We propose Graph-Coupled Oscillator Networks (GraphCON), a novel framework for deep learning on graphs. It is based on discretizations of a second-order system of ordinary differential equations (ODEs), which model a network of nonlinear controlled and damped oscillators, coupled via the adjacency structure of the underlying graph. The flexibility of our framework permits any basic GNN layer (e.g. convolutional or attentional) as the coupling function, from which a multi-layer deep neural network is built up via the dynamics of the proposed ODEs. We relate the oversmoothing problem, commonly encountered in GNNs, to the stability of steady states of the underlying ODE and show that zero-Dirichlet energy steady states are not stable for our proposed ODEs. This demonstrates that the proposed framework mitigates the oversmoothing problem. Moreover, we prove that GraphCON mitigates the exploding and vanishing gradients problem to facilitate training of deep multi-layer GNNs. Finally, we show that our approach offers competitive performance with respect to the state-of-the-art on a variety of graph-based learning tasks.

Cellular sheaves equip graphs with a ``geometrical'' structure by assigning vector spaces and linear maps to nodes and edges. Graph Neural Networks (GNNs) implicitly assume a graph with a trivial underlying sheaf. This choice is reflected in the structure of the graph Laplacian operator, the properties of the associated diffusion equation, and the characteristics of the convolutional models that discretise this equation. In this paper, we use cellular sheaf theory to show that the underlying geometry of the graph is deeply linked with the performance of GNNs in heterophilic settings and their oversmoothing behaviour. By considering a hierarchy of increasingly general sheaves, we study how the ability of the sheaf diffusion process to achieve linear separation of the classes in the infinite time limit expands. At the same time, we prove that when the sheaf is non-trivial, discretised parametric diffusion processes have greater control than GNNs over their asymptotic behaviour. On the practical side, we study how sheaves can be learned from data. The resulting sheaf diffusion models have many desirable properties that address the limitations of classical graph diffusion equations (and corresponding GNN models) and obtain competitive results in heterophilic settings. Overall, our work provides new connections between GNNs and algebraic topology and would be of interest to both fields.

We present Graph Neural Diffusion (GRAND) that approaches deep learning on graphs as a continuous diffusion process and treats Graph Neural Networks (GNNs) as discretisations of an underlying PDE. In our model, the layer structure and topology correspond to the discretisation choices of temporal and spatial operators. Our approach allows a principled development of a broad new class of GNNs that are able to address the common plights of graph learning models such as depth, oversmoothing, and bottlenecks. Key to the success of our models are stability with respect to perturbations in the data and this is addressed for both implicit and explicit discretisation schemes. We develop linear and nonlinear versions of GRAND, which achieve competitive results on many standard graph benchmarks.

We propose a novel class of graph neural networks based on the discretized Beltrami flow, a non-Euclidean diffusion PDE. In our model, node features are supplemented with positional encodings derived from the graph topology and jointly evolved by the Beltrami flow, producing simultaneously continuous feature learning, topology evolution. The resulting model generalizes many popular graph neural networks and achieves state-of-the-art results on several benchmarks.

The workshop features presentations of accepted contributions to the RecSys Challenge 2021, organized by Politecnico di Bari, ETH Zürich, Jönköping University, and the data set is provided by Twitter. The challenge focuses on a real-world task of tweet engagement prediction in a dynamic environment. For 2021, the challenge considers four different engagement types: Likes, Retweet, Quote, and replies. This year’s challenge brings the problem even closer to Twitter’s real recommender systems by introducing latency constraints. We also increases the data size to encourage novel methods. Also, the data density is increased in terms of the graph where users are considered to be nodes and interactions as edges. The goal is twofold: to predict the probability of different engagement types of a target user for a set of Tweets based on heterogeneous input data while providing fair recommendations. In fact, multi-goal optimization considering accuracy and fairness is particularly challenging. However, we believed that the recommendation community was nowadays mature enough to face the challenge of providing accurate and, at the same time, fair recommendations. To this end, Twitter has released a public dataset of close to 1 billion data points, > 40 million each day over 28 days. Week 1 − 3 will be used for training and week 4 for evaluation and testing. Each datapoint contains the tweet along with engagement features, user features, and tweet features. A peculiarity of this challenge is related to keeping the dataset updated with the platform: if a user deletes a Tweet, or their data from Twitter, the dataset is promptly updated. Moreover, each change in the dataset implied new evaluations of all submissions and the update of the leaderboard metrics. The challenge was well received with 578 registered users, and 386 submissions.

Word2vec is a powerful machine learning tool that emerged from Natural Language Processing (NLP) and is now applied in multiple domains, including recommender systems, forecasting, and network analysis. As Word2vec is often used off the shelf, we address the question of whether the default hyperparameters are suitable for recommender systems. The answer is emphatically no. In this paper, we first elucidate the importance of hyperparameter optimization and show that unconstrained optimization yields an average 221% improvement in hit rate over the default parameters. However, unconstrained optimization leads to hyperparameter settings that are very expensive and not feasible for large scale recommendation tasks. To this end, we demonstrate 138% average improvement in hit rate with a runtime budget-constrained hyperparameter optimization. Furthermore, to make hyperparameter optimization applicable for large scale recommendation problems where the target dataset is too large to search over, we investigate generalizing hyperparameters settings from samples. We show that applying constrained hyperparameter optimization using only a 10% sample of the data still yields a 91% average improvement in hit rate over the default parameters when applied to the full datasets. Finally, we apply hyperparameters learned using our method of constrained optimization on a sample to the Who To Follow recommendation service at Twitter and are able to increase follow rates by 15%.

Abstract Experimentation and Measurement (E&M) capabilities allow organizations to accurately assess the impact of new propositions and to experiment with many variants of existing products. However, until now, the question of measuring the measurer, or valuing the contribution of an E&M capability to organizational success has not been addressed. We tackle this problem by analyzing how, by decreasing estimation uncertainty, E&M platforms allow for better prioritization. We quantify this benefit in terms of expected relative improvement in the performance of all new propositions and provide guidance for how much an E&M capability is worth and when organizations should invest in one.

Experimentation and Measurement (E&M) capabilities allow organizations to accurately assess the impact of new propositions and to experiment with many variants of existing products. However, until now, the question of measuring the measurer, or valuing the contribution of an E&M capability to organizational success has not been addressed. We tackle this problem by analyzing how, by decreasing estimation uncertainty, E&M platforms allow for better prioritization. We quantify this benefit in terms of expected relative improvement in the performance of all new propositions and provide guidance for how much an E&M capability is worth and when organizations should invest in one.

We describe the Customer LifeTime Value (CLTV) prediction system deployed at ASOS.com, a global online fashion retailer. CLTV prediction is an important problem in e-commerce where an accurate estimate of future value allows retailers to effectively allocate marketing spend, identify and nurture high value customers and mitigate exposure to losses. The system at ASOS provides daily estimates of the future value of every customer and is one of the cornerstones of the personalised shopping experience. The state of the art in this domain uses large numbers of handcrafted features and ensemble regressors to forecast value, predict churn and evaluate customer loyalty. Recently, domains including language, vision and speech have shown dramatic advances by replacing handcrafted features with features that are learned automatically from data. We detail the system deployed at ASOS and show that learning feature representations is a promising extension to the state of the art in CLTV modelling. We propose a novel way to generate embeddings of customers, which addresses the issue of the ever changing product catalogue and obtain a significant improvement over an exhaustive set of handcrafted features.