Learning and optimization with cascaded VLSI neural network building-block chips

To demonstrate the versatility of the building-block approach, two neural network applications were implemented on cascaded analog VLSI chips. Weights were implemented using 7-b multiplying digital-to-analog converter (MDAC) synapse circuits, with 31 x 32 and 32 x 32 synapses per chip. A novel learning algorithm compatible with analog VLSI was applied to the two-input parity problem. The algorithm combines dynamically evolving architecture with limited gradient-descent backpropagation for efficient and versatile supervised learning. To implement the learning algorithm in hardware, synapse circuits were paralleled for additional quantization levels. The hardware-in-the-loop learning system allocated 2-5 hidden neurons for parity problems. Also, a 7 x 7 assignment problem was mapped onto a cascaded 64-neuron fully connected feedback network. In 100 randomly selected problems, the network found optimal or good solutions in most cases, with settling times in the range of 7-100 microseconds.