# Neuro-symbolic framework

Automatic glaucoma screening degrades when a model moves to another hospital and camera; a neuro-symbolic framework combines anatomical graph reasoning with differentiable fuzzy clinical rules in one network, trained on 9,100 fundus images drawn from a corpus of 12,619 images across eight datasets in eight countries and tested on 485 fully held-out RIM-ONE images from a different Spanish hospital and camera. On the in-distribution test set, EfficientNet-B4 with a graph attention network reaches an AUC of 0.9612 (95% CI 0.951–0.972) versus 0.9472 for EfficientNet-B4 alone, yet the combined full model scores 0.6155 cross-hospital, 8.1 points below the baseline.

Automatic glaucoma screening degrades when a model moves to another hospital and camera; a neuro-symbolic framework combines anatomical graph reasoning with differentiable fuzzy clinical rules in one network, trained on 9,100 fundus images drawn from a corpus of 12,619 images across eight datasets in eight countries and tested on 485 fully held-out RIM-ONE images from a different Spanish hospital and camera. On the in-distribution test set, EfficientNet-B4 with a graph attention network reaches an AUC of 0.9612 (95% CI 0.951–0.972) versus 0.9472 for EfficientNet-B4 alone, yet the combined full model scores 0.6155 cross-hospital, 8.1 points below the baseline.

SymAnt merges a scene graph and a knowledge graph into one joint graph and uses the symbolic context found by graph search as the starting point for iterative decoding, so it can predict long action sequences from very short observation windows. In the short-observation settings of Breakfast and 50 Salads, its mean accuracy over classes exceeds the neuro-symbolic baseline NeSCA and several large-model baselines; on EPIC-KITCHENS, the 3M-parameter model performs comparably to fine-tuned models with billions of parameters. Because predictions are anchored in an editable graph, users can add or remove nodes at inference time to change predictions without retraining.

SymAnt merges a scene graph and a knowledge graph into one joint graph and uses the symbolic context found by graph search as the starting point for iterative decoding, so it can predict long action sequences from very short observation windows. In the short-observation settings of Breakfast and 50 Salads, its mean accuracy over classes exceeds the neuro-symbolic baseline NeSCA and several large-model baselines; on EPIC-KITCHENS, the 3M-parameter model performs comparably to fine-tuned models with billions of parameters. Because predictions are anchored in an editable graph, users can add or remove nodes at inference time to change predictions without retraining.

The work proposes Law&Order, a neuro-symbolic framework that combines large language model synthesis with cell-level verification and iterative localized error repair using human-written OpenTaxSolver tax returns to automatically formalize tax forms and instructions into executable symbolic programs, establishing structural correspondence aligning legal and symbolic components such as cells and schedules and denotational correspondence requiring symbolic components to implement the computations specified by their legal counterparts; evaluated on independently authored, held-out TaxCalcBench returns never exposed during generation or repair, the most advanced LLM achieves only 66% accuracy while Law&Order achieves 100% cell-level and form-level accuracy on 51 held-out returns.

The work proposes Law&Order, a neuro-symbolic framework that combines large language model synthesis with cell-level verification and iterative localized error repair using human-written OpenTaxSolver tax returns to automatically formalize tax forms and instructions into executable symbolic programs, establishing structural correspondence aligning legal and symbolic components such as cells and schedules and denotational correspondence requiring symbolic components to implement the computations specified by their legal counterparts; evaluated on independently authored, held-out TaxCalcBench returns never exposed during generation or repair, the most advanced LLM achieves only 66% accuracy while Law&Order achieves 100% cell-level and form-level accuracy on 51 held-out returns.