Based on the predictive coding theory in neuro- science, we designed a bi-directional and recur- rent neural net, namely deep predictive coding networks (PCN), that has feedforward, feedback, and recurrent connections. Feedback connections from a higher layer carry the prediction of its lower-layer representation; feedforward connec- tions carry the prediction errors to its higher-layer. Given image input, PCN runs recursive cycles of bottom-up and top-down computation to update its internal representations and reduce the differ- ence between bottom-up input and top-down pre- diction at every layer. After multiple cycles of recursive updating, the representation is used for image classification. With benchmark datasets (CIFAR-10/100, SVHN, and MNIST), PCN was found to always outperform its feedforward-only counterpart: a model without any mechanism for recurrent dynamics, and its performance tended to improve given more cycles of computation over time. In short, PCN reuses a single architecture to recursively run bottom-up and top-down pro- cesses to refine its representation towards more accurate and definitive object recognition.

Inspired by "predictive coding" - a theory in neuroscience, we develop a bi-directional and dynamic neural network with local recurrent processing, namely predictive coding network (PCN). Unlike feedforward-only convolutional neural networks, PCN includes both feedback connections, which carry top-down predictions, and feedforward connections, which carry bottom-up errors of prediction. Feedback and feedforward connections enable adjacent layers to interact locally and recurrently to refine representations towards minimization of layer-wise prediction errors. When unfolded over time, the recurrent processing gives rise to an increasingly deeper hierarchy of non-linear transformation, allowing a shallow network to dynamically extend itself into an arbitrarily deep network. We train and test PCN for image classification with SVHN, CIFAR and ImageNet datasets. Despite notably fewer layers and parameters, PCN achieves competitive performance compared to classical and state-of-the-art models. Further analysis shows that the internal representations in PCN converge over time and yield increasingly better accuracy in object recognition. Errors of top-down prediction also reveal visual saliency or bottom-up attention.