Can Topological Deep Learning (TDL) models compute fundamental topological invariants? 🔎🌐. Our new paper suggests that in many cases the answer is surprisingly NO. To mitigate this, we develop two new TDL architectures inspired by expressive graph networks. 1/11

RT @GuyBarSh: 📢 Introducing:. Learning on LLM Output Signatures for Gray-box LLM Behavior Analysis [.A joint work w….

What do you want to know?.

Topological blindspots is an ICLR oral presentation! Come check it out 🔥.

RT @neribr: "Balancing Efficiency and Expressiveness: Subgraph GNNs with Walk-Based Centrality" by @JoshSouthern13, @ytn_ym, Guy Bar-Shalom….

RT @yoav_gelberg: 🧠 Can we train models to manipulate NN weights?. Join us at the first Weight Space Learning Workshop @ICLR_conf to explor….

Check out our new paper!.

RT @miniapeur: Topological machine learning and topological data analysis are two of the most interesting and fast-growing fields if you're….

Extremely honored to be on this list! Thanks @miniapeur for the support!.

A collaboration with an incredible group of people: @yoav_gelberg @GuyBarSh @ffabffrasca @mmbronstein @HaggaiMaron. Inspired by works by: @HajijMustafa @ninamiolane .@Pseudomanifold @crisbodnar @naturecomputes and more.

See for the full paper, where we additionally present a topological criterion for HOMP indistinguishability, compare HOMP to hypergraph architectures, and more!. Stay tuned for more experimental results on real-world datasets 🚀.

Using a novel synthetic dataset called the Torus Dataset, we empirically evaluate the expressivity of these architectures, taking the first step towards benchmarking the expressivity of TDL models. 9/11.

To mitigate these limitations, we introduce two new TDL architectures: multi-cellular networks (MCN), that can reach full expressivity but are computationally expensive, and scalable MCN (SMCN), an efficient alternative that still mitigates many of HOMPs limitations. 8/11

Finally, we discuss the homology groups of a complex, which encode the structure of the high dimensional holes in the space (e.g. a circle has a 1-dimensional hole, a sphere has a 2-dimentional hole etc.). We demonstrate that HOMP is unable to compute ANY homology group. 7/11

Additionally, we note that the Möbius strip cannot be embedded in the plane while the cylinder can, demonstrating that HOMP is also unable to detect planarity. 6/11

We then explore whether HOMP can compute orientability, a topological property that captures whether a space has consistent “sides”, e.g. a cylinder is orientable while a Möbius strip is not. We prove that HOMP cannot separate the two and thus can't detect orientability. 5/11

Our first example focuses on the diameter, a natural metric invariant which intuitively measures how “spread out” a topological object is. We show that HOMP models are unable to distinguish between complexes based on their diameters. 4/11

Exploring the expressive power of HOMP, we demonstrate its inability to compute several fundamental metric and topological properties such as diameter, orientability, planarity and homology, implying that HOMP cannot fully leverage basic topological facts about the data. 3/11.

TDL enables learning from topological data such as simplicial, cellular and combinatorial complexes. The most popular TDL architecture is Higher-Order Message Passing (HOMP), which extends classic graph neural networks to topological domains. 2/11