arXiv subjects

Diego Febbe

Publications and source records attributed to Diego Febbe.

11 recordsLinked to original sources

arXiv2026

Optimal Navigation on Simplicial Complexes

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 in the network science field. In this work, we study an extension of these topological measures for simplicial complexes: a specific type of geometric and algebraic structures that encapsulates higher-order interactions. Here, the explorability analysis of simplicial complexes has been conducted in terms of the mean first passage times between nodes, i.e. the 0th-order simplices, with the inclusion of a long-range stochastic teleportation term modulated with respect to the local random walk hopping across the various dimensions. We also provide a perturbative approximation scheme recovering the modulation parameter between pure random walk and teleportation mode (for higher-order setting) acting as the expansion parameter.

cond-mat.stat-mech↗

arXiv2026

Spectral Higher-Order Neural Networks Have Sharp Expressivity Bounds

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 weighted hyperedges required leads to an intractable parameter explosion. However, a novel parametrization that leverages spectral attributes for neural hypergraphs has been recently proposed, that enables to recycle parameters via a weight sharing scheme and consequently yields a significant reduction of the associated computational cost. Preliminary tests carried out on spectral higher-order architectures pointed to meaningful improvements in both performance and interpretability. Building on these results, we advance the benchmarking efforts by evaluating the spectral higher order framework on N-bit parity tasks, a well-established testbed known to be particularly challenging. As we will convincingly argue, Spectral Higher-Order Neural Networks (SHONNs) possess a versatile and highly tunable hypothesis space.

cs.LG↗

arXiv2026

Approximating velocity fields with planted attractors via Neural-ODEs for classification purposes

In this work, Neural ODEs equipped with a curated collection of equilibrium points have been successfully employed for classification tasks. The planted attractors serve as indicators for the target classes, while the velocity field leveraging the universal approximation capabilities of the architecture shapes the dynamical landscape. This process defines the basins of attraction of the trained model, effectively directing each input (provided as an initial condition) toward its corresponding destination target.

cond-mat.dis-nn↗

arXiv2026

Model of Simplicial Complexes with dimension-wise preferential attachment

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 constituting basic element of the system. Recently scholars have brought to the fore the relevance of higher-order networks, namely structures allowing to encode for many-body interaction, differently from the pairwise case handled by networks. This novel research field opens new avenues of research with applications ranging from neurosciences to social sciences; there is thus a need for generative models of higher-order network capable to reproduce features present in empirical data. In this work we present a model for growing simplicial complex rooted on a preferential attachment process acting dimension-wise, i.e., returning a power law distribution for the generalized degree of simplexes of different dimension.

cond-mat.stat-mech↗

arXiv2026

Exact Fixed-Point Constraints in Neural-ODEs with Provable Universality

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 accommodate for a finite collection of points in the reference multi-dimensional space of the Neural-ODE where the velocity field is exactly equal to zero. In this way, the gradient-based training is rigorously constrained inside the prescribed hypothesis class while leaving the expressive power of the Neural-ODE unaltered. We rigorously prove the universality of the Neural-ODE under any local constraints in the velocity field and give a computationally convenient way of imposing the fixed points. Our method is then tested on two paradigmatic physical models.

cond-mat.dis-nn↗

arXiv2026

Spectral Higher-Order Neural Networks

Neural networks are fundamental tools of modern machine learning. The standard paradigm assumes binary interactions (across feedforward linear passes) between inter-tangled units, organized in sequential layers. Generalized architectures have been also designed that move beyond pairwise interactions, so as to account for higher-order couplings among computing neurons. Higher-order networks are however usually deployed as augmented graph neural networks (GNNs), and, as such, prove solely advantageous in contexts where the input exhibits an explicit hypergraph structure. Here, we present Spectral Higher-Order Neural Networks (SHONNs), a new algorithmic strategy to incorporate higher-order interactions in general-purpose, feedforward, network structures. SHONNs leverages a reformulation of the model in terms of spectral attributes. This allows to mitigate the common stability and parameter scaling problems that come along weighted, higher-order, forward propagations.

cs.LG↗

arXiv2026

Random Walks Across Dimensions: Exploring Simplicial Complexes

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 edges, and edges to triangles, via a nested organization that hierarchically extends to higher structures of arbitrary large, but finite, dimension. The asymptotic distribution of the walkers provides a natural ranking to gauge the relative importance of higher order simplices. Optimal search strategies in presence of stochastic teleportation are addressed and the peculiar interplay of noise with higher order structures unraveled.

cond-mat.stat-mech↗

arXiv2025

Train Stochastic Non Linear Coupled ODEs to Classify and Generate

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 attractors of the deterministic model. Optimizing the dynamical system amounts to shaping the architecture of inter-nodes connection to steer the evolution towards the assigned equilibrium, as a function of the class to which the item - supplied as an initial condition - belongs to. Under the stochastic perspective, point attractors are turned into probability distributions, made analytically accessible via the linear noise approximation. The addition of noise proves beneficial to oppose adversarial attacks, a property that gets engraved into the trained adjacency matrix and therefore also inherited by the deterministic counterpart of the optimized stochastic model. By providing samples from the target distribution as an input to a feedforward neural network (or even to a dynamical model of the same typology of the adopted for classification purposes), yields a fully generative scheme. Conditional generation is also possible by merging classification and generation modalities. Automatic disentanglement of isolated key features is finally proven.

cond-mat.dis-nn↗

arXiv2024

Deterministic versus stochastic dynamical classifiers: opposing random adversarial attacks with noise

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 a veritable dynamically assisted classifier. To this end the model is supplied with a set of planted attractors which are self-consistently embedded in the inter-nodes coupling matrix, via its spectral decomposition. Learning to classify amounts to sculp the basin of attraction of the imposed equilibria, directing different items towards the corresponding destination target, which reflects the class of respective pertinence. A stochastic variant of the CVFR model is also studied and found to be robust to aversarial random attacks, which corrupt the items to be classified. This remarkable finding is one of the very many surprising effects which arise when noise and dynamical attributes are made to mutually resonate.

cs.LG↗

arXiv2024

Learning in Wilson-Cowan model for metapopulation

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 types of structural, functional, or effective neuronal connectivity between these regions. Each region comprises interacting populations of excitatory and inhibitory cells, consistent with the standard Wilson-Cowan model. By incorporating stable attractors into such a metapopulation model's dynamics, we transform it into a learning algorithm capable of achieving high image and text classification accuracy. We test it on MNIST and Fashion MNIST, in combination with convolutional neural networks, on CIFAR-10 and TF-FLOWERS, and, in combination with a transformer architecture (BERT), on IMDB, always showing high classification accuracy. These numerical evaluations illustrate that minimal modifications to the Wilson-Cowan model for metapopulation can reveal unique and previously unobserved dynamics.

q-bio.NC↗

arXiv2024

Estimating Global Input Relevance and Enforcing Sparse Representations with a Scalable Spectral Neural Network Approach

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 to elaborate on the process of decision making. Here, we propose a novel method to estimate the relative importance of the input components for a Deep Neural Network. This is achieved by leveraging on a spectral re-parametrization of the optimization process. Eigenvalues associated to input nodes provide in fact a robust proxy to gauge the relevance of the supplied entry features. Notably, the spectral features ranking is performed automatically, as a byproduct of the network training, with no additional processing to be carried out. Moreover, by leveraging on the regularization of the eigenvalues, it is possible to enforce solutions making use of a minimum subset of the input components, increasing the explainability of the model and providing sparse input representations. The technique is compared to the most common methods in the literature and is successfully challenged against both synthetic and real data.

cs.LG↗