We propose a bio-inspired concept based on the maximization of entropy in neural networks for memory storage and high-order cognitive skills.We emphasize the role of information structure to cut into smaller pieces high resolution inputs into extremely low resolution neurons.Despite the unreliability of neurons due to intrinsic noise and limitations, their interaction allows error-free reconstruction.In particular, we show that the necessary number of neurons for reconstruction grows linearly while the resolution of the input grows exponentially.Playing with the information structure of neurons, we can make them sensitive to symbolic information in signals, like hierarchical binary trees or the relative order of elements in sequences. These features are a hallmark of symbolic systems and of higher-order cognitive skills.