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Regional Adaptive Hierarchical Transform (RAHT) is an effective point cloud attribute compression (PCAC) method. However, its application in deep learning lacks research. This paper proposes an end-to-end RAHT framework for lossy PCAC based on the sparse tensor, called DeepRAHT. The RAHT transform is performed within the end-to-end reconstruction process, without requiring manual RAHT for pre-processing. We also introduce the predictive RAHT to reduce bitrates and design a learning-based prediction model to enhance the performance. Moreover, we devise a bitrate proxy that applies run-length coding to entropy coding, achieving seamless variable-rate coding and improving the robustness. DeepRAHT is a reversible and distortion-controllable framework, ensuring its lower bound performance and offering significant application potential. The experiments demonstrate that DeepRAHT is a high-performance, faster, and more robust framework than the baseline solutions.