Neuro-Symbolic Artificial Intelligence: A Task-Directed Survey in the Black-Box Models Era

Neuro-Symbolic (NeSy) AI has recently emerged as a novel paradigm to enable trustworthy AI, aiming at integrating sub-symbolic neural perception with grounded symbolic reasoning. The neuro-symbolic integration process that characterizes these models has been proven beneficial to achieve more transparent, explainable and efficient AI systems. Meanwhile, their properties under adversarial settings have been overlooked being frequently deemed robust-by-design. However, the neural-symbolic integration process they leverage constitutes an additional layer of complexity that may provide an attack entry-point. Therefore, in this paper, we claim that an in-depth investigation of the adversarial robustness of NeSy models is necessary and provide the first systematic evaluation of backdoor attacks against NeSy. To this end, we compare the most popular NeSy framework, namely DeepProbLog, against baseline neural networks across a total of eight backdoor settings and four reasoning tasks. Our experimental results show that while NeSy models are indeed more robust than their neural counterpart on average, their robustness vastly depend on the strictness of the reasoning process being enforced and its compatibility with the chosen adversarial target. The source code to reproduce our experiments is made available at https://github.com/marcoantoniocorallo/NeSy-Backdoor.

Neurosymbolic (NeSy) models integrate neural networks and symbolic reasoning for robust and interpretable AI. State-of-the-art NeSy models require that the symbolic component is expressed in a differentiable way, often complicating the use of approximate inference. We propose EM-NeSy which casts probabilistic NeSy learning as an instance of the Expectation-Maximization (EM) algorithm. In the expectation step, we compute the posterior over the neurally predicted symbols conditioned on the label via probabilistic inference. In the maximization step, we update the neural parameters based on this posterior using gradient descent only through the neural component. This formulation unlocks the full potential of the EM algorithm for NeSy learning. It allows NeSy to extend naturally to approximate reasoning without any additional modifications or differentiability requirements of the symbolic component. Furthermore, it recovers the standard end-to-end gradient-based NeSy setting under exact inference. Our experimental results demonstrate the scalability and computational efficiency of EM-NeSy.

Neuro-Symbolic (NeSy) predictors incorporate prior knowledge into the prediction process of neural networks, ensuring that outputs satisfy specified constraints, making them particularly suitable for high-stakes applications where compliance with domain knowledge is essential. A key bottleneck in this paradigm is the acquisition of symbolic constraints: encoding domain knowledge into logical formulas remains a manual and expert-intensive process. In this work, we investigate the extent to which auto-formalization via LLMs can systematically translate textual knowledge into symbolic knowledge that can be plugged into NeSy predictors. To this end, we introduce auto-nesy-bench, a new benchmark for evaluating constraint formalization and its impact on downstream accuracy of NeSy predictors. Through an extensive evaluation across several domains, we find that LLMs can formalize constraints to a meaningful extent, generating formulas that are often similar to those provided by human experts. Moreover, when the generated formulas are syntactically valid, they can lead to high-quality downstream predictions. The code and benchmark are available at https://unitn-sml.github.io/auto-nesy-bench/.