Towards a Health-Based Power Grid Optimization in the Artificial Intelligence Era

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 demand driven by the so-called Artificial Intelligence (AI) revolution. Although AI has and will continue to have a transformative impact, its environmental and health impacts are often overlooked. The standard approach to power grid optimization aims to minimize CO$_2$ emissions. In this paper, we propose a new holistic paradigm. Our proposed optimization directly targets the minimization of adverse health outcomes under energy efficiency and emission constraints. We show the first example of an optimal fuel mix allocation problem aiming to minimize the average number of adverse health effects resulting from exposure to hazardous air pollutants with constraints on the average and marginal emissions. We argue that this new health-based power grid optimization is essential to promote truly sustainable technological advances that align both with global climate goals and public health priorities.

TopoTune : A Framework for Generalized Combinatorial Complex Neural Networks

Graph Neural Networks (GNNs) excel in learning from relational datasets, processing node and edge features in a way that preserves the symmetries of the graph domain. However, many complex systems--such as biological or social networks--involve multiway complex interactions that are more naturally represented by higher-order topological spaces. The emerging field of Topological Deep Learning (TDL) aims to accommodate and leverage these higher-order structures. Combinatorial Complex Neural Networks (CCNNs), fairly general TDL models, have been shown to be more expressive and better performing than GNNs. However, differently from the graph deep learning ecosystem, TDL lacks a principled and standardized framework for easily defining new architectures, restricting its accessibility and applicability. To address this issue, we introduce Generalized CCNNs (GCCNs), a novel simple yet powerful family of TDL models that can be used to systematically transform any (graph) neural network into its TDL counterpart. We prove that GCCNs generalize and subsume CCNNs, while extensive experiments on a diverse class of GCCNs show that these architectures consistently match or outperform CCNNs, often with less model complexity. In an effort to accelerate and democratize TDL, we introduce TopoTune, a lightweight software that allows practitioners to define, build, and train GCCNs with unprecedented flexibility and ease.

Higher-Order Topological Directionality and Directed Simplicial Neural Networks

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 complexes. Although many complex systems have an asymmetric relational structure, most TDL models forcibly symmetrize these relationships. In this paper, we first introduce a novel notion of higher-order directionality and we then design Directed Simplicial Neural Networks (Dir-SNNs) based on it. Dir-SNNs are message-passing networks operating on directed simplicial complexes able to leverage directed and possibly asymmetric interactions among the simplices. To our knowledge, this is the first TDL model using a notion of higher-order directionality. We theoretically and empirically prove that Dir-SNNs are more expressive than their directed graph counterpart in distinguishing isomorphic directed graphs. Experiments on a synthetic source localization task demonstrate that Dir-SNNs outperform undirected SNNs when the underlying complex is directed, and perform comparably when the underlying complex is undirected.

ICML Topological Deep Learning Challenge 2024: Beyond the Graph Domain

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 Learning and Generative Modeling (GRaM). The challenge focused on the problem of representing data in different discrete topological domains in order to bridge the gap between Topological Deep Learning (TDL) and other types of structured datasets (e.g. point clouds, graphs). Specifically, participants were asked to design and implement topological liftings, i.e. mappings between different data structures and topological domains --like hypergraphs, or simplicial/cell/combinatorial complexes. The challenge received 52 submissions satisfying all the requirements. This paper introduces the main scope of the challenge, and summarizes the main results and findings.

E(n) Equivariant Topological Neural Networks

Graph neural networks excel at modeling pairwise interactions, but they cannot flexibly accommodate higher-order interactions and features. Topological deep learning (TDL) has emerged recently as a promising tool for addressing this issue. TDL enables the principled modeling of arbitrary multi-way, hierarchical higher-order interactions by operating on combinatorial topological spaces, such as simplicial or cell complexes, instead of graphs. However, little is known about how to leverage geometric features such as positions and velocities for TDL. This paper introduces E(n)-Equivariant Topological Neural Networks (ETNNs), which are E(n)-equivariant message-passing networks operating on combinatorial complexes, formal objects unifying graphs, hypergraphs, simplicial, path, and cell complexes. ETNNs incorporate geometric node features while respecting rotation and translation equivariance. Moreover, ETNNs are natively ready for settings with heterogeneous interactions. We provide a theoretical analysis to show the improved expressiveness of ETNNs over architectures for geometric graphs. We also show how several E(n) equivariant variants of TDL models can be directly derived from our framework. The broad applicability of ETNNs is demonstrated through two tasks of vastly different nature: i) molecular property prediction on the QM9 benchmark and ii) land-use regression for hyper-local estimation of air pollution with multi-resolution irregular geospatial data. The experiment results indicate that ETNNs are an effective tool for learning from diverse types of richly structured data, highlighting the benefits of principled geometric inductive bias.

Attending to Topological Spaces: The Cellular Transformer

Topological Deep Learning seeks to enhance the predictive performance of neural network models by harnessing topological structures in input data. Topological neural networks operate on spaces such as cell complexes and hypergraphs, that can be seen as generalizations of graphs. In this work, we introduce the Cellular Transformer (CT), a novel architecture that generalizes graph-based transformers to cell complexes. First, we propose a new formulation of the usual self- and cross-attention mechanisms, tailored to leverage incidence relations in cell complexes, e.g., edge-face and node-edge relations. Additionally, we propose a set of topological positional encodings specifically designed for cell complexes. By transforming three graph datasets into cell complex datasets, our experiments reveal that CT not only achieves state-of-the-art performance, but it does so without the need for more complex enhancements such as virtual nodes, in-domain structural encodings, or graph rewiring.

Dynamic Relative Representations for Goal-Oriented Semantic Communications

In future 6G wireless networks, semantic and effectiveness aspects of communications will play a fundamental role, incorporating meaning and relevance into transmissions. However, obstacles arise when devices employ diverse languages, logic, or internal representations, leading to semantic mismatches that might jeopardize understanding. In latent space communication, this challenge manifests as misalignment within high-dimensional representations where deep neural networks encode data. This paper presents a novel framework for goal-oriented semantic communication, leveraging relative representations to mitigate semantic mismatches via latent space alignment. We propose a dynamic optimization strategy that adapts relative representations, communication parameters, and computation resources for energy-efficient, low-latency, goal-oriented semantic communications. Numerical results demonstrate our methodology's effectiveness in mitigating mismatches among devices, while optimizing energy consumption, delay, and effectiveness.

TopoX: A Suite of Python Packages for Machine Learning on Topological Domains

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: hypergraphs, simplicial, cellular, path and combinatorial complexes. topox consists of three packages: toponetx facilitates constructing and computing on these domains, including working with nodes, edges and higher-order cells; topoembedx provides methods to embed topological domains into vector spaces, akin to popular graph-based embedding algorithms such as node2vec; topomodelx is built on top of PyTorch and offers a comprehensive toolbox of higher-order message passing functions for neural networks on topological domains. The extensively documented and unit-tested source code of topox is available under MIT license at https://github.com/pyt-team.

Stability of Graph Convolutional Neural Networks through the lens of small perturbation analysis

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 limited number of insertions or deletions of edges. We derive a novel bound on the expected difference between the outputs of unperturbed and perturbed GCNs. The proposed bound explicitly depends on the magnitude of the perturbation of the eigenpairs of the Laplacian matrix, and the perturbation explicitly depends on which edges are inserted or deleted. Then, we provide a quantitative characterization of the effect of perturbing specific edges on the stability of the network. We leverage tools from small perturbation analysis to express the bounds in closed, albeit approximate, form, in order to enhance interpretability of the results, without the need to compute any perturbed shift operator. Finally, we numerically evaluate the effectiveness of the proposed bound.

Goal-oriented Communications for the IoT: System Design and Adaptive Resource Optimization

Internet of Things (IoT) applications combine sensing, wireless communication, intelligence, and actuation, enabling the interaction among heterogeneous devices that collect and process considerable amounts of data. However, the effectiveness of IoT applications needs to face the limitation of available resources, including spectrum, energy, computing, learning and inference capabilities. This paper challenges the prevailing approach to IoT communication, which prioritizes the usage of resources in order to guarantee perfect recovery, at the bit level, of the data transmitted by the sensors to the central unit. We propose a novel approach, called goal-oriented (GO) IoT system design, that transcends traditional bit-related metrics and focuses directly on the fulfillment of the goal motivating the exchange of data. The improvement is then achieved through a comprehensive system optimization, integrating sensing, communication, computation, learning, and control. We provide numerical results demonstrating the practical applications of our methodology in compelling use cases such as edge inference, cooperative sensing, and federated learning. These examples highlight the effectiveness and real-world implications of our proposed approach, with the potential to revolutionize IoT systems.