Graph representation learning has become a ubiquitous component in many scenarios, ranging from social network analysis to energy forecasting in smart grids. In several applications, ensuring the fairness of the node (or graph) representations with respect to some protected attributes is crucial for their correct deployment. Yet, fairness in graph deep learning remains underexplored, with few solutions available. In particular, the tendency of similar nodes to cluster on several real-world graphs (i.e., homophily) can dramatically worsen the fairness of these procedures. In this article, we propose a novel biased edge dropout algorithm (FairDrop) to counter-act homophily and improve fairness in graph representation learning. FairDrop can be plugged in easily on many existing algorithms, is efficient, adaptable, and can be combined with other fairness-inducing solutions. After describing the general algorithm, we demonstrate its application on two benchmark tasks, specifically, as a random walk model for producing node embeddings, and to a graph convolutional network for link prediction. We prove that the proposed algorithm can successfully improve the fairness of all models with only a small or negligible drop in accuracy, and compares favourably with existing state-of-the-art solutions. In an ablation study, we demonstrate that our algorithm can flexibly interpolate between biasing towards fairness and an unbiased edge dropout. Furthermore, to better evaluate the gains, we propose a new dyadic group definition to measure the bias of a link prediction task when paired with group-based fairness metrics. In particular, we extend the metric used to measure the bias in node embeddings by taking account of the graph structure.

Graph convolutional networks (GCNs) are a family of neural network models that perform inference on graph data by interleaving vertexwise operations and message-passing exchanges across nodes. Concerning the latter, two key questions arise: 1) how to design a differentiable exchange protocol (e.g., a one-hop Laplacian smoothing in the original GCN) and 2) how to characterize the tradeoff in complexity with respect to the local updates. In this brief, we show that the state-of-the-art results can be achieved by adapting the number of communication steps independently at every node. In particular, we endow each node with a halting unit (inspired by Graves' adaptive computation time [1]) that after every exchange decides whether to continue communicating or not. We show that the proposed adaptive propagation GCN (AP-GCN) achieves superior or similar results to the best proposed models so far on a number of benchmarks while requiring a small overhead in terms of additional parameters. We also investigate a regularization term to enforce an explicit tradeoff between communication and accuracy. The code for the AP-GCN experiments is released as an open-source library.

In this article, we investigate the degree of explainability of graph neural networks (GNNs). The existing explainers work by finding global/local subgraphs to explain a prediction, but they are applied after a GNN has already been trained. Here, we propose a meta-explainer for improving the level of explainability of a GNN directly at training time, by steering the optimization procedure toward minima that allow post hoc explainers to achieve better results, without sacrificing the overall accuracy of GNN. Our framework (called MATE, MetA-Train to Explain) jointly trains a model to solve the original task, e.g., node classification, and to provide easily processable outputs for downstream algorithms that explain the model's decisions in a human-friendly way. In particular, we meta-train the model's parameters to quickly minimize the error of an instance-level GNNExplainer trained on-the-fly on randomly sampled nodes. The final internal representation relies on a set of features that can be ``better'' understood by an explanation algorithm, e.g., another instance of GNNExplainer. Our model-agnostic approach can improve the explanations produced for different GNN architectures and use any instance-based explainer to drive this process. Experiments on synthetic and real-world datasets for node and graph classification show that we can produce models that are consistently easier to explain by different algorithms. Furthermore, this increase in explainability comes at no cost to the accuracy of the model.

The aim of this work is to develop a fully-distributed algorithmic framework for training graph convolutional networks (GCNs). The proposed method is able to exploit the meaningful relational structure of the input data, which are collected by a set of agents that communicate over a sparse network topology. After formulating the centralized GCN training problem, we first show how to make inference in a distributed scenario where the underlying data graph is split among different agents. Then, we propose a distributed gradient descent procedure to solve the GCN training problem. The resulting model distributes computation along three lines: during inference, during back-propagation, and during optimization. Convergence to stationary solutions of the GCN training problem is also established under mild conditions. Finally, we propose an optimization criterion to design the communication topology between agents in order to match with the graph describing data relationships. A wide set of numerical results validate our proposal. To the best of our knowledge, this is the first work combining graph convolutional neural networks with distributed optimization.

Objective. Deep learning tools applied to high-resolution neurophysiological data have significantly progressed, offering enhanced decoding, real-time processing, and readability for practical applications. However, the design of artificial neural networks to analyze neural activity in vivo remains a challenge, requiring a delicate balance between efficiency in low-data regimes and the interpretability of the results. Approach. To address this challenge, we introduce a novel specialized transformer architecture to analyze single-neuron spiking activity. The model is tested on multi-electrode recordings from the dorsal premotor cortex of non-human primates performing a motor inhibition task. Main results. The proposed architecture provides an early prediction of the correct movement direction, achieving accurate results no later than 230 ms after the Go signal presentation across animals. Additionally, the model can forecast whether the movement will be generated or withheld before a stop signal, unattended, is actually presented. To further understand the internal dynamics of the model, we compute the predicted correlations between time steps and between neurons at successive layers of the architecture, with the evolution of these correlations mirrors findings from previous theoretical analyses. Significance. Overall, our framework provides a comprehensive use case for the practical implementation of deep learning tools in motor control research, highlighting both the predictive capabilities and interpretability of the proposed architecture.