Concept Bottleneck Models (CBMs), which break down the reasoning process into the input-to-concept mapping and the concept-to-label prediction, have garnered significant attention due to their remarkable interpretability achieved by the interpretable concept bottleneck. However, despite the transparency of the concept-to-label prediction, the mapping from the input to the intermediate concept remains a black box, giving rise to concerns about the trustworthiness of the learned concepts (i.e., these concepts may be predicted based on spurious cues). The issue of concept untrustworthiness greatly hampers the interpretability of CBMs, thereby hindering their further advancement. To conduct a comprehensive analysis on this issue, in this study we establish a benchmark to assess the trustworthiness of concepts in CBMs. A pioneering metric, referred to as concept trustworthiness score, is proposed to gauge whether the concepts are derived from relevant regions. Additionally, an enhanced CBM is introduced, enabling concept predictions to be made specifically from distinct parts of the feature map, thereby facilitating the exploration of their related regions. Besides, we introduce three modules, namely the cross-layer alignment (CLA) module, the cross-image alignment (CIA) module, and the prediction alignment (PA) module, to further enhance the concept trustworthiness within the elaborated CBM. The experiments on five datasets across ten architectures demonstrate that without using any concept localization annotations during training, our model improves the concept trustworthiness by a large margin, meanwhile achieving superior accuracy to the state-of-the-arts. Our code is available at https://github.com/hqhQAQ/ProtoCBM.

Sensor placement plays an important role in terrain deformation monitoring systems and has an essential effect on data collection. The difficulty of sensor placement entails obtaining the most adequate and reliable information with the fewest number of sensors. Most sensor placement schemes are currently based on randomized non-uniform sampling and probability statistics, such as structural modality and optimization methods, which are difficult to directly apply due to the randomness and spatial heterogeneity of terrain deformation. In this study, the placement conditions of two-dimensional non-uniform sampling with equal arc length were deduced for underwater terrain deformation monitoring based on the MEMS accelerometer network. In order to completely reconstruct the underwater terrain, the arc length interval of the sensors should be less than $\frac{1}{2\mathsf{\Omega }}$ ($\mathsf{\Omega }$ is the maximum frequency of the detected terrain). The maximum MRE and maximum RMSE were both less than seven percent in a terrain deformation monitoring experiment and a water tank test. The research results help technicians apply contact sensor arrays for underwater terrain monitoring.

Concept Bottleneck Models (CBMs), which break down the reasoning process into the input-to-concept mapping and the concept-to-label prediction, have garnered significant attention due to their remarkable interpretability achieved by the interpretable concept bottleneck. However, despite the transparency of the concept-to-label prediction, the mapping from the input to the intermediate concept remains a black box, giving rise to concerns about the trustworthiness of the learned concepts (i.e., these concepts may be predicted based on spurious cues). The issue of concept untrustworthiness greatly hampers the interpretability of CBMs, thereby hindering their further advancement. To conduct a comprehensive analysis on this issue, in this study we establish a benchmark to assess the trustworthiness of concepts in CBMs. A pioneering metric, referred to as concept trustworthiness score, is proposed to gauge whether the concepts are derived from relevant regions. Additionally, an enhanced CBM is introduced, enabling concept predictions to be made specifically from distinct parts of the feature map, thereby facilitating the exploration of their related regions. Besides, we introduce three modules, namely the cross-layer alignment (CLA) module, the cross-image alignment (CIA) module, and the prediction alignment (PA) module, to further enhance the concept trustworthiness within the elaborated CBM. The experiments on five datasets across ten architectures demonstrate that without using any concept localization annotations during training, our model improves the concept trustworthiness by a large margin, meanwhile achieving superior accuracy to the state-of-the-arts. Our code is available at https://github.com/hqhQAQ/ProtoCBM.