Experiencing certain events triggers the acquisition of new memories. Although necessary, however, actual experience is not sufficient for memory formation. One-trial learning is also gated by knowledge of appropriate background information to make sense of the experienced occurrence. Strong neurobiological evidence suggests that long-term memory storage involves formation of new synapses. On the short time scale, this form of structural plasticity requires that the axon of the pre-synaptic neuron be physically proximal to the dendrite of the post-synaptic neuron. We surmise that such axonal-dendritic overlap (ADO) constitutes the neural correlate of background information-gated (BIG) learning. The hypothesis is based on a fundamental neuroanatomical constraint: an axon must pass close to the dendrites that are near other neurons it contacts. The topographic organization of the mammalian cortex ensures that nearby neurons encode related information. Using neural network simulations, we demonstrate that ADO is a suitable mechanism for BIG learning. We model knowledge as associations between terms, concepts or indivisible units of thought via directed graphs. The simplest instantiation encodes each concept by single neurons. Results are then generalized to cell assemblies. The proposed mechanism results in learning real associations better than spurious co-occurrences, providing definitive cognitive advantages. 