  Tensor analytics lays mathematical basis for the prosperous promotion of
multiway signal processing. To increase computing throughput, mainstream
processors transform tensor convolutions to matrix multiplications to enhance
parallelism of computing. However, such order-reducing transformation produces
data duplicates and consumes additional memory. Here, we demonstrate an
integrated photonic tensor flow processor without tensor-matrix transformation,
which outputs the convolved tensor as the input tensor 'flows' through the
processor. The hybrid manipulation of optical dimensions of wavelength, time,
and space enables the direct representation and processing of high-order
tensors in optical domain. In the proof-of-concept experiment, processing of
multi-channel images and videos is accomplished at the frequency of 20 GHz. A
convolutional neural network is demonstrated on the processor, which achieves
an accuracy of 97.9 percent on action recognition.
