Most explanation methods are designed in an empirical manner, so exploring whether there exists a first-principles explanation of a deep neural network (DNN) becomes the next core scientific problem in explainable artificial intelligence (XAI). Although it is still an open problem, in this paper, we discuss whether the interaction-based explanation can serve as the first-principles explanation of a DNN. The strong explanatory power of interaction theory comes from the following aspects: (1) it establishes a new axiomatic system to quantify the decision-making logic of a DNN into a set of symbolic interaction concepts; (2) it simultaneously explains various deep learning phenomena, such as generalization power, adversarial sensitivity, representation bottleneck, and learning dynamics; (3) it provides mathematical tools that uniformly explain the mechanisms of various empirical attribution methods and empirical adversarial-transferability-boosting methods; (4) it explains the extremely complex learning dynamics of a DNN by analyzing the two-phase dynamics of interaction complexity, which further reveals the internal mechanism of why and how the generalization power/adversarial sensitivity of a DNN changes during the learning process.

The cross-correlation of high-frequency ambient noise (>1 Hz) is usually interpreted as the empirical Green's function between two stations and used for imaging the near surface. However, high-frequency ambient noise mainly originates from human activities with nonuniform distributions, which may lead to spurious arrival in cross-correlation and bias the analysis of surface waves. Here, we develop an algorithm for improving high-frequency surface wave cross-correlation using an attention mechanism-based neural network, CCformer. The CCformer takes two-station cross-correlations of different time segments as input. Instead of directly producing an improved cross-correlation, the CCformer integrates the process of stacking individual cross-correlations to enhance its explainability. By identifying coherent information between each segment and generating stacking weights, the CCformer improves desired coherent signals and attenuates spurious and incoherent noises, ultimately resulting in a well-stacked cross-correlation. After training with a synthetic dataset of 200,000 labeled samples, the CCformer presents a good ability to improve the quality of stacked cross-correlation for a synthetic noise-added test dataset with dispersion, source distribution, and acquisition parameters different from the training dataset. The dispersion spectrum of the improved cross-correlation is more continuous than the results of linear stack and phase-weighted stack, and the spectral maxima agree with the theoretical dispersion curve. Moreover, a real dataset acquired from a test site also indicates the generalizability of CCformer for laterally varying media according to the symmetry of improved cross-correlation, dispersion spectrum maxima consistent with that of active data, and inversion results validated by known targets. Therefore, the proposed algorithm provides a practical solution for automatically extracting effective surface wave signals from high-frequency ambient noise.

This paper explains the generalization power of a deep neural network (DNN) from the perspective of interactions. Although there is no universally accepted definition of the concepts encoded by a DNN, the sparsity of interactions in a DNN has been proved, i.e., the output score of a DNN can be well explained by a small number of interactions between input variables. In this way, to some extent, we can consider such interactions as interactive concepts encoded by the DNN. Therefore, in this paper, we derive an analytic explanation of inconsistency of concepts of different complexities. This may shed new lights on using the generalization power of concepts to explain the generalization power of the entire DNN. Besides, we discover that the DNN with stronger generalization power usually learns simple concepts more quickly and encodes fewer complex concepts. We also discover the detouring dynamics of learning complex concepts, which explains both the high learning difficulty and the low generalization power of complex concepts. The code will be released when the paper is accepted.

Rhythmic auditory stimulation (RAS) has been shown to be beneficial for the gait initiation (GI) in Parkinson's disease (PD) patients with freezing of gait. However, the underlying neurophysiological mechanisms are still poorly understood. In this study, we utilized electroencephalography (EEG) and surface electromyography (sEMG) to investigate differences in neural and muscular activity during the gait initiation phase of 20 healthy participants, under conditions with and without RAS. We analyzed contingent negative variation (CNV) amplitude in EEG during gait initiation and the behaviorally relevant onset time of sEMG initiation, primarily from a time-domain analysis perspective. Additionally, we employed a two-tailed t-test to compare the CNV amplitude and sEMG onset time between the two conditions (with RAS vs. without RAS). The results revealed that CNV was induced in the middle pre-frontal, frontal, central, and temporal regions under both rhythmic and non-rhythmic auditory stimulation (Non_ RAS) conditions. Significant differences in CNV amplitude were observed in the temporal region between conditions with and without RAS, with higher CNV amplitudes observed under RAS conditions. Additionally, sEMG data indicated that the onset of gait was earlier in participants exposed to RAS.

Multifrequency ground penetrating radar (GPR) data fusion integrates complementary information from multiple single central frequency measurements into a composite radargram, broadening the spectral bandwidth of signals and improving interpretation efficiency and accuracy. Here, we develop an indicator-guided multifrequency GPR data fusion algorithm with the transformer network. Instead of generating the fusion result directly, we design the fusion network to integrate the fusion process of combining original multifrequency GPR data with the main idea of learning to understand the difference between different single central frequency data and then producing fusion weights, ultimately resulting in the fused GPR data. The indicator we used, which is the 1-D Laplacian operator gradient representing the importance of each central frequency data at different time windows, guides the network to preserve as much high-resolution information as possible in the overlapping area. The results of synthetic, experimental, and field data indicate that, compared with the recently developed long short-term memory network (LSTM)-based fusion algorithm, the proposed algorithm shows high efficiency and provides better fusion results that retain more high-resolution information from high-frequency data without losing deep signals from low-frequency data. Moreover, it presents a good generalization capability for datasets with a similar acquisition situation. Therefore, it provides an effective real-time multifrequency GPR fusion solution, especially for cases where a large amount of multifrequency GPR data measured under similar circumstances needs to be fused.

Seismic full-waveform inversion (FWI) is a powerful technique for high-resolution imaging of subsurface physical properties. However, it suffers from the possibility of falling into local minimum due to the inherent nonlinearity and ill-posedness. Recently, the data-driven deep learning approach has been used to solve ill-posed inverse problems, with the limitations of high data collection costs and poor model generalization capabilities. To alleviate these difficulties, we unroll the iterative optimization algorithm based on the augmented Lagrangian method into a layer-wise network architecture to solve seismic FWI, called ALFWI-Net. The ALFWI-Net decomposes the constrained optimization problem into three unconstrained subproblems. Correspondingly, the velocity model is updated by three alternating iterative formulations implemented by four modules in the network. One of the modules uses the Lagrange multiplier method to solve for the gradient of FWI, while the others correspond to the solution of the three subproblems. A soft-threshold-based convolutional neural network is used to learn the proximal operator in the implicit regularized optimization subproblem. Therefore, ALFWI-Net alleviates limitations in applicability since both the regularization function and parameters, step size and thresholds are automatically learned in the training process. Experiments were conducted on two geologic models, with the SEG salt model posing a challenge due to its limited data samples. Nevertheless, we successfully derived improved velocity models from seismic full-waveform recordings. Numerical experiments on two kinds of geological models demonstrated that ALFWI-Net outperforms classical FWI and data-driven methods in reconstruction accuracy, convergence speed, and out-of-distribution generalization.

Given the obstacle in accentuating the reconstruction accuracy for diagnostically significant tissues, most existing MRI reconstruction methods perform targeted reconstruction of the entire MR image without considering fine details, especially when dealing with highly under-sampled images. Therefore, a considerable volume of efforts has been directed towards surmounting this challenge, as evidenced by the emergence of numerous methods dedicated to preserving high-frequency content as well as fine textural details in the reconstructed image. In this case, exploring the merits associated with each method of mining high-frequency information and formulating a reasonable principle to maximize the joint utilization of these approaches will be a more effective solution to achieve accurate reconstruction. Specifically, this work constructs an innovative principle named Correlated and Multi-frequency Diffusion Model (CM-DM) for highly under-sampled MRI reconstruction. In essence, the rationale underlying the establishment of such principle lies not in assembling arbitrary models, but in pursuing the effective combinations and replacement of components. It also means that the novel principle focuses on forming a correlated and multi-frequency prior through different high-frequency operators in the diffusion process. Moreover, multi-frequency prior further constraints the noise term closer to the target distribution in the frequency domain, thereby making the diffusion process converge faster. Experimental results verify that the proposed method achieved superior reconstruction accuracy, with a notable enhancement of approximately 2dB in PSNR compared to state-of-the-art methods.

Compressive sensing theory have been proposed in the field of radar for target detection. The challenge of compressive sensing applied to passive bistatic radar lies in the high computational complexity aggravated by the transmitted signal dependent time-varying sparse model. So, we propose a transmitted-signal-free and time-invariant sparse model for passive radar based on orthogonal frequency division multiplexing waveforms. We first generate the sparse model by using the surveillance signal and pilot information only, and exploiting the sparsity of scene including only a few targets and clutter. Then, range-Doppler profile for target detection can be implemented based on our proposed sparse model. Finally, simulation and experimental results illustrate that our proposed sparse model has high detection performance.

Clutter rejection is a key technique for high-frequency passive radar (HFPR). To solve this problem, the traditional signal processing methods have been used, which mainly depend on prior information of the feature differences between target and clutter in time, space, or frequency domain. As a new attempt to deep-mine the clutter feature automatically and reject it by only data-driven processing, a novel clutter rejection method based on graph-relational mapping using a deep learning network is proposed in this letter. In this method, the clutter rejection problem is turned into an image-to-image translation problem between the range-Doppler (RD) spectrograms before and after clutter rejection. A deep-learning-enabled image translation network (CycleGAN) is exploited to learn from training data of RD spectrograms and to establish the mapping relationship. When processing clutter rejection tasks, the trained network can automatically extract clutter features without prior information and save manpower. The performance evaluations of the novel clutter rejection method are also investigated, and the experimental results confirm that the proposed method can effectively reject clutter in HFPR.

The clutter encountered in the ground-penetrating radar (GPR) system severely obscures the visibility of subsurface objects, especially in the case of overlapping target responses and clutter. In this letter, a novel self-supervised learning strategy with dual-network architecture and pseudolabels is proposed. First, the dual-network consists of two subnetworks: one is to simulate the low-rank part, and another simulates the sparse part. Second, the raw GPR data are decomposed as the sum of low-rank and sparse matrices by robust nonnegative matrix factorization (RNMF), termed two pseudolabels. Then, these pseudolabels guide the two subnetworks to accurately reconstruct the target response and clutter trace by trace, respectively. Results based on simulated data by gprMax and real datasets demonstrate that the proposed method is effective in separating target response from clutter and can achieve a similar effect as RNMF in less time without any prior information.

This paper proposes a method to disentangle and quantify interactions among words that are encoded inside a DNN for natural language processing. We construct a tree to encode salient interactions extracted by the DNN. Six metrics are proposed to analyze properties of interactions between constituents in a sentence. The interaction is defined based on Shapley values of words, which are considered as an unbiased estimation of word contributions to the network prediction. Our method is used to quantify word interactions encoded inside the BERT, ELMo, LSTM, CNN, and Transformer networks. Experimental results have provided a new perspective to understand these DNNs, and have demonstrated the effectiveness of our method.

This paper proposes a generic method to learn interpretable convolutional filters in a deep convolutional neural network (CNN) for object classification, where each interpretable filter encodes features of a specific object part. Our method does not require additional annotations of object parts or textures for supervision. Instead, we use the same training data as traditional CNNs. Our method automatically assigns each interpretable filter in a high conv-layer with an object part of a certain category during the learning process. Such explicit knowledge representations in conv-layers of the CNN help people clarify the logic encoded in the CNN, i.e., answering what patterns the CNN extracts from an input image and uses for prediction. We have tested our method using different benchmark CNNs with various architectures to demonstrate the broad applicability of our method. Experiments have shown that our interpretable filters are much more semantically meaningful than traditional filters.

Cognitive radio is a promising technology to improve spectral efficiency. However, communication security of a secondary network is limited by its transmit power and channel fading. In order to tackle this issue, by exploiting the high flexibility and the possibility of establishing line-of-sight links, a cognitive unmanned aerial vehicle (UAV) communication network is studied. The average secrecy rate of the secondary network is maximized by robustly optimizing the UAVs trajectory and transmit power. Our formulated problem takes into account practical imperfect location estimation. To solve the non-convex problem, an iterative suboptimal algorithm based on the Bernstein-type inequalities is presented. Our simulation results demonstrate that the proposed scheme can improve the secure communication performance significantly compared to a benchmark scheme based on fixed trajectory.

When observing from a spaceborne or unmanned airborne platform, aperture synthesis radiometric imaging (ASRI) is sometimes configured with an irregularly distributed array. In the previous study, the array factor forming (AFF) has been proposed to reconstruct the brightness temperature (BT) image of the observed scene. However, it is found that AFF is invalid when system noise is taken into account. In order to solve the problem, AFF with regularization is proposed in this letter. The reason why the conventional AFF becomes invalid is analyzed, and how AFF with regularization provides a stable solution is discussed. Numerical simulation and experimental results show that the BT image reconstructed by AFF with regularization is more accurate than that reconstructed by the conventional AFF, which demonstrates the validation of the method.

Cognitive radio is a promising technology to improve spectral efficiency. However, the secure performance of a secondary network achieved by using physical layer security techniques is limited by its transmit power and channel fading. In order to tackle this issue, a cognitive unmanned aerial vehicle (UAV) communication network is studied by exploiting the high flexibility of a UAV and the possibility of establishing line-of-sight links. The average secrecy rate of the secondary network is maximized by robustly optimizing the UAV's trajectory and transmit power. Our problem formulation takes into account two practical inaccurate location estimation cases, namely, the worst case and the outage-constrained case. In order to solve those challenging non-convex problems, an iterative algorithm based on S-Procedure is proposed for the worst case while an iterative algorithm based on Bernstein-type inequalities is proposed for the outage-constrained case. The proposed algorithms can obtain effective suboptimal solutions of the corresponding problems. Our simulation results demonstrate that the algorithm under the outage-constrained case can achieve a higher average secrecy rate with a low computational complexity compared to that of the algorithm under the worst case. Moreover, the proposed schemes can improve the secure communication performance significantly compared to other benchmark schemes.

Mirrored aperture synthesis (MAS) has been proposed to utilize a few antennas to provide high spatial resolution for atmospheric remote sensing. In order to verify the fundamentals of mirrored aperture synthesis (MAS) further, a prototype working at V band was developed in the past two years. In this paper, the prototype is briefly introduced, and then some indoor experiments and the experimental results for one-dimensional MAS based on the prototype are presented, mainly including the fringe pattern experiment for verifying the correlation output and the imaging experiment based on two point sources for evaluating the spatial resolution of MAS.

Because the principle of mirrored interferometric aperture synthesis (MIAS) is different from that of the conventional interferometric aperture synthesis, the antenna array for 1-D MIAS should be redesigned. And in order to get a precise estimation of the cosine visibilities, the maximum rank of the transfer matrix should be set as the key constraint condition of the array optimization model, but this has not been clearly presented before. In this letter, the maximum rank of the transfer matrix is discussed and proved by the mathematical induction method. When the position of each antenna in the array is an even multiple of 0.5, the value for the maximum rank is proven to be M - 2, and when the position of each antenna is an odd multiple of 0.5, the value for the maximum rank is proven to be M - 1, where M is the number of the spatial frequencies provided by the array. This conclusion is significant for the array design of 1-D MIAS.

In order to catch the iterated growth and evolution of the future mobile communications, this paper has proposed to study on a novel prediction model for radio propagation as well with its applications based on the radio propagation theory and the inverse theory. The prediction of radio propagation in a mobile network can be treated as an inverse problem. Instead of through the high-precision geometric modeling of wireless environments, this problem can be solved by an inversion of the measured data (under all priori constraints). So a complicated propagation prediction problem can be simplified to a system of large scale ill-condition equations, which can be solved by genetic algorithm appropriately. The effectiveness of the proposed method has been demonstrated using experiments under various radio environments in Guang Dong, China. It was shown that the prediction results were approximately consistent with independent checking samples. The advantages of the proposed strategies compared with existing approaches are well demonstrated.