For scientific machine learning tasks with a lot of custom code, picking the right Automatic Differentiation (AD) system matters. Our Julia package DifferentiationInterface.jl provides a common frontend to a dozen AD backends, unlocking easy comparison and modular development. In particular, its built-in preparation mechanism leverages the strengths of each backend by amortizing one-time computations. This is key to enabling sophisticated features like sparsity handling without putting additional burdens on the user.

We investigate popular resampling methods for estimating the uncertainty of statistical models, such as subsampling, bootstrap and the jackknife, and their performance in high-dimensional supervised regression tasks. We provide a tight asymptotic description of the biases and variances estimated by these methods in the context of generalized linear models, such as ridge and logistic regression, taking the limit where the number of samples $n$ and dimension $d$ of the covariates grow at a comparable rate: $\alpha=n/d$ fixed. Our findings are three-fold: i) resampling methods are fraught with problems in high dimensions and exhibit the double-descent-like behavior typical of these situations; ii) only when $\alpha$ is large enough do they provide consistent and reliable error estimations (we give convergence rates); iii) in the over-parametrized regime $\alpha<1$ relevant to modern machine learning practice, their predictions are not consistent, even with optimal regularization.