Flood and Echo: Algorithmic Alignment of GNNs with Distributed Computing

Graph Neural Networks are a natural fit for learning algorithms. They can directly represent tasks through an abstract but versatile graph structure and handle inputs of different sizes. This opens up the possibility for scaling and extrapolation to larger graphs, one of the most important advantages of an algorithm. However, this raises two core questions i) How can we enable nodes to gather the required information in a given graph ($\textit{information exchange}$), even if is far away and ii) How can we design an execution framework which enables this information exchange for extrapolation to larger graph sizes ($\textit{algorithmic alignment for extrapolation}$). We propose a new execution framework that is inspired by the design principles of distributed algorithms: Flood and Echo Net. It propagates messages through the entire graph in a wave like activation pattern, which naturally generalizes to larger instances. Through its sparse but parallel activations it is provably more efficient in terms of message complexity. We study the proposed model and provide both empirical evidence and theoretical insights in terms of its expressiveness, efficiency, information exchange and ability to extrapolate.

Euler Characteristic Transform Based Topological Loss for Reconstructing 3D Images from Single 2D Slices

The computer vision task of reconstructing 3D images, i.e., shapes, from their single 2D image slices is extremely challenging, more so in the regime of limited data. Deep learning models typically optimize geometric loss functions, which may lead to poor reconstructions as they ignore the structural properties of the shape. To tackle this, we propose a novel topological loss function based on the Euler Characteristic Transform. This loss can be used as an inductive bias to aid the optimization of any neural network toward better reconstructions in the regime of limited data. We show the effectiveness of the proposed loss function by incorporating it into SHAPR, a state-of-the-art shape reconstruction model, and test it on two benchmark datasets, viz., Red Blood Cells and Nuclei datasets. We also show a favourable property, namely injectivity and discuss the stability of the topological loss function based on the Euler Characteristic Transform.

A Robust Classification Framework for Byzantine-Resilient Stochastic Gradient Descent

This paper proposes a Robust Gradient Classification Framework (RGCF) for Byzantine fault tolerance in distributed stochastic gradient descent. The framework consists of a pattern recognition filter which we train to be able to classify individual gradients as Byzantine by using their direction alone. This filter is robust to an arbitrary number of Byzantine workers for convex as well as non-convex optimisation settings, which is a significant improvement on the prior work that is robust to Byzantine faults only when up to 50% of the workers are Byzantine. This solution does not require an estimate of the number of Byzantine workers; its running time is not dependent on the number of workers and can scale up to training instances with a large number of workers without a loss in performance. We validate our solution by training convolutional neural networks on the MNIST dataset in the presence of Byzantine workers.