Content Loss Computation

easyPRONeural Style TransferStyle TransferCV: Computational Photography

Compute the content loss between feature maps.

Content loss ensures the generated image preserves the high-level structure of the content image. Unlike style, we want to preserve spatial layout, so we directly compare feature activations:

$L_{content} = \frac{1}{2} \sum_{i,j} (F_{ij}^{gen} - F_{ij}^{content})^2$

where:

$F^{gen}$ is the feature map of the generated image
$F^{content}$ is the feature map of the content image

By matching features (not pixels), we preserve semantic content while allowing stylistic changes. Content loss is typically computed from a mid-level CNN layer that captures shapes and objects.

Example

Input

content_loss([[1, 2], [3, 4]], [[1, 2], [3, 4]])

Output

0.0

Reasoning

Comparing identical feature maps:
Differences: all zeros
Squared differences: all zeros
Sum: 0
Content loss: 0 / 2 = 0.0
Identical features mean identical content - zero loss.

Constraints

F_generated and F_content: feature maps with same shape
Return loss value rounded to 4 decimal places
Loss should be 0 when feature maps are identical

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Concept primerPREVIEW

The task is to compute the content loss as the squared difference between the feature maps of the generated image and the content image, averaged with a factor of \frac{1}{2}.

1. Background Knowledge

In neural style transfer (NST), you generate an image that combines the content (objects, layout) of one image with the style (colors, textures, brush strokes) of another. Content and style are represented not in pixel space but in the feature space of a pretrained CNN (e.g., VGG).

A feature map is the activation output of a convolutional layer when you feed an image through the CNN. Mid-level layers (e.g., conv4_2 in VGG) tend to capture object shapes and spatial structure, which is why they are used for content representation in NST. The content loss measures how different the feature maps of the generated image are from those of the content image at these layers.

2. Algorithm / General Approach

The general pattern for computing content loss:

Pass the content image through a pretrained CNN and store the feature map from a chosen content layer.
Pass the generated image through the same CNN and extract the feature map from the same layer.
Compute the squared difference between these two feature maps, summed over all spatial positions and channels.
Multiply by \frac{1}{2} (as given in the formula) to get $L_{$ \text{content} $}$ .

Mathematically (for one layer):

L_{\text{content}} = \frac{1}{2} \sum_{i,j} \big(F_{ij}^{gen} - F_{ij}^{content}\big)^2

Where $F^{gen}$ and $F^{content}$ have shape $(C, H, W)$ or $(N, C, H, W)$ depending on framework.

3. Step-by-Step Strategy

Assume you’re using PyTorch-like tensors; adapt similarly for NumPy or TensorFlow.

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solution.py

Python 3.13

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