Petar Veličković

Graph neural networks (GNNs) are typically applied to static graphs that are assumed to be known upfront. This static input structure is often informed purely by insight of the machine learning practitioner, and might not be optimal for the actual task the GNN is solving. In absence of reliable domain expertise, one might resort to inferring the latent graph structure, which is often difficult due to the vast search space of possible graphs. Here we introduce Pointer Graph Networks (PGNs) which… Show more

Graph neural networks (GNNs) are typically applied to static graphs that are assumed to be known upfront. This static input structure is often informed purely by insight of the machine learning practitioner, and might not be optimal for the actual task the GNN is solving. In absence of reliable domain expertise, one might resort to inferring the latent graph structure, which is often difficult due to the vast search space of possible graphs. Here we introduce Pointer Graph Networks (PGNs) which augment sets or graphs with additional inferred edges for improved model expressivity. PGNs allow each node to dynamically point to another node, followed by message passing over these pointers. The sparsity of this adaptable graph structure makes learning tractable while still being sufficiently expressive to simulate complex algorithms. Critically, the pointing mechanism is directly supervised to model long-term sequences of operations on classical data structures, incorporating useful structural inductive biases from theoretical computer science. Qualitatively, we demonstrate that PGNs can learn parallelisable variants of pointer-based data structures, namely disjoint set unions and link/cut trees. PGNs generalise out-of-distribution to 5x larger test inputs on dynamic graph connectivity tasks, outperforming unrestricted GNNs and Deep Sets. Show less

Graph Neural Networks (GNNs) are a powerful representational tool for solving problems on graph-structured inputs. In almost all cases so far, however, they have been applied to directly recovering a final solution from raw inputs, without explicit guidance on how to structure their problem-solving. Here, instead, we focus on learning in the space of algorithms: we train several state-of-the-art GNN architectures to imitate individual steps of classical graph algorithms, parallel (breadth-first… Show more

Graph Neural Networks (GNNs) are a powerful representational tool for solving problems on graph-structured inputs. In almost all cases so far, however, they have been applied to directly recovering a final solution from raw inputs, without explicit guidance on how to structure their problem-solving. Here, instead, we focus on learning in the space of algorithms: we train several state-of-the-art GNN architectures to imitate individual steps of classical graph algorithms, parallel (breadth-first search, Bellman-Ford) as well as sequential (Prim's algorithm). As graph algorithms usually rely on making discrete decisions within neighbourhoods, we hypothesise that maximisation-based message passing neural networks are best-suited for such objectives, and validate this claim empirically. We also demonstrate how learning in the space of algorithms can yield new opportunities for positive transfer between tasks---showing how learning a shortest-path algorithm can be substantially improved when simultaneously learning a reachability algorithm. Show less

We present Deep Graph Infomax (DGI), a general approach for learning node representations within graph-structured data in an unsupervised manner. DGI relies on maximizing mutual information between patch representations and corresponding high-level summaries of graphs---both derived using established graph convolutional network architectures. The learnt patch representations summarize subgraphs centered around nodes of interest, and can thus be reused for downstream node-wise learning tasks. In… Show more

We present Deep Graph Infomax (DGI), a general approach for learning node representations within graph-structured data in an unsupervised manner. DGI relies on maximizing mutual information between patch representations and corresponding high-level summaries of graphs---both derived using established graph convolutional network architectures. The learnt patch representations summarize subgraphs centered around nodes of interest, and can thus be reused for downstream node-wise learning tasks. In contrast to most prior approaches to unsupervised learning with GCNs, DGI does not rely on random walk objectives, and is readily applicable to both transductive and inductive learning setups. We demonstrate competitive performance on a variety of node classification benchmarks, which at times even exceeds the performance of supervised learning. Show less

Machine learning with deep neural networks ("deep learning") allows for learning complex features directly from raw input data, completely eliminating hand-crafted, "hard-coded" feature extraction from the learning pipeline. This has lead to state-of-the-art performance being achieved across several---previously disconnected---problem domains, including computer vision, natural language processing, reinforcement learning and generative modelling. These success stories nearly universally go… Show more

Machine learning with deep neural networks ("deep learning") allows for learning complex features directly from raw input data, completely eliminating hand-crafted, "hard-coded" feature extraction from the learning pipeline. This has lead to state-of-the-art performance being achieved across several---previously disconnected---problem domains, including computer vision, natural language processing, reinforcement learning and generative modelling. These success stories nearly universally go hand-in-hand with availability of immense quantities of labelled training examples ("big data") exhibiting simple grid-like structure (e.g. text or images), exploitable through convolutional or recurrent layers. This is due to the extremely large number of degrees-of-freedom in neural networks, leaving their generalisation ability vulnerable to effects such as overfitting. However, there remain many domains where extensive data gathering is not always appropriate, affordable, or even feasible. Furthermore, data is generally organised in more complicated kinds of structure---which most existing approaches would simply discard. Examples of such tasks are abundant in the biomedical space; with e.g. small numbers of subjects available for any given clinical study, or relationships between proteins specified via interaction networks. I hypothesise that, if deep learning is to reach its full potential in such environments, we need to reconsider "hard-coded" approaches---integrating assumptions about inherent structure in the input data directly into our architectures and learning algorithms, through structural inductive biases. In this dissertation, I directly validate this hypothesis by developing three structure-infused neural network architectures (operating on sparse multimodal and graph-structured data), and a structure-informed learning algorithm for graph neural networks, demonstrating significant outperformance of conventional baseline models and algorithms. Show less

We analyse multimodal time-series data corresponding to weight, sleep and steps measurements. We focus on predicting whether a user will successfully achieve his/her weight objective. For this, we design several deep long short-term memory (LSTM) architectures, including a novel cross-modal LSTM (X-LSTM), and demonstrate their superiority over baseline approaches. The X-LSTM improves parameter efficiency by processing each modality separately and allowing for information flow between them by… Show more

We analyse multimodal time-series data corresponding to weight, sleep and steps measurements. We focus on predicting whether a user will successfully achieve his/her weight objective. For this, we design several deep long short-term memory (LSTM) architectures, including a novel cross-modal LSTM (X-LSTM), and demonstrate their superiority over baseline approaches. The X-LSTM improves parameter efficiency by processing each modality separately and allowing for information flow between them by way of recurrent cross-connections. We present a general hyperparameter optimisation technique for X-LSTMs, which allows us to significantly improve on the LSTM and a prior state-of-the-art cross-modal approach, using a comparable number of parameters. Finally, we visualise the model’s predictions, revealing implications about latent variables in this task. Show less

We present graph attention networks (GATs), novel neural network architectures that operate on graph-structured data, leveraging masked self-attentional layers to address the shortcomings of prior methods based on graph convolutions or their approximations. By stacking layers in which nodes are able to attend over their neighborhoods' features, we enable (implicitly) specifying different weights to different nodes in a neighborhood, without requiring any kind of computationally intensive matrix… Show more

We present graph attention networks (GATs), novel neural network architectures that operate on graph-structured data, leveraging masked self-attentional layers to address the shortcomings of prior methods based on graph convolutions or their approximations. By stacking layers in which nodes are able to attend over their neighborhoods' features, we enable (implicitly) specifying different weights to different nodes in a neighborhood, without requiring any kind of computationally intensive matrix operation (such as inversion) or depending on knowing the graph structure upfront. In this way, we address several key challenges of spectral-based graph neural networks simultaneously, and make our model readily applicable to inductive as well as transductive problems. Our GAT models have achieved or matched state-of-the-art results across four established transductive and inductive graph benchmarks: the Cora, Citeseer and Pubmed citation network datasets, as well as a protein-protein interaction dataset (wherein test graphs remain unseen during training). Show less

In this paper we propose cross-modal convolutional neural networks (X-CNNs), a novel biologically inspired type of CNN architectures, treating gradient descent-specialised CNNs as individual units of processing in a larger-scale network topology, while allowing for unconstrained information flow and/or weight sharing between analogous hidden layers of the network---thus generalising the already well-established concept of neural network ensembles (where information typically may flow only… Show more

In this paper we propose cross-modal convolutional neural networks (X-CNNs), a novel biologically inspired type of CNN architectures, treating gradient descent-specialised CNNs as individual units of processing in a larger-scale network topology, while allowing for unconstrained information flow and/or weight sharing between analogous hidden layers of the network---thus generalising the already well-established concept of neural network ensembles (where information typically may flow only between the output layers of the individual networks). The constituent networks are individually designed to learn the output function on their own subset of the input data, after which cross-connections between them are introduced after each pooling operation to periodically allow for information exchange between them. This injection of knowledge into a model (by prior partition of the input data through domain knowledge or unsupervised methods) is expected to yield greatest returns in sparse data environments, which are typically less suitable for training CNNs. For evaluation purposes, we have compared a standard four-layer CNN as well as a sophisticated FitNet4 architecture against their cross-modal variants on the CIFAR-10 and CIFAR-100 datasets with differing percentages of the training data being removed, and find that at lower levels of data availability, the X-CNNs significantly outperform their baselines (typically providing a 2--6% benefit, depending on the dataset size and whether data augmentation is used), while still maintaining an edge on all of the full dataset tests. Show less