Gradient descent during the learning process of a neural network can be subject to many instabilities. The spectral density of the Jacobian is a key component for analyzing robustness. Following the works of Pennington et al., such Jacobians are modeled using free multiplicative convolutions from Free Probability Theory. We present a reliable and very fast method for computing the associated spectral densities. This method has a controlled and proven convergence. Our technique is based on an adaptative Newton-Raphson scheme, by finding and chaining basins of attraction: the Newton algorithm finds contiguous lilypad-like basins and steps from one to the next, heading towards the objective. We demonstrate the applicability of our method by using it to assess how the learning process is affected by network depth, layer widths and initialization choices: empirically, final test losses are very correlated to our Free Probability metrics.

This work introduces a geometric framework and a novel network architecture for creating correspondences between samples of different conditions. Under this formalism, the latent space is a fiber bundle stratified into a base space encoding conditions, and a fiber space encoding the variations within conditions. The correspondences between conditions are obtained by minimizing an energy functional, resulting in diffeomorphism flows between fibers. We illustrate this approach using MNIST and Olivetti and benchmark its performances on the task of batch correction, which is the problem of integrating multiple biological datasets together.

A team of researchers hailing from Harvard and Université de Montréal today launched Epitopes.world, It's built atop an algorithm -- CAMAP -- that generates predictions for potential vaccine targets, enabling researchers to identify which parts of the virus are more likely to be exposed at the surface (epitopes) of infected cells. Project lead Dr. Tariq Daouda, who worked alongside doctorates in machine learning, immunobiologists, and bioinformaticians to build Epitopes.world, Fewer than 12% of all drugs entering clinical trials end up in pharmacies, and it takes at least 10 years for medicines to complete the journey from discovery to the marketplace. Clinical trials alone take six to seven years, on average, putting the cost of R&D at roughly $2.6 billion, according to the Pharmaceutical Research and Manufacturers of America.