Neurosymbolic systems promise to combine deep neural network's (DNN) processing of raw sensor inputs with few-shot performance of symbolic artificial intelligence. Two-stage approaches explicitly decouple DNN based perception from subsequent rule based reasoning. This avoids optimization and interpretability issues of end to end differentiable approaches, but requires costly labels for the perception output. This paper introduces an efficient weak supervision scheme for the perception stage to ground its output symbols for logical induction in object-centric reasoning tasks. It combines a slot-based architecture for object-centricity with a Variational Autoencoder (VAE) for self-supervision, competing with concept guidance on latent dimensions for human interpretable grounding. The resulting predictions are translated into symbolic background knowledge for reasoning frameworks, such as Inductive Logic Programming (ILP), Decision Trees, and Bayesian Networks. Our extensive empirical evaluation on synthetic and real world datasets shows that our approach can discover complex, abstract rules for object centric reasoning whilst reducing supervision to as little as 1% of labels, and being robust even under substantial domain shift. Notably, at 1% supervision it even outperforms state of the art foundation model baselines in domain generalization
Weak supervision enables machine learning models to learn from limited or noisy labels, but it introduces challenges in reliability and semantic clarity, particularly in multi-instance partial label learning (MI-PLL), where models must resolve both ambiguous supervision signals and uncertain instance-label mappings. This paper proposes a semantics for a neuro-symbolic framework that integrates inductive logic programming (ILP) to structure MI-PLL through relational constraints. In this formulation, ILP defines a hypothesis space over label transitions, formalizes the semantics of per-instance classifiers and provides a relational scaffold for reasoning about weak supervision. Two inductive tasks are studied in this framework: inferring the transition predicate from the observed and classifier predicates, and inferring instance-level classifier assignments from the observed and transition predicates. This formal semantics facilitates constraint specification, consistency checking and the diagnosis of semantic failure modes that bag-level accuracy alone may conceal.
Vision-Language Models (VLMs) have been applied to a wide range of reasoning tasks, yet it remains unclear whether they can reason robustly under distribution shifts. In this paper, we study covariate shifts in which the perceptual input distribution changes while the underlying prediction rules do not. To investigate this question, we consider visual deductive reasoning tasks, where a model is required to answer a query given an image and logical rules defined over the object concepts in the image. Empirically, we find that VLMs fine-tuned through gradient-based end-to-end training can achieve high in-distribution accuracy but fail to generalize under such shifts, suggesting that fine-tuning does not reliably induce the underlying reasoning function. This motivates a neuro-symbolic perspective that decouples perception from reasoning. However, we further observe that recent neuro-symbolic approaches that rely on black-box components for reasoning can still exhibit inconsistent robustness across tasks. To address this issue, we propose VLC, a neuro-symbolic method that combines VLM-based concept recognition with circuit-based symbolic reasoning. In particular, task rules are compiled into a symbolic program, specifically a circuit, which executes the rules exactly over the object concepts recognized by the VLM. Experiments on three simple visual deductive reasoning tasks with distinct rule sets show that VLC consistently achieves higher task accuracy on out-of-distribution data than other reasoning paradigms. Code is available at https://github.com/uiuctml/VLC.
Neuro-symbolic models are usually trained with supervision only on final labels, leaving the intermediate concepts unobserved. Since many concept assignments are consistent with a given label, training can predict labels correctly while recovering the wrong concepts, a failure known as a reasoning shortcut. Prototypical networks reduce shortcuts by anchoring each concept to a few labeled examples, but existing methods still couple perception and reasoning through a hand-crafted, task-specific differentiable loss that must be redesigned for every task. We introduce \textbf{Soft-PNet}, which removes this loss: it reframes concept grounding as a Metropolis walk over a precomputed cache of feasible symbolic solutions, guided by a prototype distribution built from a single labeled anchor per concept, and trains against one KL objective between the prototype-weighted cache and the network's concept predictions. The objective is identical across tasks and remains applicable when the solution space cannot be enumerated. On \texttt{MNIST-EvenOdd}, Visual Sudoku, and \texttt{Kand-Logic} under scarce supervision, Soft-PNet matches loss-engineered prototypical networks at the concept and label levels and recovers concepts that soft-grounding baselines miss, with no loss engineering and lower training time.