5 papers
Algebraic Networks and Architectural Degenerations
Giacomo Graziani
We study the geometry of polynomial neural networks with monomial activation functions and no bias. We introduce a general framework of algebraic networks, together with their real…
On the Stable Euclidean Distance Degree of Algebraic Layers
Giacomo Graziani
We study the projective geometry of algebraic neural layers, namely families of maps induced by a polynomial activation function, with particular emphasis on the generic Euclidean…
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…
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…
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…