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 the internal generative model and the external environmental. Inspired by this, we enforce consistency in neural networks by incorporating generative recurrent feedback. We instantiate it on convolutional neural networks (CNNs). The proposed framework, termed Convolutional Neural Networks with Feedback (CNN-F), introduces a generative feedback with latent variables into existing CNN architectures, making consistent predictions via alternating MAP inference under a Bayesian framework. CNN-F shows considerably better adversarial robustness over regular feedforward CNNs on standard benchmarks. In addition, With higher V4 and IT neural predictivity, CNN-F produces object representations closer to primate vision than conventional CNNs.
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