用可微分的软答案集替代传统符号求解器，实现端到端神经符号推理。
AS2 -- Attention-Based Soft Answer Sets: An End-to-End Differentiable Neuro-Soft-Symbolic Reasoning Architecture
- 以概率分布形式连续逼近答案集程序的立即后果算子，实现全程可微。
- 在视觉数独上达99.89%单元准确率，100%满足约束条件，无需外部求解器。
- 通过约束组嵌入编码问题结构，对位置顺序不敏感，适合可解释推理任务。
神经符号人工智能系统通常通过非可微边界将神经感知模块与离散符号求解器耦合，导致约束满足反馈无法回传至感知编码器。本文提出AS2（基于注意力的软答案集），一种全可微的神经符号架构，用答案集编程（ASP）立即后果算子 $T_P$ 的软连续近似替代离散求解器。AS2在前向传播中保持每个位置的符号域概率分布，并通过最小化 $T_P$ 的概率推广固定点残差实现端到端训练，无需在训练或推理时调用外部求解器。该架构完全不使用传统位置嵌入，而是通过反映声明式ASP规范的约束组成员嵌入编码问题结构，使模型对任意位置索引无感。在视觉数独上，AS2在1,000个测试板上达到99.89%单元准确率和100%约束满足（经Clingo验证），采用贪心约束解码且无需外部求解器；在包含 $N \in \{2, 4, 8\}$ 个加数的MNIST加法任务中，所有尺度下数字准确率均超99.7%。结果表明，结合约束感知注意力与声明式约束规范的软可微固定点算子，可匹敌或超越流水线及求解器依赖型神经符号系统，同时保持全端到端可微性。
原文摘要 · Abstract (English)
Neuro-symbolic artificial intelligence (AI) systems typically couple a neural perception module to a discrete symbolic solver through a non-differentiable boundary, preventing constraint-satisfaction feedback from reaching the perception encoder during training. We introduce AS2 (Attention-Based Soft Answer Sets), a fully differentiable neuro-symbolic architecture that replaces the discrete solver with a soft, continuous approximation of the Answer Set Programming (ASP) immediate consequence operator $T_P$. AS2 maintains per-position probability distributions over a finite symbol domain throughout the forward pass and trains end-to-end by minimizing the fixed-point residual of a probabilistic lift of $T_P$, thereby differentiating through the constraint check without invoking an external solver at either training or inference time. The architecture is entirely free of conventional positional embeddings. Instead, it encodes problem structure through constraint-group membership embeddings that directly reflect the declarative ASP specification, making the model agnostic to arbitrary position indexing. On Visual Sudoku, AS2 achieves 99.89% cell accuracy and 100% constraint satisfaction (verified by Clingo) across 1,000 test boards, using a greedy constrained decoding procedure that requires no external solver. On MNIST Addition with $N \in \{2, 4, 8\}$ addends, AS2 achieves digit accuracy above 99.7% across all scales. These results demonstrate that a soft differentiable fixpoint operator, combined with constraint-aware attention and declarative constraint specification, can match or exceed pipeline and solver-based neuro-symbolic systems while maintaining full end-to-end differentiability.
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