Kalyan Varma Nadimpalli

Kalyan Varma Nadimpalli, Amit Chattopadhyay, Bastian Rieck

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.

Joël Mathys, Florian Grötschla, Kalyan Varma Nadimpalli et al.

Most Graph Neural Networks follow the standard message-passing framework where, in each step, all nodes simultaneously communicate with each other. We want to challenge this paradigm by aligning the computation more closely to the execution of distributed algorithms and propose the Flood and Echo Net. A single round of a Flood and Echo Net consists of an origin node and a flooding phase followed by an echo phase. First, during the flooding, messages are sent from the origin and propagated outwards throughout the entire graph. Then, during the echo, the message flow reverses and messages are sent back towards the origin. As nodes are only sparsely activated upon receiving a message, this leads to a wave-like activation pattern that traverses the graph. Through these sparse but parallel activations, the Net becomes more expressive than traditional MPNNs which are limited by the 1-WL test and also is provably more efficient in terms of message complexity. Moreover, the mechanism's inherent ability to generalize across graphs of varying sizes positions it as a practical architecture for the task of algorithmic learning. We test the Flood and Echo Net on a variety of synthetic tasks and the SALSA-CLRS benchmark and find that the algorithmic alignment of the execution improves generalization to larger graph sizes.

Shashank Reddy Chirra, Kalyan Varma Nadimpalli, Shrisha Rao

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.