aiqbench analysis
This paper introduces AS², a fully differentiable neuro-symbolic architecture that eliminates the need for external discrete solvers by approximating Answer Set Programming operators with continuous functions. By deriving embeddings directly from declarative ASP specifications, the model achieves high accuracy on spatial constraint tasks like Visual Sudoku and CLEVR-Hans while maintaining end-to-end trainability. The work represents a significant methodological advance in bridging neural perception with symbolic reasoning for complex logical inference problems.
AS2 -- Attention-Based Soft Answer Sets: An End-to-End Differentiable Neuro-Soft-Symbolic Reasoning Architecture
arXiv:2603.18436v2 Announce Type: replace 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.
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.
Artificial Intelligence (cs.AI)
arXiv:2603.18436 [cs.AI]
(or arXiv:2603.18436v2 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2603.18436 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 249 words