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2020


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Sampling on networks: estimating spectral centrality measures and their impact in evaluating other relevant network measures

Ruggeri, N., De Bacco, C.

Applied Network Science, 5:81, October 2020 (article)

Abstract
We perform an extensive analysis of how sampling impacts the estimate of several relevant network measures. In particular, we focus on how a sampling strategy optimized to recover a particular spectral centrality measure impacts other topological quantities. Our goal is on one hand to extend the analysis of the behavior of TCEC [Ruggeri2019], a theoretically-grounded sampling method for eigenvector centrality estimation. On the other hand, to demonstrate more broadly how sampling can impact the estimation of relevant network properties like centrality measures different than the one aimed at optimizing, community structure and node attribute distribution. Finally, we adapt the theoretical framework behind TCEC for the case of PageRank centrality and propose a sampling algorithm aimed at optimizing its estimation. We show that, while the theoretical derivation can be suitably adapted to cover this case, the resulting algorithm suffers of a high computational complexity that requires further approximations compared to the eigenvector centrality case.

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Code Preprint pdf DOI [BibTex]


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Optimal transport for multi-commodity routing on networks

Lonardi, A., Facca, E., Putti, M., De Bacco, C.

October 2020 (article) Submitted

Abstract
We present a model for finding optimal multi-commodity flows on networks based on optimal transport theory. The model relies on solving a dynamical system of equations. We prove that its stationary solution is equivalent to the solution of an optimization problem that generalizes the one-commodity framework. In particular, it generalizes previous results in terms of optimality, scaling, and phase transitions obtained in the one-commodity case. Remarkably, for a suitable range of parameters, the optimal topologies have loops. This is radically different to the one-commodity case, where within an analogous parameter range the optimal topologies are trees. This important result is a consequence of the extension of Kirkchoff's law to the multi-commodity case, which enforces the distinction between fluxes of the different commodities. Our results provide new insights into the nature and properties of optimal network topologies. In particular, they show that loops can arise as a consequence of distinguishing different flow types, and complement previous results where loops, in the one-commodity case, were arising as a consequence of imposing dynamical rules to the sources and sinks or when enforcing robustness to damage. Finally, we provide an efficient implementation for each of the two equivalent numerical frameworks, both of which achieve a computational complexity that is more efficient than that of standard optimization methods based on gradient descent. As a result, our model is not merely abstract but can be efficiently applied to large datasets. We give an example of concrete application by studying the network of the Paris metro.

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Code Preprint [BibTex]


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Community detection with node attributes in multilayer networks

Contisciani, M., Power, E. A., De Bacco, C.

Nature Scientific Reports, 10, pages: 15736, September 2020 (article)

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Code Preprint pdf [BibTex]

Code Preprint pdf [BibTex]


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Deep Graph Matching via Blackbox Differentiation of Combinatorial Solvers

Rolinek, M., Swoboda, P., Zietlow, D., Paulus, A., Musil, V., Martius, G.

In Computer Vision – ECCV 2020, Springer International Publishing, Cham, August 2020 (inproceedings)

Abstract
Building on recent progress at the intersection of combinatorial optimization and deep learning, we propose an end-to-end trainable architecture for deep graph matching that contains unmodified combinatorial solvers. Using the presence of heavily optimized combinatorial solvers together with some improvements in architecture design, we advance state-of-the-art on deep graph matching benchmarks for keypoint correspondence. In addition, we highlight the conceptual advantages of incorporating solvers into deep learning architectures, such as the possibility of post-processing with a strong multi-graph matching solver or the indifference to changes in the training setting. Finally, we propose two new challenging experimental setups.

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Code Arxiv [BibTex]

Code Arxiv [BibTex]


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Analytical classical density functionals from an equation learning network

Lin, S., Martius, G., Oettel, M.

The Journal of Chemical Physics, 152(2):021102, 2020, arXiv preprint \url{https://arxiv.org/abs/1910.12752} (article)

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Preprint_PDF DOI [BibTex]

Preprint_PDF DOI [BibTex]


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A Real-Robot Dataset for Assessing Transferability of Learned Dynamics Models

Agudelo-España, D., Zadaianchuk, A., Wenk, P., Garg, A., Akpo, J., Grimminger, F., Viereck, J., Naveau, M., Righetti, L., Martius, G., Krause, A., Schölkopf, B., Bauer, S., Wüthrich, M.

IEEE International Conference on Robotics and Automation (ICRA), 2020 (conference) Accepted

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Project Page PDF [BibTex]

Project Page PDF [BibTex]


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Sample-efficient Cross-Entropy Method for Real-time Planning

Pinneri, C., Sawant, S., Blaes, S., Achterhold, J., Stueckler, J., Rolinek, M., Martius, G.

In Conference on Robot Learning 2020, 2020 (inproceedings)

Abstract
Trajectory optimizers for model-based reinforcement learning, such as the Cross-Entropy Method (CEM), can yield compelling results even in high-dimensional control tasks and sparse-reward environments. However, their sampling inefficiency prevents them from being used for real-time planning and control. We propose an improved version of the CEM algorithm for fast planning, with novel additions including temporally-correlated actions and memory, requiring 2.7-22x less samples and yielding a performance increase of 1.2-10x in high-dimensional control problems.

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Paper Code [BibTex]

Paper Code [BibTex]


Differentiation of Blackbox Combinatorial Solvers
Differentiation of Blackbox Combinatorial Solvers

Vlastelica, M., Paulus, A., Musil, V., Martius, G., Rolı́nek, M.

In International Conference on Learning Representations, ICLR’20, 2020 (incollection)

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link (url) Project Page [BibTex]

link (url) Project Page [BibTex]


Optimizing Rank-based Metrics with Blackbox Differentiation
Optimizing Rank-based Metrics with Blackbox Differentiation

Rolinek, M., Musil, V., Paulus, A., Vlastelica, M., Michaelis, C., Martius, G.

In Proceedings IEEE Conf. on Computer Vision and Pattern Recognition (CVPR), pages: 7620-7630, IEEE International Conference on Computer Vision and Pattern Recognition (CVPR) 2020, 2020, Best paper nomination (inproceedings)

Abstract
Rank-based metrics are some of the most widely used criteria for performance evaluation of computer vision models. Despite years of effort, direct optimization for these metrics remains a challenge due to their non-differentiable and non-decomposable nature. We present an efficient, theoretically sound, and general method for differentiating rank-based metrics with mini-batch gradient descent. In addition, we address optimization instability and sparsity of the supervision signal that both arise from using rank-based metrics as optimization targets. Resulting losses based on recall and Average Precision are applied to image retrieval and object detection tasks. We obtain performance that is competitive with state-of-the-art on standard image retrieval datasets and consistently improve performance of near state-of-the-art object detectors.

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Paper @ CVPR Long Oral Short Oral Arxiv Code Pdf Project Page [BibTex]

Paper @ CVPR Long Oral Short Oral Arxiv Code Pdf Project Page [BibTex]


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Network extraction by routing optimization

Baptista, T. D., Leite, D., Facca, E., Putti, M., De Bacco, C.

Nature Scientific Reports , 10, 2020 (article)

Abstract
Routing optimization is a relevant problem in many contexts. Solving directly this type of optimization problem is often computationally unfeasible. Recent studies suggest that one can instead turn this problem into one of solving a dynamical system of equations, which can instead be solved efficiently using numerical methods. This results in enabling the acquisition of optimal network topologies from a variety of routing problems. However, the actual extraction of the solution in terms of a final network topology relies on numerical details which can prevent an accurate investigation of their topological properties. In this context, theoretical results are fully accessible only to an expert audience and ready-to-use implementations for non-experts are rarely available or insufficiently documented. In particular, in this framework, final graph acquisition is a challenging problem in-and-of-itself. Here we introduce a method to extract networks topologies from dynamical equations related to routing optimization under various parameters’ settings. Our method is made of three steps: first, it extracts an optimal trajectory by solving a dynamical system, then it pre-extracts a network and finally, it filters out potential redundancies. Remarkably, we propose a principled model to address the filtering in the last step, and give a quantitative interpretation in terms of a transport-related cost function. This principled filtering can be applied to more general problems such as network extraction from images, thus going beyond the scenarios envisioned in the first step. Overall, this novel algorithm allows practitioners to easily extract optimal network topologies by combining basic tools from numerical methods, optimization and network theory. Thus, we provide an alternative to manual graph extraction which allows a grounded extraction from a large variety of optimal topologies.

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Code Preprint link (url) DOI [BibTex]

Code Preprint link (url) DOI [BibTex]

2012


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Variants of guided self-organization for robot control

Martius, G., Herrmann, J.

Theory in Biosci., 131(3):129-137, Springer Berlin / Heidelberg, 2012 (article)

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link (url) DOI [BibTex]

2012


link (url) DOI [BibTex]


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The Playful Machine - Theoretical Foundation and Practical Realization of Self-Organizing Robots

Der, R., Martius, G.

Springer, Berlin Heidelberg, 2012 (book)

Abstract
Autonomous robots may become our closest companions in the near future. While the technology for physically building such machines is already available today, a problem lies in the generation of the behavior for such complex machines. Nature proposes a solution: young children and higher animals learn to master their complex brain-body systems by playing. Can this be an option for robots? How can a machine be playful? The book provides answers by developing a general principle---homeokinesis, the dynamical symbiosis between brain, body, and environment---that is shown to drive robots to self-determined, individual development in a playful and obviously embodiment-related way: a dog-like robot starts playing with a barrier, eventually jumping or climbing over it; a snakebot develops coiling and jumping modes; humanoids develop climbing behaviors when fallen into a pit, or engage in wrestling-like scenarios when encountering an opponent. The book also develops guided self-organization, a new method that helps to make the playful machines fit for fulfilling tasks in the real world.

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link (url) [BibTex]