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Neural networks are based on a simplified model of the brain. In thisproject, we wanted to relax the simplifying assumptions of a traditional neuralnetwork by making a model that more closely emulates the low level interactionsof neurons. Like in an RNN, our model has a state that persists between timesteps, so that the energies of neurons persist. However, unlike an RNN, ourstate consists of a 2 dimensional matrix, rather than a 1 dimensional vector,thereby introducing a concept of distance to other neurons within the state. Inour model, neurons can only fire to adjacent neurons, as in the brain. Like inthe brain, we only allow neurons to fire in a time step if they contain enoughenergy, or excitement. We also enforce a notion of conservation of energy, sothat a neuron cannot excite its neighbors more than the excitement it alreadycontained at that time step. Taken together, these two features allow signalsin the form of activations to flow around in our network over time, making ourneural mesh more closely model signals traveling through the brain the brain.Although our main goal is to design an architecture to more closely emulate thebrain in the hope of having a correct internal representation of information bythe time we know how to properly train a general intelligence, we did benchmarkour neural mash on a specific task. We found that by increasing the runtime ofthe mesh, we were able to increase its accuracy without increasing the numberof parameters.

Neural Mesh: Introducing a Notion of Space and Conservation of Energy to Neural Networks