11 papers
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…
Train Stochastic Non Linear Coupled ODEs to Classify and Generate
Stefano Gagliani, Feliciano Giuseppe Pacifico, Lorenzo Chicchi +4
A general class of dynamical systems which can be trained to operate in classification and generation modes are introduced. A procedure is proposed to plant asymptotic stationary a…
Deterministic versus stochastic dynamical classifiers: opposing random adversarial attacks with noise
Lorenzo Chicchi, Duccio Fanelli, Diego Febbe +4
The Continuous-Variable Firing Rate (CVFR) model, widely used in neuroscience to describe the intertangled dynamics of excitatory biological neurons, is here trained and tested as…
Learning in Wilson-Cowan model for metapopulation
Raffaele Marino, Lorenzo Buffoni, Lorenzo Chicchi +4
The Wilson-Cowan model for metapopulation, a Neural Mass Network Model, treats different subcortical regions of the brain as connected nodes, with connections representing various…
Estimating Global Input Relevance and Enforcing Sparse Representations with a Scalable Spectral Neural Network Approach
Lorenzo Chicchi, Lorenzo Buffoni, Diego Febbe +3
In machine learning practice it is often useful to identify relevant input features. Isolating key input elements, ranked according their respective degree of relevance, can help t…