human
Solve the following python programming problem given the following code:
# Layers to use. We will use these layers as advised in the paper.
# To have softer features, increase the weight of the higher layers
# (conv5_1) and decrease the weight of the lower layers (conv1_1).
# To have harder features, decrease the weight of the higher layers
# (conv5_1) and increase the weight of the lower layers (conv1_1).
STYLE_LAYERS = [
    ('conv1_1', 0.5),
    ('conv2_1', 0.5),
    ('conv3_1', 0.5),
    ('conv4_1', 0.5),
    ('conv5_1', 0.5),
]

def style_loss_func(sess, model):
    """
    Style loss function as defined in the paper.
    """
    def _gram_matrix(feat):
        """
        Compute the Gram matrix from features.

        Inputs:
        - feat: Tensor of shape (1, H, W, C) giving features for a single image.

        Returns:
        - gram: Tensor of shape (C, C) giving the (optionally normalized) Gram matrices for the input image.
        """
        #############################################################################
        # TODO: Compute gram matrix                                                 #
        #############################################################################
        gram = None
        #############################################################################
        #                             END OF YOUR CODE                              #
        #############################################################################
        return gram
    
    def _style_loss(current_feat, style_feat):
        """
        Inputs:
        - current_feat: features of the current image, Tensor with shape [1, height, width, channels]
        - style_feat: features of the style image, Tensor with shape [1, height, width, channels]

        Returns:
        - scalar style loss
        """
        assert (current_feat.shape == style_feat.shape)
        #############################################################################
        # TODO: Compute style loss function                                         #
        # HINT: Call the...
Given the above code, generate some markdown instructions for it.
assistant
#Here is Python program to compute the Gram matrix from features.

Style Loss
Now we can tackle the style loss of equation (5) from the paper. For a given layer $\ell$, the style loss is defined as follows:
First, compute the Gram matrix G which represents the correlations between the responses of each filter, where F is as above. The Gram matrix is an approximation to the covariance matrix -- we want the activation statistics of our generated image to match the activation statistics of our style image, and matching the (approximate) covariance is one way to do that. There are a variety of ways you could do this, but the Gram matrix is nice because it's easy to compute and in practice shows good results.
Given a feature map $F^\ell$ of shape $(1, M_\ell,  N_\ell)$, the Gram matrix has shape $(1, N_\ell, N_\ell)$ and its elements are given by:
$$G_{ij}^\ell  = \sum_k F^{\ell}{ik} F^{\ell}{jk}$$
Assuming $G^\ell$ is the Gram matrix from the feature map of the current image, $A^\ell$ is the Gram Matrix from the feature map of the source style image, then the style loss for the layer $\ell$ is simply the Euclidean distance between the two Gram matrices:
$$E_\ell = \frac{1}{4 N^2_\ell M^2_\ell} \sum_{i, j} \left(G^\ell_{ij} - A^\ell_{ij}\right)^2$$
In practice we usually compute the style loss at a set of layers $\mathcal{L}$ rather than just a single layer $\ell$; then the total style loss is the weighted sum of style losses at each layer by $w_\ell$:
$$L_s = \sum_{\ell \in \mathcal{L}}  w_\ell E_\ell$$
In our case it is a summation from conv1_1 (lower layer) to conv5_1 (higher layer). Intuitively, the style loss across multiple layers captures lower level features (hard strokes, points, etc) to higher level features (styles, patterns, even objects).