Deep learning as performed by artificial deep neural networks (DNNs) has achieved great successes recently in many important areas that deal with text, images, videos, graphs, and so on. However, the black-box nature of DNNs has become one of the primary obstacles for their wide adoption in mission-critical applications such as medical diagnosis and therapy. Because of the huge potentials of deep learning, the interpretability of DNNs has recently attracted much research attention. In this article, we propose a simple but comprehensive taxonomy for interpretability, systematically review recent studies on interpretability of neural networks, describe applications of interpretability in medicine, and discuss future research directions, such as in relation to fuzzy logic and brain science.

Inspired by complexity and diversity of biological neurons, our group proposed quadratic neurons by replacing the inner product in current artificial neurons with a quadratic operation on input data, thereby enhancing the capability of an individual neuron. Along this direction, we are motivated to evaluate the power of quadratic neurons in popular network architectures, simulating human-like learning in the form of “quadratic-neuron-based deep learning”. Our prior theoretical studies have shown important merits of quadratic neurons and networks in representation, efficiency, and interpretability. In this paper, we use quadratic neurons to construct an encoder-decoder structure, referred as the quadratic autoencoder, and apply it to low-dose CT denoising. The experimental results on the Mayo low-dose CT dataset demonstrate the utility and robustness of quadratic autoencoder in terms of image denoising and model efficiency. To our best knowledge, this is the first time that the deep learning approach is implemented with a new type of neurons and demonstrates a significant potential in the medical imaging field.

Image denoising is a prerequisite for downstream tasks in many fields. Low-dose and photon-counting computed tomography (CT) denoising can optimize diagnostic performance at minimized radiation dose. Supervised deep denoising methods are popular but require paired clean or noisy samples that are often unavailable in practice. Limited by the independent noise assumption, current self-supervised denoising methods cannot process correlated noises as in CT images. Here we propose the first-of-its-kind similarity-based self-supervised deep denoising approach, referred to as Noise2Sim, that works in a nonlocal and nonlinear fashion to suppress not only independent but also correlated noises. Theoretically, Noise2Sim is asymptotically equivalent to supervised learning methods under mild conditions. Experimentally, Nosie2Sim recovers intrinsic features from noisy low-dose CT and photon-counting CT images as effectively as or even better than supervised learning methods on practical datasets visually, quantitatively and statistically. Noise2Sim is a general self-supervised denoising approach and has great potential in diverse applications.

Bearing fault diagnosis is of great importance to decrease the damage risk of rotating machines and further improve economic profits. Recently, machine learning, represented by deep learning, has made great progress in bearing fault diagnosis. However, applying deep learning to such a task still faces major challenges such as effectiveness and interpretability: i) When bearing signals are highly corrupted by noise, the performance of deep learning models drops dramatically; ii) A deep network is notoriously a black box. It is difficult to know how a model classifies faulty signals from the normal and the physics principle behind the classification. To solve these issues, first, we prototype a convolutional network with recently-invented quadratic neurons. This quadratic neuron-empowered network can qualify the noisy bearing data due to the strong feature representation ability of quadratic neurons. Moreover, we independently derive the attention mechanism from a quadratic neuron, referred to as qttention, by factorizing the learned quadratic function in analogue to the attention, making the model made of quadratic neurons inherently interpretable. Experiments on the public and our datasets demonstrate that the proposed network can facilitate effective and interpretable bearing fault diagnosis. Our code is available at https://github.com/asdvfghg/ QCNN_for_bearing_diagnosis.