SlowGuess/NeurIPS_2023_OCR huggingface dataset:
Its evaluation on finite sets  $\mathcal{X}$  and  $\tilde{\mathcal{X}}$  follows verbatim by computing their empirical mean and covariance matrix. The value of FID is between 0 and  $+\infty$ . The lower the FID value is, the closer two distributions are.
Relationship between  $\ell_2$  and cosine similarity.
The  $\ell_2$  norm can be used as a tool to measure the distance between vectors, often embeddings of images like those produced by our SimSem model:
$$
\ell_ {2} (\mathbf {u}, \mathbf {v}) = \| \mathbf {u} - \mathbf {v} \| _ {2}, \tag {6}
$$
The issue with distances to estimate the similarity between vectors is that they are only bounded below by zero (when  $\mathbf{u} = \mathbf{v}$ ). This makes it hard to set a threshold above which vectors  $\mathbf{u}$  and  $\mathbf{v}$  can be considered dissimilar. Thus, cosine similarity is often preferred to  $\ell_2$  distance as its values belong to the interval  $[-1, 1]$ , 1 indicating proportional vectors and  $-1$  vectors of opposite directions. Let  $\mathbf{u}, \mathbf{v}$  be normalized vectors, then the relationship between cosine similarity and  $\ell_2$  norm is
$$
\ell_ {2} (\mathbf {u}, \mathbf {v}) = \sqrt {2 (1 - \operatorname {c o s s i m} (\mathbf {u} , \mathbf {v}))}. \tag {7}
$$
E More Discussions
How much extra effort needs to be paid to extend the current approach? The effort required to extend the current method to other tasks also depends on the nature of the tasks. If we evaluate privacy leakage for the counting task, it would be useful to ask human annotators to count the number of objects in the reconstructed image: if it equals the number of objects in the original image, then privacy may be considered leaked. For this particular counting task, we speculate that manageable efforts will be needed to extend our current approach. On the other hand, tasks that need specialized or professional annotations will likely require more effort, such as medical image understanding.
<https://torchmetrics.readthedocs.io/en/stable/image/learned_perceptual_imagePatch_satisfaction.html>