Title: Learning the Connections in Direct Feedback Alignment. Abstract: Feedback alignment was proposed to address the biological implausibility of the backpropagation algorithm which requires the transportation of the weight transpose during the backwards pass. The idea was later built upon with the proposal of direct feedback alignment (DFA), which propagates the error directly from the output layer to each hidden layer in the backward path using a fixed random weight matrix. This contribution was significant because it allowed for the parallelization of the backwards pass by the use of these feedback connections. However, just as feedback alignment, DFA does not perform well in deep convolutional networks. We propose to learn the backward weight matrices in DFA, adopting the methodology of Kolen-Pollack learning, to improve training and inference accuracy in deep convolutional neural networks by updating the direct feedback connections such that they come to estimate the forward path. The proposed method improves the accuracy of learning by direct feedback connections and reduces the gap between parallel training to serial training by means of backpropagation.