Recurrent backpropagation and the dynamical approach to adaptive neural computation

Error backpropagation in feedforward neural network models is a popular learning algorithm that has its roots in nonlinear estimation and optimization. It is being used routinely to calculate error gradients in nonlinear systems with hundreds of thousands of parameters. However, the classical architecture for backpropagation has severe restrictions. The extension of backpropagation to networks with recurrent connections will be reviewed. It is now possible to efficiently compute the error gradients for networks that have temporal dynamics, which opens applications to a host of problems in systems identification and control

Deep learning with asymmetric connections and Hebbian updates

We show that deep networks can be trained using Hebbian updates yielding similar performance to ordinary back-propagation on challenging image datasets. To overcome the unrealistic symmetry in connections between layers, implicit in back-propagation, the feedback weights are separate from the feedforward weights. The feedback weights are also updated with a local rule, the same as the feedforward weights - a weight is updated solely based on the product of activity of the units it connects. With fixed feedback weights as proposed in Lillicrap et. al (2016) performance degrades quickly as the depth of the network increases. If the feedforward and feedback weights are initialized with the same values, as proposed in Zipser and Rumelhart (1990), they remain the same throughout training thus precisely implementing back-propagation. We show that even when the weights are initialized differently and at random, and the algorithm is no longer performing back-propagation, performance is comparable on challenging datasets. We also propose a cost function whose derivative can be represented as a local Hebbian update on the last layer. Convolutional layers are updated with tied weights across space, which is not biologically plausible. We show that similar performance is achieved with untied layers, also known as locally connected layers, corresponding to the connectivity implied by the convolutional layers, but where weights are untied and updated separately. In the linear case we show theoretically that the convergence of the error to zero is accelerated by the update of the feedback weights

Learning long-range spatial dependencies with horizontal gated-recurrent units

Progress in deep learning has spawned great successes in many engineering applications. As a prime example, convolutional neural networks, a type of feedforward neural networks, are now approaching -- and sometimes even surpassing -- human accuracy on a variety of visual recognition tasks. Here, however, we show that these neural networks and their recent extensions struggle in recognition tasks where co-dependent visual features must be detected over long spatial ranges. We introduce the horizontal gated-recurrent unit (hGRU) to learn intrinsic horizontal connections -- both within and across feature columns. We demonstrate that a single hGRU layer matches or outperforms all tested feedforward hierarchical baselines including state-of-the-art architectures which have orders of magnitude more free parameters. We further discuss the biological plausibility of the hGRU in comparison to anatomical data from the visual cortex as well as human behavioral data on a classic contour detection task.Comment: Published at NeurIPS 2018 https://papers.nips.cc/paper/7300-learning-long-range-spatial-dependencies-with-horizontal-gated-recurrent-unit