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

## TL;DR

This paper introduces SpineNeuroSym, a new framework for spinal X-ray analysis that combines geometry-aware learning and symbolic reasoning to improve accuracy and explainability in medical imaging.

## Contribution

The novel contribution is the integration of a differentiable radiographic geometry module and neuro-symbolic constraints for interpretable spinal X-ray analysis.

## Key findings

- SpineNeuroSym achieved 89.4% classification accuracy on a dataset of 1613 spinal radiographs.
- The framework outperformed eight state-of-the-art imaging baselines in classification metrics.
- The model computes clinically relevant indices like slip ratio and disc asymmetry for interpretable predictions.

## Abstract

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 (n = 496), infection (n = 322), spondyloarthropathy (n = 275), normal cervical (n = 192), normal thoracic (n = 70), and normal lumbar spine (n = 258)—SpineNeuroSym achieved 89.4% classification accuracy, a macro-F1 of 0.872, and an AUROC of 0.941, outperforming eight state-of-the-art imaging baselines. These results highlight how integrating neuro-geometric modeling, symbolic constraints, and counterfactual validation advances explainable, trustworthy, and reproducible medical imaging AI, establishing a pathway toward transparent image analysis systems.