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Modular neural network computing apparatus are provided with distributed neural network storage. In various embodiments, a neural inference processor comprises a plurality of neural inference cores, at least one model network interconnecting the plurality of neural inference cores, and at least one activation network interconnecting the plurality of neural inference cores. Each of the plurality of neural inference cores comprises memory adapted to store input activations, output activations, and a neural network model. The neural network model comprises synaptic weights, neuron parameters, and neural network instructions. The at least one model network is configured to distribute the neural network model among the plurality of neural inference cores. Each of the plurality of neural inference cores is configured to apply the synaptic weights to input activations from its memory to produce a plurality of output …