  Neural networks are vulnerable to input perturbations such as additive noise
and adversarial attacks. In contrast, human perception is much more robust to
such perturbations. The Bayesian brain hypothesis states that human brains use
an internal generative model to update the posterior beliefs of the sensory
input. This mechanism can be interpreted as a form of self-consistency between
the maximum a posteriori (MAP) estimation of an internal generative model and
the external environment. Inspired by such hypothesis, we enforce
self-consistency in neural networks by incorporating generative recurrent
feedback. We instantiate this design on convolutional neural networks (CNNs).
The proposed framework, termed Convolutional Neural Networks with Feedback
(CNN-F), introduces a generative feedback with latent variables to existing CNN
architectures, where consistent predictions are made through alternating MAP
inference under a Bayesian framework. In the experiments, CNN-F shows
considerably improved adversarial robustness over conventional feedforward CNNs
on standard benchmarks.
