Differentiable Symbolic Planning: A Neural Architecture for Constraint Reasoning with Learned Feasibility

TL;DR

This paper introduces Differentiable Symbolic Planning (DSP), a neural architecture that performs constraint reasoning by combining symbolic logic with differentiability, enabling better generalization and interpretability.

Contribution

The authors propose DSP integrated into a Universal Cognitive Kernel, achieving state-of-the-art results on constraint reasoning benchmarks with interpretable feasibility signals.

Findings

Achieves 97.4% accuracy on planning with 4x size generalization.

Attains 96.4% accuracy on SAT problems with 2x generalization.

Global feasibility aggregation is critical for high accuracy.

Abstract

Neural networks excel at pattern recognition but struggle with constraint reasoning -- determining whether configurations satisfy logical or physical constraints. We introduce Differentiable Symbolic Planning (DSP), a neural architecture that performs discrete symbolic reasoning while remaining fully differentiable. DSP maintains a feasibility channel (phi) that tracks constraint satisfaction evidence at each node, aggregates this into a global feasibility signal (Phi) through learned rule-weighted combination, and uses sparsemax attention to achieve exact-zero discrete rule selection. We integrate DSP into a Universal Cognitive Kernel (UCK) that combines graph attention with iterative constraint propagation. Evaluated on three constraint reasoning benchmarks -- graph reachability, Boolean satisfiability, and planning feasibility -- UCK+DSP achieves 97.4% accuracy on planning under 4x size generalization (vs. 59.7% for ablated baselines), 96.4% on SAT under 2x generalization, and maintains balanced performance on both positive and negative classes where standard neural approaches collapse. Ablation studies reveal that global phi aggregation is critical: removing it causes accuracy to drop from 98% to 64%. The learned phi signal exhibits interpretable semantics, with values of +18 for feasible cases and -13 for infeasible cases emerging without supervision.