Fake News Detection on Social Media using Geometric Deep Learning

Social media are nowadays one of the main news sources for millions of people around the globe due to their low cost, easy access and rapid dissemination. This however comes at the cost of dubious trustworthiness and significant risk of exposure to 'fake news', intentionally written to mislead the readers. Automatically detecting fake news poses challenges that defy existing content-based analysis approaches. One of the main reasons is that often the interpretation of the news requires the knowledge of political or social context or 'common sense', which current NLP algorithms are still missing. Recent studies have shown that fake and real news spread differently on social media, forming propagation patterns that could be harnessed for the automatic fake news detection. Propagation-based approaches have multiple advantages compared to their content-based counterparts, among which is language independence and better resilience to adversarial attacks. In this paper we show a novel automatic fake news detection model based on geometric deep learning. The underlying core algorithms are a generalization of classical CNNs to graphs, allowing the fusion of heterogeneous data such as content, user profile and activity, social graph, and news propagation. Our model was trained and tested on news stories, verified by professional fact-checking organizations, that were spread on Twitter. Our experiments indicate that social network structure and propagation are important features allowing highly accurate (92.7% ROC AUC) fake news detection. Second, we observe that fake news can be reliably detected at an early stage, after just a few hours of propagation. Third, we test the aging of our model on training and testing data separated in time. Our results point to the promise of propagation-based approaches for fake news detection as an alternative or complementary strategy to content-based approaches.

Isospectralization, or how to hear shape, style, and correspondence

The question whether one can recover the shape of a geometric object from its Laplacian spectrum (`hear the shape of the drum') is a classical problem in spectral geometry with a broad range of implications and applications. While theoretically the answer to this question is negative (there exist examples of iso-spectral but non-isometric manifolds), little is known about the practical possibility of using the spectrum for shape reconstruction and optimization. In this paper, we introduce a numerical procedure called {\em isospectralization}, consisting of deforming one shape to make its Laplacian spectrum match that of another. We implement the isospectralization procedure using modern differentiable programming techniques and exemplify its applications in some of the classical and notoriously hard problems in geometry processing, computer vision, and graphics such as shape reconstruction, pose and style transfer, and dense deformable correspondence.

CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filters

The rise of graph-structured data such as social networks, regulatory networks, citation graphs, and functional brain networks, in combination with resounding success of deep learning in various applications, has brought the interest in generalizing deep learning models to non-Euclidean domains. In this paper, we introduce a new spectral domain convolutional architecture for deep learning on graphs. The core ingredient of our model is a new class of parametric rational complex functions (Cayley polynomials) allowing to efficiently compute spectral filters on graphs that specialize on frequency bands of interest. Our model generates rich spectral filters that are localized in space, scales linearly with the size of the input data for sparsely-connected graphs, and can handle different constructions of Laplacian operators. Extensive experimental results show the superior performance of our approach, in comparison to other spectral domain convolutional architectures, on spectral image classification, community detection, vertex classification and matrix completion tasks.

Nonisometric Surface Registration via Conformal Laplace-Beltrami Basis Pursuit

Surface registration is one of the most fundamental problems in geometry processing. Many approaches have been developed to tackle this problem in cases where the surfaces are nearly isometric. However, it is much more challenging to compute correspondence between surfaces which are intrinsically less similar. In this paper, we propose a variational model to align the Laplace-Beltrami (LB) eigensytems of two non-isometric genus zero shapes via conformal deformations. This method enables us compute to geometric meaningful point-to-point maps between non-isometric shapes. Our model is based on a novel basis pursuit scheme whereby we simultaneously compute a conformal deformation of a 'target shape' and its deformed LB eigensytem. We solve the model using an proximal alternating minimization algorithm hybridized with the augmented Lagrangian method which produces accurate correspondences given only a few landmark points. We also propose a reinitialization scheme to overcome some of the difficulties caused by the non-convexity of the variational problem. Intensive numerical experiments illustrate the effectiveness and robustness of the proposed method to handle non-isometric surfaces with large deformation with respect to both noise on the underlying manifolds and errors within the given landmarks.

Graph Neural Networks for IceCube Signal Classification

Tasks involving the analysis of geometric (graph- and manifold-structured) data have recently gained prominence in the machine learning community, giving birth to a rapidly developing field of geometric deep learning. In this work, we leverage graph neural networks to improve signal detection in the IceCube neutrino observatory. The IceCube detector array is modeled as a graph, where vertices are sensors and edges are a learned function of the sensors' spatial coordinates. As only a subset of IceCube's sensors is active during a given observation, we note the adaptive nature of our GNN, wherein computation is restricted to the input signal support. We demonstrate the effectiveness of our GNN architecture on a task classifying IceCube events, where it outperforms both a traditional physics-based method as well as classical 3D convolution neural networks.

Geodesic convolutional neural networks on Riemannian manifolds

Feature descriptors play a crucial role in a wide range of geometry analysis and processing applications, including shape correspondence, retrieval, and segmentation. In this paper, we introduce Geodesic Convolutional Neural Networks (GCNN), a generalization of the convolutional networks (CNN) paradigm to non-Euclidean manifolds. Our construction is based on a local geodesic system of polar coordinates to extract "patches", which are then passed through a cascade of filters and linear and non-linear operators. The coefficients of the filters and linear combination weights are optimization variables that are learned to minimize a task-specific cost function. We use GCNN to learn invariant shape features, allowing to achieve state-of-the-art performance in problems such as shape description, retrieval, and correspondence.

Dual-Primal Graph Convolutional Networks

In recent years, there has been a surge of interest in developing deep learning methods for non-Euclidean structured data such as graphs. In this paper, we propose Dual-Primal Graph CNN, a graph convolutional architecture that alternates convolution-like operations on the graph and its dual. Our approach allows to learn both vertex- and edge features and generalizes the previous graph attention (GAT) model. We provide extensive experimental validation showing state-of-the-art results on a variety of tasks tested on established graph benchmarks, including CORA and Citeseer citation networks as well as MovieLens, Flixter, Douban and Yahoo Music graph-guided recommender systems.

PeerNets: Exploiting Peer Wisdom Against Adversarial Attacks

Deep learning systems have become ubiquitous in many aspects of our lives. Unfortunately, it has been shown that such systems are vulnerable to adversarial attacks, making them prone to potential unlawful uses. Designing deep neural networks that are robust to adversarial attacks is a fundamental step in making such systems safer and deployable in a broader variety of applications (e.g. autonomous driving), but more importantly is a necessary step to design novel and more advanced architectures built on new computational paradigms rather than marginally building on the existing ones. In this paper we introduce PeerNets, a novel family of convolutional networks alternating classical Euclidean convolutions with graph convolutions to harness information from a graph of peer samples. This results in a form of non-local forward propagation in the model, where latent features are conditioned on the global structure induced by the graph, that is up to 3 times more robust to a variety of white- and black-box adversarial attacks compared to conventional architectures with almost no drop in accuracy.

MotifNet: a motif-based Graph Convolutional Network for directed graphs

Deep learning on graphs and in particular, graph convolutional neural networks, have recently attracted significant attention in the machine learning community. Many of such techniques explore the analogy between the graph Laplacian eigenvectors and the classical Fourier basis, allowing to formulate the convolution as a multiplication in the spectral domain. One of the key drawback of spectral CNNs is their explicit assumption of an undirected graph, leading to a symmetric Laplacian matrix with orthogonal eigendecomposition. In this work we propose MotifNet, a graph CNN capable of dealing with directed graphs by exploiting local graph motifs. We present experimental evidence showing the advantage of our approach on real data.

Dynamic Graph CNN for Learning on Point Clouds

Point clouds provide a flexible and scalable geometric representation suitable for countless applications in computer graphics; they also comprise the raw output of most 3D data acquisition devices. Hence, the design of intelligent computational models that act directly on point clouds is critical, especially when efficiency considerations or noise preclude the possibility of expensive denoising and meshing procedures. While hand-designed features on point clouds have long been proposed in graphics and vision, however, the recent overwhelming success of convolutional neural networks (CNNs) for image analysis suggests the value of adapting insight from CNN to the point cloud world. To this end, we propose a new neural network module dubbed EdgeConv suitable for CNN-based high-level tasks on point clouds including classification and segmentation. EdgeConv is differentiable and can be plugged into existing architectures. Compared to existing modules operating largely in extrinsic space or treating each point independently, EdgeConv has several appealing properties: It incorporates local neighborhood information; it can be stacked or recurrently applied to learn global shape properties; and in multi-layer systems affinity in feature space captures semantic characteristics over potentially long distances in the original embedding. Beyond proposing this module, we provide extensive evaluation and analysis revealing that EdgeConv captures and exploits fine-grained geometric properties of point clouds. The proposed approach achieves state-of-the-art performance on standard benchmarks including ModelNet40 and S3DIS.