How does Naïve Bayes relate to information geometry and exponential family manifolds?

Naïve Bayes can be interpreted as a projection onto a submanifold of independent distributions within the exponential family.

From an information geometry perspective, probability distributions form a curved manifold. Naïve Bayes restricts this space to a submanifold where features are conditionally independent given the class. Learning NB corresponds to projecting empirical distributions onto this constrained manifold using KL divergence minimization. This explains both its efficiency and its bias: it trades geometric expressiveness for tractability.