AS2 achieves a fully differentiable neuro-symbolic bridge by replacing discrete solvers with a soft, continuous approximation of the Answer Set Programming operator.
March 20, 2026
Original Paper
AS2 -- Attention-Based Soft Answer Sets: An End-to-End Differentiable Neuro-Soft-Symbolic Reasoning Architecture
arXiv · 2603.18436
The Takeaway
It removes the non-differentiable boundary typical of neuro-symbolic systems, allowing constraint-satisfaction signals to flow back to the neural encoder during training. This enables complex logical reasoning tasks (like Visual Sudoku) to be solved end-to-end without external solver calls at inference.
From the abstract
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 ope