Reference for ultralytics/utils/loss.py

@staticmethod
def forward(pred_score, gt_score, label, alpha=0.75, gamma=2.0):
    """Computes varfocal loss."""
    weight = alpha * pred_score.sigmoid().pow(gamma) * (1 - label) + gt_score * label
    with autocast(enabled=False):
        loss = (
            (F.binary_cross_entropy_with_logits(pred_score.float(), gt_score.float(), reduction="none") * weight)
            .mean(1)
            .sum()
        )
    return loss

@staticmethod
def forward(pred, label, gamma=1.5, alpha=0.25):
    """Calculates and updates confusion matrix for object detection/classification tasks."""
    loss = F.binary_cross_entropy_with_logits(pred, label, reduction="none")
    # p_t = torch.exp(-loss)
    # loss *= self.alpha * (1.000001 - p_t) ** self.gamma  # non-zero power for gradient stability

    # TF implementation https://github.com/tensorflow/addons/blob/v0.7.1/tensorflow_addons/losses/focal_loss.py
    pred_prob = pred.sigmoid()  # prob from logits
    p_t = label * pred_prob + (1 - label) * (1 - pred_prob)
    modulating_factor = (1.0 - p_t) ** gamma
    loss *= modulating_factor
    if alpha > 0:
        alpha_factor = label * alpha + (1 - label) * (1 - alpha)
        loss *= alpha_factor
    return loss.mean(1).sum()

def __call__(self, pred_dist, target):
    """
    Return sum of left and right DFL losses.

    Distribution Focal Loss (DFL) proposed in Generalized Focal Loss
    https://ieeexplore.ieee.org/document/9792391
    """
    target = target.clamp_(0, self.reg_max - 1 - 0.01)
    tl = target.long()  # target left
    tr = tl + 1  # target right
    wl = tr - target  # weight left
    wr = 1 - wl  # weight right
    return (
        F.cross_entropy(pred_dist, tl.view(-1), reduction="none").view(tl.shape) * wl
        + F.cross_entropy(pred_dist, tr.view(-1), reduction="none").view(tl.shape) * wr
    ).mean(-1, keepdim=True)

def forward(self, pred_dist, pred_bboxes, anchor_points, target_bboxes, target_scores, target_scores_sum, fg_mask):
    """IoU loss."""
    weight = target_scores.sum(-1)[fg_mask].unsqueeze(-1)
    iou = bbox_iou(pred_bboxes[fg_mask], target_bboxes[fg_mask], xywh=False, CIoU=True)
    loss_iou = ((1.0 - iou) * weight).sum() / target_scores_sum

    # DFL loss
    if self.dfl_loss:
        target_ltrb = bbox2dist(anchor_points, target_bboxes, self.dfl_loss.reg_max - 1)
        loss_dfl = self.dfl_loss(pred_dist[fg_mask].view(-1, self.dfl_loss.reg_max), target_ltrb[fg_mask]) * weight
        loss_dfl = loss_dfl.sum() / target_scores_sum
    else:
        loss_dfl = torch.tensor(0.0).to(pred_dist.device)

    return loss_iou, loss_dfl

def forward(self, pred_dist, pred_bboxes, anchor_points, target_bboxes, target_scores, target_scores_sum, fg_mask):
    """IoU loss."""
    weight = target_scores.sum(-1)[fg_mask].unsqueeze(-1)
    iou = probiou(pred_bboxes[fg_mask], target_bboxes[fg_mask])
    loss_iou = ((1.0 - iou) * weight).sum() / target_scores_sum

    # DFL loss
    if self.dfl_loss:
        target_ltrb = bbox2dist(anchor_points, xywh2xyxy(target_bboxes[..., :4]), self.dfl_loss.reg_max - 1)
        loss_dfl = self.dfl_loss(pred_dist[fg_mask].view(-1, self.dfl_loss.reg_max), target_ltrb[fg_mask]) * weight
        loss_dfl = loss_dfl.sum() / target_scores_sum
    else:
        loss_dfl = torch.tensor(0.0).to(pred_dist.device)

    return loss_iou, loss_dfl

def forward(self, pred_kpts, gt_kpts, kpt_mask, area):
    """Calculates keypoint loss factor and Euclidean distance loss for predicted and actual keypoints."""
    d = (pred_kpts[..., 0] - gt_kpts[..., 0]).pow(2) + (pred_kpts[..., 1] - gt_kpts[..., 1]).pow(2)
    kpt_loss_factor = kpt_mask.shape[1] / (torch.sum(kpt_mask != 0, dim=1) + 1e-9)
    # e = d / (2 * (area * self.sigmas) ** 2 + 1e-9)  # from formula
    e = d / ((2 * self.sigmas).pow(2) * (area + 1e-9) * 2)  # from cocoeval
    return (kpt_loss_factor.view(-1, 1) * ((1 - torch.exp(-e)) * kpt_mask)).mean()

def __call__(self, preds, batch):
    """Calculate the sum of the loss for box, cls and dfl multiplied by batch size."""
    loss = torch.zeros(3, device=self.device)  # box, cls, dfl
    feats = preds[1] if isinstance(preds, tuple) else preds
    pred_distri, pred_scores = torch.cat([xi.view(feats[0].shape[0], self.no, -1) for xi in feats], 2).split(
        (self.reg_max * 4, self.nc), 1
    )

    pred_scores = pred_scores.permute(0, 2, 1).contiguous()
    pred_distri = pred_distri.permute(0, 2, 1).contiguous()

    dtype = pred_scores.dtype
    batch_size = pred_scores.shape[0]
    imgsz = torch.tensor(feats[0].shape[2:], device=self.device, dtype=dtype) * self.stride[0]  # image size (h,w)
    anchor_points, stride_tensor = make_anchors(feats, self.stride, 0.5)

    # Targets
    targets = torch.cat((batch["batch_idx"].view(-1, 1), batch["cls"].view(-1, 1), batch["bboxes"]), 1)
    targets = self.preprocess(targets.to(self.device), batch_size, scale_tensor=imgsz[[1, 0, 1, 0]])
    gt_labels, gt_bboxes = targets.split((1, 4), 2)  # cls, xyxy
    mask_gt = gt_bboxes.sum(2, keepdim=True).gt_(0.0)

    # Pboxes
    pred_bboxes = self.bbox_decode(anchor_points, pred_distri)  # xyxy, (b, h*w, 4)

    _, target_bboxes, target_scores, fg_mask, _ = self.assigner(
        pred_scores.detach().sigmoid(),
        (pred_bboxes.detach() * stride_tensor).type(gt_bboxes.dtype),
        anchor_points * stride_tensor,
        gt_labels,
        gt_bboxes,
        mask_gt,
    )

    target_scores_sum = max(target_scores.sum(), 1)

    # Cls loss
    # loss[1] = self.varifocal_loss(pred_scores, target_scores, target_labels) / target_scores_sum  # VFL way
    loss[1] = self.bce(pred_scores, target_scores.to(dtype)).sum() / target_scores_sum  # BCE

    # Bbox loss
    if fg_mask.sum():
        target_bboxes /= stride_tensor
        loss[0], loss[2] = self.bbox_loss(
            pred_distri, pred_bboxes, anchor_points, target_bboxes, target_scores, target_scores_sum, fg_mask
        )

    loss[0] *= self.hyp.box  # box gain
    loss[1] *= self.hyp.cls  # cls gain
    loss[2] *= self.hyp.dfl  # dfl gain

    return loss.sum() * batch_size, loss.detach()  # loss(box, cls, dfl)

def bbox_decode(self, anchor_points, pred_dist):
    """Decode predicted object bounding box coordinates from anchor points and distribution."""
    if self.use_dfl:
        b, a, c = pred_dist.shape  # batch, anchors, channels
        pred_dist = pred_dist.view(b, a, 4, c // 4).softmax(3).matmul(self.proj.type(pred_dist.dtype))
        # pred_dist = pred_dist.view(b, a, c // 4, 4).transpose(2,3).softmax(3).matmul(self.proj.type(pred_dist.dtype))
        # pred_dist = (pred_dist.view(b, a, c // 4, 4).softmax(2) * self.proj.type(pred_dist.dtype).view(1, 1, -1, 1)).sum(2)
    return dist2bbox(pred_dist, anchor_points, xywh=False)

def preprocess(self, targets, batch_size, scale_tensor):
    """Preprocesses the target counts and matches with the input batch size to output a tensor."""
    nl, ne = targets.shape
    if nl == 0:
        out = torch.zeros(batch_size, 0, ne - 1, device=self.device)
    else:
        i = targets[:, 0]  # image index
        _, counts = i.unique(return_counts=True)
        counts = counts.to(dtype=torch.int32)
        out = torch.zeros(batch_size, counts.max(), ne - 1, device=self.device)
        for j in range(batch_size):
            matches = i == j
            n = matches.sum()
            if n:
                out[j, :n] = targets[matches, 1:]
        out[..., 1:5] = xywh2xyxy(out[..., 1:5].mul_(scale_tensor))
    return out

def __call__(self, preds, batch):
    """Calculate and return the loss for the YOLO model."""
    loss = torch.zeros(4, device=self.device)  # box, cls, dfl
    feats, pred_masks, proto = preds if len(preds) == 3 else preds[1]
    batch_size, _, mask_h, mask_w = proto.shape  # batch size, number of masks, mask height, mask width
    pred_distri, pred_scores = torch.cat([xi.view(feats[0].shape[0], self.no, -1) for xi in feats], 2).split(
        (self.reg_max * 4, self.nc), 1
    )

    # B, grids, ..
    pred_scores = pred_scores.permute(0, 2, 1).contiguous()
    pred_distri = pred_distri.permute(0, 2, 1).contiguous()
    pred_masks = pred_masks.permute(0, 2, 1).contiguous()

    dtype = pred_scores.dtype
    imgsz = torch.tensor(feats[0].shape[2:], device=self.device, dtype=dtype) * self.stride[0]  # image size (h,w)
    anchor_points, stride_tensor = make_anchors(feats, self.stride, 0.5)

    # Targets
    try:
        batch_idx = batch["batch_idx"].view(-1, 1)
        targets = torch.cat((batch_idx, batch["cls"].view(-1, 1), batch["bboxes"]), 1)
        targets = self.preprocess(targets.to(self.device), batch_size, scale_tensor=imgsz[[1, 0, 1, 0]])
        gt_labels, gt_bboxes = targets.split((1, 4), 2)  # cls, xyxy
        mask_gt = gt_bboxes.sum(2, keepdim=True).gt_(0.0)
    except RuntimeError as e:
        raise TypeError(
            "ERROR ❌ segment dataset incorrectly formatted or not a segment dataset.\n"
            "This error can occur when incorrectly training a 'segment' model on a 'detect' dataset, "
            "i.e. 'yolo train model=yolov8n-seg.pt data=coco8.yaml'.\nVerify your dataset is a "
            "correctly formatted 'segment' dataset using 'data=coco8-seg.yaml' "
            "as an example.\nSee https://docs.ultralytics.com/datasets/segment/ for help."
        ) from e

    # Pboxes
    pred_bboxes = self.bbox_decode(anchor_points, pred_distri)  # xyxy, (b, h*w, 4)

    _, target_bboxes, target_scores, fg_mask, target_gt_idx = self.assigner(
        pred_scores.detach().sigmoid(),
        (pred_bboxes.detach() * stride_tensor).type(gt_bboxes.dtype),
        anchor_points * stride_tensor,
        gt_labels,
        gt_bboxes,
        mask_gt,
    )

    target_scores_sum = max(target_scores.sum(), 1)

    # Cls loss
    # loss[1] = self.varifocal_loss(pred_scores, target_scores, target_labels) / target_scores_sum  # VFL way
    loss[2] = self.bce(pred_scores, target_scores.to(dtype)).sum() / target_scores_sum  # BCE

    if fg_mask.sum():
        # Bbox loss
        loss[0], loss[3] = self.bbox_loss(
            pred_distri,
            pred_bboxes,
            anchor_points,
            target_bboxes / stride_tensor,
            target_scores,
            target_scores_sum,
            fg_mask,
        )
        # Masks loss
        masks = batch["masks"].to(self.device).float()
        if tuple(masks.shape[-2:]) != (mask_h, mask_w):  # downsample
            masks = F.interpolate(masks[None], (mask_h, mask_w), mode="nearest")[0]

        loss[1] = self.calculate_segmentation_loss(
            fg_mask, masks, target_gt_idx, target_bboxes, batch_idx, proto, pred_masks, imgsz, self.overlap
        )

    # WARNING: lines below prevent Multi-GPU DDP 'unused gradient' PyTorch errors, do not remove
    else:
        loss[1] += (proto * 0).sum() + (pred_masks * 0).sum()  # inf sums may lead to nan loss

    loss[0] *= self.hyp.box  # box gain
    loss[1] *= self.hyp.box  # seg gain
    loss[2] *= self.hyp.cls  # cls gain
    loss[3] *= self.hyp.dfl  # dfl gain

    return loss.sum() * batch_size, loss.detach()  # loss(box, cls, dfl)

def calculate_segmentation_loss(
    self,
    fg_mask: torch.Tensor,
    masks: torch.Tensor,
    target_gt_idx: torch.Tensor,
    target_bboxes: torch.Tensor,
    batch_idx: torch.Tensor,
    proto: torch.Tensor,
    pred_masks: torch.Tensor,
    imgsz: torch.Tensor,
    overlap: bool,
) -> torch.Tensor:
    """
    Calculate the loss for instance segmentation.

    Args:
        fg_mask (torch.Tensor): A binary tensor of shape (BS, N_anchors) indicating which anchors are positive.
        masks (torch.Tensor): Ground truth masks of shape (BS, H, W) if `overlap` is False, otherwise (BS, ?, H, W).
        target_gt_idx (torch.Tensor): Indexes of ground truth objects for each anchor of shape (BS, N_anchors).
        target_bboxes (torch.Tensor): Ground truth bounding boxes for each anchor of shape (BS, N_anchors, 4).
        batch_idx (torch.Tensor): Batch indices of shape (N_labels_in_batch, 1).
        proto (torch.Tensor): Prototype masks of shape (BS, 32, H, W).
        pred_masks (torch.Tensor): Predicted masks for each anchor of shape (BS, N_anchors, 32).
        imgsz (torch.Tensor): Size of the input image as a tensor of shape (2), i.e., (H, W).
        overlap (bool): Whether the masks in `masks` tensor overlap.

    Returns:
        (torch.Tensor): The calculated loss for instance segmentation.

    Notes:
        The batch loss can be computed for improved speed at higher memory usage.
        For example, pred_mask can be computed as follows:
            pred_mask = torch.einsum('in,nhw->ihw', pred, proto)  # (i, 32) @ (32, 160, 160) -> (i, 160, 160)
    """
    _, _, mask_h, mask_w = proto.shape
    loss = 0

    # Normalize to 0-1
    target_bboxes_normalized = target_bboxes / imgsz[[1, 0, 1, 0]]

    # Areas of target bboxes
    marea = xyxy2xywh(target_bboxes_normalized)[..., 2:].prod(2)

    # Normalize to mask size
    mxyxy = target_bboxes_normalized * torch.tensor([mask_w, mask_h, mask_w, mask_h], device=proto.device)

    for i, single_i in enumerate(zip(fg_mask, target_gt_idx, pred_masks, proto, mxyxy, marea, masks)):
        fg_mask_i, target_gt_idx_i, pred_masks_i, proto_i, mxyxy_i, marea_i, masks_i = single_i
        if fg_mask_i.any():
            mask_idx = target_gt_idx_i[fg_mask_i]
            if overlap:
                gt_mask = masks_i == (mask_idx + 1).view(-1, 1, 1)
                gt_mask = gt_mask.float()
            else:
                gt_mask = masks[batch_idx.view(-1) == i][mask_idx]

            loss += self.single_mask_loss(
                gt_mask, pred_masks_i[fg_mask_i], proto_i, mxyxy_i[fg_mask_i], marea_i[fg_mask_i]
            )

        # WARNING: lines below prevents Multi-GPU DDP 'unused gradient' PyTorch errors, do not remove
        else:
            loss += (proto * 0).sum() + (pred_masks * 0).sum()  # inf sums may lead to nan loss

    return loss / fg_mask.sum()

@staticmethod
def single_mask_loss(
    gt_mask: torch.Tensor, pred: torch.Tensor, proto: torch.Tensor, xyxy: torch.Tensor, area: torch.Tensor
) -> torch.Tensor:
    """
    Compute the instance segmentation loss for a single image.

    Args:
        gt_mask (torch.Tensor): Ground truth mask of shape (n, H, W), where n is the number of objects.
        pred (torch.Tensor): Predicted mask coefficients of shape (n, 32).
        proto (torch.Tensor): Prototype masks of shape (32, H, W).
        xyxy (torch.Tensor): Ground truth bounding boxes in xyxy format, normalized to [0, 1], of shape (n, 4).
        area (torch.Tensor): Area of each ground truth bounding box of shape (n,).

    Returns:
        (torch.Tensor): The calculated mask loss for a single image.

    Notes:
        The function uses the equation pred_mask = torch.einsum('in,nhw->ihw', pred, proto) to produce the
        predicted masks from the prototype masks and predicted mask coefficients.
    """
    pred_mask = torch.einsum("in,nhw->ihw", pred, proto)  # (n, 32) @ (32, 80, 80) -> (n, 80, 80)
    loss = F.binary_cross_entropy_with_logits(pred_mask, gt_mask, reduction="none")
    return (crop_mask(loss, xyxy).mean(dim=(1, 2)) / area).sum()

def __call__(self, preds, batch):
    """Calculate the total loss and detach it."""
    loss = torch.zeros(5, device=self.device)  # box, cls, dfl, kpt_location, kpt_visibility
    feats, pred_kpts = preds if isinstance(preds[0], list) else preds[1]
    pred_distri, pred_scores = torch.cat([xi.view(feats[0].shape[0], self.no, -1) for xi in feats], 2).split(
        (self.reg_max * 4, self.nc), 1
    )

    # B, grids, ..
    pred_scores = pred_scores.permute(0, 2, 1).contiguous()
    pred_distri = pred_distri.permute(0, 2, 1).contiguous()
    pred_kpts = pred_kpts.permute(0, 2, 1).contiguous()

    dtype = pred_scores.dtype
    imgsz = torch.tensor(feats[0].shape[2:], device=self.device, dtype=dtype) * self.stride[0]  # image size (h,w)
    anchor_points, stride_tensor = make_anchors(feats, self.stride, 0.5)

    # Targets
    batch_size = pred_scores.shape[0]
    batch_idx = batch["batch_idx"].view(-1, 1)
    targets = torch.cat((batch_idx, batch["cls"].view(-1, 1), batch["bboxes"]), 1)
    targets = self.preprocess(targets.to(self.device), batch_size, scale_tensor=imgsz[[1, 0, 1, 0]])
    gt_labels, gt_bboxes = targets.split((1, 4), 2)  # cls, xyxy
    mask_gt = gt_bboxes.sum(2, keepdim=True).gt_(0.0)

    # Pboxes
    pred_bboxes = self.bbox_decode(anchor_points, pred_distri)  # xyxy, (b, h*w, 4)
    pred_kpts = self.kpts_decode(anchor_points, pred_kpts.view(batch_size, -1, *self.kpt_shape))  # (b, h*w, 17, 3)

    _, target_bboxes, target_scores, fg_mask, target_gt_idx = self.assigner(
        pred_scores.detach().sigmoid(),
        (pred_bboxes.detach() * stride_tensor).type(gt_bboxes.dtype),
        anchor_points * stride_tensor,
        gt_labels,
        gt_bboxes,
        mask_gt,
    )

    target_scores_sum = max(target_scores.sum(), 1)

    # Cls loss
    # loss[1] = self.varifocal_loss(pred_scores, target_scores, target_labels) / target_scores_sum  # VFL way
    loss[3] = self.bce(pred_scores, target_scores.to(dtype)).sum() / target_scores_sum  # BCE

    # Bbox loss
    if fg_mask.sum():
        target_bboxes /= stride_tensor
        loss[0], loss[4] = self.bbox_loss(
            pred_distri, pred_bboxes, anchor_points, target_bboxes, target_scores, target_scores_sum, fg_mask
        )
        keypoints = batch["keypoints"].to(self.device).float().clone()
        keypoints[..., 0] *= imgsz[1]
        keypoints[..., 1] *= imgsz[0]

        loss[1], loss[2] = self.calculate_keypoints_loss(
            fg_mask, target_gt_idx, keypoints, batch_idx, stride_tensor, target_bboxes, pred_kpts
        )

    loss[0] *= self.hyp.box  # box gain
    loss[1] *= self.hyp.pose  # pose gain
    loss[2] *= self.hyp.kobj  # kobj gain
    loss[3] *= self.hyp.cls  # cls gain
    loss[4] *= self.hyp.dfl  # dfl gain

    return loss.sum() * batch_size, loss.detach()  # loss(box, cls, dfl)

def calculate_keypoints_loss(
    self, masks, target_gt_idx, keypoints, batch_idx, stride_tensor, target_bboxes, pred_kpts
):
    """
    Calculate the keypoints loss for the model.

    This function calculates the keypoints loss and keypoints object loss for a given batch. The keypoints loss is
    based on the difference between the predicted keypoints and ground truth keypoints. The keypoints object loss is
    a binary classification loss that classifies whether a keypoint is present or not.

    Args:
        masks (torch.Tensor): Binary mask tensor indicating object presence, shape (BS, N_anchors).
        target_gt_idx (torch.Tensor): Index tensor mapping anchors to ground truth objects, shape (BS, N_anchors).
        keypoints (torch.Tensor): Ground truth keypoints, shape (N_kpts_in_batch, N_kpts_per_object, kpts_dim).
        batch_idx (torch.Tensor): Batch index tensor for keypoints, shape (N_kpts_in_batch, 1).
        stride_tensor (torch.Tensor): Stride tensor for anchors, shape (N_anchors, 1).
        target_bboxes (torch.Tensor): Ground truth boxes in (x1, y1, x2, y2) format, shape (BS, N_anchors, 4).
        pred_kpts (torch.Tensor): Predicted keypoints, shape (BS, N_anchors, N_kpts_per_object, kpts_dim).

    Returns:
        (tuple): Returns a tuple containing:
            - kpts_loss (torch.Tensor): The keypoints loss.
            - kpts_obj_loss (torch.Tensor): The keypoints object loss.
    """
    batch_idx = batch_idx.flatten()
    batch_size = len(masks)

    # Find the maximum number of keypoints in a single image
    max_kpts = torch.unique(batch_idx, return_counts=True)[1].max()

    # Create a tensor to hold batched keypoints
    batched_keypoints = torch.zeros(
        (batch_size, max_kpts, keypoints.shape[1], keypoints.shape[2]), device=keypoints.device
    )

    # TODO: any idea how to vectorize this?
    # Fill batched_keypoints with keypoints based on batch_idx
    for i in range(batch_size):
        keypoints_i = keypoints[batch_idx == i]
        batched_keypoints[i, : keypoints_i.shape[0]] = keypoints_i

    # Expand dimensions of target_gt_idx to match the shape of batched_keypoints
    target_gt_idx_expanded = target_gt_idx.unsqueeze(-1).unsqueeze(-1)

    # Use target_gt_idx_expanded to select keypoints from batched_keypoints
    selected_keypoints = batched_keypoints.gather(
        1, target_gt_idx_expanded.expand(-1, -1, keypoints.shape[1], keypoints.shape[2])
    )

    # Divide coordinates by stride
    selected_keypoints /= stride_tensor.view(1, -1, 1, 1)

    kpts_loss = 0
    kpts_obj_loss = 0

    if masks.any():
        gt_kpt = selected_keypoints[masks]
        area = xyxy2xywh(target_bboxes[masks])[:, 2:].prod(1, keepdim=True)
        pred_kpt = pred_kpts[masks]
        kpt_mask = gt_kpt[..., 2] != 0 if gt_kpt.shape[-1] == 3 else torch.full_like(gt_kpt[..., 0], True)
        kpts_loss = self.keypoint_loss(pred_kpt, gt_kpt, kpt_mask, area)  # pose loss

        if pred_kpt.shape[-1] == 3:
            kpts_obj_loss = self.bce_pose(pred_kpt[..., 2], kpt_mask.float())  # keypoint obj loss

    return kpts_loss, kpts_obj_loss

@staticmethod
def kpts_decode(anchor_points, pred_kpts):
    """Decodes predicted keypoints to image coordinates."""
    y = pred_kpts.clone()
    y[..., :2] *= 2.0
    y[..., 0] += anchor_points[:, [0]] - 0.5
    y[..., 1] += anchor_points[:, [1]] - 0.5
    return y

def __call__(self, preds, batch):
    """Compute the classification loss between predictions and true labels."""
    loss = F.cross_entropy(preds, batch["cls"], reduction="mean")
    loss_items = loss.detach()
    return loss, loss_items

def __call__(self, preds, batch):
    """Calculate and return the loss for the YOLO model."""
    loss = torch.zeros(3, device=self.device)  # box, cls, dfl
    feats, pred_angle = preds if isinstance(preds[0], list) else preds[1]
    batch_size = pred_angle.shape[0]  # batch size, number of masks, mask height, mask width
    pred_distri, pred_scores = torch.cat([xi.view(feats[0].shape[0], self.no, -1) for xi in feats], 2).split(
        (self.reg_max * 4, self.nc), 1
    )

    # b, grids, ..
    pred_scores = pred_scores.permute(0, 2, 1).contiguous()
    pred_distri = pred_distri.permute(0, 2, 1).contiguous()
    pred_angle = pred_angle.permute(0, 2, 1).contiguous()

    dtype = pred_scores.dtype
    imgsz = torch.tensor(feats[0].shape[2:], device=self.device, dtype=dtype) * self.stride[0]  # image size (h,w)
    anchor_points, stride_tensor = make_anchors(feats, self.stride, 0.5)

    # targets
    try:
        batch_idx = batch["batch_idx"].view(-1, 1)
        targets = torch.cat((batch_idx, batch["cls"].view(-1, 1), batch["bboxes"].view(-1, 5)), 1)
        rw, rh = targets[:, 4] * imgsz[0].item(), targets[:, 5] * imgsz[1].item()
        targets = targets[(rw >= 2) & (rh >= 2)]  # filter rboxes of tiny size to stabilize training
        targets = self.preprocess(targets.to(self.device), batch_size, scale_tensor=imgsz[[1, 0, 1, 0]])
        gt_labels, gt_bboxes = targets.split((1, 5), 2)  # cls, xywhr
        mask_gt = gt_bboxes.sum(2, keepdim=True).gt_(0.0)
    except RuntimeError as e:
        raise TypeError(
            "ERROR ❌ OBB dataset incorrectly formatted or not a OBB dataset.\n"
            "This error can occur when incorrectly training a 'OBB' model on a 'detect' dataset, "
            "i.e. 'yolo train model=yolov8n-obb.pt data=dota8.yaml'.\nVerify your dataset is a "
            "correctly formatted 'OBB' dataset using 'data=dota8.yaml' "
            "as an example.\nSee https://docs.ultralytics.com/datasets/obb/ for help."
        ) from e

    # Pboxes
    pred_bboxes = self.bbox_decode(anchor_points, pred_distri, pred_angle)  # xyxy, (b, h*w, 4)

    bboxes_for_assigner = pred_bboxes.clone().detach()
    # Only the first four elements need to be scaled
    bboxes_for_assigner[..., :4] *= stride_tensor
    _, target_bboxes, target_scores, fg_mask, _ = self.assigner(
        pred_scores.detach().sigmoid(),
        bboxes_for_assigner.type(gt_bboxes.dtype),
        anchor_points * stride_tensor,
        gt_labels,
        gt_bboxes,
        mask_gt,
    )

    target_scores_sum = max(target_scores.sum(), 1)

    # Cls loss
    # loss[1] = self.varifocal_loss(pred_scores, target_scores, target_labels) / target_scores_sum  # VFL way
    loss[1] = self.bce(pred_scores, target_scores.to(dtype)).sum() / target_scores_sum  # BCE

    # Bbox loss
    if fg_mask.sum():
        target_bboxes[..., :4] /= stride_tensor
        loss[0], loss[2] = self.bbox_loss(
            pred_distri, pred_bboxes, anchor_points, target_bboxes, target_scores, target_scores_sum, fg_mask
        )
    else:
        loss[0] += (pred_angle * 0).sum()

    loss[0] *= self.hyp.box  # box gain
    loss[1] *= self.hyp.cls  # cls gain
    loss[2] *= self.hyp.dfl  # dfl gain

    return loss.sum() * batch_size, loss.detach()  # loss(box, cls, dfl)

def bbox_decode(self, anchor_points, pred_dist, pred_angle):
    """
    Decode predicted object bounding box coordinates from anchor points and distribution.

    Args:
        anchor_points (torch.Tensor): Anchor points, (h*w, 2).
        pred_dist (torch.Tensor): Predicted rotated distance, (bs, h*w, 4).
        pred_angle (torch.Tensor): Predicted angle, (bs, h*w, 1).

    Returns:
        (torch.Tensor): Predicted rotated bounding boxes with angles, (bs, h*w, 5).
    """
    if self.use_dfl:
        b, a, c = pred_dist.shape  # batch, anchors, channels
        pred_dist = pred_dist.view(b, a, 4, c // 4).softmax(3).matmul(self.proj.type(pred_dist.dtype))
    return torch.cat((dist2rbox(pred_dist, pred_angle, anchor_points), pred_angle), dim=-1)