AS²：基于注意力的软答案集端到端可微神经-软-符号推理架构
AS2 -- Attention-Based Soft Answer Sets: An End-to-End Differentiable Neuro-Soft-Symbolic Reasoning Architecture
AI 导读
研究者提出 AS²（Attention-Based Soft Answer Sets），一种完全可微的神经-符号推理架构，用 ASP 算子 $T_P$ 的连续近似替代离散求解器，训练和推理均无需外部求解器。
正文 · 原文
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.
| Subjects: | Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2603.18436 [cs.AI] |
| (or arXiv:2603.18436v2 [cs.AI] for this version) | |
| https://doi.org/10.48550/arXiv.2603.18436 arXiv-issued DOI via DataCite |
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)
来源：arXiv cs.AI · arxiv.org