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In a physical neural system, learning rules must be local both in space andtime. In order for learning to occur, non-local information must becommunicated to the deep synapses through a communication channel, the deeplearning channel. We identify several possible architectures for this learningchannel (Bidirectional, Conjoined, Twin, Distinct) and six symmetry challenges:1) symmetry of architectures; 2) symmetry of weights; 3) symmetry of neurons;4) symmetry of derivatives; 5) symmetry of processing; and 6) symmetry oflearning rules. Random backpropagation (RBP) addresses the second and thirdsymmetry, and some of its variations, such as skipped RBP (SRBP) address thefirst and the fourth symmetry. Here we address the last two desirablesymmetries showing through simulations that they can be achieved and that thelearning channel is particularly robust to symmetry variations. Specifically,random backpropagation and its variations can be performed with the samenon-linear neurons used in the main input-output forward channel, and theconnections in the learning channel can be adapted using the same algorithmused in the forward channel, removing the need for any specialized hardware inthe learning channel. Finally, we provide mathematical results in simple casesshowing that the learning equations in the forward and backward channelsconverge to fixed points, for almost any initial conditions. In symmetricarchitectures, if the weights in both channels are small at initialization,adaptation in both channels leads to weights that are essentially symmetricduring and after learning. Biological connections are discussed.

Learning in the Machine: the Symmetries of the Deep Learning Channel