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We present Capse.jl, a novel emulator that utilizes neural networks topredict Cosmic Microwave Background (CMB) temperature, polarization and lensingangular power spectra. The emulator computes predictions in just a fewmicroseconds with emulation errors below 0.1 $\sigma$ for all the scalesrelevant for the planned CMB-S4 survey. Capse.jl can also be trained in anhour's time on a CPU. As a test case, we use Capse.jl to analyze Planck 2018data and ACT DR4 data. We obtain the same result as standard analysis methodswith a computational efficiency 3 to 6 order of magnitude higher. We takeadvantage of the differentiability of our emulators to use gradients-basedmethods, such as Pathfinder and Hamiltonian Monte Carlo (HMC), which speed upthe convergence and increase sampling efficiency. Together, these features makeCapse.jl a powerful tool for studying the CMB and its implications forcosmology. When using the fastest combination of our likelihoods, emulators,and analysis algorithm, we are able to perform a Planck TT + TE + EE analysisin less than a second. To ensure full reproducibility, we provide open accessto the codes and data required to reproduce all the results of this work.

Capse.jl: efficient and auto-differentiable CMB power spectra emulation