22 citations · 61 across the 30 of their papers we have counts for
32 papers
CoVariance Filters and Neural Networks over Hilbert Spaces
Claudio Battiloro, Andrea Cavallo, Elvin Isufi
CoVariance Neural Networks (VNNs) perform graph convolutions on the empirical covariance matrix of signals defined over finite-dimensional Hilbert spaces, motivated by robustness a…
Algorithmic Collective Action with Multiple Collectives
Claudio Battiloro, Pietro Greiner, Bret Nestor +2
As learning systems increasingly influence everyday decisions, user-side steering via Algorithmic Collective Action (ACA)-coordinated changes to shared data-offers a complement to…
Frame-Based Zero-Shot Semantic Channel Equalization for AI-Native Communications
Simone Fiorellino, Claudio Battiloro, Emilio Calvanese Strinati +1
In future AI-native wireless networks, the presence of mismatches between the latent spaces of independently designed and trained deep neural network (DNN) encoders may impede mutu…
Topological Adaptive Least Mean Squares Algorithms over Simplicial Complexes
Lorenzo Marinucci, Claudio Battiloro, Paolo Di Lorenzo
This paper introduces a novel adaptive framework for processing dynamic flow signals over simplicial complexes, extending classical least-mean-squares (LMS) methods to high-order t…
Directed Semi-Simplicial Learning with Applications to Brain Activity Decoding
Manuel Lecha, Andrea Cavallo, Francesca Dominici +5
Graph Neural Networks (GNNs) excel at learning from pairwise interactions but often overlook multi-way and hierarchical relationships. Topological Deep Learning (TDL) addresses thi…
Topological Dictionary Learning
Enrico Grimaldi, Claudio Battiloro, Paolo Di Lorenzo
The aim of this paper is to introduce a novel dictionary learning algorithm for sparse representation of signals defined over combinatorial topological spaces, specifically, regula…
The Relativity of Causal Knowledge
Gabriele D'Acunto, Claudio Battiloro
Recent advances in artificial intelligence reveal the limits of purely predictive systems and call for a shift toward causal and collaborative reasoning. Drawing inspiration from t…
Topological Neural Networks over the Air
Simone Fiorellino, Claudio Battiloro, Paolo Di Lorenzo
Topological neural networks (TNNs) are information processing architectures that model representations from data lying over topological spaces (e.g., simplicial or cell complexes)…
Quantum Simplicial Neural Networks
Simone Piperno, Claudio Battiloro, Andrea Ceschini +3
Graph Neural Networks (GNNs) excel at learning from graph-structured data but are limited to modeling pairwise interactions, insufficient for capturing higher-order relationships p…
Towards a Health-Based Power Grid Optimization in the Artificial Intelligence Era
Claudio Battiloro, Gianluca Guidi, Falco J. Bargagli-Stoffi +1
The electric power sector is one of the largest contributors to greenhouse gas emissions in the world. In recent years, there has been an unprecedented increase in electricity dema…
TopoTune : A Framework for Generalized Combinatorial Complex Neural Networks
Mathilde Papillon, Guillermo Bernárdez, Claudio Battiloro +1
Graph Neural Networks (GNNs) effectively learn from relational data by leveraging graph symmetries. However, many real-world systems -- such as biological or social networks -- fea…
ICML Topological Deep Learning Challenge 2024: Beyond the Graph Domain
Guillermo Bernárdez, Lev Telyatnikov, Marco Montagna +70
This paper describes the 2nd edition of the ICML Topological Deep Learning Challenge that was hosted within the ICML 2024 ELLIS Workshop on Geometry-grounded Representation Learnin…
Higher-Order Topological Directionality and Directed Simplicial Neural Networks
Manuel Lecha, Andrea Cavallo, Francesca Dominici +2
Topological Deep Learning (TDL) has emerged as a paradigm to process and learn from signals defined on higher-order combinatorial topological spaces, such as simplicial or cell com…
TopoBench: A Framework for Benchmarking Topological Deep Learning
Lev Telyatnikov, Guillermo Bernardez, Marco Montagna +34
This work introduces TopoBench, an open-source library designed to standardize benchmarking and accelerate research in topological deep learning (TDL). TopoBench decomposes TDL int…
Attending to Topological Spaces: The Cellular Transformer
Rubén Ballester, Pablo Hernández-García, Mathilde Papillon +6
Topological Deep Learning seeks to enhance the predictive performance of neural network models by harnessing topological structures in input data. Topological neural networks opera…
E(n) Equivariant Topological Neural Networks
Claudio Battiloro, Ege Karaismailoğlu, Mauricio Tec +3
Graph neural networks excel at modeling pairwise interactions, but they cannot flexibly accommodate higher-order interactions and features. Topological deep learning (TDL) has emer…
Dynamic Relative Representations for Goal-Oriented Semantic Communications
Simone Fiorellino, Claudio Battiloro, Emilio Calvanese Strinati +1
In future 6G wireless networks, semantic and effectiveness aspects of communications will play a fundamental role, incorporating meaning and relevance into transmissions. However,…
TopoX: A Suite of Python Packages for Machine Learning on Topological Domains
Mustafa Hajij, Mathilde Papillon, Florian Frantzen +40
We introduce TopoX, a Python software suite that provides reliable and user-friendly building blocks for computing and machine learning on topological domains that extend graphs: h…
Stability of Graph Convolutional Neural Networks through the lens of small perturbation analysis
Lucia Testa, Claudio Battiloro, Stefania Sardellitti +1
In this work, we study the problem of stability of Graph Convolutional Neural Networks (GCNs) under random small perturbations in the underlying graph topology, i.e. under a limite…
Goal-oriented Communications for the IoT: System Design and Adaptive Resource Optimization
Paolo Di Lorenzo, Mattia Merluzzi, Francesco Binucci +4
Internet of Things (IoT) applications combine sensing, wireless communication, intelligence, and actuation, enabling the interaction among heterogeneous devices that collect and pr…
ICML 2023 Topological Deep Learning Challenge : Design and Results
Mathilde Papillon, Mustafa Hajij, Helen Jenne +53
This paper presents the computational challenge on topological deep learning that was hosted within the ICML 2023 Workshop on Topology and Geometry in Machine Learning. The competi…
Generalized Simplicial Attention Neural Networks
Claudio Battiloro, Lucia Testa, Lorenzo Giusti +3
Graph machine learning methods excel at leveraging pairwise relations present in the data. However, graphs are unable to fully capture the multi-way interactions inherent in many c…
From Latent Graph to Latent Topology Inference: Differentiable Cell Complex Module
Claudio Battiloro, Indro Spinelli, Lev Telyatnikov +3
Latent Graph Inference (LGI) relaxed the reliance of Graph Neural Networks (GNNs) on a given graph topology by dynamically learning it. However, most of LGI methods assume to have…
Tangent Bundle Convolutional Learning: from Manifolds to Cellular Sheaves and Back
Claudio Battiloro, Zhiyang Wang, Hans Riess +2
In this work we introduce a convolution operation over the tangent bundle of Riemann manifolds in terms of exponentials of the Connection Laplacian operator. We define tangent bund…