Database query optimizers benefit greatly from accurate cardinality estimation; however, this is hard to achieve on tables with correlated and/or skewed columns. We present a novel approach using neural networks to learn and approximate selectivity functions that take a bounded range on each column as input, effectively estimating selectivities for all relational operators. Experimental results with a simplified prototype show a significant improvement over state-of-the-art cardinality estimators on constructed datasets in terms of accuracy, efficiency, and amount of user input required.