Inspired by neuronal diversity in the biological neural system, a plethora of studies proposed to design novel types of artificial neurons and introduce neuronal diversity into artificial neural networks. Recently proposed quadratic neuron, which replaces the inner-product operation in conventional neurons with a quadratic one, have achieved great success in many essential tasks. Despite the promising results of quadratic neurons, there is still an unresolved issue: Is the superior performance of quadratic networks simply due to the increased parameters or due to the intrinsic expressive capability? Without clarifying this issue, the performance of quadratic networks is always suspicious. Additionally, resolving this issue is reduced to finding killer applications of quadratic networks. In this paper, with theoretical and empirical studies, we show that quadratic networks enjoy parametric efficiency, thereby confirming that the superior performance of quadratic networks is due to the intrinsic expressive capability. This intrinsic expressive ability comes from that quadratic neurons can easily represent nonlinear interaction, while it is hard for conventional neurons. Theoretically, we derive the approximation efficiency of quadratic networks over conventional ones in terms of real space and manifolds. Moreover, from the perspective of the Barron space, we demonstrate that there exists a functional space whose functions can be approximated by quadratic networks in a dimension-free error, but the approximation error of conventional networks is dependent on dimensions. Empirically, experimental results on synthetic data, classic benchmarks, and real-world applications show that quadratic models broadly enjoy parametric efficiency, and the gain of efficiency depends on the task.

Accurate and reliable prediction of bearing remaining useful life (RUL) is crucial to the prognostics and health management of rotation machinery. Despite the rapid progress of data-driven methods, the generalizability of data-driven models remains an open issue to be addressed. In this article, we tackle this challenge by resolving the feature misalignment problem that arises in extracting features from the raw vibration signals. Toward this goal, we introduce a logarithmic cumulative transformation (LCT) operator consisting of cumulative, logarithmic, and another cumulative transformation for feature extraction. In addition, we propose a novel method to estimate the reliability associated with each RUL prediction by integrating a linear regression model and an auxiliary exponential model. The linear regression model rectifies bias from neural network's point predictions while the auxiliary exponential model fits the differential slopes of the linear models and generates the upper and lower bounds for building the reliability indicator. The proposed approach comprised of LCT, an attention GRU-based encoder–decoder network, and reliability evaluation is validated on the FEMETO-ST dataset. Computational results demonstrate the superior performance of the proposed approach several other state-of-the-art methods.

Truth and Privacy-preserving service are two key issues for data collection in Mobile Crowd Sensing (MCS). However, most of the existing data collection studies use CRH to calculate the truth value, which is difficult to guarantee the data accuracy. The proposed privacy-preserving service methods either neglect the truth-value computation or still adopt the CRH method. To solve the challenge, we propose a Reputation and Privacy-Preserving Service based Truth Data Collection (RPPS-TDC) scheme to achieve the privacy-preserving accurate data collection for MCS. RPPS-TDC scheme consists of two steps: worker trust calculation and reputation-based truth value calculation. Firstly, data requester performs the initial weights calculation on the received data using DBCRH method. Secondly, reputation center uses the initial weights to update the reputation, which is based on the trustworthy worker inference. Finally, the workers are reweighted according to their reputation. We select workers based on trust_MaxHeap, thus obtaining more accurate data. At the same time, we give workers payments based on their trust weights. All the above operations are completed under data encryption, ensuring that only the data requesters have access to the workers’ submitted data. The platform consists of mining nodes, and reputation center resides on the blockchain, thus achieving distributed computing which overcomes the shortcomings of the traditional MCS system. Extensive experiments demonstrate that RPPS-TDC is effective and outperforms previous strategies in two key performance metrics: data accuracy and compensation rationality allocation.