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Neonatal mortality remains a critical global challenge, particularly in resource-limited settings with restricted access to advanced diagnostic tools. Early detection of life-threatening conditions like Sepsis and Respiratory Distress Syndrome (RDS), which significantly contribute to neonatal deaths, is crucial for timely interventions and improved survival rates. This study investigates the use of newborn cry sounds, specifically the expiratory segments (the most informative parts of cry signals) as non-invasive biomarkers for early disease diagnosis. We utilized an expanded and balanced cry dataset, applying Self-Supervised Learning (SSL) models—wav2vec 2.0, WavLM, and HuBERT—to extract feature representations directly from raw cry audio signals. This eliminates the need for manual feature extraction while effectively capturing complex patterns associated with sepsis and RDS. A classifier consisting of a single fully connected layer was placed on top of the SSL models to classify newborns into Healthy, Sepsis, or RDS groups. We fine-tuned the SSL models and classifiers by optimizing hyperparameters using two learning rate strategies: linear and annealing. Results demonstrate that the annealing strategy consistently outperformed the linear strategy, with wav2vec 2.0 achieving the highest accuracy of approximately 90% (89.76%). These findings highlight the potential of integrating this method into Newborn Cry Diagnosis Systems (NCDSs). Such systems could assist medical staff in identifying critically ill newborns, prioritizing care, and improving neonatal outcomes through timely interventions. Full article