cs.LGFeb 19, 2026

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

Authors: Venkatakrishna Reddy Oruganti

Organizations: Sithara Inc., Plano, Texas, USA

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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.

Figures & tables

Figure 1: Universal Cognitive Kernel (UCK) with DSP Module. The system processes graph-structured inputs through TT rollout steps, alternating between graph attention and DSP updates. The DSP module maintains learnable rule embeddings, computes sparse rule activation ( α\alpha ) and node selection ( β\beta ) using sparsemax, and aggregates local feasibility into a global signal ( Φ\Phi ).
Figure 2: DSP Module detailed architecture. The module computes global summaries, applies sparsemax for discrete rule activation ( α\alpha ) and node selection ( β\beta ), computes gated effects, and aggregates local feasibility into the critical global Φ\Phi signal. Ablation evidence shows removing global ϕ\phi causes 34-point accuracy collapse.
Figure 3: Comparison of softmax vs sparsemax attention. Softmax distributes weight across all rules, causing interference. Sparsemax produces exact zeros, enabling discrete rule selection. This difference accounts for 26 percentage points in accuracy (71.1% vs 97.4%).
TaskModelOverallPositiveNegativeBalance
Planning (8 ×\times 8 →\to 16 ×\times 16)UCK (no DSP)59.7%20.1%99.3%0.203
GIN81.1%92.3%69.9%0.757
UCK+DSP97.4% ±\pm 0.1%99.9%94.8%0.949
SAT (10 →\to 20 vars)GIN93.8% ±\pm 0.5%93.7%93.9%0.999
UCK+DSP96.4% ±\pm 0.7%99.6%93.2%0.936
Reachability (12 →\to 30 nodes)UCK (no DSP)73.4%56.2%90.6%0.620
Table 1: Results across three constraint reasoning benchmarks with significant size generalization. UCK+DSP achieves highest accuracy with balanced performance on both positive and negative classes.
Configuration8 ×\times 8 Acc16 ×\times 16 Acc16 ×\times 16 INFEAS
Full DSP97.0%98.0%96.0%
No ϕ\phi channel96.8%58.8%17.6%
No global ϕ\phi96.6%64.0%28.0%
ϕ\phi in keys only97.0%98.0%96.0%
ϕ\phi in effects only96.4%98.2%96.4%
No DSP (baseline)82.8%78.4%85.2%
Table 2: Ablation study on the planning task. Global ϕ\phi aggregation is critical for generalization.
Attention Type16 ×\times 16 AccuracyVariance
Sparsemax97.4%±\pm 0.1%
Softmax71.1%±\pm 2.8%
Entmax ( α\alpha =1.5)60.1%±\pm 8.3%
Table 3: Comparison of attention mechanisms. Sparsemax is essential for stable, high-accuracy performance.
ClassGlobal ϕ\phi MeanGlobal ϕ\phi Std
FEASIBLE+18.0+18.06.4
INFEASIBLE−13.5-13.515.9
Separation31.5—
Table 4: The global ϕ\phi signal learns interpretable semantics without supervision.
Figure 4: Learned ϕ\phi semantics. The global feasibility signal learns to separate feasible ( μ=+18\mu=+18 ) from infeasible ( μ=−13\mu=-13 ) cases with 31.5-point separation, emerging purely from training without explicit supervision of ϕ\phi values.
MetricValue
Parameters∼\sim 64,000
Training time∼\sim 11 min (T4 GPU)
Inference<< 1ms per sample
Table 5: Computational requirements. DSP adds minimal overhead while providing substantial accuracy gains.
Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

ParameterValue
dmodeld_{\text{model}}64
druled_{\text{rule}}64
Number of rules ( KK )12
Rollout steps ( TT )4
ϕmax⁡\phi_{\max}6.0
Dropout0.1
Appendix
Table 6: Hyperparameters used across all experiments.
DatasetTrain SizeTest SizeTrain ExamplesTest Examples
Planning8 ×\times 816 ×\times 1610,0002,000
SAT10 vars20 vars10,0002,000
Reachability12 nodes30 nodes10,0002,000
Appendix
Table 7: Dataset statistics for all three benchmarks.
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