Miguel Carrasco

Guillermo Bernárdez, Lev Telyatnikov, Marco Montagna et al.

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.

Martin Carrasco, Guillermo Bernardez, Marco Montagna et al.

While Graph Neural Networks (GNNs) have proven highly effective at modeling relational data, pairwise connections cannot fully capture multi-way relationships naturally present in complex real-world systems. In response to this, Topological Deep Learning (TDL) leverages more general combinatorial representations -- such as simplicial or cellular complexes -- to accommodate higher-order interactions. Existing TDL methods often extend GNNs through Higher-Order Message Passing (HOMP), but face critical \emph{scalability challenges} due to \textit{(i)} a combinatorial explosion of message-passing routes, and \textit{(ii)} significant complexity overhead from the propagation mechanism. This work presents HOPSE (Higher-Order Positional and Structural Encoder), an alternative method to solve tasks involving higher-order interactions \emph{without message passing}. Instead, HOPSE breaks \emph{arbitrary higher-order domains} into their neighborhood relationships using a Hasse graph decomposition. This method shows that decoupling the representation learning of neighborhood topology from that of attributes results in lower computational complexity, casting doubt on the need for HOMP. The experiments on molecular graph tasks and topological benchmarks show that HOPSE matches performance on traditional TDL datasets and outperforms HOMP methods on topological tasks, achieving up to $7\times$ speedups over HOMP-based models, opening a new path for scalable TDL.

Jorge E. León, Miguel Carrasco

On one hand, recent advances in chatbots has led to a rising popularity in using these models for coding tasks. On the other hand, modern generative image models primarily rely on text encoders to translate semantic concepts into visual representations, even when there is clear evidence that audio can be employed as input as well. Given the previous, in this work, we explore whether state-of-the-art conversational agents can design effective audio encoders to replace the CLIP text encoder from Stable Diffusion 1.5, enabling image synthesis directly from sound. We prompted five publicly available chatbots to propose neural architectures to work as these audio encoders, with a set of well-explained shared conditions. Each valid suggested encoder was trained on over two million context related audio-image-text observations, and evaluated on held-out validation and test sets using various metrics, together with a qualitative analysis of their generated images. Although almost all chatbots generated valid model designs, none achieved satisfactory results, indicating that their audio embeddings failed to align reliably with those of the original text encoder. Among the proposals, the Gemini audio encoder showed the best quantitative metrics, while the Grok audio encoder produced more coherent images (particularly, when paired with the text encoder). Our findings reveal a shared architectural bias across chatbots and underscore the remaining coding gap that needs to be bridged in future versions of these models. We also created a public demo so everyone could study and try out these audio encoders. Finally, we propose research questions that should be tackled in the future, and encourage other researchers to perform more focused and highly specialized tasks like this one, so the respective chatbots cannot make use of well-known solutions and their creativity/reasoning is fully tested.