  We propose and study a new projection formula for training binary weight
convolutional neural networks. The projection formula measures the error in
approximating a full precision (32 bit) vector by a 1-bit vector in the l_1
norm instead of the standard l_2 norm. The l_1 projector is in closed
analytical form and involves a median computation instead of an arithmatic
average in the l_2 projector. Experiments on 10 keywords classification show
that the l_1 (median) BinaryConnect (BC) method outperforms the regular BC,
regardless of cold or warm start. The binary network trained by median BC and a
recent blending technique reaches test accuracy 92.4%, which is 1.1% lower than
the full-precision network accuracy 93.5%. On Android phone app, the trained
binary network doubles the speed of full-precision network in spoken keywords
recognition.
