What the Yoneda lemma says: an object is determined by its relationships to all other objects

What the Y combinator does: enables recursion in languages without named functions

The Y combinator enables recursive function definitions in lambda calculus and similar functional languages

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

How does the concept of homotopy type theory (HoTT) enable the unification of homotopy theory and higher category theory in mathematical foundations?

HoTT unifies homotopy theory and higher category theory by using types as mathematical objects, enabling homotopical and categorical structures to coexist

What IS (Inception Score) measures: diversity and quality of generated images

Inception Score quantifies image diversity and generated images' quality

What the underdetermination of theory by data means — evidence is always compatible with multiple theories

Underdetermination implies that evidence does not uniquely determine a single theory

What nominalism claims — only particular things exist, universals are just names

Nominalism posits that only individual objects exist, universals are mere linguistic constructs