Bayesian posterior inference of modern multiprobe cosmological analyses incurs massive computational costs. These computational costs have severe environmental impacts and the long wallclock time slows scientific productivity. To address these difficulties, we introduce LINNA: the Likelihood Inference Neural Network Accelerator. Relative to the baseline of modern survey cosmological analyses, LINNA reduces the computational cost associated with posterior inference by a factor of 8–50. To accomplish these reductions, LINNA automatically builds training data sets, creates neural network emulators, and produces a Markov chain that samples the posterior. We explicitly verify that LINNA accurately reproduces the first-year DES cosmological constraints derived from a variety of different data vectors with our default code settings, without needing to retune the algorithm every time. Further, we find that LINNA is sufficient for enabling accurate and efficient sampling for LSST Y10 multi-probe analyses.