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Classifying hyperspectral images (HSIs) is a complex task in remote sensing due to the high-dimensional nature and volume of data involved. To address these challenges, we propose the Spectral-Spatial non-Linear Model, a novel framework that significantly reduces data volume while enhancing classification accuracy. Our model employs a bidirectional reversed convolutional neural network (CNN) to efficiently extract spectral features, complemented by a specialized block for spatial feature analysis. This hybrid approach leverages the operational efficiency of CNNs and incorporates dynamic feature extraction inspired by attention mechanisms, optimizing performance without the high computational demands typically associated with transformer-based models. The SS non-Linear Model is designed to process hyperspectral data bidirectionally, achieving notable classification and efficiency improvements by fusing spectral and spatial features effectively. This approach yields superior classification accuracy compared to existing benchmarks while maintaining computational efficiency, making it suitable for resource-constrained environments. We validate the SS non-Linear Model on three widely recognized datasets, Houston 2013, Indian Pines, and Pavia University, demonstrating its ability to outperform current state-of-the-art models in HSI classification and efficiency. This work highlights the innovative methodology of the SS non-Linear Model and its practical benefits for remote sensing applications, where both data efficiency and classification accuracy are critical. For further details, please refer to our code repository on GitHub: HSILinearModel.