Write the formula for PageRank equation

How does the Page Rank algorithm map and rank the importance of individual web pages within the vast network of the World Wide Web, considering the entire history of the internet as its microcosm?

Page Rank algorithm assigns importance based on link structures, iteratively calculating web pages' relevance

Write the equation for cross-entropy loss

H(y, p) = -Σ(y_i * log(p_i)) for all i

Write the formula for Pearson correlation coefficient

r = Σ((xi - x̄)(yi - ȳ)) / (√Σ(xi - x̄)² * √Σ(yi - ȳ)²)

Write the formula for Mahalanobis distance

D^2 = (x - μ)^T Σ^(-1) (x - μ)

What weight tying does in language models: shares embedding and output projection matrices

Language models use tied weights to share embedding and output projection matrices, enhancing parameter efficiency

What is the formula for calculating the mutual information between two discrete random variables X and Y?

I(X;Y) = ∑∑ P(x,y) log(P(x,y)/(P(x)P(y)))