arXiv subjects

Gianluca Peri

Publications and source records attributed to Gianluca Peri.

6 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

On rankings in multiplayer games with an application to the game of Whist

We propose a novel extension of the Bradley-Terry model to multiplayer games and adapt a recent algorithm by Newman [1] to our model. We demonstrate the use of our proposed method on synthetic datasets and on a real dataset of games of cards.

cs.GT↗

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

Smart Walkers in Discrete Space

We study the statistical properties of trainable agents moving in discrete space. After introducing the mathematical framework, we first analyze the dynamics of two completely random walkers, mutually competing in a chaser-target interaction scheme. The statistics of the encounters is analytically obtained and the predictions tested versus numerical simulations. We then move forward to extend the baseline case to agents capable of learning and adapting to an external reward signal, using reinforcement learning. Smart walkers morph the statistics of the encounter, to maximize their cumulated reward, as confirmed by combined numerical and analytical insights. More interestingly, configuration entropy proves a reliable proxy to gauge the acquired ability of the agents to cope with the assigned task when no other information about them (i.e. reward signal, policy, etc) is present. We further test the proposed measure of learned skills by operating the Stockfish chess engine against a quasi-random untrained opponent. The obtained conclusions corroborate our claim. Summing up, our primary contribution is to propose and test a quantitative measure of agents' awareness that naturally correlates with the inherent complexity of the task being performed.

cond-mat.stat-mech↗

arXiv2025

Spectral Architecture Search for Neural Network Models

Architecture design and optimization are challenging problems in the field of artificial neural networks. Working in this context, we here present SPARCS (SPectral ARchiteCture Search), a novel architecture search protocol which exploits the spectral attributes of the inter-layer transfer matrices. SPARCS allows one to explore the space of possible architectures by spanning continuous and differentiable manifolds, thus enabling for gradient-based optimization algorithms to be eventually employed. With reference to simple benchmark models, we show that the newly proposed method yields a self-emerging architecture with a minimal degree of expressivity to handle the task under investigation and with a reduced parameter count as compared to other viable alternatives.

cs.LG↗