Lipschitzness Effect of a Loss Function on Generalization Performance of Deep Neural Networks Trained by Adam and AdamW Optimizers

The generalization performance of deep neural networks with regard to the optimization algorithm is one of the major concerns in machine learning. This performance can be affected by various factors. In this paper, we theoretically prove that the Lipschitz constant of a loss function is an important factor to diminish the generalization error of the output model obtained by Adam or AdamW. The results can be used as a guideline for choosing the loss function when the optimization algorithm is Adam or AdamW. In addition, to evaluate the theoretical bound in a practical setting, we choose the human age estimation problem in computer vision. For assessing the generalization better, the training and test datasets are drawn from different distributions. Our experimental evaluation shows that the loss function with lower Lipschitz constant and maximum value improves the generalization of the model trained by Adam or AdamW.Comment: 13 pages, 6 figures, 3 table

Linkage of modules over Cohen-Macaulay rings

Inspired by the works in linkage theory of ideals, the concept of sliding depth of extension modules is defined to prove the Cohen-Macaulyness of linked module if the base ring is merely Cohen-Macaulay. Some relations between this new condition and other module-theory conditions such as G-dimension and sequentially Cohen-Macaulay are established. By the way several already known theorems in linkage theory are improved or recovered by new approaches.Comment: 12 Page

A novel AI-based approach for modelling the fate, transportation and prediction of chromium in rivers and agricultural crops: A case study in Iran

Chromium (Cr) pollution caused by the discharge of industrial wastewater into rivers poses a significant threat to the environment, aquatic and human life, as well as agricultural crops irrigated by these rivers. This paper employs artificial intelligence (AI) to introduce a new framework for modeling the fate, transport, and estimation of Cr from its point of discharge into the river until it is absorbed by agricultural products. The framework is demonstrated through its application to the case study River, which serves as the primary water resource for tomato production irrigation in Mashhad city, Iran. Measurements of Cr concentration are taken at three different river depths and in tomato leaves from agricultural lands irrigated by the river, allowing for the identification of bioaccumulation effects. By employing boundary conditions and smart algorithms, various aspects of control systems are evaluated. The concentration of Cr in crops exhibits an accumulative trend, reaching up to 1.29 µg/g by the time of harvest. Using data collected from the case study and exploring different scenarios, AI models are developed to estimate the Cr concentration in tomato leaves. The tested AI models include linear regression (LR), neural network (NN) classifier, and NN regressor, yielding goodness-of-fit values (R2) of 0.931, 0.874, and 0.946, respectively. These results indicate that the NN regressor is the most accurate model, followed by the LR, for estimating Cr levels in tomato leaves

One-step hydrothermal synthesis of a green NiCo-LDHs-rGO composite for the treatment of lead ion in aqueous solutions

In this study,, we have synthesised a microspherical nickel-cobalt-layered double hydroxides-reduced graphene oxide composite (NiCo-LDHs-rGO) through a one-step hydrothermal method. We subsequently used this composite as an adsorbent to remove Pb2+ from aqueous solutions. The instruments used for the characterisation of adsorbent included Fourier Transform Infrared Spectrophotometry (FT-IR), Field Emission Scanning Electron Microscopy (FESEM), Mapping Elemental Analysis, Electron Dispersive X-Ray spectroscopy (EDX), X-Ray Diffraction Analysis (XRD) and Brunauer-Emmett-Teller (BET)analysis. We conducted a series of experiments to investigate the factors affecting the adsorption of Pb2+ ions in batch mode such as solution pH, adsorbent dosage, contact time, competing ion and regeneration by NiCo-LDHs-rGO. Under optimised conditions determined using the Taguchi method (pH = 5.0, adsorbent dosage = 20 mg and contact time = 30 min), the best removal rate of 99.7% was achieved for 100 mg L-1 of Pb2+. According to the results, NiCo-LDHs-rGO exhibited a high preference for Pb2+ over Cu2+, Zn2+ and Cd2+. This adsorbent was regenerated for several cycles (using 0.01 M HCl) with no significant deterioration in performance. The analyses of the adsorption isotherm models revealed that the adsorption of Pb2+ followed Freundlich isotherm with a maximum adsorption capacity of 200 mg g-1. The kinetic data also confirmed that pseudo second order kinetic equation is the most accurate model for predicting the adsorption kinetics. Furthermore, the Simulink modelling illustrated that the adsorption kinetics of Pb2+ onto NiCo-LDHs-rGO could be accurately represented in a continuous stirred-tank reactor. Finally, dual interactions of the effective parameters can be modelled by polynomial equations in MATLAB, and according to the Taguchi model, pH emerged as the most influential factor among all the parameters

A novel smart framework for optimal design of green roofs in buildings conforming with energy conservation and thermal comfort

The rise in greenhouse gas emissions in cities and the excessive consumption of fossil energy resources has made the development of green spaces, such as green roofs, an increasingly important focus in urban areas. This study proposes a novel smart energy-comfort system for green roofs in housing estates that utilises integrated machine learning (ML), DesignBuilder (DB) software and Taguchi design computations for optimising green roof design and operation in buildings. The optimisation process maximises energy conservation and thermal comfort of the green roof buildings for effective parameters of green roofs including Leaf Area Index (P1), leaf reflectivity (P2), leaf emissivity (P3), and stomatal resistance (P4). The optimal solutions can result in a 12.8% increase in comfort hours and a 14% reduction in energy consumption compared to the base case. The ML analysis revealed that the adaptive network-based fuzzy inference system is the most appropriate method for predicting Energy-Comfort functions based on effective parameters, with a correlation coefficient greater than 97%. This novel smart framework for the optimal design of green roofs in buildings offers an innovative approach to achieving energy conservation and thermal comfort in urban areas

Developing a smart and clean technology for bioremediation of antibiotic contamination in arable lands

This study presents a smart technological framework to efficiently remove azithromycin from natural soil resources using bioremediation techniques. The framework consists of several modules, each with different models such as Penicillium Simplicissimum (PS) bioactivity, soft computing models, statistical optimisation, Machine Learning (ML) algorithms, and Decision Tree (DT) control system based on Removal Percentage (RP). The first module involves designing experiments using a literature review and the Taguchi Orthogonal design method for cultural conditions. The RP is predicted as a function of cultural parameters using Response Surface Methodology (RSM) and three ML algorithms: Instance-Based K (IBK), KStar, and Locally Weighted Learning (LWL). The sensitivity analysis shows that pH is the most important factor among all parameters, including pH, Aeration Intensity (AI), Temperature, Microbial/Food (M/F) ratio, and Retention Time (RT), with a p-value of < 0.0001. AI is the next most significant parameter, also with a p-value of < 0.0001. The optimal biological conditions for removing azithromycin from soil resources are a temperature of 32°C, pH of 5.5, M/F ratio of 1.59 mg/g, and AI of 8.59 m3/h. During the 100-day bioremediation process, RP was found to be an insignificant factor for more than 25 days, which simplifies the conditions. Among the ML algorithms, the IBK model provided the most accurate prediction of RT, with a correlation coefficient of over 95%