Equivariant neural networks for recovery of Hadamard matrices

We propose a message passing neural network architecture designed to be equivariant to column and row permutations of a matrix. We illustrate its advantages over traditional architectures like multi-layer perceptrons (MLPs), convolutional neural networks (CNNs) and even Transformers, on the combinatorial optimization task of recovering a set of deleted entries of a Hadamard matrix. We argue that this is a powerful application of the principles of Geometric Deep Learning to fundamental mathematics, and a potential stepping stone toward more insights on the Hadamard conjecture using Machine Learning techniques.

Cost-based Feature Transfer for Vehicle Occupant Classification

Knowledge of human presence and interaction in a vehicle is of growing interest to vehicle manufacturers for design and safety purposes. We present a framework to perform the tasks of occupant detection and occupant classification for automatic child locks and airbag suppression. It operates for all passenger seats, using a single overhead camera. A transfer learning technique is introduced to make full use of training data from all seats whilst still maintaining some control over the bias, necessary for a system designed to penalize certain misclassifications more than others. An evaluation is performed on a challenging dataset with both weighted and unweighted classifiers, demonstrating the effectiveness of the transfer process.