7 papers · 1 filter
Optimal Navigation on Simplicial Complexes
Diego Febbe, Duccio Fanelli, Gianluca Peri +1
The navigation time and optimal search strategies deriving from random dynamical processes on binary graphs have been extensively explored and analyzed, being of prominent interest…
Spectral Higher-Order Neural Networks Have Sharp Expressivity Bounds
Gianluca Peri, Diego Febbe, Duccio Fanelli
Neural hypergraphs are a natural generalization of neural networks, the reference models in modern machine learning. Yet, their deployment has proven demanding: the number of weigh…
Approximating velocity fields with planted point attractors via Neural-ODE for classification purposes
Feliciano Giuseppe Pacifico, Duccio Fanelli, Lorenzo Buffoni +3
In this work, Neural ODEs equipped with a curated collection of equilibrium points have been successfully employed for classification tasks. The planted fixed points serve as indic…
Exact Fixed-Point Constraints in Neural-ODEs with Provable Universality
Feliciano Giuseppe Pacifico, Duccio Fanelli, Lorenzo Buffoni +3
We introduce a technique that enables Neural-ODEs to approximate arbitrary velocity fields with a priori planted fixed-points. Specifically, a recipe is given to explicitly accommo…
Model of Simplicial Complexes with dimension-wise preferential attachment
Diego Febbe, Duccio Fanelli, Timoteo Carletti
Network science is a powerful framework allowing to model complex systems, it is capable to describe and take into account the intricate web of connections existing among the const…
Spectral Higher-Order Neural Networks
Gianluca Peri, Timoteo Carletti, Duccio Fanelli +1
Neural networks are fundamental tools of modern machine learning. The standard paradigm assumes binary interactions (across feedforward linear passes) between inter-tangled units,…
Random Walks Across Dimensions: Exploring Simplicial Complexes
Diego Febbe, Duccio Fanelli, Timoteo Carletti
We introduce a novel operator to describe a random walk process on a simplicial complex. Walkers are allowed to wonder across simplices of various dimensions, bridging nodes to edg…