The backpropagation of error algorithm (BP) is often said to be impossible to implement in a real brain. The recent success of deep networks in machine learning and AI, however, has inspired a number of proposals for understanding how the brain might learn across multiple layers, and hence how it might implement or approximate BP. As of yet, none of these proposals have been rigorously evaluated on tasks where BP-guided deep learning has proved critical, or in architectures more structured than simple fully-connected networks. Here we present the first results on scaling up a biologically motivated model of deep learning to datasets which need deep networks with  appropriate architectures to achieve good performance. We present results on CIFAR-10 and ImageNet.   For CIFAR-10 we show that our algorithm, a straightforward, weight-transport-free variant of difference target-propagation (DTP) modified to remove backpropagation from the penultimate layer, is competitive with BP in training deep networks with locally defined receptive fields that have untied weights.   For ImageNet we find that both DTP and our algorithm perform significantly worse than BP, opening questions about whether different architectures or algorithms are required to scale these approaches. Our results and implementation details help establish baselines for biologically motivated deep learning schemes going forward. The suitability of the backpropagation of error (BP) algorithm BID27 for explaining learning in the brain was questioned soon after its popularization BID8 BID5 . Weaker objections included undesirable characteristics of artificial networks in general, such as their violation of Dale's Law, their lack of cell-type variability, and the need for the gradient signals to be both positive and negative. Much more serious objections were: (1) The need for the feedback connections carrying the gradient to have the same weights as the corresponding feedforward connections and (2) The need for a distinct form of information propagation (error propagation) that does not influence neural activity, and hence does not conform to known biological feedback mechanisms underlying neural communication.Researchers have long sought biologically plausible and empirically powerful learning algorithms that avoid some of these flaws BID1 BID25 BID0 BID23 Xie & Seung, 2003; BID12 BID14 BID10 BID21 . A common theme of some of the most promising approaches -such as Contrastive Hebbian Learning BID22 , and Generalized Recirculation BID23 -is to use feedback connections to influence neural activity, and to use differences in feedfoward-driven and feedback-driven activities or products of activities to locally approximate gradients BID0 BID26 BID23 Xie & Seung, 2003; BID30 Whittington & Bogacz, 2017) . Since these activity propagation methods don't require explicit propagation of gradients through the network, they go a long way towards answering the second serious objection noted above. However, many of these methods require long "positive" and "negative" settling phases for computing the activities or activity products whose differences provide the learning signal. Proposals for shortening the phases BID11 BID4 are not entirely satisfactory as they still fundamentally depend on a settling process, and, in general, any settling process will likely be too slow for a brain that needs to quickly compute hidden activities. Indeed, for the same reason, only a handful of the algorithms that require settling have ever been used on large scale problems in machine learning.Perhaps the most practical among this family of "activity propagation" algorithms is target propagation (TP) and its variants BID17 BID11 BID2 . The intuition for TP is as follows: Suppose you have a feedforward neural network and have the capacity to compute perfect inverses backwards through the network (i.e., given the activities in layer h l+1 , we can compute h l = f −1 (h l+1 ; θ l+1 )). If we impose an output target (for a given input) on the output layer, then we can propagate activity backwards through the network to infer what the activities should be to produce the output target. These backwards propagated activities are denoted the layer targets, or simply targets. Then, when computing a feedfoward propagation through the network given some input, we can layer-wise compare the feedforward activations to what they should have been (i.e., the targets), and use the differences to compute weight changes. TP algorithms do not require settling dynamics, and thus can compute forward passes and updates quickly. As well, for one TP variant , it has been shown that weight changes that cause future feedforward activity to be nudged towards their targets approximate the weight changes computed by BP.While TP and its variants are promising as biologically-plausible algorithms, there are some lingering questions about their applicability to the brain. First, the only variant explored empirically -difference target propagation (DTP) -still depends on explicit gradient computation via backpropagation for learning the penultimate layer's outgoing synaptic weights (see Algorithm Box 1 in ). Second, they have not been tested on datasets more difficult than MNIST. And third, they have not been incorporated into architectures more complicated than simple multi-layer perceptrons (MLPs).In this work we address each of these issues. Our contribution is threefold: (1) We examine the learning and performance of a biologically-motivated algorithm, Difference Target-propagation (DTP), on MNIST, CIFAR, and ImageNet, (2) We develop a variant of DTP called Simplified Difference Target Propagation (SDTP), which eliminates significant lingering biologically implausible features from DTP, and (3) We investigate the role of weight-sharing convolutions, which are key to performance on difficult datasets in artificial neural networks, by testing the effectiveness of locally connected architectures trained with BP, DTP, and SDTP.Sharing the weights of locally connected units greatly reduces the number of free parameters and this has several very beneficial effects on computer simulations of large neural nets. It improves generalization and it drastically reduces both the amount of memory needed to store the parameters and the amount of communication required between replicas of the same model running on different subsets of the data on different processors. From a biological perspective we are interested in how STDP compares with BP without using weight sharing, so both our BP results and our SDTP results are considerably worse than convolutional neural nets and take far longer to produce. Historically, there has been significant disagreement about whether BP can tell us anything interesting about learning in the brain BID5 BID8 . Indeed, from the mid 1990s to 2010, work on applying BP to the brain all but disappeared. Recent progress in machine learning has prompted a revival of this debate; where other approaches have failed, deep networks trained via BP have been key to achieving impressive performance on difficult datasets such as ImageNet. It is once again natural to wonder whether some approximation of BP might underlie learning in the brain.However, none of the algorithms proposed as approximations of BP have been tested on the datasets that were instrumental in convincing the machine learning and neuroscience communities to revisit these questions.Here we introduced a straightforward variant of difference target-propogation that completely removed gradient propagation and weight transport and tested it on the challenging task of classifying CIFAR and ImageNet images. We also investigated and reported results on the use of local connectivity. We demonstrated that networks trained with SDTP without any weight sharing (i.e. weight transport in the backward pass or weight tying in convolutions) are generally able to compete with those trained with BP on difficult tasks such as CIFAR. However, BP significantly outperforms both DTP and SDTP on ImageNet, and more work is required to understand why this issue arises at scale.We note that although activity-propagation-based algorithms go a long way towards biological plausibility, there are still many biological constraints that we did not address here. For example, we've set aside the question of spiking neurons entirely to focus on asking whether variants of TP can scale up to solve difficult problems at all. The question of spiking networks is an important one BID29 BID9 ), but it is nevertheless possible to gain algorithmic insight to the brain without tackling all of the elements of biological complexity simultaneously. Similarly, we also ignore Dale's law in all of our experiments BID24 . In general, we've aimed at the simplest models that allow us to address questions around (1) weight sharing, and (2) the form and function of feedback communication.Algorithms that contend for a role in helping us understand learning in cortex should be able to perform well on difficult domains without relying on weight transport or tying. Thus, our results offer a new benchmark for future work looking to evaluate the effectiveness of potential biologically plausible algorithms in more powerful architectures and on more difficult datasets.
Benchmarks for biologically plausible learning algorithms on complex datasets and architectures
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