An adversarial example is a modified input image designed to cause a Machine Learning (ML) model to make a mistake; these perturbations are often invisible or subtle to human observers and highlight vulnerabilities in a model's ability to generalize from its training data. Several adversarial attacks can create such examples, each with a different perspective, effectiveness, and perceptibility of changes. Conversely, defending against such adversarial attacks improves the robustness of ML models in image processing and other domains of deep learning. Most defence mechanisms require either a level of model awareness, changes to the model, or access to a comprehensive set of adversarial examples during training, which is impractical. Another option is to use an auxiliary model in a preprocessing manner without changing the primary model. This study presents a practical and effective solution -- using predictive coding networks (PCnets) as an auxiliary step for adversarial defence. By seamlessly integrating PCnets into feed-forward networks as a preprocessing step, we substantially bolster resilience to adversarial perturbations. Our experiments on MNIST and CIFAR10 demonstrate the remarkable effectiveness of PCnets in mitigating adversarial examples with about 82% and 65% improvements in robustness, respectively. The PCnet, trained on a small subset of the dataset, leverages its generative nature to effectively counter adversarial efforts, reverting perturbed images closer to their original forms. This innovative approach holds promise for enhancing the security and reliability of neural network classifiers in the face of the escalating threat of adversarial attacks.

Transformer has shown promise in reinforcement learning to model time-varying features for obtaining generalized low-level robot policies on diverse robotics datasets in embodied learning. However, it still suffers from the issues of low data efficiency and high inference latency. In this paper, we propose to investigate the task from a new perspective of the frequency domain. We first observe that the energy density in the frequency domain of a robot's trajectory is mainly concentrated in the low-frequency part. Then, we present the Fourier Controller Network (FCNet), a new network that uses Short-Time Fourier Transform (STFT) to extract and encode time-varying features through frequency domain interpolation. In order to do real-time decision-making, we further adopt FFT and Sliding DFT methods in the model architecture to achieve parallel training and efficient recurrent inference. Extensive results in both simulated (e.g., D4RL) and real-world environments (e.g., robot locomotion) demonstrate FCNet's substantial efficiency and effectiveness over existing methods such as Transformer, e.g., FCNet outperforms Transformer on multi-environmental robotics datasets of all types of sizes (from 1.9M to 120M). The project page and code can be found https://thkkk.github.io/fcnet.

We propose a neural-layer architecture based on Householder weighting and absolute-value activating, hence called Householder-absolute neural layer or simply Han-layer. Compared to a fully connected layer with $d$-neurons and $d$ outputs, a Han-layer reduces the number of parameters and the corresponding complexity from $O(d^2)$ to $O(d)$. The Han-layer structure guarantees two desirable properties: (1) gradient stability (free of vanishing or exploding gradient), and (2) 1-Lipschitz continuity. Extensive numerical experiments show that one can strategically use Han-layers to replace fully connected (FC) layers, reducing the number of model parameters while maintaining or even improving the generalization performance. We will also showcase the capabilities of the Han-layer architecture on a few small stylized models, and discuss its current limitations.