What is meant by correlation structure?

I know only about the Pearson's correlation coefficient in literature.

Covariance between two random variables $$X$$ and $$Y$$ is defined as

$$Cov[X, Y] = \mathbb{E}[(X - \mathbb{E}[X])(Y-\mathbb{E}[Y])]$$

(Linear) Correlation between two random variables $$X$$ and $$Y$$ is defined as

$$Corr[X, Y] = \dfrac{Cov[X, Y]}{\sigma(X)\sigma(Y)}$$

Covariance is a measure of association between two random variables whereas correlation measures how much dependent they both are on each other.

Consider the following excerpt mentioning "correlation structure" from section 2: General Design Principles of the research paper titled Rethinking the Inception Architecture for Computer Vision

Theoretically, information content cannot be assessed merely by the dimensionality of the representation as it discards important factors like correlation structure; the dimensionality merely provides a rough estimate of information content.

What is meant by the "correlation structure" mentioned here? Is it a graph on input random variables? Is it in any way related to the aforementioned correlation?