A speech recognition model includes an encoder network, a prediction network, and a joint network. The encoder network is configured to receive a sequence of acoustic frames characterizing an input utterance; and generate, at each of a plurality of output steps, a higher order feature representation for a corresponding acoustic frame in the sequence of acoustic frames. The prediction network is configured to: receive a sequence of non-blank symbols output by a final Softmax layer; and generate, at each of the plurality of output steps, a dense representation. The joint network is configured to generate, at each of the plurality of output steps based on the higher order feature representation and the dense representation, a probability distribution over possible speech recognition hypotheses. The joint network includes a stack of gating and bilinear pooling to fuse the dense representation and the higher order feature representation.