3 papers
math.AG2025
On the Euclidean Distance Degree of Quadratic Two-Neuron Neural Networks
Giacomo Graziani
We study the Euclidean Distance degree of algebraic neural network models from the perspective of algebraic geometry. Focusing on shallow networks with two neurons, quadratic activ…
math.AG2025
Grothendieck's proof of Hirzebruch-Riemann-Roch theorem
Giacomo Graziani
The Riemann-Roch Theorem is one of the cornerstones of algebraic geometry, connecting algebraic data (sheaf cohomology) with geometric ones (intersection theory). This survey paper…
math.AG2025
Ruled and rational surfaces and their models
Giacomo Graziani
One of the most powerful ideas in the study and classification of algebraic varieties is the notion of a model: that is, to single out an object, in the appropriate isomorphism cla…