@article{14739, abstract = {Attempts to incorporate topological information in supervised learning tasks have resulted in the creation of several techniques for vectorizing persistent homology barcodes. In this paper, we study thirteen such methods. Besides describing an organizational framework for these methods, we comprehensively benchmark them against three well-known classification tasks. Surprisingly, we discover that the best-performing method is a simple vectorization, which consists only of a few elementary summary statistics. Finally, we provide a convenient web application which has been designed to facilitate exploration and experimentation with various vectorization methods.}, author = {Ali, Dashti and Asaad, Aras and Jimenez, Maria-Jose and Nanda, Vidit and Paluzo-Hidalgo, Eduardo and Soriano Trigueros, Manuel}, issn = {1939-3539}, journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence}, keywords = {Applied Mathematics, Artificial Intelligence, Computational Theory and Mathematics, Computer Vision and Pattern Recognition, Software}, number = {12}, pages = {14069--14080}, publisher = {IEEE}, title = {{A survey of vectorization methods in topological data analysis}}, doi = {10.1109/tpami.2023.3308391}, volume = {45}, year = {2023}, } @article{12128, abstract = {We introduce a machine-learning (ML) framework for high-throughput benchmarking of diverse representations of chemical systems against datasets of materials and molecules. The guiding principle underlying the benchmarking approach is to evaluate raw descriptor performance by limiting model complexity to simple regression schemes while enforcing best ML practices, allowing for unbiased hyperparameter optimization, and assessing learning progress through learning curves along series of synchronized train-test splits. The resulting models are intended as baselines that can inform future method development, in addition to indicating how easily a given dataset can be learnt. Through a comparative analysis of the training outcome across a diverse set of physicochemical, topological and geometric representations, we glean insight into the relative merits of these representations as well as their interrelatedness.}, author = {Poelking, Carl and Faber, Felix A and Cheng, Bingqing}, issn = {2632-2153}, journal = {Machine Learning: Science and Technology}, keywords = {Artificial Intelligence, Human-Computer Interaction, Software}, number = {4}, publisher = {IOP Publishing}, title = {{BenchML: An extensible pipelining framework for benchmarking representations of materials and molecules at scale}}, doi = {10.1088/2632-2153/ac4d11}, volume = {3}, year = {2022}, } @article{12134, abstract = {Standard epidemic models exhibit one continuous, second order phase transition to macroscopic outbreaks. However, interventions to control outbreaks may fundamentally alter epidemic dynamics. Here we reveal how such interventions modify the type of phase transition. In particular, we uncover three distinct types of explosive phase transitions for epidemic dynamics with capacity-limited interventions. Depending on the capacity limit, interventions may (i) leave the standard second order phase transition unchanged but exponentially suppress the probability of large outbreaks, (ii) induce a first-order discontinuous transition to macroscopic outbreaks, or (iii) cause a secondary explosive yet continuous third-order transition. These insights highlight inherent limitations in predicting and containing epidemic outbreaks. More generally our study offers a cornerstone example of a third-order explosive phase transition in complex systems.}, author = {Börner, Georg and Schröder, Malte and Scarselli, Davide and Budanur, Nazmi B and Hof, Björn and Timme, Marc}, issn = {2632-072X}, journal = {Journal of Physics: Complexity}, keywords = {Artificial Intelligence, Computer Networks and Communications, Computer Science Applications, Information Systems}, number = {4}, publisher = {IOP Publishing}, title = {{Explosive transitions in epidemic dynamics}}, doi = {10.1088/2632-072x/ac99cd}, volume = {3}, year = {2022}, } @article{12147, abstract = {Continuous-time neural networks are a class of machine learning systems that can tackle representation learning on spatiotemporal decision-making tasks. These models are typically represented by continuous differential equations. However, their expressive power when they are deployed on computers is bottlenecked by numerical differential equation solvers. This limitation has notably slowed down the scaling and understanding of numerous natural physical phenomena such as the dynamics of nervous systems. Ideally, we would circumvent this bottleneck by solving the given dynamical system in closed form. This is known to be intractable in general. Here, we show that it is possible to closely approximate the interaction between neurons and synapses—the building blocks of natural and artificial neural networks—constructed by liquid time-constant networks efficiently in closed form. To this end, we compute a tightly bounded approximation of the solution of an integral appearing in liquid time-constant dynamics that has had no known closed-form solution so far. This closed-form solution impacts the design of continuous-time and continuous-depth neural models. For instance, since time appears explicitly in closed form, the formulation relaxes the need for complex numerical solvers. Consequently, we obtain models that are between one and five orders of magnitude faster in training and inference compared with differential equation-based counterparts. More importantly, in contrast to ordinary differential equation-based continuous networks, closed-form networks can scale remarkably well compared with other deep learning instances. Lastly, as these models are derived from liquid networks, they show good performance in time-series modelling compared with advanced recurrent neural network models.}, author = {Hasani, Ramin and Lechner, Mathias and Amini, Alexander and Liebenwein, Lucas and Ray, Aaron and Tschaikowski, Max and Teschl, Gerald and Rus, Daniela}, issn = {2522-5839}, journal = {Nature Machine Intelligence}, keywords = {Artificial Intelligence, Computer Networks and Communications, Computer Vision and Pattern Recognition, Human-Computer Interaction, Software}, number = {11}, pages = {992--1003}, publisher = {Springer Nature}, title = {{Closed-form continuous-time neural networks}}, doi = {10.1038/s42256-022-00556-7}, volume = {4}, year = {2022}, } @article{9234, abstract = {In this paper, we present two new inertial projection-type methods for solving multivalued variational inequality problems in finite-dimensional spaces. We establish the convergence of the sequence generated by these methods when the multivalued mapping associated with the problem is only required to be locally bounded without any monotonicity assumption. Furthermore, the inertial techniques that we employ in this paper are quite different from the ones used in most papers. Moreover, based on the weaker assumptions on the inertial factor in our methods, we derive several special cases of our methods. Finally, we present some experimental results to illustrate the profits that we gain by introducing the inertial extrapolation steps.}, author = {Izuchukwu, Chinedu and Shehu, Yekini}, issn = {1572-9427}, journal = {Networks and Spatial Economics}, keywords = {Computer Networks and Communications, Software, Artificial Intelligence}, number = {2}, pages = {291--323}, publisher = {Springer Nature}, title = {{New inertial projection methods for solving multivalued variational inequality problems beyond monotonicity}}, doi = {10.1007/s11067-021-09517-w}, volume = {21}, year = {2021}, }