Weaknesses: The absence of any explaining figures makes it hard for the reader to fully understand the underlying architecture of BPNNs. Specifically, it is not clear what the actual target of a BPNN acting on a particular factor graph is! Is it the partition function? Moreover, the intention of the Bethe Free Energy Layer remains obscure. In lines 121-125 you mention: 'When convergence to a fixed point is unnecessary, we can increase the flexibility [...] Additionally we define a Bethe free energy layer using two MLPs that take the trajectories of learned beliefs from each factor and variable as input and output scalars.'

Glass with good processability, chemical inertness, and optical transparency has been widely used in optical and aesthetic products, many of which require curve pro-files with high precision. To meet the increasingly tightened geometrical tolerances and fast product updating rates, the traditional approach of developing a thermoform-ing process through trials and errors can cause a large waste of time and resources and often end up with failure. Hence, there is a need to develop an efficient predictive model, replacing the costly simulations or experiments, to assist the design of preci-sion glass thermoforming. In this work, we report a dimensionless back-propagation neural network (BPNN) that can adequately predict the form errors and thus compen-sate for these errors in mold design to achieve precision glass molding. Based on the precision molds, also discussed is the issue of error magnification considering that cover glass for AR/VR glasses or smartphones, with extremely large scale of produc-tion, may require a lower level of mold machining accuracy. It is expected that this BPNN will also be implementable in the glass-manufacturing industry, i.e., trained using industrial data for precision mold designs.

Diabetes, resulting from inadequate insulin production or utilization, causes extensive harm to the body. Existing diagnostic methods are often invasive and come with drawbacks, such as cost constraints. Although there are machine learning models like Classwise k Nearest Neighbor (CkNN) and General Regression Neural Network (GRNN), they struggle with imbalanced data and result in under-performance. Leveraging advancements in sensor technology and machine learning, we propose a non-invasive diabetes diagnosis using a Back Propagation Neural Network (BPNN) with batch normalization, incorporating data re-sampling and normalization for class balancing. Our method addresses existing challenges such as limited performance associated with traditional machine learning. Experimental results on three datasets show significant improvements in overall accuracy, sensitivity, and specificity compared to traditional methods. Notably, we achieve accuracies of 89.81% in Pima diabetes dataset, 75.49% in CDC BRFSS2015 dataset, and 95.28% in Mesra Diabetes dataset. This underscores the potential of deep learning models for robust diabetes diagnosis. See project website https://steve-zeyu-zhang.github.io/DiabetesDiagnosis/

In recent years, machine learning (ML) has brought effective approaches and novel techniques to economic decision, investment forecasting, and risk management, etc., coping the variable and intricate nature of economic and financial environments. For the investment in stock market, this research introduces a pioneering quantitative fusion model combining stock timing and picking strategy by leveraging the Multivariate Gaussian-Hidden Markov Model (MGHMM) and Back Propagation Neural Network optimized by Particle Swarm (PSO-BPNN). After the information coefficients (IC) between fifty-two factors that have been winsorized, neutralized and standardized and the return of CSI 300 index are calculated, a given amount of factors that rank ahead are choose to be candidate factors heading for the input of PSO-BPNN after dimension reduction by Principal Component Analysis (PCA), followed by a certain amount of constituent stocks outputted. Subsequently, we conduct the prediction and trading on the basis of the screening stocks and stock market state outputted by MGHMM trained using inputting CSI 300 index data after Box-Cox transformation, bespeaking eximious performance during the period of past four years. Ultimately, some conventional forecast and trading methods are compared with our strategy in Chinese stock market. Our fusion strategy incorporating stock picking and timing presented in this article provide a innovative technique for financial analysis.