Fwd: Networks seminar: BrAINs season 2024/2025. Talk at 4pm 21st November

[Liubov]

Dear all,

On the 21st November at 4pm CET we will have Pr. Francesco Vaccarino speaking about: Topological Constraints in Shallow ReLU Neural Networks: A Journey through Optimization Obstacles

Abstract:

This talk explores the topological properties of the parameter space in shallow neural networks, specifically those using ReLU activation functions. We present the discovery of a topological obstruction that limits gradient-based optimization within the network's loss landscape. Focusing on two-layer ReLU networks, we demonstrate how neurons’ gradient flow trajectories are confined to products of quadric hypersurfaces and examine how these constraints emerge from the network's initialization and symmetries. Calculating the invariant set's Betti numbers reveals conditions where the network's connected components limit optimal learning. The analysis draws connections between these obstructions, Segre varieties, and invariant theory, providing insights into navigating and potentially mitigating such obstacles. Joint work with Marco Nurisso and Pierrick Leroy.
To appear in Advances in Neural Information Processing Systems (NeurIPS 2024).

The recordings of the seminar BrAINs season are on the website and new youtube channel.

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Best regards,

Liubov TUPIKINA

On behalf of the organisers of the seminar

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Bests,

Liubov

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[Liubov]

Hello everyone,

On the 28th November at 12pm CET we will have Xingyu Pan speaking about his work on Robustness of interdependent hypergraphs: A bipartite network framework.

Abstract:

We develop a bipartite network framework to study the robustness of interdependent hypergraphs. From such a perspective, nodes and hyperedges of a hypergraph are equivalent to each other, a property that largely simplifies their mathematical treatment. We develop a general percolation theory based on this representation and apply it to study the robustness of interdependent hypergraphs against random damage, which we verify with numerical simulations. We analyze a variety of interacting patterns, from heterogeneous to correlated hyperstructures, and from full- to partial-dependency couplings between an arbitrary number of hypergraphs, and characterize their structural stability via their phase diagrams. Given its generality, we expect that our framework will provide useful insights for the development of more realistic venues to characterize cascading failures in interdependent higher-order systems.https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.6.013049

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[Liubov]

Dear everyone,

It is our pleasure to welcome Mario Rosario Guarracino (University of Cassino, Italy).

On the 5th December at 5pm CET he will be speaking about a novel unsupervised approach to hypergraphs-ensemble embedding.

Abstract: Hypergraphs model higher-order dependencies of complex systems which simple network models fail to capture. We introduce a framework for the unsupervised embedding of hypergraphs based on their transition probability matrices. In this article, we focus on the problem of multiple hypergraph similarity learning by projecting each hypergraph into a vector space. We demonstrate the effectiveness of our approach in classifying simulated and real-world metabolic hypergraphs.

This work is in collaboration with Ichcha Manipur, University of Cambridge.

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The coming seminar won't be recorded. The recordings of the previous seminars of BrAINs season are on the website and new youtube channel.

[Liubov]

Dear everyone,

Happy New Year!

It is our pleasure to welcome Yin-Jie Ma (East China University of Science and Technology, Shanghai, China), our first speaker this season.

On the 16th January at 5pm CET he will be speaking about a novel unsupervised approach to hypergraphs-ensemble embedding.

Title: Reconstructing simplicial complexes from evolutionary games

Abstract: Prior knowledge on network structure is a prerequisite to depict the intricate dynamics in various systems. While existing research has predominantly focused on reconstructing complex networks based on pairwise interactions between entities, the prevalence and significance of higher-order interactions in real-world networks have been increasingly recognized. Interactions beyond simple dyads remain largely unexplored in the context of network reconstruction. We here introduce three methods to reconstruct higher-order networks embedded in evolutionary games. We demonstrate their high accuracy and excellent overall performance of reconstruction in three synthetic and three empirical higher-order networks. Our global estimation method with triadic constraints requires fewer observations of data, thereby reducing the costs of data collection while maintaining robustness against measurement noise. Our research provides valuable insights of addressing the inverse problem in network science through the lens of network reconstruction in higher-order dynamics.