The research introduces Soft-PNet, a novel approach to prototyping concept grounding within neuro-symbolic models. Existing methods typically rely on hand-crafted, task-specific differentiable losses to mitigate reasoning shortcuts. Soft-PNet removes this requirement by reframing the problem as a Metropolis walk over a precomputed cache of symbolic solutions. This cache is built from a single labeled anchor per concept, creating a prototype distribution. The model is then trained using a KL divergence objective between this prototype-weighted cache and the network’s concept predictions. This approach maintains consistency across different tasks and remains applicable even when the solution space cannot be fully enumerated.
Experiments were conducted on MNIST-EvenOdd, Visual Sudoku, and Kand-Logic under conditions of scarce supervision. The results demonstrate that Soft-PNet matches the performance of loss-engineered prototypical networks at both the concept and label levels. Notably, Soft-PNet recovers concepts that standard soft-grounding baselines fail to identify. The training process for Soft-PNet requires significantly less time compared to methods that necessitate loss engineering.
Soft-PNet’s architecture utilizes a Metropolis walk, a stochastic optimization technique, to navigate the concept space. This approach eliminates the need for explicit enumeration of the solution space, offering flexibility across diverse tasks. The KL divergence objective ensures that the network’s concept predictions align with the prototype-weighted cache, reinforcing the grounding process. The model’s design prioritizes adaptability and robustness, reducing the reliance on task-specific loss functions.
The Soft-PNet model has a context window size of 1 per concept. The model is trained on a single labeled anchor per concept. The model achieves comparable loss-engineered prototypical networks on MNIST-EvenOdd, Visual Sudoku, and Kand-Logic.
Source: https://arxiv.org/abs/2609.12247