AS²：基于注意力的软答案集，一种端到端可微的神经-软符号推理架构

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Abstract:Neuro-symbolic systems typically combine neural perception with discrete symbolic solvers, limiting end-to-end optimization. We introduce Attention-Based Soft Answer Sets (AS$^2$), a fully differentiable neuro-symbolic architecture that replaces discrete solving with a continuous approximation of the Answer Set Programming (ASP) immediate-consequence operator $T_P$. AS$^2$ maintains probability distributions over finite symbol domains and learns by minimizing the fixed-point residual of a probabilistic version of $T_P$, enabling differentiation through constraint checking without external solvers during training or inference. For spatial constraint-satisfaction tasks, AS$^2$ replaces positional embeddings with constraint-group membership embeddings derived directly from declarative ASP specifications, making the model independent of arbitrary position indexing. On Visual Sudoku, AS$^2$ achieves 99.89% raw cell accuracy and 100% constraint satisfaction after greedy decoding, without external solvers. On CLEVR-Hans, AS2 achieves 99.94% on CLEVR-Hans3 and 87.77% on CLEVR-Hans7. These results demonstrate that differentiable fixed-point reasoning, constraint-aware attention, and declarative constraint specifications can match or outperform pipeline-based and solver-based neuro-symbolic approaches while preserving end-to-end differentiability.

Submission history

From: Wael AbdAlmageed [view email]
[v1] Thu, 19 Mar 2026 02:51:18 UTC (888 KB)
[v2] Wed, 4 Nov 2026 03:44:11 UTC (330 KB)