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[Submitted on 10 Sep 2026]
Abstract: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.
Submission history
From: Marcos Galván López [view email]
[v1]
Thu, 10 Sep 2026 22:10:33 UTC (188 KB)
추출 본문 · 출처: arxiv.org · https://arxiv.org/abs/2609.12247