Early diagnosis of Alzheimer’s Disease (AD) holds key in delaying cognitive decline and managing the progression of dementia. The Mini-Mental State Examination (MMSE) serves as a valuable tool for evaluating cognitive impairment, aiding in the identification of AD severity and early-stage diagnosis. Traditionally, prediction models aiming to predict MMSE scores from speech have utilized the mean squared error (MSE) as the loss function. However, MSE tends to bias predictions towards the average, which limits its ability to discriminate AD severity effectively. To address this limitation, we propose a novel Weighted MSE-CE loss function aimed at improving AD discrimination by accurately predicting MMSE scores. It reaches the goal through the integration of cross entropy (CE) into mean squared error (MSE), leveraging the Bernoulli penalty and distance-based weights. Furthermore, our approach relies solely on language-agnostic acoustic features, eliminating the requirement for transcription. Consequently, it gains the potential to be applied to individuals speaking various languages. Experimental results on the ADReSSo dataset demonstrate that our method reduces the RMSE to 4.55, outperforming other acoustic-based approaches. Additionally, our predictions achieved an impressive 77.46% accuracy in AD detection, highlighting its effectiveness in assessing AD severity.