Current algorithms for deep learning probably cannot run in the brain because they rely on weight transport, where forward-path neurons transmit their synaptic weights to a feedback path, in a way that is likely impossible biologically. An algorithm called feedback alignment achieves deep learning without weight transport by using random feedback weights, but it performs poorly on hard visual-recognition tasks. Here we describe two mechanisms — a neural circuit called a weight mirror and a modification of an algorithm proposed by Kolen and Pollack in 1994 — both of which let the feedback path learn appropriate synaptic weights quickly and accurately even in large networks, without weight transport or complex wiring. Tested on the ImageNet visual-recognition task, these mechanisms outperform both feedback alignment and the newer sign-symmetry method, and nearly match backprop, the standard algorithm of deep learning, which uses weight transport.

Recent work in computer science has shown the power of deep learning driven by the backpropagation algorithm in networks of artificial neurons. But real neurons in the brain are different from most of these artificial ones in at least three crucial ways: they emit spikes rather than graded outputs, their inputs and outputs are related dynamically rather than by piecewise-smooth functions, and they have no known way to coordinate arrays of synapses in separate forward and feedback pathways so that they change simultaneously and identically, as they do in backpropagation. Given these differences, it is unlikely that current deep learning algorithms can operate in the brain, but we that show these problems can be solved by two simple devices: learning rules can approximate dynamic input-output relations with piecewise-smooth functions, and a variation on the feedback alignment algorithm can train deep networks without having to coordinate forward and feedback synapses. Our results also show that deep spiking networks learn much better if each neuron computes an intracellular teaching signal that reflects that cell's nonlinearity. With this mechanism, networks of spiking neurons show useful learning in synapses at least nine layers upstream from the output cells and perform well compared to other spiking networks in the literature on the MNIST digit recognition task.

Many neural control systems are at least roughly optimized, but how is optimal control learned? There are algorithms for this purpose, but in their current forms, they are not suited for biological neural networks because they rely on a type of communication that is not available in the brain, namely, weight transport-transmitting the strengths, or "weights," of individual synapses to other synapses and neurons. Here we show how optimal control can be learned without weight transport. Our method involves a set of simple mechanisms that can compensate for the absence of weight transport in the brain and so may be useful for neural computation generally.

When we learn something new, our brain may store the information in synapses or in reverberating loops of electrical activity, but current theories of motor learning focus almost entirely on the synapses. Here we show that loops could also play a role and would bring advantages: loop-based algorithms can learn complex control tasks faster, with exponentially fewer neurons, and avoid the problem of weight transport. They do all this at a cost: in the presence of long feedback delays, loop algorithms cannot control very fast movements, but in this case, loop and synaptic mechanisms can complement each other-mixed systems quickly learn to make accurate but not very fast motions and then gradually speed up. Loop algorithms explain aspects of consolidation, the role of attention, and the relapses that are sometimes seen after a task has apparently been learned, and they make further predictions.

To learn effectively, an adaptive controller needs to know its sensitivity derivatives--the variables that quantify how system performance depends on the commands from the controller. In the case of biological sensorimotor control, no one has explained how those derivatives themselves might be learned, and some authors suggest they are not learned at all but are known innately. Here we show that this knowledge cannot be solely innate, given the adaptive flexibility of neural systems. And we show how it could be learned using forms of information transport that are available in the brain. The mechanism, which we call implicit supervision, helps explain the flexibility and speed of sensorimotor learning and our ability to cope with high-dimensional work spaces and tools.