E(n) Equivariant Topological Neural Networks
Claudio Battiloro, Ege Karaismailo\u{g}lu, Mauricio Tec, George, Dasoulas, Michelle Audirac, Francesca Dominici
TL;DR
This paper introduces E(n)-Equivariant Topological Neural Networks (ETNNs), which operate on combinatorial complexes to model higher-order interactions with geometric features, improving expressiveness and efficiency over existing models.
Contribution
The paper proposes a novel class of E(n)-equivariant neural networks that operate on topological complexes, incorporating geometric features and demonstrating superior performance and theoretical advantages.
Findings
ETNNs outperform state-of-the-art equivariant TDL models on molecular property prediction.
ETNNs effectively model heterogeneous multi-way interactions in complex data.
ETNNs achieve comparable or better results with lower computational costs.
Abstract
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, reflection, and translation…
Peer Reviews
Decision·ICLR 2025 Poster
Presentation, clarity and experimental transparency I found the paper to be written clearly, and the mathematical statements and proofs were precise, well formulated and easy to follow. Further, the authors included a lot of helpful background about topological deep learning, and explained concepts clearly. One of the biggest strengths of this paper is the much appreciated transparency around testing in the appendix. This allowed a confident and clear understanding of what the authors actuall
TDL vs GDL: novelty as a conceptual framework For me personally I find it hard to understand the framing of this as a part of an entirely new conceptual field of topological deep learning beyond GNNs, and question the genuine novelty of papers like this. This is a concern I have of the field of TDL more generally, but I hope that the authors may be able to help clarify given their excellent communication skills demonstrated in the paper. Unless I’m mistaken, the basic content of proposition (
The authors add an important piece of work for the Topological Deep Learning (TDL) community as there is not much literature on Equivariant TDL. The work is well-formulated with clear motivations. The theoretical contributions are well-written. The paper is also self-contained and easy to follow, given the substantial explanations from related prior literature. The ablation studies are well-conducted via many synthetic graphs and additional information (hyperparameters, data statistics, etc.) ar
Novelty is the key disadvantage of the paper. It seems that the work just extends prior works on graphs to TDL. Even though the theoretical insights are important, yet they are mostly an extension from graphs. Another important weakness is scalability and practicability of the problem. There are only two real-world datasets evaluated, and in both cases, graph sizes are small. Furthermore, the performance isn’t convincing given there are only minor improvements over the graph counterparts. The p
1. The paper offers a simple and straightforward way to adapt higher order message passing to respect $O(d)$ symmetries. 2. The experimental section effectively demonstrates the architecture's performance and introduces two new, interesting real-world TDL benchmarks, addressing a need highlighted in a recent position paper [1]. [1] Theodore Papamarkou, Tolga Birdal, Michael M Bronstein, Gunnar E Carlsson, Justin Curry, Yue Gao, Mustafa Hajij, Roland Kwitt, Pietro Lio, Paolo Di Lorenzo, et a
1. The novelty of the proposed architecture and the theoretical section is somewhat limited. The architecture closely resembles those presented in [4] and [2]. Additionally, the theoretical contributions feel somewhat straightforward, offering limited new insights. 2. Building on the previous comment about the theoretical section, the paper lacks an analysis of how the choice of invariant function (see Equation (6)) affects the architecture's expressivity. It would be valuable to examine whethe
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TopicsNeural Networks and Applications