3D Weighted Geometric Graph Neural Networks for Sheep Facial Pain Assessment

Automated pain recognition from facial expression could make continuous welfare assessment practical in sheep, but adoption depends on trust: a stockperson cannot act on a score that arrives without justification. We ground a model in the Sheep Pain Facial Expression Scale (SPFES) by letting each detected facial region attend over text embeddings of the clinical descriptors and then test whether the resulting explanations mean anything. They do not. Ablating an entire descriptor changes the predicted logit by about $10^{-4}$, and the most-attended cue agrees with the predicted pain level in only $32.6\%$ of regions, although the attention maps, the learned gate, and the generated text all proposed otherwise. We therefore remove the appearance bypass with a concept bottleneck whose classifier reads only SPFES concept scores, supervised by per-region state annotations that image-level pipelines discard. This costs $0.05$--$0.10$ in Cohen's $κ$ but yields concepts that are demonstrably learned: minority pain-indicating states are recovered at $3.5$--$8.3\times$ their base rates, and the ear and eye severity orderings emerge without severity supervision. Removing the supervision alone leaves $κ$ unchanged while concept accuracy falls to $0.109$, showing that architectural necessity does not imply semantic validity. We also show that pooled concept accuracy is misleading under clinical imbalance and provide a cross-validated, protocol-matched benchmark of seven methods on this dataset.

Graph neural networks face two fundamental challenges rooted in the linear structure of Euclidean vector spaces: (1) Current architectures represent geometry through vectors (directions, gradients), yet many tasks require matrix-valued representations that capture relationships between directions-such as how atomic orientations covary in a molecule. These second-order representations are naturally captured by points on the symmetric positive definite matrices (SPD) manifold; (2) Standard message passing applies shared transformations across edges. Sheaf neural networks address this via edge-specific transformations, but existing formulations remain confined to vector spaces and therefore cannot propagate matrix-valued features. We address both challenges by developing the first sheaf neural network operates natively on the SPD manifold. Our key insight is that the SPD manifold admits a Lie group structure, enabling well-posed analogs of sheaf operators without projecting to Euclidean space. Theoretically, we prove that SPD-valued sheaves are strictly more expressive than Euclidean sheaves: they admit consistent configurations (global sections) that vector-valued sheaves cannot represent, directly translating to richer learned representations. Empirically, our sheaf convolution transforms effectively rank-1 directional inputs into full-rank matrices encoding local geometric structure. Our dual-stream architecture achieves SOTA on 6/7 MoleculeNet benchmarks, with the sheaf framework providing consistent depth robustness.

Automatic pain assessment from facial video remains challenging due to the spatial heterogeneity of pain-related facial cues. This study proposes ReFace, a spatial reorganization pipeline that divides facial input into four spatial quadrants before tokenization, rather than processing the entire face as a single region. Evaluated on the AI4Pain dataset, the proposed approach achieves $56.00\%$ accuracy on the test set using video only, achieving the highest reported accuracy under the fixed AI4Pain benchmark protocol among the compared methods. Notably, the four-quadrant configuration processes the same total pixel budget as the full-face input, yet achieves higher accuracy, suggesting that spatial reorganization can improve performance under the proposed tokenization design. A single quadrant region, processing just one quarter of those pixels, remains competitive at a fraction of the computational cost.