Application of deep neural network is a rapidly expanding field now reaching many disciplines including genomics. In particular, convolutional neural networks have been exploited for identifying the functional role of short genomic sequences. These approaches rely on gathering large sets of sequences with known functional role, extracting those sequences from whole-genome-annotations. These sets are then split into learning, test and validation sets in order to train the networks. While the obtained networks perform well on validation sets, they often perform poorly when applied on whole genomes in which the ratio of positive over negative examples can be very different than in the training set. We here address this issue by assessing the genome-wide performance of networks trained with sets exhibiting different ratios of positive to negative examples. As a case study, we use sequences encompassing gene starts from the RefGene database as positive examples and random genomic sequences as negative examples. We then demonstrate that models trained using data from one organism can be used to predict gene-start sites in a related species, when using training sets providing good genome-wide performance. This cross-species application of convolutional neural networks provides a new way to annotate any genome from existing high-quality annotations in a related reference species. It also provides a way to determine whether the sequence motifs recognised by chromatin-associated proteins in different species are conserved or not.