The proposed algorithm is a differentiable approximate truncation robust computed tomography (ATRACT) reconstruction algorithm for end-to-end trainable cone-beam CT reconstruction, offering enhanced robustness to truncated geometries and a significant reduction of truncation artifacts. The proposed method utilizes known operator learning to map the analytical reconstruction into a neural network. This approach preserves physical consistency while enabling data-driven optimization of redundancy weights under the 180◦ limited-angle condition. The experimental results demonstrate that the proposed frame work surpasses the Parker-weighted analytical reconstruction, achieving a 1.5% higher SSIM and a 1.1% lower MSE. This outcome validates the accuracy and efficacy of the analytical-to-neural mapping procedure. The differentiable formulation integrates the interpretability of analytical reconstruction with the adaptability of learning-based methods, thereby providing a robust and extensible foundation for imaging applications under truncated geometries.