arXiv subjects

Liliya Imasheva

Publications and source records attributed to Liliya Imasheva.

5 recordsLinked to original sources

arXiv2025

TopoBench: A Framework for Benchmarking Topological Deep Learning

This work introduces TopoBench, an open-source library designed to standardize benchmarking and accelerate research in topological deep learning (TDL). TopoBench decomposes TDL into a sequence of independent modules for data generation, loading, transforming and processing, as well as model training, optimization and evaluation. This modular organization provides flexibility for modifications and facilitates the adaptation and optimization of various TDL pipelines. A key feature of TopoBench is its support for transformations and lifting across topological domains. Mapping the topology and features of a graph to higher-order topological domains, such as simplicial and cell complexes, enables richer data representations and more fine-grained analyses. The applicability of TopoBench is demonstrated by benchmarking several TDL architectures across diverse tasks and datasets.

cs.LG↗

arXiv2025

A Remedy for Over-Squashing in Graph Learning via Forman-Ricci Curvature based Graph-to-Hypergraph Structural Lifting

Graph Neural Networks are highly effective at learning from relational data, leveraging node and edge features while maintaining the symmetries inherent to graph structures. However, many real-world systems, such as social or biological networks, exhibit complex interactions that are more naturally represented by higher-order topological domains. The emerging field of Geometric and Topological Deep Learning addresses this challenge by introducing methods that utilize and benefit from higher-order structures. Central to TDL is the concept of lifting, which transforms data representations from basic graph forms to more expressive topologies before the application of GNN models for learning. In this work, we propose a structural lifting strategy using Forman-Ricci curvature, which defines an edge-based network characteristic based on Riemannian geometry. Curvature reveals local and global properties of a graph, such as a network's backbones, i.e. coarse, structure-preserving graph geometries that form connections between major communities - most suitably represented as hyperedges to model information flows between clusters across large distances in the network. To this end, our approach provides a remedy to the problem of information distortion in message passing across long distances and graph bottlenecks - a phenomenon known in graph learning as over-squashing.

cs.LG↗

arXiv2025

Comparison of Three Methods for Triggering Core-collapse Supernova Explosions in Spherical Symmetry

Despite the three-dimensional nature of core-collapse supernovae (CCSNe), simulations in spherical symmetry (1D) play an important role to study large model sets for the progenitor-remnant connection, explosion properties, remnant masses, and CCSN nucleosynthesis. To trigger explosions in 1D, various numerical recipes have been applied, mostly with gross simplifications of the complex microphysics governing stellar core collapse, the formation of the compact remnant, and the mechanism of the explosion. Here we investigate the two most popular treatments, piston-driven and thermal-bomb explosions, in comparison to 1D explosions powered by a parametric neutrino engine in the P-HOTB code. For this comparison we calculate CCSNe for eight stars and evolution times up to 10,000 s, targeting the same progenitor-specific explosion energies as obtained by the neutrino-engine results. Otherwise we employ widely-used ("classic") modelling assumptions, and alternatively to the standard contraction-expansion trajectory for pistons, we also test suitably selected Lagrangian mass shells adopted from the neutrino-driven explosions as "special trajectories." Although the 56Ni production agrees within roughly a factor of two between the different explosion triggers, neither piston nor thermal bombs can reproduce the correlation of 56Ni yields and explosion energies found in neutrino-driven explosions. This shortcoming as well as the problem of massive fallback witnessed in classical piston models, which diminishes or extinguishes the ejected nickel, can be largely cured by the special trajectories. These and the choice of the explosion energies, however, make the modelling dependent on pre-existing neutrino-driven explosion results.

astro-ph.HE↗

arXiv2024

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.

cs.LG↗

arXiv2022

Parameterisations of thermal bomb explosions for core-collapse supernovae and 56Ni production

Thermal bombs are a widely used method to artificially trigger explosions of core-collapse supernovae (CCSNe) to determine their nucleosynthesis or ejecta and remnant properties. Recently, their use in spherically symmetric (1D) hydrodynamic simulations led to the result that {56,57}Ni and 44Ti are massively underproduced compared to observational estimates for Supernova 1987A, if the explosions are slow, i.e., if the explosion mechanism of CCSNe releases the explosion energy on long timescales. It was concluded that rapid explosions are required to match observed abundances, i.e., the explosion mechanism must provide the CCSN energy nearly instantaneously on timescales of some ten to order 100 ms. This result, if valid, would disfavor the neutrino-heating mechanism, which releases the CCSN energy on timescales of seconds. Here, we demonstrate by 1D hydrodynamic simulations and nucleosynthetic post-processing that these conclusions are a consequence of disregarding the initial collapse of the stellar core in the thermal-bomb modelling before the bomb releases the explosion energy. We demonstrate that the anti-correlation of 56Ni yield and energy-injection timescale vanishes when the initial collapse is included and that it can even be reversed, i.e., more 56Ni is made by slower explosions, when the collapse proceeds to small radii similar to those where neutrino heating takes place in CCSNe. We also show that the 56Ni production in thermal-bomb explosions is sensitive to the chosen mass cut and that a fixed mass layer or fixed volume for the energy deposition cause only secondary differences. Moreover, we propose a most appropriate setup for thermal bombs.

astro-ph.HE↗