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Neural nets have become popular to accelerate parameter inferences,especially for the upcoming generation of galaxy surveys in cosmology. Asneural nets are approximative by nature, a recurrent question has been how topropagate the neural net's approximation error, in order to avoid biases in theparameter inference. We present a Bayesian solution to propagating a neuralnet's approximation error and thereby debiasing parameter inference. We exploitthat a neural net reports its approximation errors during the validation phase.We capture the thus reported approximation errors via the highest-order summarystatistics, allowing us to eliminate the neural net's bias during inference,and propagating its uncertainties. We demonstrate that our method is quicklyimplemented and successfully infers parameters even for strongly biased neuralnets. In summary, our method provides the missing element to judge the accuracyof a posterior if it cannot be computed based on an infinitely accuratelytheory code.

Bayesian error propagation for neural-net based parameter inference