gt_bbox_mask in zip(
                  bbox_preds, bbox_targets_list, inside_gt_bbox_mask_list):
              temp_num_gt = gt_bboxe.size(1)
              expand_mlvl_points = mlvl_points[:, None, :].expand(
                  num_points, temp_num_gt, 2).reshape(-1, 2)
              gt_bboxe = gt_bboxe.reshape(-1, 4)
              expand_bbox_pred = bbox_pred[:, None, :].expand(
                  num_points, temp_num_gt, 4).reshape(-1, 4)
              decoded_bbox_preds = distance2bbox(expand_mlvl_points,
                                                 expand_bbox_pred)
              decoded_target_preds = distance2bbox(expand_mlvl_points, gt_bboxe)
              with torch.no_grad():
                  ious = bbox_overlaps(
                      decoded_bbox_preds, decoded_target_preds, is_aligned=True)
                  ious = ious.reshape(num_points, temp_num_gt)
                  if temp_num_gt:
                      ious = ious.max(
                          dim=-1, keepdim=True).values.repeat(1, temp_num_gt)
                  else:
                      ious = ious.new_zeros(num_points, temp_num_gt)
                  ious[~inside_gt_bbox_mask] = 0
                  ious_list.append(ious)
              loss_bbox = self.loss_bbox(
                  decoded_bbox_preds,
                  decoded_target_preds,
                  weight=None,
                  reduction_override='none')
              reg_loss_list.append(loss_bbox.reshape(num_points, temp_num_gt))
  
          cls_scores = [item.sigmoid() for item in cls_scores]
          objectnesses = [item.sigmoid() for item in objectnesses]
          pos_loss_list, = multi_apply(self.get_pos_loss_single, cls_scores,
                                       objectnesses, reg_loss_list, gt_labels,
                                       center_prior_weight_list)
          pos_avg_factor = reduce_mean(
              bbox_pred.new_tensor(all_num_gt)).clamp_(min=1)
          pos_loss = sum(pos_loss_list) / pos_avg_factor
  
          neg_loss_list, = multi_apply(self.get_neg_loss_single, cls_scores,
                                       objectnesses, gt_labels, ious_list,
                                       inside_gt_bbox_mask_list)
          neg_avg_factor = sum(item.data.sum()
                               for item in center_prior_weight_list)
          neg_avg_factor = reduce_mean(neg_avg_factor).clamp_(min=1)
          neg_loss = sum(neg_loss_list) / neg_avg_factor
  
          center_loss = []
          for i in range(len(img_metas)):
  
              if inside_gt_bbox_mask_list[i].any():
                  center_loss.append(
                      len(gt_bboxes[i]) /
                      center_prior_weight_list[i].sum().clamp_(min=EPS))
              # when width or height of gt_bbox is smaller than stride of p3
              else:
                  center_loss.append(center_prior_weight_list[i].sum() * 0)
  
          center_loss = torch.stack(center_loss).mean() * self.center_loss_weight
  
          # avoid dead lock in DDP
          if all_num_gt == 0:
              pos_loss = bbox_preds[0].sum() * 0
              dummy_center_prior_loss = self.center_prior.mean.sum(
              ) * 0 + self.center_prior.sigma.sum() * 0
              center_loss = objectnesses[0].sum() * 0 + dummy_center_prior_loss
  
          loss = dict(
              loss_pos=pos_loss, loss_neg=neg_loss, loss_center=center_loss)
  
          return loss
  
      def get_targets(self, points, gt_bboxes_list):
          """Compute regression targets and each point inside or outside gt_bbox
          in multiple images.
  
          Args:
              points (list[Tensor]): Points of all fpn level, each has shape
                  (num_points, 2).
              gt_bboxes_list (list[Tensor]): Ground truth bboxes of each image,
                  each has shape (num_gt, 4).
  
          Returns:
              tuple(list[Tensor]):
  
                  - inside_gt_bbox_mask_list (list[Tensor]): Each
                    Tensor is with bool type and shape of
                    (num_points, num_gt), each value
                    is used to mark whether this point falls
                    within a certain gt.
                  - concat_lvl_bbox_targets (list[Tensor]): BBox
                    targets of each level. Each tensor has shape
                    (num_points, num_gt, 4).
          """
  
          concat_points = torch.cat(points, dim=0)
          # the number of points per img, per lvl
          inside_gt_bbox_mask_list, bbox_targets_list = multi_apply(
              self._get_target_single, gt_bboxes_list, points=concat_points)
          return inside_gt_bbox_mask_list, bbox_targets_list
  
      def _get_target_single(self, gt_bboxes, points):
          """Compute regression targets and each point inside or outside gt_bbox
          for a single image.
  
          Args:
              gt_bboxes (Tensor): gt_bbox of single image, has shape
                  (num_gt, 4).
              points (Tensor): Points of all fpn level, has shape
                  (num_points, 2).
  
          Returns:
              tuple[Tensor]: Containing the following Tensors:
  
                  - inside_gt_bbox_mask (Tensor): Bool tensor with shape
                    (num_points, num_gt), each value is used to mark
                    whether this point falls within a certain gt.
                  - bbox_targets (Tensor): BBox targets of each points with
                    each gt_bboxes, has shape (num_points, num_gt, 4).
          """
          num_points = points.size(0)
          num_gts = gt_bboxes.size(0)
          gt_bboxes = gt_bboxes[None].expand(num_points, num_gts, 4)
          xs, ys = points[:, 0], points[:, 1]
          xs = xs[:, None]
          ys = ys[:, None]
          left = xs - gt_bboxes[..., 0]
          right = gt_bboxes[..., 2] - xs
          top = ys - gt_bboxes[..., 1]
          bottom = gt_bboxes[..., 3] - ys
          bbox_targets = torch.stack((left, top, right, bottom), -1)
          if num_gts:
              inside_gt_bbox_mask = bbox_targets.min(-1)[0] > 0
          else:
              inside_gt_bbox_mask = bbox_targets.new_zeros((num_points, num_gts),
                                                           dtype=torch.bool)
  
          return inside_gt_bbox_mask, bbox_targets
  