Although adversarial training has been the state-of-the-art approach to defend against adversarial examples (AEs), it suffers from a robustness-accuracy trade-off, where high robustness is achieved at the cost of clean accuracy. In this work, we leverage invariance regularization on latent representations to learn discriminative yet adversarially invariant representations, aiming to mitigate this trade-off. We analyze two key issues in representation learning with invariance regularization: (1) a "gradient conflict" between invariance loss and classification objectives, leading to suboptimal convergence, and (2) the mixture distribution problem arising from diverged distributions of clean and adversarial inputs. To address these issues, we propose Asymmetrically Representation-regularized Adversarial Training (AR-AT), which incorporates asymmetric invariance loss with stop-gradient operation and a predictor to improve the convergence, and a split-BatchNorm (BN) structure to resolve the mixture distribution problem. Our method significantly improves the robustness-accuracy trade-off by learning adversarially invariant representations without sacrificing discriminative ability. Furthermore, we discuss the relevance of our findings to knowledge-distillation-based defense methods, contributing to a deeper understanding of their relative successes.

Inverse problems in image reconstruction are fundamentally complicated by unknown noise properties. Classical iterative deconvolution approaches amplify noise and require careful parameter selection for an optimal trade-off between sharpness and grain. Deep learning methods allow for flexible parametrization of the noise and learning its properties directly from the data. Recently, self-supervised blind-spot neural networks were successfully adopted for image deconvolution by including a known point-spread function in the end-to-end training. However, their practical application has been limited to 2D images in the biomedical domain because it implies large kernels that are poorly optimized. We tackle this problem with Fast Fourier Transform convolutions that provide training speed-up in 3D microscopy deconvolution tasks. Further, we propose to adopt a Siamese invariance loss for deconvolution and empirically identify its optimal position in the neural network between blind-spot and full image branches. The experimental results show that our improved framework outperforms the previous state-of-the-art deconvolution methods with a known point spread function.

The training data distribution is often biased towards objects in certain orientations and illumination conditions. While humans have a remarkable capability of recognizing objects in out-of-distribution (OoD) orientations and illuminations, Deep Neural Networks (DNNs) severely suffer in this case, even when large amounts of training examples are available. In this paper, we investigate three different approaches to improve DNNs in recognizing objects in OoD orientations and illuminations. Namely, these are (i) training much longer after convergence of the in-distribution (InD) validation accuracy, i.e., late-stopping, (ii) tuning the momentum parameter of the batch normalization layers, and (iii) enforcing invariance of the neural activity in an intermediate layer to orientation and illumination conditions. Each of these approaches substantially improves the DNN's OoD accuracy (more than 20% in some cases). We report results in four datasets: two datasets are modified from the MNIST and iLab datasets, and the other two are novel (one of 3D rendered cars and another of objects taken from various controlled orientations and illumination conditions). These datasets allow to study the effects of different amounts of bias and are challenging as DNNs perform poorly in OoD conditions. Finally, we demonstrate that even though the three approaches focus on different aspects of DNNs, they all tend to lead to the same underlying neural mechanism to enable OoD accuracy gains -- individual neurons in the intermediate layers become more selective to a category and also invariant to OoD orientations and illuminations.