Source code for torchvision.models.detection.ssd

import warnings
from collections import OrderedDict
from typing import Any, Dict, List, Optional, Tuple

import torch
import torch.nn.functional as F
from torch import nn, Tensor

from ..._internally_replaced_utils import load_state_dict_from_url
from ...ops import boxes as box_ops
from ...utils import _log_api_usage_once
from .. import vgg
from . import _utils as det_utils
from .anchor_utils import DefaultBoxGenerator
from .backbone_utils import _validate_trainable_layers
from .transform import GeneralizedRCNNTransform

__all__ = ["SSD", "ssd300_vgg16"]

model_urls = {
    "ssd300_vgg16_coco": "https://download.pytorch.org/models/ssd300_vgg16_coco-b556d3b4.pth",
}

backbone_urls = {
    # We port the features of a VGG16 backbone trained by amdegroot because unlike the one on TorchVision, it uses the
    # same input standardization method as the paper. Ref: https://s3.amazonaws.com/amdegroot-models/vgg16_reducedfc.pth
    # Only the `features` weights have proper values, those on the `classifier` module are filled with nans.
    "vgg16_features": "https://download.pytorch.org/models/vgg16_features-amdegroot-88682ab5.pth"
}


def _xavier_init(conv: nn.Module):
    for layer in conv.modules():
        if isinstance(layer, nn.Conv2d):
            torch.nn.init.xavier_uniform_(layer.weight)
            if layer.bias is not None:
                torch.nn.init.constant_(layer.bias, 0.0)


class SSDHead(nn.Module):
    def __init__(self, in_channels: List[int], num_anchors: List[int], num_classes: int):
        super().__init__()
        self.classification_head = SSDClassificationHead(in_channels, num_anchors, num_classes)
        self.regression_head = SSDRegressionHead(in_channels, num_anchors)

    def forward(self, x: List[Tensor]) -> Dict[str, Tensor]:
        return {
            "bbox_regression": self.regression_head(x),
            "cls_logits": self.classification_head(x),
        }


class SSDScoringHead(nn.Module):
    def __init__(self, module_list: nn.ModuleList, num_columns: int):
        super().__init__()
        self.module_list = module_list
        self.num_columns = num_columns

    def _get_result_from_module_list(self, x: Tensor, idx: int) -> Tensor:
        """
        This is equivalent to self.module_list[idx](x),
        but torchscript doesn't support this yet
        """
        num_blocks = len(self.module_list)
        if idx < 0:
            idx += num_blocks
        out = x
        for i, module in enumerate(self.module_list):
            if i == idx:
                out = module(x)
        return out

    def forward(self, x: List[Tensor]) -> Tensor:
        all_results = []

        for i, features in enumerate(x):
            results = self._get_result_from_module_list(features, i)

            # Permute output from (N, A * K, H, W) to (N, HWA, K).
            N, _, H, W = results.shape
            results = results.view(N, -1, self.num_columns, H, W)
            results = results.permute(0, 3, 4, 1, 2)
            results = results.reshape(N, -1, self.num_columns)  # Size=(N, HWA, K)

            all_results.append(results)

        return torch.cat(all_results, dim=1)


class SSDClassificationHead(SSDScoringHead):
    def __init__(self, in_channels: List[int], num_anchors: List[int], num_classes: int):
        cls_logits = nn.ModuleList()
        for channels, anchors in zip(in_channels, num_anchors):
            cls_logits.append(nn.Conv2d(channels, num_classes * anchors, kernel_size=3, padding=1))
        _xavier_init(cls_logits)
        super().__init__(cls_logits, num_classes)


class SSDRegressionHead(SSDScoringHead):
    def __init__(self, in_channels: List[int], num_anchors: List[int]):
        bbox_reg = nn.ModuleList()
        for channels, anchors in zip(in_channels, num_anchors):
            bbox_reg.append(nn.Conv2d(channels, 4 * anchors, kernel_size=3, padding=1))
        _xavier_init(bbox_reg)
        super().__init__(bbox_reg, 4)


class SSD(nn.Module):
    """
    Implements SSD architecture from `"SSD: Single Shot MultiBox Detector" <https://arxiv.org/abs/1512.02325>`_.

    The input to the model is expected to be a list of tensors, each of shape [C, H, W], one for each
    image, and should be in 0-1 range. Different images can have different sizes but they will be resized
    to a fixed size before passing it to the backbone.

    The behavior of the model changes depending if it is in training or evaluation mode.

    During training, the model expects both the input tensors, as well as a targets (list of dictionary),
    containing:
        - boxes (``FloatTensor[N, 4]``): the ground-truth boxes in ``[x1, y1, x2, y2]`` format, with
          ``0 <= x1 < x2 <= W`` and ``0 <= y1 < y2 <= H``.
        - labels (Int64Tensor[N]): the class label for each ground-truth box

    The model returns a Dict[Tensor] during training, containing the classification and regression
    losses.

    During inference, the model requires only the input tensors, and returns the post-processed
    predictions as a List[Dict[Tensor]], one for each input image. The fields of the Dict are as
    follows, where ``N`` is the number of detections:

        - boxes (``FloatTensor[N, 4]``): the predicted boxes in ``[x1, y1, x2, y2]`` format, with
          ``0 <= x1 < x2 <= W`` and ``0 <= y1 < y2 <= H``.
        - labels (Int64Tensor[N]): the predicted labels for each detection
        - scores (Tensor[N]): the scores for each detection

    Args:
        backbone (nn.Module): the network used to compute the features for the model.
            It should contain an out_channels attribute with the list of the output channels of
            each feature map. The backbone should return a single Tensor or an OrderedDict[Tensor].
        anchor_generator (DefaultBoxGenerator): module that generates the default boxes for a
            set of feature maps.
        size (Tuple[int, int]): the width and height to which images will be rescaled before feeding them
            to the backbone.
        num_classes (int): number of output classes of the model (including the background).
        image_mean (Tuple[float, float, float]): mean values used for input normalization.
            They are generally the mean values of the dataset on which the backbone has been trained
            on
        image_std (Tuple[float, float, float]): std values used for input normalization.
            They are generally the std values of the dataset on which the backbone has been trained on
        head (nn.Module, optional): Module run on top of the backbone features. Defaults to a module containing
            a classification and regression module.
        score_thresh (float): Score threshold used for postprocessing the detections.
        nms_thresh (float): NMS threshold used for postprocessing the detections.
        detections_per_img (int): Number of best detections to keep after NMS.
        iou_thresh (float): minimum IoU between the anchor and the GT box so that they can be
            considered as positive during training.
        topk_candidates (int): Number of best detections to keep before NMS.
        positive_fraction (float): a number between 0 and 1 which indicates the proportion of positive
            proposals used during the training of the classification head. It is used to estimate the negative to
            positive ratio.
    """

    __annotations__ = {
        "box_coder": det_utils.BoxCoder,
        "proposal_matcher": det_utils.Matcher,
    }

    def __init__(
        self,
        backbone: nn.Module,
        anchor_generator: DefaultBoxGenerator,
        size: Tuple[int, int],
        num_classes: int,
        image_mean: Optional[List[float]] = None,
        image_std: Optional[List[float]] = None,
        head: Optional[nn.Module] = None,
        score_thresh: float = 0.01,
        nms_thresh: float = 0.45,
        detections_per_img: int = 200,
        iou_thresh: float = 0.5,
        topk_candidates: int = 400,
        positive_fraction: float = 0.25,
    ):
        super().__init__()
        _log_api_usage_once(self)

        self.backbone = backbone

        self.anchor_generator = anchor_generator

        self.box_coder = det_utils.BoxCoder(weights=(10.0, 10.0, 5.0, 5.0))

        if head is None:
            if hasattr(backbone, "out_channels"):
                out_channels = backbone.out_channels
            else:
                out_channels = det_utils.retrieve_out_channels(backbone, size)

            assert len(out_channels) == len(anchor_generator.aspect_ratios)

            num_anchors = self.anchor_generator.num_anchors_per_location()
            head = SSDHead(out_channels, num_anchors, num_classes)
        self.head = head

        self.proposal_matcher = det_utils.SSDMatcher(iou_thresh)

        if image_mean is None:
            image_mean = [0.485, 0.456, 0.406]
        if image_std is None:
            image_std = [0.229, 0.224, 0.225]
        self.transform = GeneralizedRCNNTransform(
            min(size), max(size), image_mean, image_std, size_divisible=1, fixed_size=size
        )

        self.score_thresh = score_thresh
        self.nms_thresh = nms_thresh
        self.detections_per_img = detections_per_img
        self.topk_candidates = topk_candidates
        self.neg_to_pos_ratio = (1.0 - positive_fraction) / positive_fraction

        # used only on torchscript mode
        self._has_warned = False

    @torch.jit.unused
    def eager_outputs(
        self, losses: Dict[str, Tensor], detections: List[Dict[str, Tensor]]
    ) -> Tuple[Dict[str, Tensor], List[Dict[str, Tensor]]]:
        if self.training:
            return losses

        return detections

    def compute_loss(
        self,
        targets: List[Dict[str, Tensor]],
        head_outputs: Dict[str, Tensor],
        anchors: List[Tensor],
        matched_idxs: List[Tensor],
    ) -> Dict[str, Tensor]:
        bbox_regression = head_outputs["bbox_regression"]
        cls_logits = head_outputs["cls_logits"]

        # Match original targets with default boxes
        num_foreground = 0
        bbox_loss = []
        cls_targets = []
        for (
            targets_per_image,
            bbox_regression_per_image,
            cls_logits_per_image,
            anchors_per_image,
            matched_idxs_per_image,
        ) in zip(targets, bbox_regression, cls_logits, anchors, matched_idxs):
            # produce the matching between boxes and targets
            foreground_idxs_per_image = torch.where(matched_idxs_per_image >= 0)[0]
            foreground_matched_idxs_per_image = matched_idxs_per_image[foreground_idxs_per_image]
            num_foreground += foreground_matched_idxs_per_image.numel()

            # Calculate regression loss
            matched_gt_boxes_per_image = targets_per_image["boxes"][foreground_matched_idxs_per_image]
            bbox_regression_per_image = bbox_regression_per_image[foreground_idxs_per_image, :]
            anchors_per_image = anchors_per_image[foreground_idxs_per_image, :]
            target_regression = self.box_coder.encode_single(matched_gt_boxes_per_image, anchors_per_image)
            bbox_loss.append(
                torch.nn.functional.smooth_l1_loss(bbox_regression_per_image, target_regression, reduction="sum")
            )

            # Estimate ground truth for class targets
            gt_classes_target = torch.zeros(
                (cls_logits_per_image.size(0),),
                dtype=targets_per_image["labels"].dtype,
                device=targets_per_image["labels"].device,
            )
            gt_classes_target[foreground_idxs_per_image] = targets_per_image["labels"][
                foreground_matched_idxs_per_image
            ]
            cls_targets.append(gt_classes_target)

        bbox_loss = torch.stack(bbox_loss)
        cls_targets = torch.stack(cls_targets)

        # Calculate classification loss
        num_classes = cls_logits.size(-1)
        cls_loss = F.cross_entropy(cls_logits.view(-1, num_classes), cls_targets.view(-1), reduction="none").view(
            cls_targets.size()
        )

        # Hard Negative Sampling
        foreground_idxs = cls_targets > 0
        num_negative = self.neg_to_pos_ratio * foreground_idxs.sum(1, keepdim=True)
        # num_negative[num_negative < self.neg_to_pos_ratio] = self.neg_to_pos_ratio
        negative_loss = cls_loss.clone()
        negative_loss[foreground_idxs] = -float("inf")  # use -inf to detect positive values that creeped in the sample
        values, idx = negative_loss.sort(1, descending=True)
        # background_idxs = torch.logical_and(idx.sort(1)[1] < num_negative, torch.isfinite(values))
        background_idxs = idx.sort(1)[1] < num_negative

        N = max(1, num_foreground)
        return {
            "bbox_regression": bbox_loss.sum() / N,
            "classification": (cls_loss[foreground_idxs].sum() + cls_loss[background_idxs].sum()) / N,
        }

    def forward(
        self, images: List[Tensor], targets: Optional[List[Dict[str, Tensor]]] = None
    ) -> Tuple[Dict[str, Tensor], List[Dict[str, Tensor]]]:
        if self.training and targets is None:
            raise ValueError("In training mode, targets should be passed")

        if self.training:
            assert targets is not None
            for target in targets:
                boxes = target["boxes"]
                if isinstance(boxes, torch.Tensor):
                    if len(boxes.shape) != 2 or boxes.shape[-1] != 4:
                        raise ValueError(f"Expected target boxes to be a tensor of shape [N, 4], got {boxes.shape}.")
                else:
                    raise ValueError(f"Expected target boxes to be of type Tensor, got {type(boxes)}.")

        # get the original image sizes
        original_image_sizes: List[Tuple[int, int]] = []
        for img in images:
            val = img.shape[-2:]
            assert len(val) == 2
            original_image_sizes.append((val[0], val[1]))

        # transform the input
        images, targets = self.transform(images, targets)

        # Check for degenerate boxes
        if targets is not None:
            for target_idx, target in enumerate(targets):
                boxes = target["boxes"]
                degenerate_boxes = boxes[:, 2:] <= boxes[:, :2]
                if degenerate_boxes.any():
                    bb_idx = torch.where(degenerate_boxes.any(dim=1))[0][0]
                    degen_bb: List[float] = boxes[bb_idx].tolist()
                    raise ValueError(
                        "All bounding boxes should have positive height and width."
                        f" Found invalid box {degen_bb} for target at index {target_idx}."
                    )

        # get the features from the backbone
        features = self.backbone(images.tensors)
        if isinstance(features, torch.Tensor):
            features = OrderedDict([("0", features)])

        features = list(features.values())

        # compute the ssd heads outputs using the features
        head_outputs = self.head(features)

        # create the set of anchors
        anchors = self.anchor_generator(images, features)

        losses = {}
        detections: List[Dict[str, Tensor]] = []
        if self.training:
            assert targets is not None

            matched_idxs = []
            for anchors_per_image, targets_per_image in zip(anchors, targets):
                if targets_per_image["boxes"].numel() == 0:
                    matched_idxs.append(
                        torch.full((anchors_per_image.size(0),), -1, dtype=torch.int64, device=anchors_per_image.device)
                    )
                    continue

                match_quality_matrix = box_ops.box_iou(targets_per_image["boxes"], anchors_per_image)
                matched_idxs.append(self.proposal_matcher(match_quality_matrix))

            losses = self.compute_loss(targets, head_outputs, anchors, matched_idxs)
        else:
            detections = self.postprocess_detections(head_outputs, anchors, images.image_sizes)
            detections = self.transform.postprocess(detections, images.image_sizes, original_image_sizes)

        if torch.jit.is_scripting():
            if not self._has_warned:
                warnings.warn("SSD always returns a (Losses, Detections) tuple in scripting")
                self._has_warned = True
            return losses, detections
        return self.eager_outputs(losses, detections)

    def postprocess_detections(
        self, head_outputs: Dict[str, Tensor], image_anchors: List[Tensor], image_shapes: List[Tuple[int, int]]
    ) -> List[Dict[str, Tensor]]:
        bbox_regression = head_outputs["bbox_regression"]
        pred_scores = F.softmax(head_outputs["cls_logits"], dim=-1)

        num_classes = pred_scores.size(-1)
        device = pred_scores.device

        detections: List[Dict[str, Tensor]] = []

        for boxes, scores, anchors, image_shape in zip(bbox_regression, pred_scores, image_anchors, image_shapes):
            boxes = self.box_coder.decode_single(boxes, anchors)
            boxes = box_ops.clip_boxes_to_image(boxes, image_shape)

            image_boxes = []
            image_scores = []
            image_labels = []
            for label in range(1, num_classes):
                score = scores[:, label]

                keep_idxs = score > self.score_thresh
                score = score[keep_idxs]
                box = boxes[keep_idxs]

                # keep only topk scoring predictions
                num_topk = min(self.topk_candidates, score.size(0))
                score, idxs = score.topk(num_topk)
                box = box[idxs]

                image_boxes.append(box)
                image_scores.append(score)
                image_labels.append(torch.full_like(score, fill_value=label, dtype=torch.int64, device=device))

            image_boxes = torch.cat(image_boxes, dim=0)
            image_scores = torch.cat(image_scores, dim=0)
            image_labels = torch.cat(image_labels, dim=0)

            # non-maximum suppression
            keep = box_ops.batched_nms(image_boxes, image_scores, image_labels, self.nms_thresh)
            keep = keep[: self.detections_per_img]

            detections.append(
                {
                    "boxes": image_boxes[keep],
                    "scores": image_scores[keep],
                    "labels": image_labels[keep],
                }
            )
        return detections


class SSDFeatureExtractorVGG(nn.Module):
    def __init__(self, backbone: nn.Module, highres: bool):
        super().__init__()

        _, _, maxpool3_pos, maxpool4_pos, _ = (i for i, layer in enumerate(backbone) if isinstance(layer, nn.MaxPool2d))

        # Patch ceil_mode for maxpool3 to get the same WxH output sizes as the paper
        backbone[maxpool3_pos].ceil_mode = True

        # parameters used for L2 regularization + rescaling
        self.scale_weight = nn.Parameter(torch.ones(512) * 20)

        # Multiple Feature maps - page 4, Fig 2 of SSD paper
        self.features = nn.Sequential(*backbone[:maxpool4_pos])  # until conv4_3

        # SSD300 case - page 4, Fig 2 of SSD paper
        extra = nn.ModuleList(
            [
                nn.Sequential(
                    nn.Conv2d(1024, 256, kernel_size=1),
                    nn.ReLU(inplace=True),
                    nn.Conv2d(256, 512, kernel_size=3, padding=1, stride=2),  # conv8_2
                    nn.ReLU(inplace=True),
                ),
                nn.Sequential(
                    nn.Conv2d(512, 128, kernel_size=1),
                    nn.ReLU(inplace=True),
                    nn.Conv2d(128, 256, kernel_size=3, padding=1, stride=2),  # conv9_2
                    nn.ReLU(inplace=True),
                ),
                nn.Sequential(
                    nn.Conv2d(256, 128, kernel_size=1),
                    nn.ReLU(inplace=True),
                    nn.Conv2d(128, 256, kernel_size=3),  # conv10_2
                    nn.ReLU(inplace=True),
                ),
                nn.Sequential(
                    nn.Conv2d(256, 128, kernel_size=1),
                    nn.ReLU(inplace=True),
                    nn.Conv2d(128, 256, kernel_size=3),  # conv11_2
                    nn.ReLU(inplace=True),
                ),
            ]
        )
        if highres:
            # Additional layers for the SSD512 case. See page 11, footernote 5.
            extra.append(
                nn.Sequential(
                    nn.Conv2d(256, 128, kernel_size=1),
                    nn.ReLU(inplace=True),
                    nn.Conv2d(128, 256, kernel_size=4),  # conv12_2
                    nn.ReLU(inplace=True),
                )
            )
        _xavier_init(extra)

        fc = nn.Sequential(
            nn.MaxPool2d(kernel_size=3, stride=1, padding=1, ceil_mode=False),  # add modified maxpool5
            nn.Conv2d(in_channels=512, out_channels=1024, kernel_size=3, padding=6, dilation=6),  # FC6 with atrous
            nn.ReLU(inplace=True),
            nn.Conv2d(in_channels=1024, out_channels=1024, kernel_size=1),  # FC7
            nn.ReLU(inplace=True),
        )
        _xavier_init(fc)
        extra.insert(
            0,
            nn.Sequential(
                *backbone[maxpool4_pos:-1],  # until conv5_3, skip maxpool5
                fc,
            ),
        )
        self.extra = extra

    def forward(self, x: Tensor) -> Dict[str, Tensor]:
        # L2 regularization + Rescaling of 1st block's feature map
        x = self.features(x)
        rescaled = self.scale_weight.view(1, -1, 1, 1) * F.normalize(x)
        output = [rescaled]

        # Calculating Feature maps for the rest blocks
        for block in self.extra:
            x = block(x)
            output.append(x)

        return OrderedDict([(str(i), v) for i, v in enumerate(output)])


def _vgg_extractor(backbone: vgg.VGG, highres: bool, trainable_layers: int):
    backbone = backbone.features
    # Gather the indices of maxpools. These are the locations of output blocks.
    stage_indices = [0] + [i for i, b in enumerate(backbone) if isinstance(b, nn.MaxPool2d)][:-1]
    num_stages = len(stage_indices)

    # find the index of the layer from which we wont freeze
    assert 0 <= trainable_layers <= num_stages
    freeze_before = len(backbone) if trainable_layers == 0 else stage_indices[num_stages - trainable_layers]

    for b in backbone[:freeze_before]:
        for parameter in b.parameters():
            parameter.requires_grad_(False)

    return SSDFeatureExtractorVGG(backbone, highres)


def ssd300_vgg16(
    pretrained: bool = False,
    progress: bool = True,
    num_classes: int = 91,
    pretrained_backbone: bool = True,
    trainable_backbone_layers: Optional[int] = None,
    **kwargs: Any,
):
    """Constructs an SSD model with input size 300x300 and a VGG16 backbone.

    Reference: `"SSD: Single Shot MultiBox Detector" <https://arxiv.org/abs/1512.02325>`_.

    The input to the model is expected to be a list of tensors, each of shape [C, H, W], one for each
    image, and should be in 0-1 range. Different images can have different sizes but they will be resized
    to a fixed size before passing it to the backbone.

    The behavior of the model changes depending if it is in training or evaluation mode.

    During training, the model expects both the input tensors, as well as a targets (list of dictionary),
    containing:

        - boxes (``FloatTensor[N, 4]``): the ground-truth boxes in ``[x1, y1, x2, y2]`` format, with
          ``0 <= x1 < x2 <= W`` and ``0 <= y1 < y2 <= H``.
        - labels (Int64Tensor[N]): the class label for each ground-truth box

    The model returns a Dict[Tensor] during training, containing the classification and regression
    losses.

    During inference, the model requires only the input tensors, and returns the post-processed
    predictions as a List[Dict[Tensor]], one for each input image. The fields of the Dict are as
    follows, where ``N`` is the number of detections:

        - boxes (``FloatTensor[N, 4]``): the predicted boxes in ``[x1, y1, x2, y2]`` format, with
          ``0 <= x1 < x2 <= W`` and ``0 <= y1 < y2 <= H``.
        - labels (Int64Tensor[N]): the predicted labels for each detection
        - scores (Tensor[N]): the scores for each detection

    Example:

        >>> model = torchvision.models.detection.ssd300_vgg16(pretrained=True)
        >>> model.eval()
        >>> x = [torch.rand(3, 300, 300), torch.rand(3, 500, 400)]
        >>> predictions = model(x)

    Args:
        pretrained (bool): If True, returns a model pre-trained on COCO train2017
        progress (bool): If True, displays a progress bar of the download to stderr
        num_classes (int): number of output classes of the model (including the background)
        pretrained_backbone (bool): If True, returns a model with backbone pre-trained on Imagenet
        trainable_backbone_layers (int): number of trainable (not frozen) resnet layers starting from final block.
            Valid values are between 0 and 5, with 5 meaning all backbone layers are trainable. If ``None`` is
            passed (the default) this value is set to 4.
    """
    if "size" in kwargs:
        warnings.warn("The size of the model is already fixed; ignoring the argument.")

    trainable_backbone_layers = _validate_trainable_layers(
        pretrained or pretrained_backbone, trainable_backbone_layers, 5, 4
    )

    if pretrained:
        # no need to download the backbone if pretrained is set
        pretrained_backbone = False

    # Use custom backbones more appropriate for SSD
    backbone = vgg.vgg16(pretrained=False, progress=progress)
    if pretrained_backbone:
        state_dict = load_state_dict_from_url(backbone_urls["vgg16_features"], progress=progress)
        backbone.load_state_dict(state_dict)

    backbone = _vgg_extractor(backbone, False, trainable_backbone_layers)
    anchor_generator = DefaultBoxGenerator(
        [[2], [2, 3], [2, 3], [2, 3], [2], [2]],
        scales=[0.07, 0.15, 0.33, 0.51, 0.69, 0.87, 1.05],
        steps=[8, 16, 32, 64, 100, 300],
    )

    defaults = {
        # Rescale the input in a way compatible to the backbone
        "image_mean": [0.48235, 0.45882, 0.40784],
        "image_std": [1.0 / 255.0, 1.0 / 255.0, 1.0 / 255.0],  # undo the 0-1 scaling of toTensor
    }
    kwargs = {**defaults, **kwargs}
    model = SSD(backbone, anchor_generator, (300, 300), num_classes, **kwargs)
    if pretrained:
        weights_name = "ssd300_vgg16_coco"
        if model_urls.get(weights_name, None) is None:
            raise ValueError(f"No checkpoint is available for model {weights_name}")
        state_dict = load_state_dict_from_url(model_urls[weights_name], progress=progress)
        model.load_state_dict(state_dict)
    return model