The backpropagation algorithm has long been the canonical training method for neural networks. Modern paradigms are implicitly optimized for it, and numerous guidelines exist to ensure its proper use. Recently, synthetic gradients methods -where the error gradient is only roughly approximated - have garnered interest. These methods not only better portray how biological brains are learning, but also open new computational possibilities, such as updating layers asynchronously. Even so, they have failed to scale past simple tasks like MNIST or CIFAR-10. This is in part due to a lack of standards, leading to ill-suited models and practices forbidding such methods from performing to the best of their abilities. In this work, we focus on direct feedback alignment and present a set of best practices justified by observations of the alignment angles. We characterize a bottleneck effect that prevents alignment in narrow layers, and hypothesize it may explain why feedback alignment methods have yet to scale to large convolutional networks.
A number of such methods have focused on enhanced biological realism. Boltzmann machine learning @cite_1 , Contrastive Hebbian Learning @cite_3 , and Generalized Recirculation @cite_22 all use local learning signals that do not require propagation of a gradient through the network.
@cite_1 @cite_22 @cite_3
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We present a new learning algorithm for Boltzmann machines that contain many layers of hidden variables. Data-dependent expectations are estimated using a variational approximation that tends to focus on a single mode, and dataindependent expectations are approximated using persistent Markov chains. The use of two quite different techniques for estimating the two types of expectation that enter into the gradient of the log-likelihood makes it practical to learn Boltzmann machines with multiple hidden layers and millions of parameters. The learning can be made more efficient by using a layer-by-layer “pre-training” phase that allows variational inference to be initialized with a single bottomup pass. We present results on the MNIST and NORB datasets showing that deep Boltzmann machines learn good generative models and perform well on handwritten digit and visual object recognition tasks. The error backpropagation learning algorithm (BP) is generally considered biologically implausible because it does not use locally available, activation-based variables. A version of BP that can be computed locally using bidirectional activation recirculation (Hinton and McClelland 1988) instead of backpropagated error derivatives is more biologically plausible. This paper presents a generalized version of the recirculation algorithm (GeneRec), which overcomes several limitations of the earlier algorithm by using a generic recurrent network with sigmoidal units that can learn arbitrary input output mappings. However, the contrastive Hebbian learning algorithm (CHL, also known as DBM or mean field learning) also uses local variables to perform error-driven learning in a sigmoidal recurrent network. CHL was derived in a stochastic framework (the Boltzmann machine), but has been extended to the deterministic case in various ways, all of which rely on problematic approximations and assumptions, leading some to conclude that it is fundamentally flawed. This paper shows that CHL can be derived instead from within the BP framework via the GeneRec algorithm. CHL is a symmetry-preserving version of GeneRec that uses a simple approximation to the midpoint or second-order accurate Runge-Kutta method of numerical integration, which explains the generally faster learning speed of CHL compared to BI. Thus, all known fully general error-driven learning algorithms that use local activation-based variables in deterministic networks can be considered variations of the GeneRec algorithm (and indirectly, of the backpropagation algorithm). GeneRec therefore provides a promising framework for thinking about how the brain might perform error-driven learning. To further this goal, an explicit biological mechanism is proposed that would be capable of implementing GeneRec-style learning. This mechanism is consistent with available evidence regarding synaptic modification in neurons in the neocortex and hippocampus, and makes further predictions. Abstract This paper shows that contrastive Hebbian, the algorithm used in mean field learning, can be applied to any continuous Hopfield model. This implies that non-logistic activation functions as well as self connections are allowed. Contrary to previous approaches, the learning algorithm is derived without considering it a mean field approximation to Boltzmann machine learning. The paper includes a discussion of the conditions under which the function that contrastive Hebbian minimizes can be considered a proper error function, and an analysis of five different training regimes. An appendix provides complete demonstrations and specific instructions on how to implement contrastive Hebbian learning in interactive activation and competition models (a convenient version of the continuous Hopfield model).