We assess the feasibility of a parenchymal texture feature fusion approach, utilizing a convolutional neural network (ConvNet) architecture, to benefit breast cancer risk assessment. Hypothesizing that by capturing sparse, subtle interactions between localized motifs present in two-dimensional texture feature maps derived from mammographic images, a multitude of texture feature descriptors can be optimally reduced to five meta-features capable of serving as a basis on which a linear classifier, such as logistic regression, can efficiently assess breast cancer risk. We combine this methodology with our previously validated lattice-based strategy for parenchymal texture analysis and we evaluate the feasibility of this approach in a case-control study with 424 digital mammograms. In a randomized split-sample setting, we optimize our framework in training/validation sets (N=300) and evaluate its descriminatory performance in an independent test set (N=124). The discriminatory capacity is assessed in terms of the the area under the curve (AUC) of the receiver operator characteristic (ROC). The resulting meta-features exhibited strong classification capability in the test dataset (AUC = 0.90), outperforming conventional, non-fused, texture analysis which previously resulted in an AUC=0.85 on the same case-control dataset. Our results suggest that informative interactions between localized motifs exist and can be extracted and summarized via a fairly simple ConvNet architecture.