Methods, systems, and computer programs are provided for training a front-end neural network (“front-end NN”) and a back-end neural network (“back-end NN”). The method includes: combining the back-end NN with the front-end NN so that an output layer of the front-end NN is also an input layer of the back-end NN to form a joint layer to thereby generate a combined NN; and training the combined NN for a speech recognition with a set of utterances as training data, a plurality of specific units in the joint layer being dropped during the training and the plurality of the specific units corresponding to one or more common frequency bands. The front-end NN may be configured to estimate clean frequency filter bank features from noisy input features; or, to estimate clean frequency filter bank features from noisy frequency filter bank input features in the same feature space.