Bayesian parameter inference is an essential tool in modern cosmology, and typically requires the calculation of 10 5–10 6 theoretical models for each inference of model parameters for a given dataset combination. Computing these models by solving the linearised Einstein-Boltzmann system usually takes tens of CPU core-seconds per model, making the entire process very computationally expensive. In this paper we present connect, a neural network framework emulating class computations as an easy-to-use plug-in for the popular sampler MontePython. connect uses an iteratively trained neural network which emulates the observables usually computed by class. The training data is generated using class, but using a novel algorithm for generating favourable points in parameter space for training data, the required number of class-evaluations can be reduced by two orders of magnitude compared to a traditional inference run. Once connect has been trained for a given model, no additional training is required for different dataset combinations, making connect many orders of magnitude faster than class (and making the inference process entirely dominated by the speed of the likelihood calculation). For the models investigated in this paper we find that cosmological parameter inference run with connect produces posteriors which differ from the posteriors derived using class by typically less than 0.01–0.1 standard deviations for all parameters. We also stress that the training data can be produced in parallel, making efficient use of all available compute resources. The connect code is publicly available for download on GitHub (https://github. com/AarhusCosmology/connect_public).