Abstract Recentneuro-symbolic approaches have successfully extracted symbolic rule-sets from Convolutional Neural Network-based models to enhance interpretability. However, applying similar techniques to Vision Transformers (ViTs) remains challenging due to their lack of modular concept detectors and reliance on global self-attention mechanisms. We propose a framework for symbolic rule extraction from ViTs by introducing a sparse concept layer inspired by Sparse Autoencoders (SAEs). This linear layer operates on attention-weighted patch representations and learns a disentangled, binarized representation in which individual neurons activate for high-level visual concepts. To encourage interpretability, we apply a combination of L1 sparsity, entropy minimization, and supervised contrastive loss. These binarized concept activations are used as input to the FOLD-SE-M algorithm, which generates a rule-set in the form of a logic program. Our method achieves a better classification accuracy than the standard ViT while enabling symbolic reasoning. Crucially, the extracted rule-set is not merely post-hoc but acts as a logic-based decision layer that operates directly on the sparse concept representations. The resulting programs are concise and semantically meaningful. This work is the first to extract executable logic programs from ViTs using sparse symbolic representations, providing a step forward in interpretable and verifiable neuro-symbolic AI.

Deep learning models such as CNNs have surpassed human performance in computer vision tasks such as image classi- fication. However, despite their sophistication, these models lack interpretability which can lead to biased outcomes re- flecting existing prejudices in the data. We aim to make pre- dictions made by a CNN interpretable. Hence, we present a novel framework called NeSyFOLD to create a neurosym- bolic (NeSy) model for image classification tasks. The model is a CNN with all layers following the last convolutional layer replaced by a stratified answer set program (ASP) derived from the last layer kernels. The answer set program can be viewed as a rule-set, wherein the truth value of each pred- icate depends on the activation of the corresponding kernel in the CNN. The rule-set serves as a global explanation for the model and is interpretable. We also use our NeSyFOLD framework with a CNN that is trained using a sparse kernel learning technique called Elite BackProp (EBP). This leads to a significant reduction in rule-set size without compromising accuracy or fidelity thus improving scalability of the NeSy model and interpretability of its rule-set. Evaluation is done on datasets with varied complexity and sizes. We also pro- pose a novel algorithm for labelling the predicates in the rule- set with meaningful semantic concept(s) learnt by the CNN. We evaluate the performance of our “semantic labelling algo- rithm” to quantify the efficacy of the semantic labelling for both the NeSy model and the NeSy-EBP model.

Abstract Recent efforts in interpreting convolutional neural networks (CNNs) focus on translating the activation of CNN filters into a stratified Answer Set Program (ASP) rule-sets. The CNN filters are known to capture high-level image concepts, thus the predicates in the rule-set are mapped to the concept that their corresponding filter represents. Hence, the rule-set exemplifies the decision-making process of the CNN w.r.t the concepts that it learns for any image classification task. These rule-sets help understand the biases in CNNs, although correcting the biases remains a challenge. We introduce a neurosymbolic framework called NeSyBiCor for bias correction in a trained CNN. Given symbolic concepts, as ASP constraints, that the CNN is biased toward, we convert the concepts to their corresponding vector representations. Then, the CNN is retrained using our novel semantic similarity loss that pushes the filters away from (or toward) learning the desired/undesired concepts. The final ASP rule-set obtained after retraining, satisfies the constraints to a high degree, thus showing the revision in the knowledge of the CNN. We demonstrate that our NeSyBiCor framework successfully corrects the biases of CNNs trained with subsets of classes from the Places dataset while sacrificing minimal accuracy and improving interpretability.