Random feedback weights support learning in deep neural networks

The brain processes information through many layers of neurons. This deep architecture is representationally powerful1,2,3,4, but it complicates learning by making it hard to identify the responsible neurons when a mistake is made1,5. In machine learning, the backpropagation algorithm1 assigns blame to a neuron by computing exactly how it contributed to an error. To do this, it multiplies error signals by matrices consisting of all the synaptic weights on the neuron’s axon and farther downstream. This operation requires a precisely choreographed transport of synaptic weight information, which is thought to be impossible in the brain1,6,7,8,9,10,11,12,13,14. Here we present a surprisingly simple algorithm for deep learning, which assigns blame by multiplying error signals by random synaptic weights. We show that a network can learn to extract useful information from signals sent through these random feedback connections. In essence, the network learns to learn. We demonstrate that this new mechanism performs as quickly and accurately as backpropagation on a variety of problems and describe the principles which underlie its function. Our demonstration provides a plausible basis for how a neuron can be adapted using error signals generated at distal locations in the brain, and thus dispels long-held assumptions about the algorithmic constraints on learning in neural circuits. 1 ar X iv :1 41 1. 02 47 v1 [ qbi o. N C ] 2 N ov 2 01 4 Networks in the brain compute via many layers of interconnected neurons15,16. To work properly neurons must adjust their synapses so that the network’s outputs are appropriate for its tasks. A longstanding mystery is how upstream synapses (e.g. the synapse between α and β in Fig. 1a) are adjusted on the basis of downstream errors (e.g. e in Fig. 1a). In artificial intelligence this problem is solved by an algorithm called backpropagation of error1. Backprop works well in real-world applications17,18,19, and networks trained with it can account for cell response properties in some areas of cortex20,21. But it is biologically implausible because it requires that neurons send each other precise information about large numbers of synaptic weights — i.e. it needs weight transport1,6,7,8,12,14,22 (Fig. 1a, b). Specifically, backprop multiplies error signals e by the matrix W T , the transpose of the forward synaptic connections, W (Fig. 1b). This implies that feedback is computed using knowledge of all the synaptic weights W in the forward path. For this reason, current theories of biological learning have turned to simpler schemes such as reinforcement learning23, and “shallow” mechanisms which use errors to adjust only the final layer of a network4,11. But reinforcement learning, which delivers the same reward signal to each neuron, is slow and scales poorly with network size5,13,24. And shallow mechanisms waste the representational power of deep networks3,4,25. Here we describe a new deep-learning algorithm that is as fast and accurate as backprop, but much simpler, avoiding all transport of synaptic weight information. This makes it a mechanism the brain could easily exploit. It is based on three insights: (i) The feedback weights need not be exactly W T . In fact, any matrix B will suffice, so long as on average,