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Brain tumors often require treatment and multiple biopsies. They are the third most common cancer among young adults in both incidence and mortality. The expression of the O6-methylguanine-DNA methyltransferase (MGMT) gene plays an important role in predicting tumor behavior. It affects how patients respond to chemotherapy and may reduce the need for invasive procedures. Machine learning can help make accurate medical predictions, but it requires large and diverse patient datasets. These datasets are difficult to access due to privacy and legal restrictions. This article proposes a Federated Learning (FL) framework to address these challenges. FL allows different institutions to train a shared model without exchanging raw data. A hybrid deep learning model combining recurrent neural networks (RNNs) and convolutional neural networks (CNNs) is developed to analyze magnetic resonance imaging (MRI) scans from the BraTS 2021 dataset. The model aims to detect glioblastoma and predict MGMT gene expression. Two swarm intelligence algorithms, the Bayesian Search Optimization Algorithm and the Sparrow Search Optimization Algorithm, are used to optimize the model’s hyperparameters. The FL system was tested across ten universities. It performed similarly to models trained on centralized data. The proposed model, BrainGeneDeepNet, achieved high performance: 0.9758 accuracy, 0.0769 loss, 0.9980 AUC, 0.9770 recall, and 0.9782 precision. These results show that federated learning is a secure and effective approach for medical imaging and biomarker prediction.