Neuro-Geometric Graph Transformers with Differentiable Radiographic Geometry for Spinal X-Ray Image Analysis.

Radiographic imaging remains a cornerstone of diagnostic practice. However, accurate interpretation faces challenges from subtle visual signatures, anatomical variability, and inter-observer inconsistency. Conventional deep learning approaches, such as convolutional neural networks and vision transformers, deliver strong predictive performance but often lack anatomical grounding and interpretability, limiting their trustworthiness in imaging applications. To address these challenges, we present SpineNeuroSym, a neuro-geometric imaging framework that unifies geometry-aware learning and symbolic reasoning for explainable medical image analysis. The framework integrates weakly supervised keypoint and region-of-interest discovery, a dual-stream graph-transformer backbone, and a Differentiable Radiographic Geometry Module (dRGM) that computes clinically relevant indices (e.g., slip ratio, disc asymmetry, sacroiliac spacing, and curvature measures). A Neuro-Symbolic Constraint Layer (NSCL) enforces monotonic logic in image-derived predictions, while a Counterfactual Geometry Diffusion (CGD) module generates rare imaging phenotypes and provides diagnostic auditing through counterfactual validation. Evaluated on a comprehensive dataset of 1613 spinal radiographs from Sunpasitthiprasong Hospital encompassing six diagnostic categories-spondylolisthesis (