Weakly supervised semantic segmentation (WSSS) trains dense pixel-level segmentation models from partial or coarse annotations such as bounding boxes, scribbles, or image-level tags. While recent work leverages foundation models such as the Segment Anything Model (SAM) to generate pseudo-labels, these approaches typically depend on heuristic prompt choices and offer limited ways to incorporate prior knowledge or heterogeneous labels. We address this gap by taking a neurosymbolic perspective: integrating differentiable fuzzy logic with deep segmentation models. Weak annotations and domain-specific priors are unified as continuous logical constraints that fine-tune SAM under weak supervision. The refined foundation model then produces improved pseudo-labels, from which we train a second-stage prompt-free segmentation model. Experiments on Pascal VOC 2012 and the REFUGE2 optic disc/cup segmentation dataset show that our logic-guided fine-tuning yields higher-quality pseudo-labels, leading to state-of-the-art segmentation accuracy that often exceeds densely supervised baselines.
Neurosymbolic learning can use symbolic rules to provide supervision for latent concepts from weak labels, but it commonly assumes that the entities referenced by these rules are already specified. Object-centric models decompose images into slot-like representations; however, such slots are not necessarily aligned with the predicates required for symbolic reasoning. We investigate object-centric neurosymbolic learning under distant supervision, where the object-level arguments of a logic program are learned directly from images using only global task labels. We introduce DeepPbjectLog, a probabilistic neurosymbolic model that integrates a slot-based perceptual encoder with a probabilistic logic layer. The encoder predicts objectness and class probabilities for candidate object representations, while the logic layer marginalizes over latent objectness and class assignments to compute the likelihood of the observed label. This formulation provides a differentiable task-level learning signal for object-centric perception without requiring per-object labels, masks, bounding boxes, or heuristic set matching. Evaluations across diverse visual reasoning tasks demonstrate that DeepObjectLog achieves superior out-of-distribution generalization to compositional, object-count, and rule shifts compared to neural object-centric and standard neurosymbolic baselines.