Jan de Gier

Max Petschack, Alexandr Garbali, Jan de Gier

Machine learning explorations can make significant inroads into solving difficult problems in pure mathematics. One advantage of this approach is that mathematical datasets do not suffer from noise, but a challenge is the amount of data required to train these models and that this data can be computationally expensive to generate. Key challenges further comprise difficulty in a posteriori interpretation of statistical models and the implementation of deep and abstract mathematical problems. We propose a method for scalable tasks, by which models trained on simpler versions of a task can then generalize to the full task. Specifically, we demonstrate that a transformer neural-network trained on predicting permutations from words formed by general transpositions in the symmetric group $S_{10}$ can generalize to the symmetric group $S_{25}$ with near 100\% accuracy. We also show that $S_{10}$ generalizes to $S_{16}$ with similar performance if we only use adjacent transpositions. We employ identity augmentation as a key tool to manage variable word lengths, and partitioned windows for training on adjacent transpositions. Finally we compare variations of the method used and discuss potential challenges with extending the method to other tasks.

Thomas Attema, Emiliano Mancini, Gabriele Spini et al.

Background: Clinical decision support systems (CDSS) are a category of health information technologies that can assist clinicians to choose optimal treatments. These support systems are based on clinical trials and expert knowledge; however, the amount of data available to these systems is limited. For this reason, CDSSs could be significantly improved by using the knowledge obtained by treating patients. This knowledge is mainly contained in patient records, whose usage is restricted due to privacy and confidentiality constraints. Methods: A treatment effectiveness measure, containing valuable information for treatment prescription, was defined and a method to extract this measure from patient records was developed. This method uses an advanced cryptographic technology, known as secure Multiparty Computation (henceforth referred to as MPC), to preserve the privacy of the patient records and the confidentiality of the clinicians' decisions. Results: Our solution enables to compute the effectiveness measure of a treatment based on patient records, while preserving privacy. Moreover, clinicians are not burdened with the computational and communication costs introduced by the privacy-preserving techniques that are used. Our system is able to compute the effectiveness of 100 treatments for a specific patient in less than 24 minutes, querying a database containing 20,000 patient records. Conclusion: This paper presents a novel and efficient clinical decision support system, that harnesses the potential and insights acquired from treatment data, while preserving the privacy of patient records and the confidentiality of clinician decisions.