  The ever-growing demand for further advances in artificial intelligence
motivated research on unconventional computation based on analog physical
devices. While such computation devices mimic brain-inspired analog information
processing, learning procedures still relies on methods optimized for digital
processing such as backpropagation. Here, we present physical deep learning by
extending a biologically plausible training algorithm called direct feedback
alignment. As the proposed method is based on random projection with arbitrary
nonlinear activation, we can train a physical neural network without knowledge
about the physical system. In addition, we can emulate and accelerate the
computation for this training on a simple and scalable physical system. We
demonstrate the proof-of-concept using a hierarchically connected
optoelectronic recurrent neural network called deep reservoir computer. By
constructing an FPGA-assisted optoelectronic benchtop, we confirmed the
potential for accelerated computation with competitive performance on
benchmarks. Our results provide practical solutions for the training and
acceleration of neuromorphic computation.
