Related papers: Principled Simplicial Neural Networks for Trajecto…

Seminal works on graph neural networks have primarily targeted semi-supervised node classification problems with few observed labels and high-dimensional signals. With the development of graph networks, this setup has become a de facto…

Convolutions encode equivariance symmetries into neural networks leading to better generalisation performance. However, symmetries provide fixed hard constraints on the functions a network can represent, need to be specified in advance, and…

We propose a fresh take on understanding the mechanisms of neural networks by analyzing the rich directional structure of optimization trajectories, represented by their pointwise parameters. Towards this end, we introduce some natural…

Using the notion of contiguity of simplicial maps, we adapt Farber's topological complexity to the realm of simplicial complexes. We show that, for a finite simplicial complex $K$, our discretized concept recovers the topological complexity…

Neural networks are omnipresent, but remain poorly understood. Their increasing complexity and use in critical systems raises the important challenge to full interpretability. We propose to address a simple well-posed learning problem:…

We study navigation with limited information in networks and demonstrate that many real-world networks have a structure which can be described as favoring communication at short distance at the cost of constraining communication at long…

Neural networks trained with SGD were recently shown to rely preferentially on linearly-predictive features and can ignore complex, equally-predictive ones. This simplicity bias can explain their lack of robustness out of distribution…

Equivariant neural networks provide a principled framework for incorporating symmetry into learning architectures and have been extensively analyzed through the lens of their separation power, that is, the ability to distinguish inputs…

The increasing interest in complex networks research has been a consequence of several intrinsic features of this area, such as the generality of the approach to represent and model virtually any discrete system, and the incorporation of…

Neural Module Networks, originally proposed for the task of visual question answering, are a class of neural network architectures that involve human-specified neural modules, each designed for a specific form of reasoning. In current…

Time series data are everywhere -- from finance to healthcare -- and each domain brings its own unique complexities and structures. While advanced models like Transformers and graph neural networks (GNNs) have gained popularity in time…

In our recent works, we developed a probabilistic framework for structural analysis in undirected networks. The key idea of that framework is to sample a network by a symmetric bivariate distribution and then use that bivariate distribution…

Objective: Brain is a fantastic organ that helps creature adapting to the environment. Network is the most essential structure of brain, but the capability of a simple network is still not very clear. In this study, we try to expound some…

The set of functions parameterized by a linear fully-connected neural network is a determinantal variety. We investigate the subvariety of functions that are equivariant or invariant under the action of a permutation group. Examples of such…

Exchangeability is a desired statistical property of network ensembles requiring their invariance upon relabelling of the nodes. However combining sparsity of network ensembles with exchangeability is challenging. Here we propose a…

Predicting vehicle trajectories, angle and speed is important for safe and comfortable driving. We demonstrate the best predicted angle, speed, and best performance overall winning the top three places of the ICCV 2019 Learning to Drive…

Neural architecture search enables automation of architecture design. Despite its success, it is computationally costly and does not provide an insight on how to design a desirable architecture. Here we propose a new way of searching neural…

There are five types of trajectory prediction tasks: deterministic, stochastic, domain adaptation, momentary observation, and few-shot. These associated tasks are defined by various factors, such as the length of input paths, data split and…

The understanding of neural activity patterns is fundamentally linked to an understanding of how the brain's network architecture shapes dynamical processes. Established approaches rely mostly on deviations of a given network from certain…

Random abstract simplicial complex representation provides a mathematical description of wireless networks and their topology. In order to reduce the energy consumption in this type of network, we intend to reduce the number of network…