5 papers · 1 filter
Exceptional Singularities in Polynomial Neural Networks
Giacomo Graziani
The singularities of a neurovariety have so far always turned out to lie at subnetworks: functions already computed by a smaller architecture of the same kind. This is what makes t…
On the Euclidean Distance Degree of Shallow Polynomial Networks
Giacomo Graziani
We study the projective geometry of shallow polynomial neural networks, namely families of homogeneous polynomial maps realised by a single hidden layer with monomial activation. T…
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…