Reference for ultralytics/utils/loss.py

class VarifocalLoss(nn.Module):
    """
    Varifocal loss by Zhang et al.

    https://arxiv.org/abs/2008.13367.
    """

    def __init__(self):
        """Initialize the VarifocalLoss class."""
        super().__init__()

    @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 torch.cuda.amp.autocast(enabled=False):
            loss = (
                (F.binary_cross_entropy_with_logits(pred_score.float(), gt_score.float(), reduction="none") * weight)
                .mean(1)
                .sum()
            )
        return loss

class FocalLoss(nn.Module):
    """Wraps focal loss around existing loss_fcn(), i.e. criteria = FocalLoss(nn.BCEWithLogitsLoss(), gamma=1.5)."""

    def __init__(self):
        """Initializer for FocalLoss class with no parameters."""
        super().__init__()

    @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()

class BboxLoss(nn.Module):
    """Criterion class for computing training losses during training."""

    def __init__(self, reg_max, use_dfl=False):
        """Initialize the BboxLoss module with regularization maximum and DFL settings."""
        super().__init__()
        self.reg_max = reg_max
        self.use_dfl = use_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 = 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.use_dfl:
            target_ltrb = bbox2dist(anchor_points, target_bboxes, self.reg_max)
            loss_dfl = self._df_loss(pred_dist[fg_mask].view(-1, self.reg_max + 1), 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

    @staticmethod
    def _df_loss(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
        """
        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)

class RotatedBboxLoss(BboxLoss):
    """Criterion class for computing training losses during training."""

    def __init__(self, reg_max, use_dfl=False):
        """Initialize the BboxLoss module with regularization maximum and DFL settings."""
        super().__init__(reg_max, use_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.use_dfl:
            target_ltrb = bbox2dist(anchor_points, xywh2xyxy(target_bboxes[..., :4]), self.reg_max)
            loss_dfl = self._df_loss(pred_dist[fg_mask].view(-1, self.reg_max + 1), 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

class KeypointLoss(nn.Module):
    """Criterion class for computing training losses."""

    def __init__(self, sigmas) -> None:
        """Initialize the KeypointLoss class."""
        super().__init__()
        self.sigmas = sigmas

    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()

class v8DetectionLoss:
    """Criterion class for computing training losses."""

    def __init__(self, model):  # model must be de-paralleled
        """Initializes v8DetectionLoss with the model, defining model-related properties and BCE loss function."""
        device = next(model.parameters()).device  # get model device
        h = model.args  # hyperparameters

        m = model.model[-1]  # Detect() module
        self.bce = nn.BCEWithLogitsLoss(reduction="none")
        self.hyp = h
        self.stride = m.stride  # model strides
        self.nc = m.nc  # number of classes
        self.no = m.nc + m.reg_max * 4
        self.reg_max = m.reg_max
        self.device = device

        self.use_dfl = m.reg_max > 1

        self.assigner = TaskAlignedAssigner(topk=10, num_classes=self.nc, alpha=0.5, beta=6.0)
        self.bbox_loss = BboxLoss(m.reg_max - 1, use_dfl=self.use_dfl).to(device)
        self.proj = torch.arange(m.reg_max, dtype=torch.float, device=device)

    def preprocess(self, targets, batch_size, scale_tensor):
        """Preprocesses the target counts and matches with the input batch size to output a tensor."""
        if targets.shape[0] == 0:
            out = torch.zeros(batch_size, 0, 5, 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(), 5, 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 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 __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)

        # 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)

class v8SegmentationLoss(v8DetectionLoss):
    """Criterion class for computing training losses."""

    def __init__(self, model):  # model must be de-paralleled
        """Initializes the v8SegmentationLoss class, taking a de-paralleled model as argument."""
        super().__init__(model)
        self.overlap = model.args.overlap_mask

    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)
        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)

    @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 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()